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FDEMINV

1. FDEMINV 1 D interpretation of frequency domain EM soundings Version 1 4a c 2012 by Markku Pirttij rvi Introduction The FDEMINV program can be used to model and to interpret geophysical frequency domain electromagnetic FDEM soundings over horizontally layered earth FDEMINV can compute various magnetic field responses derived from the vertical and the horizontal component of the magnetic field due to a vertical and or a horizontal magnetic dipole Parameter optimization which is based on linearized inversion method can be utilized in 1 D interpretations The FDEMINV program is a 32 bit application that can be run on Windows 9x XP 7 with a graphics display of at least 1024x800 resolution Memory requirements and processor speed and are not critical factors since large data arrays are not used and the EM solution is quite fast to compute even on older computers The FDEMINV program has a simple graphical user interface GUI that can be used to change the parameter values to handle file input and output and to visualize the EM response and the model The user interface and the data visualization are based on the DISLIN graphics library http www dislin de Despite its inversion capabilities FDEMINV is intended primarily for forward modeling and testing One of the main reasons for me to create this program was to develop a general method to transform FDEM responses into apparent resistivity and phase using the ve
2. Department of Physics Tel 358 8 5531409 FIN 90014 University of Oulu URL https wiki oulu fi display mpi oulu fi Finland E mail markku pirttijarv at oulu fi 14 IX Append Mid W Aq yuea parare q uo s upunos W3q4 Depth m uuo 3sis q OT OL OL OL OI L T 01 401 en o _ SIYSI2M ON 6L0L99 0 ueeur dure q FL88S0 0 40113 SINY ro S res 919C6l Ly oT i4 TST ELOTE TI u ssewxomp wayo ise aseyd pue jansisa1 ddy suods g 00 u3 w 0009 1 zeuejdoo GINA 3Surpunos Kou nb rq uondinsep spou pue uiojs g z asuodsay 1 3suods got SUIPUNOS So0y xeutrger odues Surpunos JN3G4 ZH amp ouonbou q sjauueyo Bou uui isa y p pul pay E Pula wisay c pulp pisay p sade sjajaweJed japoyy bas4 doo7 15
3. such a value of the resistivity or conductivity of the homogeneous half space that produces the same EM response as the layered earth Since the loop spacing and frequency are known the host conductivity which now represents the apparent resistivity can be solved simply as p 2zu f r fe Ohmm The phase response related to the apparent resistivity is computed in the FDEMINV program as tan Im Hz Hx Re Hz Hx rad or deg Log10 Abs Imag Hz Hx 2 3 0 001 0 01 0 1 1 10 100 1000 10000 100000 Ind parameter kr 2 Figure 2 The F ratio used to interpolate the apparent resistivity for a VMD source on the surface of homogeneous halfspace Note that the method used to compute apparent resistivity could be used to transform measured data as well This requires however that both the vertical and the horizontal magnetic field have been measured The transformation method works with coplanar HMD system which has an F ratio curve very similar to that in Figure 2 Note also that the magnetic field used to compute the F ratio is the sum of free space and homogeneous half space magnetic fields and for some dipole dipole systems the vertical magnetic field is zero Therefore the interpolation of the F ratio cannot be used to compute the apparent resistivity for the coaxial HMD system for example Using the program On startup the program reads the model parameters from the FDEMINV INP file and the DISLIN graphi
4. 0 14607E 02 64 00 0 32212E 01 0 13006E 02 128 00 0 63994E 01 0 13824E 02 256 00 0 17812E 02 0 18135E 02 512 00 0 47480E 02 0 27415E 02 1024 00 0 10998E 03 0 42078E 02 2048 00 0 17153E 03 0 58351E 02 4096 00 0 10288E 03 0 50792E 02 8192 00 0 93610E 02 0 45630E 02 Lines 2 and 6 are used for comments The first line defines a header text max 30 characters The third line defines the source type ISYS response type IMOD and sounding type IOPT The source is either a VMD ISYS 1 or a HMD ISYS 2 or 3 The response type is one of the nine possibilities IMOD 1 2 or 9 defined in the Using the program chapter The sounding type is either frequency sounding IOPT 1 or geometric sounding IOPT 2 The 4 th line defines first the loop spacing m or frequency Hz used in the frequency or geometric soundings respectively The second parameter on the 4 th line defines the height in meters of the dipole dipole system from the surface of the earth Note that the source and the receiver are always on the same height level above or on the surface The 5 th line defines the number of frequencies NOF and the column indices ICO1 ICO2 and ICO3 for the two response components in this case apparent resistivity and phase since IMOD 1 and weights used in the inversion A data component can be omitted if its column index is set to zero ICO1 0 or ICO2 0 Likewise weights are not read at all if ICO3 0 as in the example above T
