User's Guide for Program EARTH
Contents
1. gt lt SHIFT gt lt HOME gt lt ENTER gt Function and Comments To find a desired point on the coordinate plane in order to enter or delete a vertex The direction of cursor moving coincides with the direction of the corresponding arrow To regulate the speed of cursor moving You may increase decrease the number of pixels which define the step of cursor moving The maximum step is equal to 10 pixels the minimum step is equal to 1 pixel To place the cursor at the upper left corner and the lower right corner of the coordinate plane respectively To realize picture scrolling in the corresponding direction To return the coordinate origin to the point 0 0 To realize the process of specification of a structure You can fix a corner vertex define its coordinates in the units of 10 km by pressing lt ENTER gt at a screen point without inputted vertex mode Draw vertex the blue cursor If you press lt ENTER gt at a screen point with existing vertex the program switches on another mode Draw fault the red cursor This vertex is assumed to be the initial point of a fault Next pressing lt ENTER gt allows to fix the end point of the fault and consequently the fault itself A vertex may be placed on the existing fault it is an end vertex intersection vertices are found automatically Remember that the situation when more than two faults begin end at the same vertex is inadmissible It is poss2. dpr files The main menu contains five items File with Block Structure View of Block Structure Numerical Parameters DPT reading amp Visualization Exit File with block structure The subdirectories and the files with extension b k from the current directory are screened in the special window You can choose a file Program DISTR loads the block structure from the selected file View of block structure This mode is used to look over the current block structure in the graphic mode on the coordinate plane Numerical parameters This mode is used to input the values of initial dimensionless time and time interval for data visualization DPT reading amp visualization If this item is selected then the subdirectories and the files with extension dpf from the current directory are screened in the special window You can choose a file If no file is selected the program returns to the main menu If the selected file does not correspond to the current block structure then the error message is imaged Otherwise the program images on the screen the moments of earthquakes loaded from the selected file for catalog preparation Exit This item needs no clarification Program LINEAM This small program allows us to specify the scheme of lineaments for some seismic zone and to save it in the file Jineam dat Specification of lineament vertices their local coordinates x and y is realized by means of the simplest
3. The range of changing is 0 500 Note that W gt We Otherwise new values of these parameters will be abrogated To specify for the fault the value of level B The range 14 of changing is 0 100 Level HF To specify for the fault the value of level H The range of changing is 0 100 Level HS To specify for the fault the value of level H The range of changing is 0 100 Note that B gt Hy gt H Otherwise new values of these parameters will be abrogated By pressing lt Esc gt it is possible to return to the second menu 2 BLOCKS to specify the values of block parameters You can select the desired block by pressing lt PgUp gt lt PgDn gt The selected block is filled on the screen by lightblue color The menu for specification of the block parameters contains the following windows Coef KU To specify for the block bottom the value in bars cm of parameter K in 2 The range of changing is 0 100 Coef WU To specify for the block bottom the value in cm bars of parameter W in 1 The range of changing is 0 500 X velocity To specify for the block the value in cm of the velocity of progressive movement of the underlying medium along axis X of the coordinate system The range of changing is 100 100 Y velocity To specify for the block the value in cm of the velocity of progressive movement of the underlying medium along axis Y of the coordinate system The range of changing is 100 10
4. belongs to another one but is not its initial or end point I intersection is a point of intersection of two faults which is not an initial or end for both of them The examples of these types of vertices are shown in Fig 1 Fig 1 Types of vertices a corner C b end E c intersection D A fault is defined by indication of its initial and end vertices The angle of dip for the fault plane is measured to the left of the fault The fault direction is the direction from its initial point to its end point The structure is separated by the faults into blocks A common part of any block with the upper plane is a polygon Boundary blocks are defined for the structure to introduce the movement of boundaries A boundary block is a continuous part of the structure boundary between two vertices which consists of some sides It is defined by the indication of its initial and end vertices A fault segment is a part of a fault plane limited by the 3 upper and lower planes and lines that connect positions on the upper and lower planes of two consecutive vertices of the fault It is a trapezium The example of the block structure on the upper plane is presented in Fig 2 Fig 2 The vertices and the faults on the upper plane This structure has 4 corner vertices with coordinates 2 1 2 5 6 5 6 1 8 end vertices with coordinates 2 2 2 3 2 4 5 1 5 5 6 2 6 3 6 4 3 in
