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the manual for gprMax

1. lmainly IBM PCs and some workstations 2mainly UNIX workstations and mainframe computers 55 t 30153 GPRMAX3D scan command file tr 30154 GPRMAXx3D snapshot command file t 30155 GPRMAX3D geometry file e bytes 4 5 contain an integer number which is the value of the number of bytes used for every integer type datum SWORD stored in the data part of the file NOT IN THE HEADER e bytes 6 7 contain an integer number which is the value of the number of bytes used for every floating point type datum SREAL stored in the data part of the file e bytes 8 9 contain an integer number which is the number of characters bytes used to store the title TITLELENGTH in the data part of the file bytes 10 11 contain an integer number which is the number of characters bytes used to store any source type specifiers GQOQURCELENGTH in the data part of the file bytes 12 13 contain an integer number which is the number of characters bytes used to store any medium identifier strings MEDIALENGTH in the data part of the file bytes 14 15 are reserved The data part of binary format output files depends on the type of file which in turn is determined by the value of the integer in bytes 2 3 It is important to note that in the data part of a GPRMAx2D 3D binary format file is E E is 6 2 All integer numbers denoted by int are SWORD bytes long All fl
2. 3D model A simple example of a 3D model is one which can be used to calculate the fields of a hertzian dipole located over a half space This problem is of great importance in GPR modelling since the model can provide the necessary information to allow the visualization of the electromagnetic fields as they propagate in the subsurface The procedure of creating a 3D model does not differ in principle from the one which should be followed for a 2D model However you should always bare in mind that a 3D model requires a rather larger amount of memory than a 2D one Hence describing fine details or modelling problems like the previous 2D examples is possible only when significant computational power is available However GPRMAX3D does not put any limit on the size of the problem that can be described The input file for this simple example is medium 3 0 0 0 0 0 0 0 1 0 0 0 sand domain 1 0 1 0 1 0 dx_dy_dz 0 02 0 02 0 02 time_window 3 35e 9 box 0 0 0 0 0 0 1 0 1 0 0 5 sand hertzian_dipole 1 0 600e6 ricker MyDipole 50 BRE example 3 0 35 T T 0 0 5 1 1 5 2 2 5 Im BRE example 4 0 2 F T T 7 0 155 J E 0 1 F t 5 4 eh 0 054 hoa 0 L L L Ng 0 0 5 1 1 5 2 2 5 m Figure 5 7 Image produced using the information in the geometry file of the BRE examples 3 and 4 Note vertical scale is exaggerated analysis 1 tx out a tx x 0 5 0 5 0 5 MyDipole 0 0 3 35e 9 rx 0 6 0 6 0
3. 0 87 0 67 0 47 0 27 Amplitude oO l Normalised Power db L L 1 60 i i i 0 2 4 6 8 0 1000 2000 3000 4000 Time ns Frequency MHz Figure 5 2 Normalized power spectrum and time waveform of the ricker excitation function The centre frequency is 900 MHz be adequate Considering the values of Az and Ay this translates to 240 x 120 cells Therefore in the input file we add domain 0 6 0 3 dx_dy 0 0025 0 0025 time_window 8 0e 9 From the 300 millimetres in the y direction let us use 50 for free space on top of the slab hence the slab can be defined by adding to the input file box 0 0 0 0 0 6 0 25 concrete The cylinder is then introduced in order to overwrite with its properties the ones of the slab Hence we add to the input file cylinder 0 3 0 175 0 025 pec Step 6 A scan of 42 5 cm length consisting of 41 GPR traces needs to be specified If the scan is centred over the rebar and we assume a separation of 50 millimetres between the transmitter and the receiver the first source should be at 0 075 0 2525 and the first receiver at 0 125 0 2525 The height of both the source and the receiver is set to be at 2 5 millimetres from the interface The step with which both source and receiver moves in the x direction scan direction is 10 millimetres From Version 2 a source definition must be inlcuded before we introduce the an
4. 000004 7 2 5 GPRMAx3D coordinate system and conventions 020004 8 2 6 Hints and tips for GPR modelling with GPRMAx2D 3D 4 8 3 GPRMAX2D input file commands 11 3 1 General notes on GPRMAX2D commands 2 0 00 000000 11 3 2 Listofallavailablecommands 0 0002 ee eee eee 12 3 3 GPRMAx2D command parameters 2 a 13 3 3 1 General commands s 2 lt seg oe Gog deh de ae a Dee Gee ee ae be ae 13 3 3 2 ABCrelatedcommands 0 00 17 3 3 3 Media and Object construction commands 000 4 19 3 3 4 Excitation and output commands 0 000000 0008 22 4 GPRMAX3D input file commands 27 4 1 General notes on GPRMAx3D commands 0 0000045 27 4 2 Listofallavailablecommands 0 00002 eee eee eee 27 4 3 GPRMAx3D command parameters 2 0 ee 29 4 3 1 Generalcommands 0 0 00 eee ee 29 4 3 2 ABC related commands 0 00000 cee ee ee 30 4 3 3 Media and Object construction commands 2 0004 4 3 4 Excitation and output commands GPRMAx2D 3D modelling examples 5 1 Single rebar in concrete 2D model 52 Other D examples s inea eaii on led OS eee a ek ee le 5 201 BRE example 2 3 a te ee nee wehbe teeta ba els feet 5 2 2 BRE example 4 30 08 ee Bid oe a a e e on eke ee Bak 5 3 Snapshots of the electric field of a horizontal dipole over a dielectric half space SD models yod ie GG eae
5. iii Chapter 1 Installation and Getting Started This chapter describes the installation procedure for GPRMAx2D 3D 1 1 Contents of the CD ROM If you have obtained a CD ROM distribution of GPRMAx then in order to install the right exe cutable for your computer locate the directory which describes your operating system and copy the file s into a suitable directory in your machine LINUX users should copy the binaries GorMax2D and GprMax3D found in the Linux directory of the CD ROM into a suitable directory on their system preferably one in your path For example at usr local bin The GPRMAx executable should work on all recent LINUX distributions but it has only been tested on REDHAT ENTERPRISE 4 MS Windows 9x 2000 NT XP users should copy the three files GprMax2D exe GprMax3D exe and cygwinl d11 found under the Windows directory into a suitable directory on the system s hard disk e g GprMax The latter file is required since GPRMAx has been compiled using Cyc WIN for the MS WINDows platform Alternatively you can copy the cygwin1 d11 file into your WINDOWS system directory Mac Os X users should copy the files found in the MacOs directory to an appropriate location on their system GPRMAX2D 3D binaries for macs have not been tested as I do not have access to a mac In the directory manual there is a copy of this manual in ADOBE PDF format If you do not have the free ADOBE ACROBAT READER you can download it from www adobe
6. specifies a line source with the ID MySource and a frequency of 600 MHz as having the waveform of a ricker wavelet and amplitude of 1 To use this line source only its ID MySource would be needed later on If the user type has been selected then the command excitation_file strl needs to be included in the model The command excitation_file allows the user to spec ify a single ASCII file that contains a list of amplitude values that can be used to excite the model These values need to be at least equal to the number of iterations that are going to be performed If they are less than this number then zero values are substituted for the missing values If more values are specified than needed they are superfluous and are ignored For example the com mand excitation_file mysource dat will read values from the file mysource dat which can be used instead of the values obtained by using one of the GPRMAxX s build in excitation functions to describe the pulse shape of the source in the model analysis and end_analysis After source types have been introduced then placing sources and output points in GPRMAx2D is accomplished using a pair of new commands analysis and end_analysis The source command tx and the receiver commands rx and or rx_box are to be placed between these two commands The syntax of the command analysis is analysis il filel cl The parameter i1 is the number of new runs
7. 1 lt il then the model will run again to calculate a new analysis step 40 In order for that to have any meaning we need to include either or both of the following com mands tx_steps f1 f2 f3 rx_steps f1 f2 f3 These commands will advance the coordinates of any tx and rx comamnds respectively by an incerement defined as parameters of the above commands The defintion of tx_steps is tx_steps f1 f2 f3 where the parameters f1 f2 and f3 are the increments in meters of the x y and z coordi nates accordingly for all the sources specified using tx commands Similarly the command rx_steps is defined as rx_steps f1 f2 3 where the parameters f1 2 and f3 are the increments in meters of the x y and z coordinates accordingly for all the receivers specified using rx For example the following statements analysis 10 testl out a tx x 0 5 0 5 0 5 MySource 0 0 10e 9 EKO V6 05 5 O45 tx_steps 0 01 0 0 0 0 rx_steps 0 01 0 0 0 0 nd_analysis will allow the simulation of 10 GPR traces The tx for the first trace is at 0 5 0 5 0 5 and the rx is at 0 6 0 5 0 5 The remaining traces are collected with a step of 0 01 metres in the x direction for both transmitter and receiver IMPORTANT NOTE The coordinates of any out put points i e receivers specified using an rx_box command do not get updated using the rx_st
8. 3 are the coordinates of the first apex of the triangle 4 5 f6 the coordi nates of the second and f7 8 9 the ones of the third The parameter st r1 is a medium identifier defined either with a medium command or in a media file currently in use Further the identi fiers free_space or pec can be used if the triangular patch is to represent a free space region or a perfect conductor In the triangle command the coordinates should define a surface and not a 3D object as with the box command For example the command triangle 0 5 0 5 0 5 0 6 0 4 0 5 0 7 0 9 0 5 pec defines a xy oriented triangular patch i e Yee cell surfaces Note that in the above example the z coordinates are identical This differs from the box command where the use of such coordinates will be illegal bowtie With the command bowtie you can introduce a bowtie antenna with specific properties in the model The antenna is made up by two triangular patches the command uses the t riangle command internally The antenna is defined as follows bowtie cl c2 f1 2 3 4 5 strl The parameter c1 is the direction i e polarization of the bowtie antenna and can be x y or z Similarly the parameter c2 denotes the remaining direction so as to define a plane where the antenna lies The parameters f1 2 and 3 are the spatial x y z coordinates of the antenna s feed point The parameter f4 is the len
9. sine ricker etc or it could be the type user if an excitation file is used The parameters f3 f4 are the angles 0 lt 6 lt m and 0 lt lt 2r in degrees that specify the direction using a spherical coordinate system with the same origin as the cartesian systen used in GPRMAX3D of the plane wave s propagation vector k The parameter f5 is the anlge 0 lt Y lt 27 that the electric field component of the pane wave makes with the vector k x 2 The parameter str2 is a huygens surface identifier see command huygens_surface The plane wave must be associated to a huygens surface in order to be sourced in the model Finally the parameter str2 is a source identifier that will be used in a t x command For example plane_wave 1 0 600e 6 gaussian 0 0 90 0 0 0 Huygensl MyPlaneWave Introduces into the model the description of a plane wave with unit amplitute centre frequency of 600 MHz and temporal variation of a gaussian pulse This plane wave will be sourced using the Huygens1 surface and according to the angles of incidence it will be coming from and be polarised in the x direction The identifier to turn this source on using a tx command is MyPlaneWave huygens_surface The command huygens_surface must be used in order to be able to source a plane wave Using this command the model s space is separated in an inner total field region bounded by the huygens surface and an outer scattered field r
10. BRE examples 3 and 4 the wet sand rectangle can either include the height of the concrete slab or not In the first case the properties of the wet sand will be replaced by the ones of concrete when the slab will be introduced In the second case the slab can be placed above the wet sand rectangle overwriting the values of the medium used to initialize the model which is always free space The first approach is preferable since it ensures that there will not be any nodes left with the properties of free space if an error on the coordinates of the slab is made In Figure 5 6 an image representation of the information stored in the geometry file is presented Observing this image the different size of the model with respect to its schematic drawing is evident First the width of the model is 100 millimetres more than in the schematic diagram This is necessary to ensure that there is enough space between the ABCs and the first source point Second there is a part of the model which represents free space and third the height of the model is less than in the schematic diagram It is not necessary to include all 600 millimetres of wet sand in the model Hence allowing for some space between the targets and the ABCs the rest of the space occupied by wet sand can be ignored This is done because it is assumed that reflections originate only within the model If the termination of the wet sand with an other medium is of importance it should be included in the
11. above command to box 0 25 0 25 0 75 0 75 pec will introduce a perfect conducting rectangle of the same size as above Note that pec does not have to be defined The size of the rectangle can not exceed the size of the model as defined by the domain command cylinder With the command cylinder you can introduce a circular disk in the 2D model simulating an infinite cylinder The syntax of the command is cylinder f1 f2 f3 strl The parameters f1 f2 are the x y coordinates of the centre of the circular disk in metres The parameter f3 is its radius r in metres and str1 is a medium identifier see box Hence the command 20 cylinder 0 5 0 5 0 2 free_space introduces in the 2D model a circular disk at the 0 5 0 5 coordinates of radius r 0 2 metres having the parameters of free space x_segment With the command x_segment you can introduce a circular segment in the 2D model simu lating an infinite segment of a cylinder The syntax of the command is x_segment f1 f2 3 f4 5 stri The parameters f 1 f 2 are the x y coordinates of the centre of the circular disk of which a segment in the x direction is going to be constructed These values are all in metres The parameters 3 and f4 are the Ziow and Xpign coordinates of the extent of the segment along the x axis The parameter 5 is the radius r in metres of the circular disk on which the segment calculation i
12. and time waveform of the ricker excitation func tion The centre frequency is 900 MHz 2 2 ee Simulated GPR scan by GPRMAX2D left and image representation of the geome try of the model right Note that the vertical scale is exaggerated Schematic drawing of the BRE examplesland2 00 Schematic drawing of the BRE examples 3and 4 00 Image produced using the information in the geometry file of the BRE examples 1 and 2 Note vertical scale is exaggerated 2 6 ee ees Image produced using the information in the geometry file of the BRE examples 3 and 4 Note vertical scale is exaggerated 6 2 es Simulated GPR scan of the BRE second example 00005 Simulated GPR scan of the BRE fourth example 0 00 Three slices through a volume of data The amplitude of the Ez field component is represented as a gray scale image The figure was created in MATLAB from the GPRMAXSD data 2 yogis ae esate a ald Bi eae are a ee Pd Schematic drawing of the 3D model of a small void after 1 GPRMAX3D simulated GPR scan over a small void 8 Representation in pseudo code of the procedure used in GPRMAX2D in order to store the values of field components in a snapshot 006 Representation in pseudo code of the procedure used in GPRMAX3D in order to store the values of field components in a snapshot 004
13. and will not function anymore in GPRMAX2D Their functionality has been replaced by new more enhanced structures and commands The commands that have been retired and are not functioning anymore are scan 12 csg xtra_tx In addition some of the old commands have changed in terms of the number of parameters they take These are tx snapshot 3 3 GPRMAx2D command parameters To aid the presentation of GPRMAX2D commands they have been grouped in four categories General commands which include the ones used to specify the size and discretization of the model ABC related commands which allow the customisation and optimisation of the absorbing boundary conditions Media and Object construction commands which are used to introduce different media in the model and construct simple geometric shapes with different constitutive parameters Excitation and Output commands which are used to place source and output points in the model Most of the commands are optional with the exception of the ones which are necessary in order to construct the simplest model possible For example none of the commands of the Media and Object construction section are necessary to run a model However without specifying any objects in the model GPRMAx2D simulates a free space air region not of particular use for GPR modelling If you have not specified a command which is essential in or