5. cs parameters from the FDEMINV DIS file If these files can not be found when the program starts new ones are created automatically using the default parameter values The program then computes the FDEM response of the initial model and builds up the user interface shown in the Appendix The FDEM response is plotted in the graph area along with a resistivity depth curve of the model and a description of the model parameters The parameters of the layered earth model and the inversion method can be altered using the controls on the left side of the FDEMINV program window As shown in Appendix the main window of the FDEMINV application contains two menus The File menu has the following nine options Open Model open an existing model file INP Save Model save the model into a file INP Read Data read in measured data for interpretation DAT Save Results save the results into a file OUT Read disp read in new graph parameters from a file DIS Save Graph as PS save the graph in Adobe s Postscript format PS Save Graph as EPS save the graph in Adobe s Encapsulated Postscript format EPS Save Graph as PDF save the graph in Adobe s Acrobat PDF format PDF Save Graph as WMF save the graph in Windows metafile format WMF Selecting these menu options brings up a typical Windows file selection dialog that can be used to provide the name of the file for open save operation Model and result files are saved in stan
6. dard ASCII text format The graphs are saved as they appear on the screen in landscape A4 size The Edit menu contains following items Comp gt Meas use the computed response as measured data Remove Meas remove information about measured data Sounding type choose between frequency and geometric Source type choose between coplanar VMD and HMD and coaxial HMD system Field component select real amp imaginary in phase and quadrature and modulus amp phase response of the first or second H1 or H2 field components see note Normalized field select Re Im and Mod Pha response of the normalized field H1 H0 or H2 HO0 where HO is primary free space field see note Ratio select Re Im and Mod Pha response of the ratio between first and second field component H1 H or H2 H1 Apparent resistivity select apparent resistivity and phase between H1 and H2 response Free space field include or exclude the free space field from the total magnetic field Response component show either both components or only the first or second component Note In case of the VMD source the first field component is vertical magnetic field and the second is horizontal axial magnetic field In case of HMD the first field component is horizontal parallel or coaxial horizontal magnetic field and the second is the vertical magnetic field which cannot be computed in case of coaxial HMD configuration Consequently the normalizing free space magnetic f
7. es are derived from the 95 confidence limits Program controls The leftmost control panel includes some push button and text field controls The Loop Freq text field defines the loop spacing when modeling frequency sounding or the frequency when modeling geometric sounding The value of the loop spacing or frequency is given multiplied by one thousand in km or kHz The other text fields are used to provide the number of layers and the resistivity and thickness values of each layer After editing the parameter values one has to apply for the changes using the Update parameters push button in the top left corner of the FDEMINV application window When increasing or decreasing the number of layers the unnecessary text field controls get hidden The maximum number of layers is six 6 The Default pushbutton resets all layer parameters to their default values 100 Qm and 100 m The text controls in the right control panel are related to the inversion These controls become active only after some data is read in using the File Read Data item The Iters text field control defines the number of successive iteration made after the Optimize button is pressed The Tres control defines the minimum singular value threshold used in the optimization This parameter actually multiplied by 1000 controls the strength of the damping Decreasing its value will loosen the damping and make the inversion method work more like a steepest descent algorithm I
8. he next NOF lines define the column formatted data frequency FREQ Hz the measured apparent resistivity Ohmm and the phase component deg The maximum amount of frequencies or loop spacings is 80 and the header text is used as a second line in the response graph title If the header text line is empty the default title in the FDEMINV DIS file is used instead The frequencies or loop spacings must be either in an ascending or in descending order Note also that the data file can contain several data columns from which one or two are read for the interpretation This means that the same data file can contain for example measurements along a profile Manual editing of the column indices is currently required to choose the correct data column for the FDEMINV program Data values equal to zero are omitted and thus used for missing data values Although there is no need to edit model files manually the following example illustrates the format of the model files FDEMINV model file 3 0 10000E 03 0 10000E 03 0 10000E 01 0 10000E 03 0 10000E 05 1 1 1 500 00 0 00 14 2 4518 16 B25 64 128 250 512 1024 2048 4096 8192 16384 Lines 1 2 and 7 in this case are used for comments and can be left empty The 3 rd line defines the number of layers NOL the maximum amount of which is 6 Lines 4 and 5 define the resistivity RH Ohmm and the thickness TH m of the two topmost layers and the 6 th line define