5. dialog You type and enter word end to complete the specification of a lineament or word exit to complete the specification of the scheme The maximum number of lineaments is equal to 20 the maximum number of vertices on a lineament is equal to 10 When the specification procedure has completed the program asks for the confirmation to save the scheme in the file Jineam dat 25
6. the number of such segments If one of last two items is selected then the subdirectories and the files with extension dpr this is the standard extension for files for catalog preparation from the current directory are screened in the special window You can choose a file If no file is selected the program returns to the previous menu If the selected file does not correspond to the current block structure then the error message is imaged The current number of records in the catalog and the mode of creation are screened in the process When the creation of the catalog is completed you can view by pressing any key the plot of dependence of the number of earthquakes on the number of quaked cells the plot of dependence of the accumulated number of earthquakes on the magnitude and the information on the total number of earthquakes on the minimum and maximum magnitudes on the maximum number of cells in one earthquake The plots are presented in the logarithmic scale see Fig 8 21 CREATION OF CATALOG Fig 8 Plots of dependencies for structure from Fig 4 Pressing lt ESC gt returns you to the previous menu V File Operations All data can be saved in and can be loaded from disk files of the special structure at every time moment during the simulation process If this item is selected then the menu of the following seven items appears 1 File for Output Structure 2 File with Initial Structure 3 File for Output Data
7. this mode and eliminates the scheme Lineaments may be useful during the geometry specification To perform verification procedure to input boundary blocks and numerical parameters of the structure The description of this possibility requires a separate section you find it after this table To return to the menu of Dynamics of Block Structure Verification procedure Functional key lt F4 gt is used to switch on verification and editing modes during specification of a block structure geometry If verification procedure defining blocks and segments is not successful then one of the messages mentioned above is screened and the illegal part of the structure 13 is marked by lightblue color Otherwise the block structure is imaged in the optimal scale and the mode of editing switches on There are two menus in the mode of editing Boundary Blocks Numerical Parameters The first menu allows us to specify boundary blocks for the structure There are three opportunities to do it 1 WHOLE this choice defines the only boundary block consisting of all boundary segments 2 SINGLE this choice defines each boundary segment as a separate boundary block If the number of boundary segments exceeds the maximum for the number of boundary blocks then all remaining segments are included in the last block Both items WHOLE and SINGLE are supplied by the color mark of boundary blocks 3 USER this choice remains def
8. 0 U velocity To specify for the block the value in 10 of a radian of the angle velocity of the underlying medium rotation around the geometrical center of the block bottom The range of changing is 100 100 By pressing lt Esc gt it is possible to return to the second menu 3 BOUNDS to specify the values of boundary block parameters You can select the desired boundary block by pressing lt PgUp gt lt PgDn gt The selected block is marked on the screen by lightblue color The menu for specification of the boundary block parameters contains the following windows X velocity To specify for the boundary block the value in cm of the velocity of its progressive movement along the axis X of the coordinate system The range of changing is 15 100 100 Y velocity To specify for the boundary block the value in cm of the velocity of its progressive movement along the axis Y of the coordinate system The range of changing is 100 100 U velocity To specify for the boundary block the value in 10 of a radian of the angle velocity of its rotation around the coordinate origin The range of changing is 100 100 By pressing lt Esc gt it is possible to return to the second menu 2 Numerical Parameters If this item is selected then the new menu appears It contains three opportunities Local Axes Parameters Time Parameters Space Parameters Local axes parameters This mode is used to input the lo
9. 4 File with Initial Data 5 File for Text Information 6 File for Catalog Preparation 7 File for Catalog You can press lt ESC gt to return to the main menu Below there is the detailed description of the items listed above 1 File for Output Structure You select this item if you want to save the block structure and all numerical parameters of the process in a text file The name of this file has to be specified in the special window The name must be without extension the standard extension for data files blk will be added automatically If the name is illegal the corresponding message is imaged If a file with the name specified already exists then the request 22 for overwriting is screened and the data are saved only after the confirmation Pressing lt ESC gt means that this file will not be created Note that data are saved twice The first operation is performed immediately after specification of the file name the second one before exit from the program to save the last version Successful execution of verification procedure is required before saving in both cases 2 File with Initial Structure The subdirectories and the files with extension blk from the current directory are screened in the special window You can choose a file Program EARTH loads the block structure from the selected file You can edit it or run the simulation process 3 File for Output Data You select this item if you want to sav