14. command geometry_file you can specify a file in which information about the model s geometry is stored in binary format This information can be used to create an image of the model and check if it is properly constructed The syntax of the command is geometry_file filel The parameter file1 is the filename of the geometry file For example the command geometry_file model geo will instruct GPRMAX2D to store information about the geometry of the model in the file model geo The structure of the geometry file is described in Chapter 6 messages Using the command messages in your input file you can partially control the amount of in formation displayed on the screen at run time The syntax of the command is messages cl The parameter c1 can be either y yes or n no which turns on or off the messages on the screen The default value is n When messages are on GPRMAX2D will display on the screen the transla tion of space and time values to cell coordinates and iteration number integer values respectively This information can be useful for error checking nips_number The command nips_number should be included in your input file only when GPRMAx2D has requested its use The syntax of the command is nips_number il where the parameter i1 is an integer number that GPRMAx2D will advise you to use This com mand controls the size of arrays used to store important information about the model
15. correspond directly to cell coordinates It is important to remember that for a given set of space coordinates x y the actual position of the electromagnetic field components are e x A2 y Su for E e a A2 y for Hy e x y St for Hy due to the staggered arrangement of field components in the FDTD algorithm Therefore the interface between two cells of different constitutive parameters is located on the positions of the magnetic field components Further it is important to remember that all sources are actually located at the positions of the E field component Allocated Cells Cell coordinates e 10 o gt ern oe 10 w s 10 0 1 2 574 5 6 7 8 9 10 Space coordinats Range for space coordinates 4 Hy Hx Ez Figure 2 3 Schematic of the GPRMAx2D coordinate system and conventions see text The components included in the oval shaped area are the ones which correspond to space coordinate 3 Ax Ay 1 metre 2 5 GPRMAx3D coordinate system and conventions The coordinate system used in GPRMAX3D is a right handed Cartesian The origin of space coordinates is 0 0 0 and the analogy between space coordinates and 3D FDTD cells is very similar to the one in GPRMAX2D explained above The difference in GPRMAX3D is that the 3D FDTD cell is rather more complicated than in the 2D case and there are no field components located at the centre of the cell At interfaces bet
16. curl equations which are applied in each FDTD cell Since these equations are discretized in both space and time the solution is obtained in an iterative fashion In each iteration the electromagnetic fields advance propagate in the FDTD grid and each iteration corresponds to an elapsed simulated time of one At Hence by specifying the number of iterations one can instruct the FDTD solver to simulate the fields for a given time window The price one has to pay of obtaining a solution directly in the time domain using the FDTD method is that the values of Az Ay Az and At can not be assigned independently FDTD is a conditionally stable numerical process The stability condition is known as the CFL condition after the initials of Courant Freidrichs and Lewy and is 2 5 At lt where c is the speed of light Hence At is bounded by the values of Ax Ay and Az The stability condition for the 2D case is easily obtained by letting Az oo One of the most challenging issues in modelling open boundary problems as the GPR one is the truncation of the computational domain at a finite distance from sources and targets where the values of the electromagnetic fields can not be calculated directly by the numerical method ap plied inside the model Hence an approximate condition known as absorbing boundary condition ABC is applied at a sufficient distance from the source to truncate and therefore limit the com putational space The role of this ABC
17. current Re is set to 0 25 t is time and f is the frequency e The sine excitation function is defined as I Rsin 2r ft and 1 iftf lt 1 R 0 iftf gt l e The gaussian excitation function is defined as I a Sttax where 27 f and x e The ricker excitation function is defined as I 26 1 e1 20 eS t x t x which is the first derivative of the gaussian function normalized to unity The parameters and y are as defined for the gaussian function 67 Appendix C MATLAB functions for GPRMAxX2D 3D In the tools subdirectory there are simple MATLAB functions which can be used to import modeled data created by GPRMAX2D 3D using the binary format option into MATLAB for further processing and visualization NOTICE These functions are not guaranteed for any particular purpose The author does not offer any warranties or representations nor does it accept any liabilities with respect to their function or application You are free to redis tribute these functions but the copyright remains with the author In each function there is a small header which explains its purpose arguments and return values 68 Bibliography 1 Giannopoulos A 1997 The investigation of Transmission Line Matrix and Finite Difference Time Domain Methods for the Forward Problem of Ground Probing Radar D Phil thesis De partment of Electronics University of York UK 2 Kunz K S and Luebbers R J 1993
18. domain method FDTD Detailed information about the use of FDTD for GPR modelling can be found in 1 and general information on the FDTD method in 2 and 3 2 1 Basic concepts of GPR modelling All electromagnetic phenomena on a macroscopic scale are described by the well known Maxwell s equations These are first order partial differential equations which express the relations between the fundamental electromagnetic field quantities and their dependence on their sources OB 2 1 VAS ae 2 2 VxH Vit 2 3 V B 0 2 4 V D qm where t is time seconds and q is the volume electric charge density coulombs cubic meter In Maxwell s equations the field vectors are assumed to be single valued bounded continuous functions of position and time In order to simulate the GPR response from a particular target or set of targets the above equations have to be solved subject to the geometry of the problem and the initial conditions The nature of the GPR forward problem classifies it as an initial value open boundary problem This means that in order to obtain a solution one has to define an initial condition i e excitation of the GPR transmitting antenna and allow for the resulting fields to propagate through space reaching a zero value at infinity since there is no specific boundary which limits the problem s geometry and where the electromagnetic fields can take a predetermined value Although the first part is easy to acco
19. f3 are the x y z coordinates in metres of the source in the model The 39 parameter str1 is the source ID that has been specified before using a source description com mand i e hertzian_dipole voltage_source etc The parameter 4 is a delay in the source s initiation If it is greater than zero then the source will be active after that time delay has passed The parameter f5 is the time of source removal If the simulation runs for longer than the source s removal time the source will stop functioning in the model after 5 seconds If the time of source removal is longer than the simulated time window then the source is active for the complete simulation and the time window value is used instead Important note If a plane wave is to be sourced a huygens surface must have been defined as well and used as an identifier in a plane_wave definition command However in order to activate the source this plane_wave definition must be used in conjuction with a tx command In that case the polarization x or y or z that has been included in the tx command as well as the coordinates specified in the tx command are ignored as the plane wave is sourced on a huygnes surface and not on a single point and its polarization is defined by the angle see plane_wave The syntax of the rx command is trki 1 2 3 and the parameters f1 2 and 3 are the x y z coordinates in
20. in the file will be used The source is active from time 0 0 until simulated time is 10 nanoseconds which could be either the end of the requested time window or earlier than that The output will be stored in ASCII format in the file test1 out The time evolution of elec tromagnetic fields at the points specified by the three rx commands at 0 5 0 7 0 5 0 8 and 0 6 0 5 will be stored in the output file In addition to the three points defined with rx com mands the output will be defined at the points defined by the rx_box command 441 points 24 Creating scans or running the model more than once If i1 of the analysis command is greater than 1 then the model will run again to calculate a new step in the current analysis In order for that to have any meaning we need to include both or at least either of the commands tx_steps rx_steps which will advance the coordinates of any tx and rx commands respectively by an incre ment defined as parameters of the above commands The definition of tx_steps is tx_steps f1 f2 where the parameters f1 and f2 are the increments in meters of the x and y coordinates accord ingly for all the sources specified using tx commands Similarly the command rx_steps is defined as rx_steps f1 f2 where the parameters f1 and f2 are the increments in meters of the x and y coordinates accord ingly for all the receivers specified using rx Fo
21. in the x direction normalized by Az stored in an int The sampling interval in the y direction normalized by Ay stored in an int The sampling interval in the z direction normalized by Az stored in an int The time instant when the snapshot has been taken normalized by At i e iteration num ber stored ina float The number of samples in the x direction in an int The number of samples in the y direction in an int The number of samples in the z direction in an int The values of the FE electromagnetic field component each stored ina float at every x y z sampling point Figure 6 2 illustrates in pseudo code the procedure used to store the values of the field component The values of the FE electromagnetic field component each stored ina float at every x y z sampling point Figure 6 2 illustrates in pseudo code the procedure used to store the values of the field component The values of the F electromagnetic field component each stored in a float at every x y z sampling point Figure 6 2 illustrates in pseudo code the procedure used to store the values of the field component The values of the H electromagnetic field component each stored ina float atevery x y z sampling point Figure 6 2 illustrates in pseudo code the procedure used to store the values of the field component The values of the H electromagnetic field component each stored ina float atevery x y z sampling point Figure 6 2 illustrates in pseudo code the p
22. is to absorb any waves impinging on it hence simulating an unbounded space The computational space i e the model limited by the ABCs should con tain all important features of the model such as sources and output points and targets Figure 2 2 antenna J Air Figure 2 2 The 2D GPR forward problem and its GPRMAx2D domain bounded by ABCs illustrates this basic difference between the problem to be modelled and the actual FDTD mod elled space In Figure 2 2 it is assumed that the half space which contains the target s is of infinite extent Therefore the only reflected waves will be the ones originating from the target In cases where the host medium is not of infinite extent e g a finite concrete slab the assumption of infi nite extent can be made as far as the actual reflections from the slab termination are not of interest or its actual size is large enough that any reflected waves which will originate at its termination will not affect the solution for the required time window In general any objects that span the size of the computational domain i e model are assumed to extend to infinity The only reflec tions which will originate from their termination at the truncation boundaries of the model are due to imperfections of the ABCs and in general are of a very small amplitude compared with the reflections from target s inside the model All other boundary conditions which apply at interfaces between different media in the FD
23. model The same approach has been used in all four examples and will save a considerable amount of computer memory and run time The result of the GPRMAX2D simulation for this example is illustrated in Figure 5 8 The simu lated GPR traces are presented using a gray scale image format To create this image the GPRMAx2D data have been imported into MATLAB 5 2 2 BRE example 4 The construction of a GPRMAXx2D model for the fourth example of the BRE set is more straight forward than the previously described one A single background medium of wet sand is used and cylinders of different size and type are employed to simulate the rebars and hollow tubes as seen in the schematic drawing of Figure 5 5 It should be noted however that the size of the 10 mil limetres rebars is quite small for a discretization step Ax and Ay of 2 5 millimetres Better results 49 BRE example 1 T f m m Figure 5 6 Image produced using the information in the geometry file of the BRE examples 1 and 2 Note vertical scale is exaggerated will be obtained using lower values However the size of the model will increase substantially Decreasing Az and Ay will not result in a different pattern for the response The result of the GPRMAX2D simulation for this example is presented in Figure 5 9 using a gray scale image format for the simulated GPR traces 5 3 Snapshots of the electric field of a horizontal dipole over a dielectric half space
24. of the model This is similar to what the number of scans was in the old scan command and it means that the model will run again after re setting all arrays and time to zero for every single i1 The parameter file1 is the name of the file where all the results for this analysis are going to be stored and the parameter c1 isa single character either a or b denoting that the format of the output file file1 will be ASCII or BINARY respectively Is is important that an analysis command is followed after other source and output con trolling commands have been inserted by the command nd_analysis which denotes the end of an analysis section that was started using an analysis command The end_analysis command has no parameters In your input file there can be any number of analysis and end_analysis pair of commands 23 tx rx and rx_box The commands tx rx and rx_box are used together in order to introduce a source po sition tx and output points rx and rx_box Any number of tx commands could be specified in the model as well as any number of rx and rx_box commands The new syntax of the tx command is tx f1 f2 strl f3 f4 The parameters f1 and f2 are the x y coordinates in metres of the source in the model The pa rameter st r1 is the source ID that has been specified before using a source descript
25. simulated GPR scan has been obtained The result is illustrated in Figure 5 3 together with an image representation of the model s space constructed using the information stored in the geometry file 5 2 Other 2D examples In the examples directory of GPRMAx2D installation disks there four input files which include the modelling instructions for four examples suggested by the Building Research Establishment BRE UK All of the examples involve rebars and hollow tubes located in concrete or sand Fur ther most of them include voids located underneath the concrete slab Schematic drawings of these examples can be found in Figures 5 4 and 5 5 Further the GPRMAx2D models of these ex amples are presented in Figures 5 6 and 5 7 as images created in MATLAB using the information stored in the geometry files of the models 1Before running any of the examples please read the input files 46 Rebar in concrete Rebar in concrete 10 20 30 40 0 0 2 0 4 0 6 Trace number m Figure 5 3 Simulated GPR scan by GPRMAX2D left and image representation of the geometry of the model right Note that the vertical scale is exaggerated 5 2 1 BRE example 2 The problem that this example represents is a more complicated modelling scenario from the first simple rebar example A schematic drawing of the problem is presented in Figure 5 4 Following the same logical steps as in the previous example the fundamental parameters of the model can be d
26. source code you could request it in writing You should state that you will not redistribute the code to anyone either verbatim or in any modified version of it Finally you should put in a few words about the reasons for needing it For any ideas or bugs or collaboration please do not hesitate to contact me Antonis Giannopoulos 2005 1PML boundaries were introduced for GPRMAX3D with Version 1 5 The executables are serial versions due to licensing of OpenMP compilers Contact me for more information Acknowledgements I would like to thank the Building Research Establishment BRE UK for providing me with the financial support to develop GPRMAXx2D 3D after completing my D Phil thesis on GPR mod elling at the University of York Without their support which helped to develop the core of the GPRMAX programmes this current release today would not have been possible Contents 1 Installation and Getting Started 1 1 1 Contents of the CD ROM 00 0 0 0000000000 0000000 1 1 2 Downloading from the Website 2 0 ee 1 13 Running GPRMAX2D 3D 2 sa a ee 2 1 4 General structure of the input file 2 2 eee 2 2 Ground Penetrating Radar modelling with GPRMAx2D 3D 4 2 1 Basic concepts of GPR modelling 2 2 ee ee 4 2 2 Assumptions for the modelling of GPR in two and three dimensions 6 2 3 Capabilities and limitations of GPRMAX2D 3D 0 0000084 7 2 4 GPRMAx2D coordinate system and conventions