9. ield HO is the vertical for VMD source and horizontal for HMD source Define freq dist item can be used to set the minimum and maximum frequency values and number of frequencies in case of frequency soundings or the minimum and maximum loop spacing and the number of loop spacings in case of geometric sounding The values are provided using an input dialog and the frequencies or loop spacings are automatically computed so that they are evenly spaced on a logarithmic scale Phase rad deg item defines if the phase component is represented as radians or degrees Weights in out item is used include or exclude the data weights in from the inversion Error bars item can be used to change the appearance of the error bars of the resistivity and thickness of the layers in the model view The error bars represent the 9596 confidence limits minimum and maximum errors obtained from the singular value decomposition used in the linearized inversion method The Exit menu has two items the first one can be used to restart the GUI and swap between traditional 3 4 display mod and widescreen mode giving an aspect ratio between 0 5 0 9 and the second is used to confirm the exit operation On exit the latest model is saved in the FDEMINV INP file replacing the original one and the results are saved in the FDEMINV OUT file Errors that are encountered before the GUI starts up are reported in the FDEMINV ERR file When operating in GUI mode run time errors arising f
10. ncreasing its value might be advantageous if the inversion gets unstable The default values of the iteration number and threshold are 10 and 1 0 1 e 3 respectively The text fields Free on the right side of each resistivity and thickness value are used to exclude 0 or to include 1 parameters from or to the inversion By default all parameters are included in the inversion If you want to fix some parameter during inversion set the corresponding parameter to zero The Sel all button can be used to fix or free all parameters for the inversion Since the inversion can easily get stuck into a local minimum the inversion should not be restarted using the previous model as a starting point When adding new layers to the model default parameter values 100 2m and 100 m are given to each new layer A single layer can also be removed by giving it a zero thickness and pressing the Update button Increasing or decreasing layers always affects the layers at the bottom File formats When using the program for interpretation purposes make sure that your input data files DA T are formatted properly before running the program Note also that there is no need to edit model files manually when interpreting field data The following example illustrates the format of the input data file Synthetic data 1 J 1 1000 0 12 2 3 0 4 00 0 14219E 01 0 30574E 02 8 00 0 12220E 01 0 23876E 02 16 00 0 15243E 01 0 18217E 02 32 00 0 22128E 01
11. or not e The 3 rd line defines parameters that define the x horizontal and y vertical position of the origin of the main graph in pixels the length of the x and y axis relative to the size of the total width and height of the total plot area eg 0 52 50 of the width or height which is equal to 2970x2100 pixels landscape A4 and the screen aspect ratio for widescreen mode e The following lines define various text items of the graph max 40 characters e Two main titles of the response graph e Three axis names of the graph When both data channels are plotted the x axis title shows both axis names Response 1 Response 2 e Four legend texts computed and measured e One title of the model description text e Two column headers of the model parameters e One additional axis title for vertical axis of the model view Note that to mimic depth sounding the response lies on the horizontal x axis and the vertical y axis is the parametric frequency or loop spacing axis Note also that by default the graph does not contain the actual names and units of all the nine different the response types Instead generic names e g Resp 1 and Resp 2 are provided and the response type is shown in the description text in the top right corner of the graph page defines Manual editing of the FDEMINV DIS file is required if printed graphs are going to be prepared for presentation purposes Note that the DISLIN graphics allows the use of
12. out any modifications At the moment however the source code is not made available and I do not intend to provide any support for the program If you find the computed results erroneous or if you have suggestions for improvements please inform me Note that the FDEMINV program has not been tested thoroughly and that its usability in data interpretation is quite modest For example currently the program does not use proper data weighting although it always works with the 10 base logarithms of both the data and the parameters Interpretation of frequency domain soundings are going to be implemented in future version of Jointem software for joint interpretation of TEM VES VLF R and AMT MT soundings For more information about the current status of Jointem and other software please visit my web page at https wiki oulu fi display mpi Q oulu fi 13 Terms of use and disclaimer You can use the FDEMINV program free of charge If you find the program useful please send me a postcard The program is provided as is The author MP and the University of Oulu disclaim all warranties expressed or implied with regard to this software In no event shall the author or the University of Oulu be liable for any indirect or consequential damages or any damages whatsoever resulting from loss of use data or profits arising out of or in connection with the use or performance of this software Contact information Markku Pirttij rvi PhD