10. Advanced School on Understanding and Prediction of Earthquakes and other Extreme Events in Complex Systems 26 September 8 October 2011 User s Guide for Program EARTH B Digas L Melnikova V Rozenberg Institute of Mathematics and Mechanics Russian Academy of Sciences Ural Branch Kovalevskoi str 16 Ekaterinburg 620990 Russian Federation www imm uran ru A Soloviev International Institute of Earthquake Prediction Theory and Mathematical Geophysics Russian Academy of Sciences Profsoyuznaya str 84 32 Moscow 117997 Russian Federation www mitp ru The Abdus Salam International Centre for Theoretical Physics Strada Costiera 11 34014 Trieste Italy 2011 Program EARTH destination and possibilities Program EARTH is destined for the numerical simulation of block structure dynamics and seismicity with two dimensional movements of blocks the 2D model A block structure is a part of lithosphere s layer between two horizontal planes consisting of perfectly rigid blocks The blocks are separated by infinitely thin plane faults and interact between themselves along the faults and with the underlying medium along the lower plane The interaction is viscous elastic The movement of the blocks is a consequence of the prescribed motion of boundaries of the block structure and the underlying medium If for some part of a fault plane the stress exceeds a certain level during simulation then a stress drop a failure occurs The fai
11. applied to the surfaces of the fault segments and to the block bottoms The discretization of a fault segment is performed as follows Each fault segment is a trapezium It is divided into rows and then into small trapeziums cells within every row so that side lengths are less than for all cells The bottom of a block is a polygon which is divided into trapeziums triangles by segments passing through its vertices and parallel to axis Y The discretization of these figures is performed in the same way as in the case of the fault segments The small trapeziums triangles are also called cells The values of coordinates displacements and forces are not distinguished for different points of the same cell Thus after space discretization cells are considered instead of points A failure occurs for a whole cell All the cells of the same fault in which the failure occurred are treated as a single earthquake Its parameters are defined by the following 7 way the origin time is the failure occurrence time the epicentral coordinates and the source depth are the weighted sums of the coordinates and depths of the cells involved in the earthquake the weight of a cell is given by its square divided by the sum of squares of all the cells the magnitude is calculated from the formula M logio S 4 01 1 02 7 where S is the total area in km of cells involved in the earthquake MODES OF WORK Program EARTH has the followin
12. ations will be performed with zero initial conditions 5 File for Text Information You select this item if you want to create a text file with the structure parameters and calculation results This file can be created in all 23 main modes of the programs The name of the file has to be specified in the special window The name must be without extension the standard extension for such files pri will be added automatically If the name is illegal the corresponding message is imaged If a file with the name specified already exists then the request for overwriting is screened and the data are saved only after the confirmation Pressing lt ESC gt means that this file will not be created 6 File for Catalog Preparation You select this item if you want to create a file which can be used for earthquake catalog preparation The name of this file has to be specified in the special window The name must be without extension the standard extension for files for catalog preparation dpf will be added automatically If the name is illegal the corresponding message is imaged If a file with the name specified already exists or it is the default file tmp dpt then the request for overwriting is screened and the file is created only after the confirmation If overwriting is prohibited then the new information will be added at the end of the file Remember that by this reason a file for catalog preparation may include data written dur
13. cal coordinates of the origin it is assumed that the unit is equal to 10 km the lengths of segments along axes OX and OY they determine the scale of graphic picture and the geographic coordinates of the origin the longitude and latitude in degrees The ranges of changing are 500 500 for the local coordinates of the origin 0 1 800 for the lengths of segments and 180 180 90 90 for the longitude and latitude respectively Time parameters This mode is used to input the values of time interval and time step Ar for the numerical simulation of dynamics of the block structure The ranges of changing are 0 9999 for the interval and 0 0001 1 for the step Note that the value of step has to be less then the value of interval Otherwise new values of these parameters will be abrogated Space parameters This mode is used to input the values of depth H of the layer step of space discretization e these values are measured in the units of 10 km and the parameter P in 5 the value of P is measured in bars When you change the depth the structure bottom is recalculated and space discretization is fulfilled then boundary blocks should be defined When you change the space step only space discretization is fulfilled The ranges of changing are 0 5 30 for the depth 0 01 5 for the step and 0 5000 for the parameter P Note that the value of step has to be less then the value of depth Otherwise new values of these para