27. unit amplitude and 600 MHz centre frequency Finally it is important to note that a file named MyLine ie st r2 is created where the output of the total and reflected voltages and currents in the line are stored The use of the t ransmission_line command should enable the construction of as faithful reproductions as is possible of real GPR antennas plane_wave The command plane_wave can be used to describe the definition of a plane wave source using the total scattered field method see 3 The plane wave source is to be used at least on this Version of GPRMAx3D only in models where the background medium is free space In order to use a plane wave the model space is partitioned to an inner total field region and an outer scattered field region In the inner total field region the plane wave is added and exists everywhere while in the outer scattered field region only scattered energy from the objects interogated by the plane wave propagates In order to define the plane wave and separate these two regions a huygens_surface command must be used which defines the surface of the box that contains the total field region The syntax of the command is plane_wave f1 f2 strl f3 f4 f5 str2 str3 The parameters f1 and f2 are the amplitute and frequency of the source s waveform The pa rameter str1 is the type of excitation in the line waveform type identifier This can be one of the build in types like gaussian
28. 6 snapshot 1 0 0 0 0 0 0 1 0 1 0 1 0 0 02 0 02 0 02 3 3e 9 snap3d out b end_analysis messages y The above input file will produce only a single GPR trace By changing 1 to a different value in the analysis command more traces can be calculated but then the tx_sptes and rx_steps must be used to move the source and receiver to different positions in the model The snapshot command as defined above produces a volume of data for each electromagnetic field component Three slices through this volume of data for the E field component the one parallel to the orientation of the source dipole are presented in Figure 5 10 Each of these slices corresponds to a constant x y and z coordinate The coordinates 0 0 0 denote the location of the source Note that the dipole is located at the interface between air and half space 5 4 GPR response of a small void 3D model This final example is taken from 1 and illustrates how a 3D model of a small rectangular void can be designed The parameters of the model are presented in a schematic drawing in Figure 5 11 A scan comprised of 21 simulated GPR traces is obtained for this target using the following input file in GPRMAx3D medium 6 0 0 0 0 0 0 001 1 0 0 0 concrete domain 0 6 1 3 0 65 dx_dy_dz 0 01 0 01 0 01 time_window 12e 9 51 BRE example 2 ns 0 5 1 1 5 2 Scan length m Figure 5 8 Simulated GPR scan of the BRE seco
29. 6 1 illustrates in pseudo code the procedure used to store the values of the field component The values of the H electromagnetic field component each stored in a float at every x y sampling point Figure 6 1 illustrates in pseudo code the procedure used to store the values of the field component Geometry output file The geometry file is always stored in binary format After the header information is stored as follows The title of the model ina st ring of TITLELENGTH bytes The number of iterations NI which have been performed in an float The spatial step Av ina float The spatial step Ay ina float The time step At ina float The number of cells NX in the z direction in an int Note that the number of cells reported in the geometry file ranges from 1 NX Internally GPRMAX2D uses the range 0 NX 1 according to the coordinate system 58 6 3 The number of cells NY in the y direction in an int The number of different media PMEDIA present in the model in an int A list PMEDIA long of medium identifiers Its medium identifier is stored in a string of MEDIALENGTH characters bytes A cell ID stored in int 2 bytes for every cell in the model The loop structure shown in Figure 6 1 is used to store these values Each cell ID corresponds to an entry 1 PMEDIA in the list of different media GPRMAx2D ASCII file formats The ASCII output files can be edited with any text editor or word processing software a
30. Although The actual limit is the highest 2 byte integer value which can be stored in the computer around 32768 16 the size of these arrays can be calculated internally the resulting number from such a calculation which takes into consideration all possible required space is usually rather larger than the one which is actually needed in most cases Hence a smaller number is used in order to conserve computer memory When GPRMAX2D detects that more space is needed it issues an error mes sage and prompts you to use this command in the input file which will set aside more space for allocation 3 3 2 ABC related commands The default values for the ABCs used in GPRMAX2D should be adequate for most simulations and are tuned to deliver a good performance without introducing any instabilities It should be noted however that a characteristic of the formulation of local ABCs such is the one used in GPRMAx2D is prone to instabilities especially when high orders are used Hence the default settings in GPRMAX2D should not be altered except if you are familiar with the formulation of the Higdon ABC used in GPRMAX2D Details about the Higdon ABC can be found in 1 In addition to local ABCs from Version 2 0 GPRMAxX2D employs the more powerful Perfectly Matched Layer PML ABC The PML works by surrounding the simulation space with a layer of non physical absorbing material which greatly absorbs all electromagnetic waves and performs very well irres
31. E LIABLE TO YOU FOR DAMAGES INCLUDING ANY GENERAL SPECIAL INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE USE OR INABILITY TO USE THE PROGRAMMES INCLUDING BUT NOT LIMITED TO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD PARTIES OR A FAILURE OF THE PROGRAMMES TO OPERATE WITH ANY OTHER PROGRAMS EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES END OF TERMS AND CONDITIONS Preface GPRMAx2D and GPRMAX3D are electromagnetic wave simulators for Ground Penetrating Radar modelling They are based on the Finite Difference Time Domain numerical method This USER s MANUAL describes the installation of GPRMAx2D 3D and the various commands which are available for the construction of 2D and 3D GPR models Some simple examples of GPR mod els are provided to illustrate the procedures that should be followed in order to obtain useful models using GPRMAX2D 3D Please do report any errors or omissions to the author If you require further information about GPRMAx2D and GPRMAX3D or you have any sugges tions for improvements to the software or to this USER s MANUAL please contact the author Dr Antonis Giannopoulos University of Edinburgh School of Engineering and Electronics Institute for Infrastructure and Environment AGB Building The King s Buildings Edinburgh EH9 3JN Scotland E mail A Giannopoulos ed ac uk Preface to Version 2 0 The GPRMAx2D 3D codes h
32. GPRMAX2D 3D USER S MANUAL VERSION 2 0 Many of the designations used by manufacturers and sellers to distinguish their products are claimed as trademarks Where those designations appear in this manual and the author was aware of a trademark claim the designations have been printed in initial caps or small caps The procedures and applications presented in this manual have been included for their instructional value They have been tested with care but are not guaranteed for any particular purpose The author does not offer any warranties or representations nor does it accept any liabilities with respect to the programmes or applications Typeset in Concrete Roman with ATEX 2e Copyright 2005 by Antonis Giannopoulos All rights reserved Permission is granted to reproduce and use this manual and GPRMAx software for academic or commercial purposes LICENCE GPRMAx2D V 2 0 Electromagnetic simulator for Ground Probing Radar GPRMAX3D V 2 0 Electromagnetic simulator for Ground Probing Radar AUTHOR Antonis Giannopoulos COPYRIGHT Antonis Giannopoulos 2005 TERMS AND CONDITIONS This Licence applies to the GPRMAx2D and GPRMAX3D executable forms object codes and to every file which is part of the GPRMAx2D and GPRMAX3D source codes The Programmes below refers to the executable images of GPRMAX2D and GPRMAX3D and to all the files which constitute the source codes for GPRMAX2D and GPRMAX3D The licensee is addressed as yo
33. GPRMAX2D is to use a media file The name and location of this file has to be supplied by the media_file command in order for GPRMAX2D to be able to use the information stored in it In this file the user can save the parameters of frequently used media and use them in GPRMAX2D by their identifiers as the internally specified free_space and pec If a medium has been already defined in a media file it does not have to be declared in GPRMAX2D with a medium command However all identifiers used in the media file and if any in medium commands must be unique Otherwise GPRMAx2D will issue an error message and terminate execution box With the command box you can introduce a rectangle of specific properties in the model The syntax of the command is box f1 2 3 4 strl the parameters f1 2 are the lower left x y coordinates of the rectangle in metres Similarly the 3 4 are the upper right x y coordinates of the rectangle The parameter st r1 is a medium identifier defined either with a medium command or in a media file currently in use Further the identifiers free_space or pec can be used if the rectangle is to represent a free space region or a perfect conductor For example the command box 0 25 0 25 0 75 0 75 my_sand introduces into the model a rectangle which is 0 5 x 0 5 metres in size and sets its properties to the ones defined to represent my_sand Changing the
34. TD model are automatically enforced in GPRMAX2D 3D 2 2 Assumptions for the modelling of GPR in two and three dimensions In constructing a GPR model in two and three dimensions some assumptions are necessaty These mainly result from the need to keep the amount of computational resources required by the model to a manageable level and to facilitate the study of the important features of the GPR response to a target without cluttering the solution with details which will obscure the fundamen tal response However GPRMAX2D 3D can easily handle more complicated GPR modelling scenarios if required The assumptions made for both GPRMAx2D and GPRMAX3D models are e all media are considered to be linear and isotropic e In GPRMAXS3D if the physical structure of the GPR antenna is not included in the model then the antenna is modelled as an ideal Hertz dipole ie a small current source In GpPRMAX2D the transmitting antenna is modelled as a line source Using a Hertz dipole in GPRMAXS3D results in reducing the computational resources required to run a 3D model in reasonable time whereas in the GPRMAX2D case the use of a line source is a consequence of the assumption of the invariance of the problem in one direction the constitutive parameters are in most cases assumed not to vary with frequency This assumption simplifies a time domain model However a formulation able to handle a Drude i e Debye plus a constant conductivity relaxati
35. The Finite Difference Time Domain Method for Electro magnetics CRC Press 3 Taflove A 1995 Computational Electrodynamics The Finite Difference Time Domain Method Artech House 4 Yee K S 1966 Numerical Solution of Initial Boundary Value Problems Involving Maxwell s Equations in Isotropic Media IEEE Transactions on Antennas and Propagation Vol 14 pp 302 307 69
36. a he all oe A og a 5 4 GPR response of a small void 3D model GPRMAX2D 3D Output File formats 6 1 GPRMAx2D 3D Binary format file header 6 2 GPRMAx2D BINARY file formats 0 0000 eee eee 6 3 GPRMAx2D ASCII file formats 0 0 0 00 eee ee ee 64 GPRMAx3D BINARY file formats 0 000 eee ee eee 6 5 GPRMAx38D ASCII file formats i s se crore skoe nii eaaa ee ee ee GPRMAX2D 3D Media file GPRMAx2D 3D Constants and excitation functions GPRMAX2D 3D Constants 0 2 0 eee Excitation functions fi bh hae oe be bak eb eS ee ers MATLAB functions for GPRMAx2D 3D Bibliography 43 43 46 47 49 50 51 55 55 56 59 59 63 64 68 69 Figures 2 1 22 23 2 4 5 1 5 2 5 3 5 4 5 5 5 6 5 7 5 8 5 9 5 10 5 11 5 12 6 1 6 2 The 3D EFDID Yee cell ic bi eee Adee ES eee a The 2D GPR forward problem and its GPRMAx2D domain bounded by ABCs Schematic of the GPRMAx2D coordinate system and conventions see text The components included in the oval shaped area are the ones which correspond to space coordinate 3 Aw Ay 1 metre 2 ee es Schematic of the GPRMAx3D coordinate system and conventions The depicted field components are the ones which correspond to space coordinate 1 Ax Ay Ag 1 metre axis eos Gals Sah eee ee eyed eee eS Schematic drawing of the rebar in concrete problem 0 4 Normalized power spectrum
37. alysis step which will calculate the scan Therefore a source defintion command is inserted in the file as line_source 1 0 900e 6 ricker MyLineSource To compute a scan then the following analysis step is inserted in the input file 45 analysis 41 rebar sca b tx 0 075 0 2525 MyLineSource 0 0 8 0e 9 Fess 01250 2525 tx_steps 0 01 0 0 rx_ steps 0 01 0 0 end_analysis The output file is called rebar sca and will be stored in binary format The model is now complete but we can add few more commands to the input file title Model of rebar in concrete messages y geometry_file rebar geo in order to obtain a geometry file and include a title for the model The final input file reads like medium 6 0 0 0 0 0 0 01 1 0 0 0 concrete domain 0 6 0 3 dx_dy 0 0025 0 0025 time_window 8 0e 9 box 0 0 0 0 0 6 0 25 concrete cylinder 0 3 0 175 0 025 pec line_source 1 0 900e6 ricker MyLineSource analysis 41 rebar sca b tx 0 075 0 2525 MyLineSource 0 0 8 0e 9 BX O15 0 2 52 5 tx_steps 0 01 0 0 rx_steps 0 01 0 0 end_analysis title Model of rebar in concrete messages y geometry_file rebar geo where lines have been drawn to separate the different steps and sections in the input file Any other comments can be included or if the order of the commands is changed it will not make a difference Using GPRMAx2D and the above input file the
38. atched layer ABC The PML works by surrounding the simulation space with a layer of non physical absorbing material which greatly absorbs all electromagnetic waves and performs very well irrespectively of the angle of incidence or the frequency of the impinging pulse In order to use the PML boundary condition instead of the default Higdon ABC the command abc_type pml 30 has to be used The command abd_type higdon sets the ABC back to its default setting At this release of GPRMAx3D the user can not influence the parameters of the PML which are determined automatically for optimum performance However the user can define the thickness or depth of the PML using the command poml_layers il where i1 is the number of Yee cells that the PML will occupy The default value is 8 cells The more cells are used the better the performance of the PML but the computational resources in crease substantially when deep PML layers are employed Further there are two important issues on using the PML t The PML layers are part of the model s geometry However the fields in the PML layers are of NO INTEREST and IT IS WRONG TO USE THEM IN CALCULATIONS Therefore DO NOT place sources or receivers in areas of the model occupied by a PML The depth of PML is defined as number of YEE CELLS and not as a distance in metres t CAUTION Currently PML works only for NON MAGNETIC media Therefore if your model needs to employ media that are to be termin
39. ated by a PML and their magnetic per meability u must be other the uo then you must use the default Higdon ABC and not the PML This restriction will be alleviated in a future release of GPRMAx3D 4 3 3 Media and Object construction commands The commands which are available in GPRMAx3D to facilitate the introduction of different media in the model and the construction of specific objects are discussed in this section GPRMAx3D after the processing of general commands sets up a model of the required size initialized to sim ulate free space air By using the commands in this section you can introduce other media and objects in the model It is important to note that as in GPRMAXx2D free space and perfect conductors are already de fined in GPRMAX3D and you do not have to redefine these two media Thus the key words free_space and pec which describe air and perfect conductors respectively are reserved and can be used directly without any definition of constitutive parameters For any other media their parameters have to be made known to GPRMAX3D by using either or both e a media file defined by the media_file command which contains the definitions of various frequently used media see Appendix A e a medium command in the input file medium The medium command has the same syntax and function as described for GPRMAx2D Further the same media files can be used either in GPRMAX2D or GPRMAX3D with no alteration to their struc