13. rom illegal parameter values are displayed on the screen during runtime After exiting the program one can look at the FDEMOUT OUT file which contains the results If data has been used in the interpretation the file contains the model parameters the RMS error and the mean of the damping factors the damped 95 confidence limits of the parameters the singular values the damping factors and the parameter eigenvectors The result file also contains the measured and computed response components and the differences If data had not been used the file just contains the model parameters some system information and the computed FDEM response Note that result files as well as model files can be saved to disk also from within a running FDEMINV application using the File Save Results menu item The FDEMINV program is not an idiot proof interpretation program It requires an initial model the parameters of which are optimized during an iterative linearized process The inversion method can easily get stuck to a local minimum and therefore the user should pay attention to the validity of the resulting model The RMS error and the mean of the damping factors can be used to assess the validity of the inversion results Optimally the RMS error should be zero and all damping factors should be equal to one Note also that after optimization the resistivity depth section shows the minimum and maximum parameter ranges using dotted lines These auxiliary curv
14. rtical and horizontal magnetic field components and to test the transformation Installing the program The program requires following files FDEMINV EXE the 32 bit executable file DISDLL DLL dynamic link library for the DISLIN graphics The distribution file FDEMINV ZIP contains also a short description file README TXT this users manual FDEMINV MANU PDPF and an example data file EXAMPLE DAT To install the program create a new directory and copy or unzip the distribution files there To be able to start the program from a shortcut that locates in a different directory move or copy the DISLIN DLL file into the WINDOWS NSYSTEM folder or someplace else where a system path has been defined The EM measurement systems Figure 1 illustrates the three measurement systems considered in FDEMINV The transmitter 7x is either a vertical VMD or a horizontal HMD magnetic dipole that is to say a horizontal or a vertical loop on or above the ground surface The receiver Rx is located at the same height level at some distance L away from the source The FDEMINV program computes two magnetic field components The first component solid black arrow is always parallel to the source dipole and the second one dashed gray arrow is perpendicular to that In case of VMD the second component is the horizontal axial component directed away from the source In case of a HMD source the second component is the vertical one Please note
15. s the resistivity of the bottom layer The 1 st line of the 2 nd paragraph defines the number of frequencies NOF The frequency values are then provided at the end of the file Note that the frequencies can be given on multiple lines The results file EDEMINV OUT contains the model parameters and depths the RMS error the mean of the damping factors the damped 95 confidence limits of the parameters the original W and normalized S singular values the damping factors T and the parameter eigenvectors 10 V matrix Some general information concerning the measurement system is also given source and sounding types loop spacing and height The results file also contains the measured and computed response components and the difference between the measured and the computed data It also contains the weights if they were used in the inversion The FDEMINV OUT file contains also the computed magnetic field components H01 H02 Re Im H1 Re Im H2 Re Im H1 H01 Re Im H2 H01 and Re Im H1 H01 H2 H02 Here H01 and H02 are free space magnetic fields H01 and H1 are the vertical or horizontal magnetic fields of a VMD or HMD H02 and H2 are the horizontal or vertical magnetic fields of a VMD or HMD Note that for historical reasons the character is used to comment out lines for the Gnuplot plotting program At the bottom the FDEMINV OUT file are given the data values required to create the model curve and the error bars u