14. ceforth the parameter Wp is used in equation 3 for this cell The values of parameters B H Hs and W may be different for different faults 6 Movements The movement of the block structure is caused by the movement of its boundaries boundary blocks and the underlying medium In the 2D model a boundary block is supposed to move progressively in the horizontal plane with a constant velocity with components V Vy and to rotate around the coordinate origin with a constant angle velocity U The medium underlying a block is supposed to move progressively in the horizontal plane with a constant velocity with components Vx Vy and to rotate around the geometrical center of the block bottom with a constant angle velocity U The system of equations that describes the movement of some block structure is a linear one and has the following form Az b 6 where the components of the unknown vector Z Zi Z2 Z3n are the components of the translation vectors of the blocks and the angles of their rotation around the geometrical centers of the bottoms n is the number of blocks It should be noted that the matrix A does not depend on time and may be calculated a priori DISCRETIZATION Time discretization is defined by a time step At The states of the structure are calculated for the discrete time moments ti t iAt i 1 2 where t is the initial moment Space discretization is defined by a space step and
15. cified the latitude and the longitude of the coordinate origin the initial year of the catalog 00h 00m of the Ist January of this year will be assigned to t 0 it is assumed in the program that the default initial year is 1900 the number of days 365 by default to be assigned to the unit of time used in the equations describing dynamics of the block structure The magnitude is calculated by formula 7 DIALOG The program uses the window interface represented in the form of hierarchical menus allowing us to specify different parameters and to choose different options The first main menu replacing the initial picture consists of the following six items I Dynamics of Block Structure 9 II Calculation of Maximum Stress II Image of Earthquake Flow IV Creation of Catalog V File Operations VI Exit To select the necessary mode you have to move the cursor to the proper item and press lt ENTER gt It is possible to terminate the program and to return to DOS command line by selecting the special item Exit and pressing lt Y gt as the answer to the confirmation question It should be noted that this is the only legal exit from the program I Dynamics of Block Structure If this item of the main menu is selected then the menu of the following four items appears 1 Geometry of Block Structure 2 Numerical Parameters 3 Simulation of Block Dynamics 4 Screening Current Variables You may press lt ESC gt to ret
16. cognized as an admissible one otherwise the procedure marks the illegal part of the structure its blocks and segments are determined automatically After this action the boundary blocks dip angles and other numerical parameters of faults blocks and boundary blocks are defined in the special menu system Thus the process of passing from geometric parameters of a real seismic region to its program approximation is rather difficult The example of model structure is presented in Fig 4 ABStISSA OROINATE BLOCK STRUCTURE ABSCISSA BRUINATE FAULTS BLOCKS BOUNDS 25 0000 Fig 4 The program approximation of the real seismic region The picture contains the following help information a the speed of cursor moving in pixels at the upper left corner of the screen b the real coordinates of the cursor at the upper right corner of the screen 11 c the number of specified vertices and faults and the number of defined segments blocks boundary blocks and boundary segments at the lower left corner of the screen if verification procedure has not worked yet then there is the expression UNDEFINED instead of the number of segments blocks and so on d the programmed keys at the lower right corner of the screen There are the following functional keys Key lt gt gt lt gt lt gt lt gt lt gt lt gt lt HOME gt lt END gt lt SHIFT gt lt gt gt lt gt Sls lt
17. e the conditions and parameters of the final or any intermediate state of the process in a file of the special structure The name of this file has to be specified in the special window The name must be without extension the standard extension for such files dd will be added automatically If the name is illegal the corresponding message is imaged If a file with the name specified already exists then the request for overwriting is screened and the data are saved only after the confirmation Pressing lt ESC gt means that this file will not be created It should be noted that file for output data includes also the information on the block structure geometry and all numerical parameters of the process for data consistency 4 File with Initial Data The subdirectories and the files with extension dd f from the current directory are screened in the special window You can choose a data file Program EARTH loads the block structure from the selected file You can continue the simulation process for this structure from the state recorded in the selected file The time parameters interval and step should be specified If a file with initial data is specified then the specifications made before for a file with initial structure and a file for output structure are cancelled The same actions are performed if you choose mode Simulation of Block Dynamics with a file with initial data specified If this file is not selected then calcul