40. ave been around for some time since their initial development in 1996 At that time 32Mb of RAM and processor speeds of 100 MHz were considered top of the range in computer technology Clearly things have moved on As computer power increases we are able to realistically model more complex GPR scenarios and even attempt models of GPR transducers Version 2 0 of GPRMAX mainly brings the 2D model in a par with the 3D in terms of development of the underlying numerical modelling technique New with Version 2 0 are Perfectly Matched Layer PML boundaries for both GPRMAx2D and GPRMAx3D User specified excitation functions for both GPRMAx2D and GPRMAx3D Huygens s Surface in GPRMAx3D Plane Wave excitation in GPRMAX3D for free space simulations which will be extended for half space simulations in future Simulation of thin wires in GPRMAx3D Voltage sources in GPRMAX3D along with 1D transmission lines for feeding models of GPR antennas New excitation structure which makes GPRMAX2D 3D more general in use and allows for multiple sources and receivers at the same time New geometry primitive in GPRMAX3D to create cylinders of any orientation in the model space Both codes have been parallelised using OpenMP The cryptic error codes of GPRMAX2D have been replaced by error messages as in GPRMAX3D I hope to continue developing GPRMAx in the future so it will become more versatile than what it is at the moment If you need to work with the
41. be out of the range of the model In such a case only the part of the model which intersects with these objects will be allocated with the desired properties 3 3 4 Excitation and output commands Starting with GPRMAX2D Version 2 0 before we start an analysis we need to specify the charac teristics of at least one source using the command line _source fl f2 stri str2 where f1 and 2 are the amplitude in amperes of the line source s current and the frequency in Hertz of the source s excitation waveform respectively The parameter st r1 controls the type of the excitation waveform The available choices for st r1 are e cont_sine which is a continuous sine waveform at the specified frequency In order to avoid introducing noise in the calculation the waveform s amplitude is modulated for the first cycle of the sine wave ramp excitation e sine which is a single cycle of a sine waveform at the specified frequency e gaussian which is a gaussian waveform e ricker which is the first derivative of the gaussian waveform e user which can used to introduce into the model User defined excitation functions In Appendix B the formulas used to calculate these waveforms are given 22 The parameter st r2 is a user supplied ID which will subsequently be used to relate the specifi cation of that source with the point of its application in the model For example line_source 1 0 600e6 ricker MySource
42. c parameters in the 2D model Its syntax is triangle f1 f2 3 4 f5 f6 strl The three apexes of the triangular patch are specified in pairs of x y coordinates in metres as e f1 f2 21 e f3 f4 e f5f6 The parameter str1 is a predefined medium identifier For example the command triangle 0 2 0 2 0 2 0 5 0 5 0 2 my_sand introduces a right angle triangle with the right angle at the lower left side of the model 0 2 0 2 A note on object construction It is important to note that GPRMAX2D process all object construction commands in the order they appear in the input file Thus model space allocated to a specific medium using for example the box command can be reallocated to another medium using the same or any other object construction command Hence the model s space can be regarded as a canvas in which objects are introduced and one can be overlaid on top of the other overwriting its properties in order to produce the desired geometry For example the sequence of commands box 0 0 0 0 1 0 1 0 concrete cylinder 0 5 0 6 0 1 pec can be used to introduce a perfectly conducting bar of r 10 cm inside a concrete slab If you reverse the order of the commands the bar will disappear from the model Objects which are introduced by a box command have to be contained within the model How ever the coordinates and radius which can be used ina cylinder and triangle com mands can
43. centres of its two faces being 0 5 0 1 0 5 and 0 5 0 8 0 5 34 cylindrical_segment With the command cylindrical_segment you can introduce a circular cylindrical segment of finite dimensions in the 3D model The syntax of the command is cylindrical_segment cl f1 f2 f3 4 5 strli c2 f6 f7 The parameter c1 denotes the direction of the cylinder s axis and it could be either x or y or z The parameters f1 and f2 are the lower and higher coordinates of the cylinder s axis For example if the cylinder is oriented in the x direction f1 f2 are the coordinates x1 x2 The parameters f3 and f4 are the remaining necessary coordinates required to describe the centres of the two circular faces of the cylinder Hence for the x oriented cylinder these are y and z respectively The following list describes all possible combinations e for an x oriented segment 1 3 4 is x1 y z and 2 3 4 is x2 y z e for an y oriented segment 3 f1 4 is x y1 z and 3 2 4 is x y2 z e for an z oriented segment 3 4 f1 is x y z1 and 3 4 2 is x y z2 The parameter 5 is the radius r in metres of the circular cylinder and st r1 is a medium identifier see Chapter 3 The parameter c2 is the direction of the segments variation The parameters f6 and f7 are the coordinates of the starting and ending points of the segment s variation For example the command cylindrical_segme
44. ch one of the Transmitters sources t x in the analysis The x coordinate of the source expressed in cell coordinates in an int The y coordinate of the source expressed in cell coordinates in an int The source type i e the source ID ina st ring of SOURCELENGTH bytes The initial source time delay as float The time of source removal as float e For each one of the number of Receivers rx in the analysis The x coordinate of the receiver expressed in cell coordinates in an int The y coordinate of the receiver expressed in cell coordinates in an int e For each one of the number of Receiver Box regions rx_box in the analysis The total number of output points for this box output region NRXBOXOUT in an int The x coordinate of each receiver in this box expressed in cell coordinates in an int The y coordinate of each receiver in this box expressed in cell coordinates in an int e The components of the electromagnetic fields L Hz Hy each stored in a float in that order for every rx output point NRX and then for every output point defined in each rx_box NRXBOXOUT at every time step for a total of NI time steps and a total of NSTEPS runs in the analysis snapshot BINARY output file After the header information is stored as follows e The title of the model ina string of TTTLELENGTH bytes e The number of iterations NI which have been performed in an float e The spatial st
45. com In the directory examples some input files used as examples in this manual have been included The directory media contain a sample media file and in the directory tools there aresome MAT LAB functions that can be used to import GPRMAx2D 3D modelled data stored in binary for mat in MATLAB 1 2 Downloading from the Website If you have downloaded the compressed zIP archive from the GPRMAX website at www goprmax org or www gprforum org or from my web page at www see ed ac uk agianno follow the same procedures as described above for the CD ROM distribution after uncompressing it to a directory of your preference 1That will require root privileges If you do not known the root password then you can run the program from a directory in your home space 1 3 Running GPRMAx2D 3D To run a 2D or 3D GPR model using GPRMAx2D 3D you have to create an input file in which the parameters of the model are specified This input file is a plain ASCII text file and should have a valid filename of your preference The structure of this input file is explained in detail in subsequent chapters To run the programs in an MS WINDOWS environment open a system DOS command window In recent MS WINDOWS OS versions you can open a command window by clicking on the Run option and typing cmd At the command window then type at the prompt GprMax2D your_path your_input_file The your_path can be the absolute path where the input file is located or the r
46. d have been retired as they are not functioning anymore These are scan CSg extra_tx There are some new commands that have been added form Version 2 which are cylinder_new thin_wire tanalysis end_analysis Htx_steps rx_steps huygens_surface thertzian_dipole voltage_source olane_wave Finally some older commands have been modified These are 28 tx snapshot transmission_line 4 3 GpRMAx3D command parameters To aid the presentation of GPRMAx3D commands they have been grouped in four categories General commands which include the ones used to specify the size and discretization of the model ABC related commands which allow the customization and optimization of the absorbing boundary conditions Media and Object construction commands which are used to introduce different media in the model and construct simple geometric shapes with different constitutive parameters Excitation and Output commands which are used to place source and output points in the model Most of the commands are optional with the exception of the ones which are necessary in order to construct the simplest model possible For example none of the commands of the Media and Object construction section are necessary to run a model However without specifying any objects in the model GPRMAX3D simulates a free space air region not of particular use for GPR modelling If y
47. deciding on the type of excitation in the follwing source definition commands The syntax of the command is very simple xcitation_file strl where str1 is the name of the ASCII file containing the values of the user specified pulse The format of the file is simply a single column of numbers For example the command xcitation_file mysource dat will read values from the file mysource dat which can be used instead of the values obtained by using GPRMAXx3D build in excitation functions to describe the pulse shape of the source in the model hertzian_dipole The command hertzian_dipole is used to define the simplest excitation in GPRMAx3D which is to specify a current density term at an electric field location This will simulate an in finitesimal dipole it does have a length of Al The syntax of the command is hertzian_dipole f1 f2 strli str2 The parameters f1 and 2 are the amplitute and frequency of the source s waveform The param eter str1 is a waveform type identifier and could be any of the ones available in GPRMAX2D or 36 the keyword user when a User specified waveform is to be employed using an excitation_file command The parameter st r2 is a source identifier that will be used in a tx command to re late this type of source to a location in the model For example hertzian_dipole 1 0 600e6 ricker MyDipole Introduces in the model the parameters of the current definiti
48. depicted field compo nents are the ones which correspond to space coordinate 1 Ax Ay Az 1 metre This manual can not serve as an in depth tutorial and a review of the FDTD method However some useful hints and tips are given here in order to cover the most fundamental aspects of using an FDTD based program and avoid the most common errors Discretization There is no specific guideline for choosing the right discretization for a given problem In general it depends on the required accuracy the frequency content of the source s pulse and the size of the targets Obviously all targets present in a model must be adequately resolved This means for example that a cylinder with radius equal to one or two spatial steps does not really look like a cylinder An other important factor which influences the discretization is the errors associated with nu merical induced dispersion This means that contrary to the real world where electromagnetic waves propagate with the same velocity irrespectively of their direction and frequency assuming no dispersive media and far field conditions in the discrete one this is not the case This error details can be found in 1 and 2 can be kept in a minimum if the following rule of thumb is satisfied the discretization step should be at least ten times smaller than the smallest wave length of the propagating electromagnetic fields Note that in general low loss media wavelengths are much smalle
49. der of the ABC see 1 Its syntax is abc_order il 3GpRMAX2D performs averaging of media properties at interfaces between regions of different constitutive parame ters Hence more space is required than the actual number of media in the model 17 The parameter i1 can take the values 1 2 or 3 The default order is 3 The lower the order of the ABC the worse its performance is For example the command abc_order 1 will force GPRMAX2D to use a first order Higdon ABC instead of the default third order one The only benefit of lower order ABCs is the increased stability that they offer abc_stability_factors The command abc_stability_factors allows you to specify small loss terms which are introduced in the ABC in order to increase its stability see 1 The syntax of the command is abc_stability_factors f1 f2 f3 The higher the parameters f1 f2 f3 are the more stable the ABC although by increasing them its performance will deteriorate If you use this command the values for the parameters should not in general be grater than 0 5 Further if you have specified a first order ABC only the first parameter f1 is effectively used and if you have specified a second order one only the first two are effectively used However values for all three parameters have to be given abc_optimization_angles The command abc_optimization_angles can be used to optimize the ABC for specific angles
50. der to run a model for example the size of the model GPRMAx2D will terminate execution issuing an appropriate error message ts The essential commands which represent the minimum set of commands required to run GPRMAX2D are e domain e dx_dy e time_window e At least one analysis with the corresponding end_analysis commands en closing at least one t x and one rx and or rx_box commands e In order for the tx command to function properly a new line_source com mand is required as well 3 3 1 General commands title With the command t it le you can include a title for your model This title is saved in the output file s The syntax of the command is title str The parameter str here can contain white space characters to separate individual words The title has to be contained in a single line 13 domain The command domain should be used to specify the size in metres of the model Its syntax is domain f1 2 The parameters f1 and f2 are the size in metres of your model in the x and y direction respec tively For example domain 1 0 1 5 will set the size of the model to be 1 0 x 1 5 metres dx_dy The command dx_dy is used to specify the discretization of space in the x and y directions respectively i e Ax and Ay The syntax of this command is dx_dy fL f2 where f1 is the spatial step in the x direction Ax and f2 is the spatial step in the y
51. direction Ay Hence a command as ax dy Osi Qwik will set the discretization steps Ax and Ay to 10 centimetres in each direction The choice of the discretization steps Ax and Ay is very important in constructing a model This command combined with the domain command determines the number of cells which are going to be used in the model and consequently the greatest part of the requirements for computer memory for the model For example using the commands domain 1 01 5 ax dys 0 1 0 1 The number of cells in the model will be 10 x 15 Changing the above to domain 1 0 1 5 dx_dy 0 01 0 01 the number of cells in the model will increase to 100 x 150 Further the spatial discretization controls the maximum permissible time step At with which the solution advances in time to reach the required simulated time window The relation between At and Az Ay is 3 1 At lt 2 1 al Cy ay By where c is the speed of light In GPRMAx2D the equality is used in 3 1 to determine At from Az and Ay As is evident from 3 1 small values of Az and Ay result in small values for At which means more iterations in order to reach a given simulated time However it is important to note that the smaller the values of Ax Ay and At are the more accurate your model will be 14 time_step_stability_factor With the command time_step_stability_factor you can alter the value of the time step At calculat
52. e can be overlaid on top of the other overwriting its properties in order to produce the desired geometry Note that commands who create surface or line objects like the plate triangle bowtie and edge commands can be similarly used to create complex shapes and configurations 4 3 4 Excitation and output commands The commands which can be used to describe the source and output points in a GPRMAx3D model are very similar with the ones used in GPRMAX2D The only differences are in the rx tx and snapshot commands in GPRMAX3D and the corresponding ones in GPRMAX2D are in the number of parameters that they need However GPRMAX3D offers a much more wider range of excitation procedures than the sin gle line_source available in GPRMAx2D The commands that define or help to define sources in GPRMAX3D are excitation_file hertzian_dipole voltage_source transmission_line plane_wave huygens_surface excitation ile The command excitation_file allows the user to specify a single ASCII file that contains a list of amplitude values that can be used to excite the model These values need to be at least equal to the number of iterations that are going to be performed If they are less than this number then zero values are substituted for the missing values If more values are specified than needed they are superfluous and are ignored To use this User specified excitation pulse use the user option when