16. sing a third party plotting program If data were not read in the output file would just contain the model parameters and the computed FDEM response Graph options Several graph parameters see Appendix can be changed by editing the FDEMINV DIS file Note that the format of the DIS file must be preserved If the format of the file becomes corrupted the program crashes while initializing the GUI In this case one should delete the file and a new one with default parameter values will be generated automatically the next time the program is started The file format and default parameter values are shown below 40 32 32 26 26 1 2 1 1 370 350 0 600 0 850 0 830 FDEM sounding Test model Response 1 Response 2 Frequency Hz Loop spacing m comp comp meas meas NS HN Fa System and model description Resist Ohmm Thickness m Depth m 11 e The l st line defines five character heights The first one is used for the main title and the graph axis titles the second height is used for the axis labels the third height is used for the plot legend text the fourth height is used for the model description text and the last height is used for the axis labels in the model view e The 2 nd line contains integer valued parameters that define 1f the info text is shown or not 1f model view is drawn or not if error bars are shown in the model view in which corner the legend is drawn and if widescreen mode is active
17. sounding system for example the method is not widely used and therefore a short description is provided in the following The 10 base logarithm of the imaginary quadrature part of the ratio of vertical and horizontal magnetic field F Log o0 Abs Im Hz Hx 1s first computed and tabulated using the homogeneous half space model over a wide range of dimensionless induction parameter a Kr where r is the loop spacing and k QOLoOn 27f is angular frequency 4j is magnetic permeability of the free space and o is the conductivity of the lower half space In practice the computation is made using fixed loop spacing and frequency and varying the host conductivity or resistivity values Figure 2 illustrates the F ratio for a VMD system on the surface of homogeneous half space Since the F ratio is a continuously decreasing function of the induction parameter the apparent resistivity of the VMD or HMD system above layered earth can be obtained using reverse interpolation Let us assume that at some frequency the computed or measured values of vertical and horizontal magnetic field are Hx and Hz which gives rise to ratio F Reverse interpolation from y to x axis of the curve shown in Figure 2 gives an induction parameter value o In practice the interpolation is made using the logio values of the induction parameter and linear extrapolation is used beyond the computed range if necessary By its definition the apparent resistivity is
18. special characters in graph texts The instructions are placed between and characters For example the text Resistivity M2 W M1 m will produce Resistivity Qm See the DISLIN documentation for further information 12 Additional information Originally I made the FDEMINV program at the University of Oulu in December 2001 when I worked as a researcher funded by a grant from Outokumpu Foundation addressed to Prof Sven Erik Hjelt Afterwards I ve updated the program every now and then The forward computation is based on the well known solution for magnetic dipole sources above 1 D layered earth e g Keller and Friscknecht 1967 The convolution algorithm and the filter coefficients used to compute the Hankel transforms are based on the work of N B Christensen Geoph Prospecting 1990 vol 38 pp 545 568 The inversion method which is based on the singular value decomposition and adaptive damping method is described in my PhD thesis M Pirttij rvi 2003 Acta Univ Oul A 403 The FDEMINV program is written in Fortran 90 and compiled with Intel Visual Fortran 11 1 The graphical user interface is based on the DISLIN graphics library version 10 2 by Helmut Michels The program distribution includes the DISDLL DLL that is required for the 32 bit GUI Since the DISLIN graphics library is independent form the operating system the FDEMINV program could be compiled on other operating systems Mac OSX Linux with
19. that in coaxial HMD configuration no vertical field is generated which prevents computation of Hx Hz Hz Hx ratios and apparent resistivity and phase VMD coplanar d L gt Rx HMD coplanar zn o L Tx R X HMD coaxial f L Figure 1 Schematic view of the commonly used VMD and HMD systems The FDEMINV program can be used to model both frequency and geometric soundings In frequency soundings the distance between the source and the receiver is kept fixed and the measurements are made using varying frequencies The attenuation of EM fields depends on the conductivity or its reciprocal the resistivity and the frequency Therefore high frequencies give information about the upper parts of the earth whereas low frequency data contains information from greater depths In geometric soundings the frequency is kept fixed and the loop spacing is varied When the loop spacing is short the data contains information near the surface When the loop spacing increases more and more information will be obtained from the deeper parts of the earth For more detailed information about the geophysical EM measurement systems please be referred to common geophysical literature e g M N Nabighian 1988 amp 1991 SEG The FDEMINV program computes the apparent resistivity and phase using the ratio of the vertical and horizontal magnetic field components Although similar method has been used in the French BRGM Melis frequency

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