18. g main modes of work I Dynamics of block structure This is the base mode If this mode is selected then the numerical simulation of dynamics of the block structure and earthquake failure sequences caused by it is performed The simulation can be started with zero initial conditions or from some intermediate state saved in a disk file of the special structure If necessary the file in which the parameters of the final or the current for the moment of process interruption state will be written can be indicated Besides it is possible to create a file for catalog preparation Below the description of operations with files is presented in detail II Calculation of maximum stress If this mode is selected then the program calculates the maximum for segment cells value of 5 in percents of the value of level B This operation is carried out for the current time moment or for some intermediate state saved in a disk file of the special structure The information about the maximum value of the stress is screened for all segments or for a selected segment III Image of earthquake flow If this mode is selected then the program images on the screen the sequence of cell failures for the fault segments In this mode the program uses the file with the information for earthquake catalog preparation The name of this file has to be indicated in the special menu arising after the selection of the mode There is a possibility to screen the plots of depe
19. he local coordinate system s origin 17 b the number of vertices faults segments blocks boundary blocks and boundary segments c the values of time and space numerical parameters d the names of files specified in File Operations If a parameter is not specified then the expression UNDEFINED is imaged You can press any key to exit II Calculation of Maximum Stress If this mode is selected then the program images on the screen the maximum for segment cells value of 5 in percents of the value of level B This operation is carried out for the current time moment if the simulation has been interrupted or for some intermediate state saved in a disk file of the special structure The information on the maximum stress is outputted by two ways for all segments and for a selected segment You can press lt TAB gt to switch over these modes In the first case there are the percents written at the middle of each segment of the block structure on the coordinate plane in the optimal scale The maximum percents are typed by red color other values by black color If the structure consists of too many segments the picture may be rather incomprehensible and it is recommended to apply the second mode In this mode the fault segments with the maximum stress for the whole structure are marked by red color Using left and right arrows you can select the segment for receiving more detailed information the selected segmen
20. ible to extend the existing fault by a natural way 12 lt DEL gt lt INS gt lt Fl gt lt F2 gt lt F3 gt lt F4 gt lt ESC gt To fulfil some deleting operations If lt DEL gt is pressed under mode Draw fault it switches off this mode If you use this key under mode Draw vertex it deletes some structure elements when the cursor indicates to the existing vertex or the whole structure when the cursor indicates to a screen point without any vertex In the first case the selected vertex and the faults having it as one of the ends are deleted after the confirmation Note that isolated vertices we call so vertices which are not one of the end points of any fault are deleted automatically during the work of verification procedure To load the standard default structure You can do it by pressing this key if your picture is empty The standard structure consists of 15 vertices 8 faults 22 segments 8 blocks and 2 boundary blocks see Fig 2 The values of coefficients and velocities are specified in such a way that there are earthquakes during the simulation process To output help information on hot keys To show the block structure on the bottom plane the mode works only after successful verification Repeated pressing switches off the bottom plane To image on the screen the scheme of lineaments prepared for some seismic zone and stored in file lineam dat Repeated pressing cancels
21. ing previous executions of the program in mode Simulation of Block Dynamics Pressing lt ENTER gt confirms your choice lt ESC gt means that the default file will be used 7 File for Catalog You select this item if you want to create a binary file in the standard 20 bytes format with an earthquake catalog The name of the file has to be specified in the special window The name must be without extension the standard extension for catalog files dat will be added automatically If the name is illegal the corresponding message is imaged If a file with the name specified already exists or it is the default file tmp dat then the request for overwriting is screened and the file is created only after the confirmation If overwriting is prohibited then the new information will be added at the end of the file Remember that by this reason a file for catalog may include data written during previous executions of the program in mode Creation of Catalog Pressing lt ENTER gt confirms your choice lt ESC gt means that the default file will be used 24 Program DISTR This program allows us to image on the screen the time distribution of earthquakes from a file for catalog preparation As in mode Simulation of Block Dynamics of program EARTH the moments of earthquakes are pictured by vertical lines of the lengths proportional to the magnitudes Program DISTR is the simple tool for visualizing data saved in