53. e in GPRMAx2D to facilitate the introduction of different media in the model and the construction of specific objects are discussed in this section GPRMAx2D after the processing of general commands sets up a model of the required size initialized to sim ulate free space air By using the commands in this section you can introduce other media and objects in the model It is important to note that free space and perfect conductors are already defined internally and you do not have to redefine these two media Thus the key words free_space and pec which describe air and perfect conductors respectively are reserved and can be used directly without any definition of constitutive parameters For any other media their parameters have to be made known to GPRMAX2D by using either or both e a media file defined by the media_file command which contains the definitions of various frequently used media see Appendix A e a medium command in the input file medium With the medium command you can introduce into the model a set of constitutive parameters describing a given medium The syntax of the command is medium f1 f2 3 f4 5 6 stri The parameters of the command are e 1 the DC static relative permittivity of the medium ers e 2 the relative permittivity at theoretically infinite frequency roo e 3 the relaxation time of the medium 7 seconds e 4 the DC static conductivity of the medium o Siemens
54. ed by GPRMAx2D However the new value should be within the allowable range for stability determined by equation 3 1 As it was mentioned above GPRMAX2D uses the equality in equation 3 1 hence the maximum permissible time step If a smaller time step is required then the command time_step_stability_factor f1 allows you to accomplish this The parameter f1 can take values 0 lt f1 lt 1 Then the actual time step that GPRMAX2D will use will be 1 At remember At is the one calculated using equality in 3 1 time_window The command t ime_window should be used to specify the total required simulated time Its syntax is time_window f1 or time_window il In the first case the f1 parameter determines the required simulated time in seconds For example if you want to simulate a GPR trace of 20 nanoseconds then time_window 20e 9 can be used GPRMAX2D will perform the necessary number of iterations in order to reach the required simulated time Alternatively if the command is specified with an i1 GPRMAx2D will interpret this value as a specified total iteration number Hence the command time_window 100 means that 100 iterations will be performed The number of iterations and the total simulated time window are related by 3 2 ty At x Ni where tu is the time window seconds At the time step and Nj the number of iterations number_of_media The command number_of_media has to be used when your model req
55. egion In essence the command defines a box inside of which is the total field region and outside the scattered field Special conditions on the surface allows the sourcing of a plane wave For details about separating the model into total and scattered field regions see 3 The syntax of the command is 38 huygens_surface f1 f2 f3 f4 5 f6 strl The parameters f1 f2 f3 are the lower left x y z coordinates of the huygens surface paral lelepiped i e box in metres Similarly the f4 5 f6 are the upper right x y z coordinates of the parallelepiped The parameter st r1 is an identifier for this surface that should be used in the plane_wave command to connect this surface to a specific plane wave source For example huygens_surface 0 2 0 2 0 2 0 8 0 8 0 8 MyHuygens defines a box of total field with lower left x y z coordinates as 0 2 0 2 0 2 and upper right 0 8 0 8 0 8 bounded by a Huygens surface The identifier MyHuygens will be used in a plane wave command analysis and end_analysis After source types have been introduced then placing sources and output points in GPRMAx3D is accomplished using a pair of new commands analysis and end_analysis The source command tx and receiver commands rx and or rx_box are to be placed between these two commands The syntax of the command analysis is analysis il filel cl The parameter i1 is the number of new ru
56. elative path where the input file is located with respect to the directory you are currently in For example assume your executable image of GPRMAX2D is located in the directory C GprMax Bin and assume that your input file is in the directory C GPRModels Inputs and is called Model1 in If your current directory is C GprMax you can issue the commands Bin GprMax2D C GPRModels Inputs Modell in or Bin GprMAx2D GPRModels Inputs Modell in in case you have included in your PATH the directory C GprMax Bin then you can type GprMax2D C GPRModels Inputs Modell in or GprMax2D GPRModels Inputs Modell in To run the programs in a LINUX environment follow the same procedure as for an MS WINDOWS system 1 4 General structure of the input file The input file which has to be supplied to GPRMAx2D 3D contains all the necessary information to run a GPR model Detailed description of the various commands available that can be used in GPRMAx2D 3D input files are described later in this manual However the general structure of an input file is the same in both programs The input file is a plain ASCII text file which can be prepared with any editor or word processing program In the input file the hash character is reserved and is used to denote the begin ning of acommand which should be passed to the programs The general syntax of all available commands is command_name parameterl parameter2 parameter3 For exam
57. ep Az ina float e The spatial step Ay ina float e The time step At ina float e The global source position number of the snapshot in an int e The lower left x coordinate of the snapshot area expressed in cell coordinates in an int 57 For all the X coordinates Lower gt Higher For all the Y coordinates Lower gt Higher E value Figure 6 1 Representation in pseudo code of the procedure used in GPRMAX2D in order to store the values of field components in a snapshot The lower left y coordinate of the snapshot area expressed in cell coordinates in an int The upper right x coordinate of the snapshot area expressed in cell coordinates in an int The upper right y coordinate of the snapshot area expressed in cell coordinates in an int The sampling interval in the x direction normalized by Az stored in an int The sampling interval in the y direction normalized by Ay stored in an int The time instant when the snapshot has been taken normalized by At i e iteration num ber stored ina float The number of samples in the x direction in an int The number of samples in the y direction in an int The values of the E electromagnetic field component each stored in a float at every x y sampling point Figure 6 1 illustrates in pseudo code the procedure used to store the values of the field component The values of the H electromagnetic field component each stored ina float at every x y sampling point Figure
58. epresent a free space region or a perfect conductor In the edge command the coordinates should define a single line and not a 3D object as with the box command For example the command dge 0 5 0 5 0 5 0 7 0 5 0 5 pec 33 defines an x directed wire i e Yee cell edges Observe that the y and z coordinates are identical This differs from the box command where the use of such coordinates will be illegal cylinder With the command cylinder you can introduce a circular cylinder of finite dimensions in the 3D model The syntax of the command is cylinder cl f1 f2 3 f4 5 strl The parameter c1 denotes the direction of the cylinder s axis and it could be either x or y or z The parameters f1 and f2 are the lower and higher coordinates of the cylinder s axis For example if the cylinder is oriented in the x direction f1 2 are the coordinates x1 x2 The parameters 3 and f4 are the remaining necessary coordinates required to describe the centres of the two circular faces of the cylinder Hence for the x oriented cylinder these are y and z respectively The following list describes all possible combinations e for an x oriented cylinder 1 3 4 is x1 y z and 2 3 4 is x2 y z e for an y oriented cylinder 3 1 4 is x y1 z and 3 2 4 is x y2 z e for an z oriented cylinder 3 4 f 1 is x y z1 and 3 4 2 is x y z2 The param
59. eps command and stay the same as defined in the input file throughout out the analysis The last command which is described bellow that can be inserted between a pair of analysis and end_analysis commands is the command snapshot snapshot In order to obtain information about the electromagnetic fields within an area of the model at a given time instant you can use the snapshot command The syntax of this command is snapshot il f1 f2 3 4 5 fO 7 8 9 10 filel cl or snapshot il f1 2 3 4 5 6 7 8 9 i2 filel cl The parameters of the command are e i1 isa counter called the global source position which is used to determine the source s po sition for which the snapshot should be taken The global source position takes a value between 1 and the number of steps defined as the first parameter in the analysis com mand 41 e f1 f2 and 3 are the lower left x y z coordinates in meters of the orthogonal parallepiped of the snapshot e 4 5 and 6 are the upper right x y z coordinates in meters of the orthogonal par allepiped of the snapshot e 7 8 and f9 are the sampling intervals in metres in the x y and z direction respectively e 10 or i2 are the snapshot time in seconds float number or the iteration number integer number respectively which denote the point in time at which the snapshot is to be taken e filel i
60. eter f5 is the radius r in metres of the circular cylinder and st r1 is a medium identifier see Chapter 3 Hence the command cylinder y 0 1 0 8 0 5 0 5 0 1 pec introduces in the 3D model a perfectly conducting circular cylinder with its axis in the y direction having a length of 0 7 metres a radius r equal to 10 cm and with the coordinates of the centres of its two faces being 0 5 0 1 0 5 and 0 5 0 8 0 5 cylinder_new With the command cylinder_new you can introduce a circular cylinder of finite dimensions in the 3D model The difference of this command with the command cylinder is that the orientation of the cylinder axis can be arbitrary i e it does not have to be one of the model s cartesian axes The syntax of the command is cylinder_new f1 f2 3 f4 5 f6 f7 strl The parameters f1 f2 and f3 are the coordinates of the centre of one of the cylinder s two faces Similarly the parameters 4 5 and f6 are the coordinates of the centre of the second face The parameter f7 is the radius r in metres of the circular cylinder and st r1 is a medium identifier see Chapter 3 Hence the command cylinder_new 0 5 0 1 0 5 0 5 0 8 0 5 0 1 pec introduces in the 3D model a perfectly conducting circular cylinder as the above example for the cylinder command with its axis in the y direction having a length of 0 7 metres a radius r equal to 10 cm and with the coordinates of the
61. etermined The problem at hand includes two different types of material con crete and wet sand Particular values for their dielectric properties were not specifically defined Therefore it will be assumed that the relative permittivity for the wet sand is e 20 and the parameters of concrete will be the ones used in the previous example The value of e 20 for wet sand may be rather high However is assumed here that it is saturated with water Using a ricker source at f 900 MHz a simple calculation reveals that a spatial step of Al 2 5 mil limetres is close to the limit set by the rule of thumb but it should be small enough for a reasonably accurate model The size of the model is set to 2600 x 800 millimetres which translates to 1040 x 320 cells The time window is set to 12 nanoseconds and a 115 GPR traces are to be calculate along a scan line of 2400 millimetres The input file for this model can thus be created and reads like medium 6 0 0 0 0 0 0 01 1 0 0 0 concrete medium 20 0 0 0 0 0 0 1 1 0 0 0 wet_sand domain 2 5 0 5 dx_dy 0 0025 0 0025 time_window 12e 9 box 0 0 0 0 2 5 0 45 wet_sand Use a cylinder of free space and then put a slab of concrete to cut it in half To calculate the smallest wavelength in wet sand a frequency of 3 x f was used 47 200 mm 100 mm 4 BRE Examle 1 300 mm Void sass 500 mm 2400 mm 200 mm BRE Example 2 t p 150 mm E a d dia 600 mm 2400
62. gth of the antenna s elements half the total length of the complete bowtie and the parameter f5 is the flare angle in degrees The parameter st r1 is a medium identifier defined either with a medium command or in a media file currently in use Further the identifiers free_space or pec can be used if the bowtie is to represent a free space region or a perfect conductor For example the command bowtie x y 0 5 0 5 0 5 0 12 60 0 pec defines a bowtie antenna that lies in the xy plane and is polarised in the x direction Further the antenna has a flare angle of 60 degrees and a total length of 0 24 metres The antenna s feed point is located at the 0 5 0 5 0 5 coordinates To succesfuly excite the antenna we need to specify a source at these coordinates which is polarised in the same direction edge With the command edge you can introduce a wire with specific properties in the model The wire is just an edge of a Yee cell and it can be useful when modelling resistors or thin wires The syntax of the command is plate f1 f2 3 f4 5 f6 strl The parameters f1 f2 f3 are the starting x y z coordinates of the edge in metres Similarly the 4 5 f6 are the ending x y z coordinates of the edge The parameter st r1 is a medium identifier defined either with a medium command or in a media file or using a thin_wire command currently in use Further the identifiers ree_space or pec can be used if the edge is to r
63. ical Speed of light c defined as 2 9979245 x 108 metre second Permittivity of free space o defined as 8 854187 x 107 Farads metre Permeability of free space uo defined as 1 256637 x 107 Henrys metre Characteristic impedance of free space Zo defined as 376 7303134 Ohms e Program related The maximum length of media identifiers MED IALENGTH is 30 characters The maximum length of filenames F ILELENGTH is 255 characters The maximum length of source types SOURCELENGTH is 30 characters The maximum length of title TITLELENGTH is 250 characters The maximum number of different media in a model is 32768 The maximum number of cells which can be allocated depends solely on the amount of available computer memory The precision of integer numbers is 2 bytes The precision of floating point numbers is 4 bytes The minimum number of cells which can be allocated in any direction is 9 The maximum number of iterations is 2147483648 which is by far more than will be required Take note that the number of iterations in binary output files and the iteration counter for binary stored snapshots is converted and stored as a float 66 Excitation functions The definitions of the source functions which can be used in GPRMAX2D are e The cont_sine excitation function is defined as I Rsin 2r ft and pa ES ifR lt 1 oyu ifR gt 1 where J is the
64. ion command i e line_source The parameter f3 is a delay in the source s initiation If it is greater than zero then the source will be active after that time delay has passed The parameter f4 is the time of source removal If the simulation runs for longer than the source s removal time the source will stop functioning in the model after 4 seconds If the time of source removal is longer than the simulated time window then the source is active for the complete simulation and the time window value is used instead The syntax of the rx command is CIO EL wD and the parameters f1 and f2 are the x y coordinates in metres of the output receiver point The syntax of the rx_box command is rx_box fl f2 3 f4 5 f6 The parameters f1 and f2 are the lower right x y coordinates of the output region The 3 and 4 are the higher right x y coordinates of the output region and finally 5 and 6 are the steps which define the number of output points in each direction The minimum value of 5 is Ax and of 6 is Ay For example with the commands analysis 1 testl out a tx 0 5 0 5 MySource 0 0 10e 9 exe 045 047 rx 0D 048 rx 06 049 EXEDOX 01 3 03 0 5 05 0 201 004 nd_analysis GPRMAXx2D will run the model once There is only one source point located at 0 5 0 5 and the excitation with ID MySource which should have been specified earlier
65. ired simulated time window The relation between At and Az Ay and Az is 1 4 1 At lt c al 3 1 1 V Ga t Woy T Be where c is the speed of light In GPRMAX3D the equality is used to determine At from Az Ay and Az As is evident from 4 1 small values of Az Ay and Az result in small values for At which means more iterations in order to reach a given simulated time However it is important to note that the smaller the values of Ax Ay Az and At are the more accurate your model will be time_step_stability_factor The use and syntax of this command is the same as the one available in GPRMAX2D The value of At that this command alters in the one calculated by equation 4 1 time_window The purpose and syntax of this command is the same as in GPRMAx2D number_of_media The use and syntax of this command is as described for GPRMAx2D geometry file The use and function of this command is as described for GPRMAx2D messages The syntax and function of this command is as described for GPRMAx2D nips_number The command nips_number should be included in your input file only when GPRMAx3D has requested its use Its syntax is the same as described for GPRMAx2D 4 3 2 ABC related commands The commands which affect the configuration and performance of the Higdon ABCs in GPRMAx3D have the same function and syntax as described for GPRMAx2D However GPRMAx3D em ploys the recently developed and more powerful PML perfectly m
66. is box expressed in cell coordinates in an int e All six components of the electromagnetic fields F Ey Ez Hz Hy and Hz as well as the currents I Iy and I calculated as V x H z V x H y V x H respectively at electric field component locations and each stored in a float in that order for every output point NRX and then for every output point defined in each rx_box NRXBOXOUT at every time step for a total of NI time steps and a total of NSTEPS runs in the analyis snapshot BINARY output file After the header information is stored as follows e The title of the model ina string of TTTLELENGTH bytes e The number of iterations NI which have been performed in an float e The spatial step Av ina float e The spatial step Ay ina float e The spatial step Az ina float e The time step At ina float e The global source position number of the snapshot in an int e The lower left x coordinate of the snapshot area expressed in cell coordinates in an int e The lower left y coordinate of the snapshot area expressed in cell coordinates in an int 60 The lower left z coordinate of the snapshot area expressed in cell coordinates in an int The upper right x coordinate of the snapshot area expressed in cell coordinates in an int The upper right y coordinate of the snapshot area expressed in cell coordinates in an int The upper right z coordinate of the snapshot area expressed in cell coordinates in an int The sampling interval
67. lity of the medium pr e 6 the magnetic conductivity of the medium o e str1 a string characterizing the medium The maximum length of the identifier st r1 is determined by a constant MEDIALENGTH and has been set to 30 characters No white spaces are allowed in the identifier Further every identi fier must be unique within a media file As an example a media file constructed for some common materials according to tabulated values 1 of their constitutive parameters at a frequency of 100 MHz is 80 0 0 0 0 0 0 01 1 0 0 0 distilled_water 80 0 0 0 0 0 0 5 1 0 0 0 fresh_water 80 0 0 0 0 0 3e4 1 0 0 0 sea_water 3 0 0 0 0 0 0 01 1 0 0 0 dry_sand_min 5 0 0 0 0 0 0 01 1 0 0 0 dry_sand_max 20 0 0 0 0 0 0 1 1 0 0 0 saturated_sand 7 0 0 0 0 0 0 5 1 0 0 0 limestone 64 Since GPRMAX2D 3D can model Debye media you can use the definition 82 3 5 5 10 9e 12 0 0 1 0 0 0 water for water in 15 C This will take into account the polarization relaxation phenomena associated with water which are described by the Debye equation 2 6 see Chapter 2 65 Appendix B GPRMAX2D 3D Constants and excitation functions GPRMAx2D 3D Constants In GPRMAX2D 3D there are some fundamental constants defined which can not be altered unless the source code is edited This is however not wise if you are not familiar with both C program ming and the FDTD method These constants are e Phys
68. ll not be affect ing the model s values they have to be supplied The order which the commands appear in the input file is not significant with the single excep tion of the analysis and end_analysis commands which since Version 2 0 specify the excitation and outputs of the model The fundamental spatial and temporal discretization steps are denoted as Ax Ay and At respec tively 11 3 2 List of all available commands In order to construct a 2D GPR model using GPRMAX2D a set of commands are available which can be used to give the necessary instructions to the program The are 32 commands available in Version 2 0 of GPRMAx2D titl domain dx_dy time_step_stability_factor time_window messages number_of_media nips_number media_file geometry_file medium abc_type abc_order abc_stability_factors abc_optimization_angles abc_mixing_parameters pml_layers box cylinder xX_segment y_segment triangle analysis nd_analysis tx UX rx_box snapshot tx_steps rx_steps line_source xcitation_file the parameters that each command requires is explained in the following section There are some GPRMAX commands that have been retired from Version 2 0 onwards
69. m 3 x f 2700 MHz The wavelength of 2700 MHz in concrete is c E Hence 4 5 cm Considering the rule of thumb described in Chapter 2 the spatial step can be set to 4 5 millimetres 5 1 A Step 3 In order to set the value for the spatial steps first a decision is made for this model to have Az Ay Al This is an obvious choice since there is no need to have a smaller step in a particular direction If we choose as Al 4 5 millimetres then the radius of the rebar will be r 6 cells This will not be considered extremely coarse but if the value is increased to 10 it will improve the model With that in mind the spatial steps are set to 5 2 Az Ay Al 2 5 milimetres The choice of Al 2 5 millimetres is well within the limit described by the rule of thumb Step 4 Since Ax Ay 2 5 millimetres the time step At calculated by 3 1 is Al cV2 which gives At 5 8967 picoseconds ps For a time window of 8 nanoseconds the model will require about 1357 iterations At Step 5 Let us further assume that a 42 5 centimetres long scan is required comprising of 41 GPR traces In order to determine the size of the model we first decide if any reflections from the termination of the slab will be important Considering its depth and the time window that is not the case Hence the concrete slab can be modelled as a half space Therefore a 600 x 300 millimetres model should 44 ricker Waveform Power spectrum
70. metre e f5 the relative permeability of the medium p e 6 the magnetic conductivity of the medium o str1 a string characterising the medium medium identifier Since GPRMAX2D has the ability to model a Debye dielectric medium the relative permittivity is described by the Debye formula see Chapter 2 and 1 Es Eoo Te eee rae 1 JwT If you do not want a debye medium you can set 3 i e T to zero In such a case GPRMAX2D will use only the values specified in 1 and f4 to describe the dielectric properties If a medium is non magnetic you can set 5 to 1 0 and 6 to zero It is important to remember that the value of r should always be higher than the time step At used in the model GPRMAX2D checks and verifies that this condition holds for all Debye media in the model If it does not then GPRMAX2D will exit raising an error The str1 parameter should be a meaningful identifier for the medium For example the com mand 19 medium 3 0 0 0 0 0 0 01 1 0 0 0 my_sand introduces a medium referenced by the identifier my_sand which has a relative permittivity fre quency independent e 3 and conductivity 0 01 Siemens metre and is non magnetic The command medium 82 3 5 5 10 9e 12 0 0 1 0 0 0 water introduces a medium with the electric parameters of water at 15 C which is described by the Debye formula An alternative or complimentary way of introducing media parameters in
71. metres of the output receiver point The syntax of the rx_box command is trx box f1 2 3 4 5 6 7 8 9 The parameters f1 2 and 3 are the lower left hand corner x y z coordinates of the output volume The 4 5 and f6 are the high right hand corner x y z coordinates of the output volume and finally 7 8 and 9 are the steps which define the number of output points in each direction The minimum value of 7 is Az of 8 is Ay and of 9 is Az For example with the commands analysis 1 testl out a tx x 0 5 0 5 0 5 MySource 0 0 10e 9 rx 025 0 5 0 7 ERE OSD 06 5 068 Bx 10 6 0 5 0V5 nd_analysis GPRMAX3D will run the model once There is only one source point located at 0 5 0 5 0 5 with polarization alonf the x direction using an excitation with ID MySource which should have been specified earlier in the file will be used The source is active from time 0 0 until simulated time has reached the value of 10 nanoseconds which could be either the end of the requested time window or earlier than that The output will be stored in ASCII format in the file test 1 out The time evolution of electro magnetic fields at the points specified by the three rx commands at 0 5 0 5 0 7 0 5 0 5 0 8 and 0 6 0 5 0 5 will be stored in the output file Creating scans or running the model more than once If i1 of the analysis command is greater than 1 i e
72. mm Figure 5 4 Schematic drawing of the BRE examples 1 and 2 cylinder 1 05 0 3 0 2 free_space box 0 0 0 3 2 5 0 45 concrete cylinder 0 25 0 375 0 0125 pec cylinder 0 45 0 375 0 0125 pec cylinder 0 65 0 375 0 0125 pec cylinder 0 85 0 375 0 0125 pec cylinder 1 05 0 375 0 0125 pec cylinder 1 25 0 375 0 0125 pec cylinder 1 45 0 375 0 0125 pec cylinder 1 65 0 375 0 0125 pec cylinder 1 85 0 375 0 0125 pec cylinder 2 05 0 375 0 0125 pec cylinder 2 25 0 375 0 0125 pec triangle 0 25 0 3 0 65 0 3 0 45 0 1 free_space triangle 1 45 0 3 1 85 0 3 1 65 0 1 free_space box 2 05 0 1 2 25 0 3 free_space cylinder 2 15125 0 10125 0 1 wet_sand line_source 1 0 900e 6 ricker MyLineSource analysis 115 bre2 out b tx 0 0875 0 4525 MyLineSource 0 0 12e 9 rx 0 1125 0 4525 tx_steps 0 02 0 0 rx_steps 0 02 0 0 end_analysis geometry_file bre2 geo title BRE Model 2 messages y It is interesting to examine the order with which the object construction commands appear in the input file For example in order to construct the semicircular void a cylinder command is used after the construction of the background rectangle of wet sand The vertical height of 48 200 mm BRE Example 3 te 150 mm 300 mm e 2400 mm Depth of Void A 0mm B 25 mm C 50mm D 55 mm E 100 mm F 100 mm G 25 mm H 0 mm BRE Examle 4 2400 mm Figure 5 5 Schematic drawing of the
73. mmodate i e specification of the source the second part can not be easily tackled using a finite computational space The FDTD approach to the numerical solution of Maxwell s equations is to discretize both the space and time continua Thus the discretization spatial Ax Ay and Az and temporal At steps play a very significant role since the smaller they are the closer the FDTD model is to a real representation of the problem However the values of the discretization steps always have to be amp j 1 k 1 E i 1 j 1 k 1 gt ij 1 k i 1 j k 1 y i k gt i Lj k Figure 2 1 The 3D FDTD Yee cell finite since computers have a limited amount of storage and finite processing speed Hence the FDTD model represents a discretized version of the real problem and of limited size The building block of this discretized FDTD grid is the Yee cell 4 named after Kane Yee who pioneered the FDTD method This is illustrated for the 3D case in Figure 2 1 The 2D FDTD cell is a simplification of the 3D one and is depicted in Figure 2 3 By assigning appropriate constitutive parameters to the locations of the electromagnetic field com ponents complex shaped targets can be included easily in the models However objects with curved boundaries are represented using a staircase approximation The numerical solution is obtained directly in the time domain by using a discretized version of Maxwell s
74. nd example box 0 0 0 0 0 0 0 6 1 3 0 5 concrete box 0 2 0 55 0 1 0 4 0 75 0 3 free_space hertzian_dipole 1 0 600e6 ricker MyDipole analysis 21 void out b tx x 0 3 0 125 0 55 MyDipole 0 0 12e 9 see 04 3 0 375 0 55 tx_steps 0 0 0 04 0 0 rx_steps 0 0 0 04 0 0 end_analysis messages n title 3D small void The result of the GPRMAXx3D simulation is presented in gray scale image format in Figure 5 12 and agrees very well with the result presented in 1 52 BRE example 4 ns 0 5 1 1 5 2 Scan length m Figure 5 9 Simulated GPR scan of the BRE fourth example X Direction of Source I 3S o 3 We oO Figure 5 10 Three slices through a volume of data The amplitude of the Ez field component is represented as a gray scale image The figure was created in MATLAB from the GPRMAX3D data 53 Tx Rx 0 25 m Yee Cells 60 130 65 fo 6 fs 600 MHz Al 0 01 m o 0 001 S m Num of traces 21 At 19 258 ps s 0 8m h 0 05 m l 0 2m d 0 2m cross section A A top view depth 0 3 m z A y A Air x scan line not to scale Figure 5 11 Schematic drawing of the 3D model of a small void after 1 Small void 0 0 1 0 2 0 3 0 5 0 6 0 7 0 8 0 4 Scan length m Figure 5 12 GPRMAX3D simulated GPR scan over a small void 54 Chapter 6 GPRMAX2D 3D Output File formats This Chapter describes the file formats used by GPRMAx2D and GPRMAX3D to
75. nd the information stored in them is in general self explanatory 6 4 GPRMAx3D BINARY file formats The file formats of GPRMAX3D differ from GPRMAX2D since information for the polarisation of the source has to be included in addition to the need to store all six components of the electro magnetic fields The basic structure of the files however is very similar analysis BINARY output file After the header information is stored as follows The title of the model ina st ring of TTTLELENGTH bytes The number of iterations NI which have been performed in an float The spatial step Av ina float The spatial step Ay ina float The spatial step Az ina float The time step At ina float The number of steps in the analysis command NSTEPS in an int The step in the x direction with which the source point moves for each trace normalized by Az stored in an int The step in the y direction with which the source point moves for each trace normalized by Ay stored in an int The step in the z direction with which the source point moves for each trace normalized by Az stored in an int The step in the x direction with which the output point receiver moves for each trace normalized by Az stored in an int The step in the y direction with which the output point receiver moves for each trace normalized by Ay stored in an int The step in the z direction with which the output point receiver moves for each trace n
76. ns of the model This is similar to what the number of scans was in the old scan command and it means that the model will run again after re setting all arrays and time to zero for every single i1 The parameter file1 is the name of the file where all the results for this analysis are going to be stored and the parameter c1 isa single character either a or b denoting that the format of the output file file1 will be ASCII or BINARY respectively It is important that an analysis command is followed after other source and output con trolling commands have been inserted by the command nd_analysis which denotes the end of an analysis section that was started using an analysis command The end_analysis command has no parameters In your input file there can be any number of analysis and end_analysis pair of commands tx rx and rx_box The commands tx rx and rx_box are used together in order to introduce a source po sition tx and output points rx and rx_box Any number of t x commands could be specified in the model as well as any number of rx and or rx_box commands The new syntax of the tx command in GPRMAX3D is very similar to the one in GPRMAx2D and is tx cel Er 2 3 strl 4 5 The parameter c1 defines the polarization of the source and could be one of x y or z The pa rameters f1 f2 and
77. nt y 0 1 0 8 0 5 0 5 0 1 pec x 0 45 0 55 introduces in the 3D model a perfectly conducting cylindrical segment with its axis in the y direc tion having a length of 0 7 metres a radius r equal to 10 cm and with the coordinates of the centres of its two faces being 0 5 0 1 0 5 and 0 5 0 8 0 5 However only cells which are located between the 0 45 and 0 55 coordinates along the x axis are allocated as a pec medium creating the required cylindrical segment sphere With the command sphere you can introduce a spherical object with specific parameters in the 3D model Its syntax is sphere f1 2 3 f4 strl The parameters 1 2 and f3 are the coordinates of the sphere s centre and f4 is its radius r in metres The parameter st r1 is a predefined medium identifier For example the command sphere 0 5 0 5 0 5 0 1 my_sand introduces a sphere of radius r 10 centimetres with its centre at 0 5 0 5 0 5 and with the con stitutive parameters of my_sand A note on object construction It is important to note that GPRMAXx3D process all the object construction commands in the order they appear in the input file in the same way GPRMAX2D does Thus model s space allocated to a specific medium using for example the box command can be reallocated to another medium using the same or any other object construction command Hence the model s space can be 35 regarded as a canvas in which objects are introduced and on
78. oating point numbers denoted by float are SREAL bytes long A character denoted by char is stored in one byte The data part of a binary format file starts at byte 16 GPRMAx2D BINARY file formats The data part of GPRMAX2D binary format files are described in this section analysis BINARY output file After the header information is stored as follows The title of the model ina st ring of TITLELENGTH bytes The number of iterations NI which have been performed in an float The spatial step Av ina float The spatial step Ay ina float The time step At ina float The number of steps in the analysis command NSTEPS in an int The step in the x direction with which the source point moves for each trace normalized by Az stored in an int 3For data formats of older Versions see their manual for details 56 e The step in the y direction with which the source point moves for each trace normalized by Ay stored in an int e The step in the x direction with which the output point receiver moves for each trace normalized by Az stored in an int e The step in the y direction with which the output point receiver moves for each trace normalized by Ay stored in an int e The number of transmitters specified with t x commands NTX in an int e The number of receivers specified with rx commands NRX in an int e The number of receiver box regions specified with rx_box commands NRXBOX in an int e For ea