22. inition of boundary blocks to the user You can do it by the following way Select the initial anticlockwise segment of the first boundary block using left and right arrows and press lt ENTER gt Specify other segments of the first boundary block by use of lt gt and lt gt Press lt ENTER gt to complete definition of the block and to start definition of a next one by analogy Press lt ESC gt to pass to specification of numerical parameters if the configuration of boundary blocks is acceptable The second menu allows us to specify all numerical parameters for the faults blocks and boundary blocks There are the following three items in this menu 1 FAULTS to specify the values of fault parameters You can select the desired fault by pressing lt PgUp gt lt PgDn gt The selected fault and its direction are marked on the screen by lightblue color The menu for specification of the fault parameters contains the following windows Dip angle Coef KF Coef WF Coef WS Level B To specify the value in degrees of a dip angle for the fault plane The range of changing is 10 170 without 89 9 90 1 To specify for the fault the value in bars cm of parameter Kr in 4 The range of changing is 0 100 To specify for the fault the value in cm bars of parameter Wp in 3 The range of changing is 0 500 To specify for the fault the value in cm bars of parameter W which is used in 3 for the creep state
23. ks Fault parameters The interaction between two adjacent blocks at any point of the fault plane separating them is described for the 2D model by the equation dAw Wf 3 f 3 where the elastic force per unit area f in the fault plane is defined by the formula f K Ar Aw 4 Here Ar is the vector of the total displacement in the fault plane between the blocks at the point Aw is the vector of the inelastic displacement in the fault plane at the point Kp and Wp are parameters that characterize interaction between the blocks in the fault plane The values of all coefficients may be different for different faults Another group of fault parameters define a failure rise Denote he If 5 where P is the parameter which may be interpreted as the difference between lithostatic and hydrostatic pressure po is the block reaction force per unit area that is normal to the fault plane at the point The value of P is the same for all faults When the value of at any part of a fault reaches the level B a failure occurs After that the components of the vector Aw are changed sharply to reduce the value of to the level He He lt B The parts of faults for which failure occurred are in the creep state It means that in equation 3 the parameter W W gt W is used instead of Wr The creep continues while the value of is higher than the level H H lt H When k lt H the cell returns to the normal state and hen
24. lures are considered as earthquakes A synthetic earthquake catalog is produced as a main result of the numerical simulation For simulation it is necessary to specify a block structure geometry values of parameters that define features of interaction between elements of the structure and movements of the underlying medium and the boundaries The output data are different visual representations of sequences of model earthquakes The program works in the interactive mode and includes the calculation and service procedures united by the system of hierarchical menus All data of the program are specified by the window interface the output is realized in the graphic form The program is supplied by the help information Program EARTH is a DOS application the programming language is Borland Pascal 7 0 IBM PC compatible with EGA VGA monitor and not less than 8M of free memory are required for the successful work of program EARTH The following files should be placed in the same directory earth exe program EARTH rtm exe dpmil6bi ovl RTM loader and overlay file egavga bgi device driver file litt chr tscr chr font files glo pcx image file The programming skill is not required from users Some experience with computers would be helpful To users The program is modified from time to time according to the experience of its applications and in order to improve user s interface Any suggestions or information on obtained