79. of incidence If you anticipate that most of the reflected energy will impinge on the ABC at specific angles you can optimize its performance for these particular angles Its syntax is abc_optimization_angles f1 f2 f3 The parameters f1 f2 f3 are the angles of optimization in degrees 0 lt 90 For example abc_optimization_angles 0 0 45 0 65 0 will optimize the ABC for normal 45 and 65 incidence It is recommended that you do not alter the default GPRMAX2D parameters abc_mixing_parameters The command abc_mixing_parameters canbe used to change the discretization of the tem poral and partial derivatives in the Higdon ABC used by GPRMAX2D see 1 The default dis cretization is the most commonly used box scheme The syntax of the command is abc_mixing_parameters fl f2 f3 f4 5 f6 The parameters f1 and f2 are the mixing parameters for the first order Higdon the f3 and f4 are used with the ones defined for the first order to determine the ABC coefficients for the second order and similarly the 5 and 6 are used with all the previous ones to determine the parameters of the third order ABC The default values for the box scheme are abc_mixing_parameters 0 5 0 5 0 5 0 5 0 5 0 5 It is strongly recommended that you not change these default values unless you are familiar with the formulation of the Higdon ABC 18 3 3 3 Media and Object construction commands The commands which are availabl
80. ommand plate you can introduce a plate with specific properties in the model The plate is just a surface of a Yee cell and it can be useful when the modelling of thinner surfaces than a Yee cell are required The syntax of the command is olate f1 f2 3 4 5 f6 stri The parameters f1 2 3 are the lower left x y z coordinates of the plate in metres Similarly the 4 5 6 are the upper right x y z coordinates of the plate The parameter st r1 is a medium identifier defined either with a medium command or in a media file currently in use Further the identifiers free_space or pec can be used if the plate is to represent a free space region or a perfect conductor In the plate command the coordinates should define a surface and not a 3D object as with the box command For example the command plate 0 5 0 5 0 5 0 7 0 8 0 5 pec defines a xy oriented plate i e Yee cell surfaces Note that in the above example the z coordinates are identical This differs from the box command where the use of such coordinates will be illegal triangle With the command triangle you can introduce a triangular patch with specific properties in the model The patch is just a triangular surface made as a collection of staircased Yee cells in the same way that is created in GPRMAX2D The syntax of the command is triangle f1 f2 3 f4 5 f6 f7 8 9 strli 32 The parameters f1 2
81. on model for the complex permittivity is included in both GPRMAx2D and GPRMAXx3D Therefore for the 2D case the governing equations reduce to the ones describing the propagation of TM mode electromagnetic waves relative to the invariance direction z of the model 2 3 Capabilities and limitations of GPRMAx2D 3D In general GPRMAX2D 3D solve numerically Maxwell s equations in two TM case and three dimensions Any linear isotropic media with constant constitutive parameters can be included in the model In addition they can model dielectrics with frequency depended permittivity de scribed by the Debye formula Es Eoo 2 6 E so t 1 JwT where is the permittivity at light frequencies is the DC permittivity and w is the angular frequency The computational domain of both GPRMAx2D 3D could be truncated either us ing a third order Higdon local absorbing boundary condition ABC or by introducing Perfectly Matched Layers PML in the model The default is the Higdon ABC however the performance of the PML is superior especially if more than six 6 layers are used The parameters of the Higdon ABC can be altered if required using simple commands In the case of PML only the number of layers of the PML is adjustable by the user Excitation of a model in GPRMAX2D is achieved by specifying the current of a line source In GPRMAX3D when a Hertzian dipole is used excitation is achieved by specifying the current and
82. on of a Hertzian Dipole with unit amplitute and centre frequency of a ricker wavelet of 600 MHz The command hertzian_dipole is the complete equivalent of the command 1ine_source that is used in GPRMAX2D voltage_source The command voltage_source is used to define a voltage source that can be introduced in the position of an electric field component either as a hard source i e replacing the electic field component s value or as having an internal lumped resistance The voltage_source command is mainly usefull in exciting GPR antennas when the physical proper of the antenna is included in the model The sysntax of the command is voltage_source f1 f2 strl f3 str2 The parameters f1 and 2 are the amplitute and frequency of the source s waveform The param eter st r1 is a waveform type identifier and could be any of the ones available in GPRMAX2D or the keyword user when a User specified waveform is to be employed using an excitation_file command The parameter f3 is the internal resistance R of the voltage source in Ohms 9 If 3 is set to zero then the voltage source is a hard source That means it prescribes exactly what the value of the electric field component would be If the waveform becomes zero then this source is perfectly reflecting The parameter st r2 is a source identifier that will be used in a tx com mand to relate this type of source to a location in the model For example voltage_source 1 0 600e6 ga
83. ormalized by Az stored in an int The number of transmitters specified with t x commands NTX in an int 59 e The number of receivers specified with rx commands NRX in an int e The number of receiver box volume regions specified with rx_box commands NRXBOX inan int e For each one of the Transmitters sources t x in the analysis The polarization of the source x y or z ina char The x coordinate of the source expressed in cell coordinates in an int The y coordinate of the source expressed in cell coordinates in an int The z coordinate of the source expressed in cell coordinates in an int The source type i e the source ID ina st ring of SOURCELENGTH bytes The initial source time delay as float The time of source removal as float e For each one of the number of Receivers rx in the analysis The x coordinate of the receiver expressed in cell coordinates in an int The y coordinate of the receiver expressed in cell coordinates in an int The z coordinate of the receiver expressed in cell coordinates in an int e For each one of the number of Receiver Box regions rx_box in the analysis The total number of output points for this box output region NRXBOXOUT in an int The x coordinate of each receiver in this box expressed in cell coordinates in an int The y coordinate of each receiver in this box expressed in cell coordinates in an int The z coordinate of each receiver in th
84. ou have not specified a command which is essential in order to run a model for example the size of the model GPRMAX3D will terminate execution issuing an appropriate error message ts The essential commands which represent the minimum set of commands required to run GPRMAXS3D are domain dx_dy time_window At least one analysis with the corresponding end_analysis commands en closing at least one tx and one rx and or rx_box commands In order for the tx command to function properly a source definition command e g Hert zian_dipole is required as well 4 3 1 General commands title The comm domain The comm domain and title has the same syntax and function as in GPRMAx2D and domain is used to specify the size in metres of the model Its syntax is 1 223 The parameters f1 f2 and f3 are the size in metres your model in the x y and z direction respectively 29 dx_dy_dz The command dx_dy_dz is used to specify the discretization of space in the x y and z direc tions respectively i e Ax Ay and Az The syntax of the command is dx_dy_dz 1 f2 3 where f1 is the spatial step in the x direction Ax f2 is the spatial step in the y direction Ay and 3 is the spatial step in the z direction Az The spatial discretization controls the maximum permissible time step At with which the solution advances in time in order to reach the requ
85. ower left x y coordinates in meters of the rectangular area of the snapshot e 3 4 are the upper right x y coordinates in meters of the rectangular area of the snapshot e f5 6 are the sampling intervals in metres in the x and y direction respectively e 7 or i2 are the snapshot time in seconds float number or the iteration number integer number respectively which denote the point in time at which the snapshot is to be taken e filel is the filename of the file where the snapshot is to be stored c1 can be a or b if the format of the snapshot file is to be ASCII or BINARY respectively For example the commands analysis 10 testl out a tx 0 5 0 5 MySource 0 0 10e 9 Tee 05 6 0 15 snapshot 5 0 0 0 0 1 0 1 0 0 1 0 1 3e 9 snapl out b tx_steps 0 01 0 0 rx_steps 0 01 0 0 nd_analysis will allow as to get a snapshot of the electromagnetic fields in the model at 3 nanoseconds while the model is calculating the fifth GPR trace 26 Chapter 4 GPRMAX3D input file commands 4 1 General notes on GPRMAx3D commands Most of the commands that can be used in GPRMAX3D input files are almost the same as the ones described for GPRMAx2D However there are some commands which are unique for GPRMAx3D For the sake of brevity only the syntactical differences of GPRMAXx3D commands that perform the same function as in GPRMAX2D will be described here Therefore please refer to Chapter 3 fo
86. pectively of the angle of incidence or the frequency of the impinging pulse In order to use the PML boundary condition instead of the default Higdon ABC the command abc_type pml has to be used The command abd_type higdon sets the ABC back to its default setting At this release of GPRMAX2D 3D the user can not influence the parameters of the PML which are determined automatically for optimum performance However the user can define the thickness or depth of the PML using the command pml_layers il where i1 is the number of Yee cells that the PML will occupy The default value is 8 cells The more cells are used the better the performance of the PML but the computational resources in crease substantially when deep PML layers are employed Further there are two important issues on using the PML t The PML layers are part of the model s geometry However the fields in the PML layers are of NO INTEREST and IT IS WRONG TO USE THEM IN CALCULATIONS Therefore DO NOT place sources or receivers in areas of the model occupied by a PML The depth of PML is defined as number of YEE cells and not as a distance in metres The following commands can be used either for experimentation with the Higdon ABCs or for further adjustments if required None of the following commands are required for any GPR mod els constructed with GPRMAx2D and should be used with caution abc_order The command abc_order determines the or
87. ple in GPRMAX2D the size of the computational domain is specified with a command Directory names are separated by a on a LINUX system and device names like C are not used domain 1 0 1 0 A command with its parameters should occupy a single line of the input file and only one com mand per line is allowed Hence the first character of a line containing a command must be the hash character If the line starts with any other character it is ignored by the program There fore user comments or descriptions can be included in the input file If a line starts with a hash character the program will expect a valid command In case the command is not spelt correctly the program will abandon execution issuing an error message When a command requires more than one parameter then these are separated using a white space character The order of introducing commands into the input file is not important with the exception of model building commands and execution i e analysis group commands which will be described in the relevant Chapter 3 Moreover as will be explained later introducing particular commands before others will facilitate the creation of any desired GPR model Chapter 2 Ground Penetrating Radar modelling with GPRMAx2D 3D This chapters discusses some basic concepts of GPR modelling using GPRMAx2D 3D To accom plish such a task GPRMAX2D 3D solve Maxwell s equations using the finite difference time
88. polarisation of the small Hertzian dipole More than one sources can be active at a given time thus making simulation of GPR arrays simple There is a choice of excitation waveforms for GPRMAx2D 3D In addition the user can specify its own excitation function The discretization of the GPRMAx2D 3D models can be different in the direction of each coordi nate axis but can not vary along this direction The smallest element in GPRMAX2D which can be allocated with user defined characteristics is an area of Ax x Ay and in GPRMAXx3D a volume of Az x Ay x Az For a list of the technical characteristics of GPRMAX2D 3D see Appendix B 2 4 GPRMAx2D coordinate system and conventions The GPRMAx2D FDTD algorithm is implemented in the x y plane The origin of the coordinate system is the lower left corner at 0 0 The smallest space that can be allocated to represent a specific medium is a 2D cell Az x Ay The reference point of the 2D cell is its centre However the space coordinates range from the left edge of the first cell to the right edge of the last one In Figure 2 3 the coordinate system of GPRMAX2D is schematically presented Only one row of cells in the x direction is depicted Assuming that Az 1 metre if one wants to allocate a rectangle with its x dimension equal to 3 metres and 1 as its lower x coordinate the x range is 1 4 The 2D cells allocated by GPRMAX2D are 1 3 When source or output positions are specified in space coordinates they
89. r a description of the conventions used to present the parameters of the commands Further it should be noted that the same essential commands have to be included in your input file in order to run a 3D model as in the case of the 2D one The fundamental spatial and temporal discretization steps are denoted as Ax Ay Az and At respectively 4 2 List of all available commands From Version 2 there are 41 commands available in GPRMAX3D which can be used to give the necessary instructions to the program for the construction of a 3D GPR model These are title domain dx_dy_dz time_step_stability_factor time_window messages number_of_media nips_number media_file geometry_file medium abc_type abc_order abc_stability_factors abc_optimization_angles abc_mixing_parameters pml_layers 27 box cylinder cylinder_new cylindrical_segment spher plat dg triangle bowti thin_wire analysis nd_analysis tx PK rx_box snapshot tx_steps rx_steps huygens_surface hertzian_dipole voltage_source transmission_line plane_wav xCitation_file There are few commands which were used in previous versions an
90. r compared to free space The above rule is described by the equation 2 7 Al 2 Absorbing boundary conditions The ABCs employed in GPRMAX2D 3D will in general perform well i e without introducing significant artificial reflections if all sources and targets are kept at least 15 cells away from them The formulation of the type of ABCs employed in GPRMAx2D 3D does not take into account any near field effects which dominate close to radiation centres i e sources and targets Form Version 2 0 Perfectly Matched Layer PML absorbing boundaries could be used in GPRMAX2D as well as in GPRMAX3D These layers which have a user adjustable thickness absorb very effi ciently most waves that propagate in them Although source and output points can be specified inside these layers it is wrong to do so from the point of view of correct modelling The fields inside these layers are not of interest to GPR modelling Placing sources inside these layers could have effects that have not been studied and will certainly provide erroneous results from a GPR modeller s point of view The above requirements have to be taken into account when the size of the model is to be decided Further for the same reason free space i e air should be always included above a source for at least 15 to 20 cells in both GPRMAx2D and GPRMAX3D GPR models Obviously the more cells there are between observation points sources targets and the absorbing boundaries the be
91. r example the following statements fanalysis 10 testl out a tx 0 5 0 5 MySource 0 0 10e 9 rx 0 6 0 5 tx_steps 0 01 0 0 xrx_steps 0 01 0 0 end_analysis will allow the simulation of 10 GPR traces The t x for the first trace is at 0 5 0 5 and the rx is at 0 6 0 5 The remaining traces are collected with a step of 0 01 metres in the x direction for both transmitter and receiver IMPORTANT NOTE The coordinates of any output points i e receivers specified using an rx_box command do not get updated using the rx_steps command and stay the same as defined in the input file throughout out the analysis The last command which is described bellow that can be inserted between a pair of analysis and end_analysis commands is the command snapshot snapshot In order to obtain information about the electromagnetic fields within an area of the model at a given time instant you can use the snapshot command The syntax of this command is snapshot il f1 f2 f3 f4 5 f6 f7 filel cl or snapshot il f1 f2 f3 f4 f5 f6 i2 filel c1 The parameters of the command are 25 i1 is a counter called the global source position which is used to determine the source s po sition for which the snapshot should be taken The global source position takes a value between 1 and the number of steps defined as the first parameter in the analysis com mand e f1 2 are the l
92. rocedure used to store the values of the field component The values of the H electromagnetic field component each stored ina float at every x y z sampling point Figure 6 2 illustrates in pseudo code the procedure used to store the values of the field component The values of the I current calculated at an electric field component location as V x H z each stored ina float at every x y z sampling point Figure 6 2 illustrates in pseudo code the procedure used to store the values of the current component The values of the J current calculated at an electric field component location as V x H each stored in a float at every x y z sampling point Figure 6 2 illustrates in pseudo code the procedure used to store the values of the current component The values of the J current calculated at an electric field component location as V x H each stored in a float at every x y z sampling point Figure 6 2 illustrates in pseudo code the procedure used to store the values of the current component 61 L the X coordinates Lower gt Higher the Y coordinates Lower gt Higher ll the Z coordinates Lower gt Higher E value Figure 6 2 Representation in pseudo code of the procedure used in GPRMAXS3D in order to store the values of field components in a snapshot Geometry output file The geometry file is always stored in binary format After the header information is stored as follows The ti
93. s based and str1 is a medium identifier see box Hence the command x_segment 0 5 0 5 0 3 0 5 0 2 pec introduces in the 2D model a segment of a circular disk at the 0 5 0 5 coordinates with a radius r 0 2 metres having an extent from 0 3 to 0 5 along the x axis and the parameters of a perfect conductor In other words it creates a semicircular disk y_segment With the command y_segment you can introduce a circular segment in the 2D model simu lating an infinite segment of a cylinder The syntax of the command is y_segment f1 f2 f3 f4 f5 strl The parameters f 1 f 2 are the x y coordinates of the centre of the circular disk of which a segment in the y direction is going to be constructed These values are all in metres The parameters 3 and f4 are the yiow and ynign coordinates of the extent of the segment along the y axis The parameter 5 is the radius r in metres of the circular disk on which the segment calculation is based and str1 is a medium identifier see box Hence the command y_segment 0 5 0 5 0 3 0 5 0 2 pec introduces in the 2D model a segment of a circular disk at the 0 5 0 5 coordinates with a radius r 0 2 metres having an extent from 0 3 to 0 5 along the y axis and the parameters of a perfect conductor In other words it creates a semicircular disk triangle With the command triangle you can introduce a triangular patch with specifi
94. s the filename of the file where the snapshot is to be stored c1 can be a or b if the format of the snapshot file is to be ASCII or BINARY respectively For example the commands analysis 10 testl out a tx 0 5 0 5 0 5 MySource 0 0 10e 9 rset 06 02 50 5 snapshot 5 0 0 0 0 0 0 1 0 1 0 1 0 0 1 0 1 0 1 3e 9 snapl out b tx_steps 0 01 0 0 0 0 rx_steps 0 01 0 0 0 0 end_analysis will save a snapshot of the electromagnetic fields in the model at a simulted time of 3 nanoseconds while the model is calculating the fifth GPR trace 42 Chapter 5 GPRMAX2D 3D modelling examples In this chapter some examples of the use of GPRMAX2D 3D for GPR modelling are presented The examples are simple but illustrate step by step the modelling process 5 1 Single rebar in concrete 2D model A schematic for this simple problem is illustrated in Figure 5 1 A GPR model is required for a per fectly conducting rebar of radius r 25 millimetres located in a concrete slab of 600 millimetres thickness at a depth of 75 millimetres Step 1 First the constitutive parameters of the media involved should be determined Since perfect conductors and free space can be modelled without the need to specify their parameters only the definition of the constitutive parameters for concrete is required Let us assume that concrete can be modelled using e 6 0 and o 0 01 S m Moreover that can be considered
95. store the results of the simulations In general the file formats of GPRMAx2D are similar to the ones used in GPRMAx3D 6 1 GPRMAx2D 3D Binary format file header All GPRMAx2D and GPRMAX3D output files stored in binary format have a 16 byte long header part and a data part The header part is the same in all GPRMAx2D 3D files and is defined as e bytes 0 1 contain the integer hexadecimal number 2B67 which identifies the file as a GPRMAX2D 3D one and provides the means to determine whether the low byte least significant bits of multi byte entities is written first or last If the first byte of the file byte 0 is the hexadecimal number 67 the file is recorded low byte first LITTLE ENDIAN but if the first byte is the hexadecimal 28 the file is recorded low byte last BIG ENDIAN e bytes 2 3 contain a positive integer number which is used to determine the particular type of the file as Current Version 2 0 t 20200 GPRMAX2D analysis command file t 20204 GPRMAX2D snapshot command file t 20205 GPRMAX2D geometry file t 30200 GPRMAXx3D analysis command file t 30204 GPRMAXx3D snapshot command file t 30205 GPRMAX3D geometry file Older Version 1 5 t 20151 GPRMAXx2D tx command file t 20152 GPRMAX2D csg command file t 20153 GPRMAXx2D scan command file 7 20154 GPRMAX2D snapshot command file t 20155 GPRMAX2D geometry file 1 30151 GPRMAx3D tx command file t 30152 GPRMAXx3D csg command file
96. tle of the model ina st ring of TTTLELENGTH bytes The number of iterations NI which have been performed in an float The spatial step Ax ina float The spatial step Ay ina float The spatial step Az ina float The time step At ina float The number of cells NX in the x direction in an int The number of cells NY in the y direction in an int The number of cells NZ in the z direction in an int The number of different media PMEDIA present in the model in an int A list PMEDIA long of medium identifiers Its medium identifier is stored in a string of MEDIALENGTH characters bytes A cell ID stored in int 2 bytes for every cell in the model The loop structure shown in Figure 6 2 is used to store these values Each cell ID corresponds to an entry 1 PMEDIA in the list of different media A component ID stored in int 2 bytes for the Ex field component This ID can be used to determine the extend of surfaces objects in GPRMAX3D The ID corresponds to an entry 1 PMEDIA in the list of different media The range of this ID is 0 NX 1 0 NY 0 NZ A component ID stored in int 2 bytes for the Ey field component This ID can be used to determine the extend of surfaces objects in GPRMAX3D The ID corresponds to an entry 1 PMEDIA in the list of different media The range of this ID is 0 NX 0 NY 1 0 NZ A component ID stored in int 2 bytes for the Ez field component This ID can be used to determine the extend of s
97. to be non magnetic Therefore uy 1 0 and o 0 0 Therefore by including in the input file medium 6 0 0 0 0 0 0 01 1 0 0 0 concrete the medium identifier concrete can be used in the model Step 2 Determine the source type and excitation frequency These should be generally known included in the problem s specification Let us assume that a ricker source can be used to simulate the GPR antenna and a centre frequency of f 900 MHz is required In order to control the nu merical dispersion see Chapter 2 the spatial steps Ax and Ay should be chosen appropriately According to the rule of thumb of Chapter 2 the wavelength of the highest frequency of interest in the model should be resolved by at least 10 cells This highest frequency of interest is not the centre frequency of the pulse used for excitation This can be easily ascertained by examining the amplitude spectrum of the source waveform which is illustrated in Figure 5 2 Examining this Figure it is apparent that the pulse contains a significant amount of energy at higher frequencies than the center one In general three to four times the centre frequency of the pulse will give a good estimate for the highest frequency which should be used in the calculations Therefore let us assume that the highest frequency which we consider significant in the pulse s spectrum is 43 GPR scan 600 mm Figure 5 1 Schematic drawing of the rebar in concrete problem f
98. tter the results will be 10 Chapter 3 GPRMAX2D input file commands 3 1 General notes on GPRMAx2D commands In order to describe the GPRMAx2D commands and their parameters the following conventions are used e f means a real number which can be entered using either a separating the integral from Es Lie E is the decimal part e g 1 5 or in scientific notation as 15e 1 or 0 15e1 i means an integer number c means a single character e g y str means a string of characters with no white spaces in between e g sand file means a filename to be supplied by the user All parameters associated with simulated space i e size of model spatial increments e t c should be specified in metres All parameters associated with time i e total simulation time time instants e t c should be specified in seconds All parameters denoting frequency should be specified in Hertz All parameters associated with spatial coordinates in the model should be specified in me tres The origin of the coordinate system 0 0 is at the lower left corner of the model It is important to note that GPRMAXx2D converts spatial and temporal parameters given in me tres and seconds respectively to integer values corresponding to FDTD cell coordinates and it eration number Therefore rounding to the nearest integer number of the user defined values is performed There are no optional parameters within a command Even if some parameters wi
99. ture thin_wire With the command thin_wire you can introduce the properties of a thin wire model in GPRMAX3D The thin wire should then be used as the medium identifier for an edge object construction command The syntax of the command is 31 thin_wire f1 strl The parameter f1 is the radius r in metres of the wire and must be much smaller than Al in order to model properly the physics of the thin wire The parameter st r1 is a medium identifier ID not currently in use A thin wire is considered to be a perfect electric conductor For example the command thin_wire 0 001 MyWire defines a PEC thin wire of radius r 1 millimetre with the identifier MyWire box With the command box you can introduce an orthogonal parallelepiped with specific proper ties in the model The syntax of the command is box f1 2 3 4 5 6 strl The parameters f1 f2 3 are the lower left x y z coordinates of the parallelepiped in metres Similarly the 4 5 6 are the upper right x y z coordinates of the parallelepiped The parameter str1isa medium identifier defined either with a medium command or ina media file currently in use Further the identifiers f ree_space or pec can be used if the parallelepiped is to represent a free space region or a perfect conductor Apart from the different number of parameters the box command serves the same purpose in GPRMAX3D as in GPRMAX2D plate With the c
100. u Any modification of the Programmes and their source code including translation to other programming languages is referred to as modification 1 You are licenced to copy and distribute only verbatim copies of the Programmes in any medium You must keep intact all the notices that refer to their Licence and all copyright notices included in the Programmes Activities other than executing copying distribution and modification are not covered by this Licence they are outside its scope 2 a You may modify your copy or copies of the Programmes or any portions of them for your own personal use only b You may not modify your copy or copies of the Programmes or any portions of them thus forming a work based on the Programmes for any other use different from the one stated in a above NO WARRANTY THERE IS NO WARRANTY FOR THE PROGRAMMES TO THE EXTENT PERMITTED BY APPLICABLE LAW EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDER PROVIDES THE PROGRAMMES AS IS WITHOUT ANY WARRANTY OF ANY KIND EITHER EXPRESSED OR IMPLIED INCLUDING BUT NOT LIMITED TO THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAMMES IS WITH YOU SHOULD THE PROGRAMMES PROVE DEFECTIVE YOU ASSUME THE COST OF ALL NECESSARY SERVICING REPAIR OR CORRECTION IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING WILL THE COPYRIGHT HOLDER B
101. uires more than a total of 10 different media to be used Initially GPRMAx2D allocates space to store the constitutive parameters for 10 media free_space pec and 8 user defined This space is usually adequate for most models but in case more media are required then you should issue the command number_of_media il 1GpRMAXx2D converts the specified time window in seconds to a number of iterations internally That is achieved using equation 3 2 An integer value is obtained by rounding the result of the division to the nearest integer 15 where the parameter i1 should be greater than 10 and at least equal to the number of different media you require There is no problem in allocating space for even a 1000 different media however valuable computer memory can be wasted If GPRMAX2D requires more space to store media parameters will terminate execution issuing an appropriate error message media_file With the command media_file you can specify the location and filename of a file containing the description of constitutive parameters of frequently used media Hence by storing these parameters in such a file you do not have to specify them in every model s input file you want to use them The syntax of the command is media_file filel where the parameter file1 is the filename of the media file including the path if necessary The structure of a media file is described in Appendix A geometry file With the
102. urfaces objects in GPRMAX3D The ID corresponds to an entry 1 PMEDIA in the list of different media The range of this ID is 0 NX 0 NY 0 NZ 1 5Note that the number of cells reported in the geometry file ranges from 1 NX Internally GPRMAX3D uses the range 0 NX 1 according to the coordinate system 62 6 5 GPRMAx3D ASCII file formats The ASCII output files can be edited with any text editor or word processing software and the information stored in them is in general self explanatory 63 Appendix A GPRMAX2D 3D Media file The media file has the role of a simple database of frequently used materials Media files can be used in the same way in both GPRMAXx2D and GPRMAX3D The structure of media files is very simple Similarly to an input file the hash character is reserved Each definition of a medium parameters should occupy a single line in the media file This line must start with the hash character The parameters of the medium follow in the same order which is required by a medium command see Chapter 3 Hence a general entry in a media file looks like 1 2 3 4 5 6 strl the parameters are e f1 the DC static relative permittivity of the medium ers e f2 the relative permittivity at theoretically infinite frequency roo e 3 the relaxation time of the medium 7 seconds e 4 the DC static conductivity of the medium Siemens metre e 5 the relative permeabi
103. ussian 50 0 MyVolt Introduces in the model the parameters of the definition of a voltage source with unit amplitute centre frequency of 600 MHz and temporal variation of a gaussian pulse The internal resistance is set to 50 Q This source can be referred to in a tx command using the identifier MyVolt transmission_line The command transmission_line defines the parameters of a 1D two wire transmission line that can be used to excite antennas in GPRMAX3D The syntax of the command has changed in Version 2 and is transmission_line f1 f2 strli f3 f4 str2 The parameters f1 and 2 are the amplitute and frequency of the source s waveform The param eter str1 is the type of excitation in the line This can be one of the build in types like gaussian sine ricker etc or it could be the type user if an excitation file is used The parameter f3 is the length of the transmission line in metres This can be important if lines of different lengths are employed in order to simulate time delays in excitations The parameter f4 is the characteristic impedance Z of the line and finally the parameter st r2 is a source identifier that will be used in a tx command For example the command transmission_line 1 0 600e6 gaussian 0 5 200 0 MyLine 37 Defines a transmission line having a length of 0 5 meters and a characteristic impedance Z 200 ohms in which a gaussian pulse will be sourced The properties of this pulse are
104. ween cells the electric field components are tangential to them and the magnetic field components are normal to them Source and output points defined in space coordinates are directly converted to cell coordinates and the corresponding field components are depicted in Figure 2 4 The actual position of field components for a given set of space coordinates x y z are e x AE y 2 for Ey e x y Su 2 for Ey x y z az for E e x y Suz a2 for H e a AE yz az for Hy e x 42 y 52 2 for H It should be noted that Hertzian dipole sources as well as other electric field excitations i e volt age sources transmission lines are actually located at the corresponding electric field compo nents 2 6 Hints and tips for GPR modelling with GPRMAx2D 3D In order to make the most of GPRMAx2D 3D in modelling GPR responses ultimately one should be familiar with the FDTD method on which these programs are based There is a very large amount of information available in the relevant literature Good starting points are 2 and 3 where as the specific application of FDTD to the GPR forward problem is described in 1 Allocated Cells 1 0 e 1 2 3 4 Cell coordinates 1 1 i 0 1 2 3 4 5 Space coordinates Range for space coordinates electric field components Z 4 magnetic field components Figure 2 4 Schematic of the GPRMAx3D coordinate system and conventions The

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