25. meters will be abrogated 3 Simulation of Block Dynamics This mode gives an opportunity to visualize results of the numerical simulation of dynamics of the block structure At every time moment the displacements and rotation angles of the blocks are recalculated the state of the structure is analyzed arising failures are processed The program images on the screen the moments of earthquakes by vertical lines of the lengths proportional to the magnitudes and the information on the current maximum value of 5 in percents of level B maximum stress for the structure including the fault segment row and column of the cell where this value is reached see Fig 5 So you can see the distribution of events in time and can compare a model earthquake flow with a real one It should be noted that dimensionless time is used in the model so it is necessary to set the correspondence between the model and real time units for example by using the seismic cycle or recurrence of strong events You can press lt ESC gt to abort the simulation and to return to the menu of Dynamics of Block Structure In this case all necessary information is saved in a file specified for output data and in a file for text information DYNAMICS OF BLOCK STRUCTURE Fig 5 Dependence of model magnitude on time for structure from Fig 4 4 Screening Current Variables Using this mode you can view the following information a the geographic coordinates of t
26. n the logarithmic scale Press lt ESC gt to return to the base picture 20 of the mode lt ESC gt To return to the main menu of the program IV Creation of Catalog This mode gives an opportunity to create an earthquake catalog in the standard 20 bytes format If this item is selected then the new menu appears It contains four opportunities Time Parameters Magnitude Parameters Creation with Unification Creation with Distinguishing Time parameters This mode is used to input the values of the initial year and the number of days per one unit of dimensionless time for determination of real time of an earthquake during creation of a catalog The ranges of changing are 2000 2000 for the initial year and 1 3650 for the number of days Magnitude parameters This mode is used to input the values of the initial magnitude and of the magnitude step for the different plots screened after creation of a catalog The ranges of changing are 3 8 for the initial magnitude and 0 01 1 for the magnitude step Creation with unification This item defines creation of a catalog with unification of all simultaneously quaked cells of the conjugated segments belonging to the same fault into one earthquake Creation with distinguishing This item defines creation of a catalog with distinguishing all simultaneously quaked cells of the different segments In this case the number of earthquakes at any time moment is equal to
27. n time is the important information for studying the phenomenon of migration of earthquakes along the faults and for investigating mechanisms of arising and spreading earthquakes 19 IMAGE OF EARTHQUAKE FLOW Selected segment CELLS Normal segment Earthquaked segnent fal Normal WU Creep Z Earthquake Fig 7 Image of earthquake flow for structure from Fig 4 There are the following functional keys Key lt gt lt lt gt gt lt ENTER gt lt Fl gt lt F2 gt lt F3 gt Function and Comments To select a segment for viewing The selected segment is marked by lightblue color To image on the screen the sequence of cell failures for the selected segment The form of imaged cell depends on its state normal creep or earthquake Segments with failed cells are marked on the picture by red There is no any information on all other segments The segment direction from left to right is marked by letters L and R Press lt ESC gt to return to the base picture of the mode To output help information on hot keys To output on the screen the plot of dependence of the number of earthquakes on the number of cells involved in an earthquake The plot is presented in the logarithmic scale Press lt ESC gt to return to the base picture of the mode To output on the screen the plot of dependence of the accumulated number of earthquakes on the number of cells involved in an earthquake The plot is presented i
28. ndence of the number of earthquakes on the number of cells failed in an earthquake IV Creation of catalog If this mode is selected then the program creates an earthquake catalog using the file with the information for earthquake catalog preparation The catalog can be produced in two ways with unification of all segments of the same fault and with distinguishing of such segments After creating the catalog the plots of dependence of the number of earthquakes on the number of cells failed in an earthquake 8 and the plot of dependence of the accumulated number of earthquakes on the magnitude are screened In all modes it is possible to save the information on the process parameters and calculation results in a text file of the special structure CATALOG Program EARTH creates an earthquake catalog stored as a binary file in the standard 20 bytes format The specification of the records in a catalog file is the following The first record consists of 20 bytes at that the first 4 bytes contain an integer which is the total number of records in the file it is the number of earthquakes plus 1 All other records have the following structure Positions of Content Type records 1 4 time of the earthquake in minutes A D integer 4 5 6 latitude 100 integer 2 7 8 longitude 100 integer 2 9 10 depth km integer 2 11 12 magnitude 100 integer 2 13 20 Are not used reserved In addition the following information has to be spe
29. simulation results will be kindly appreciated Please send both to 1 Prof A Soloviev International Institute of Earthquake Prediction Theory and Mathematical Geophysics Russian Academy of Sciences Profsoyuznaya str 84 32 Moscow 117997 RUSSIA e mail soloviev mitp ru 2 Dr V Rozenberg Institute of Mathematics and Mechanics Ural Branch Russian Academy of Sciences S Kovalevskoi str 16 Ekaterinburg 620990 RUSSIA e mail rozen imm uran ru BLOCK STRUCTURE GEOMETRY A layer with depth thickness H between two horizontal planes is considered A block structure is a part of this layer limited and divided into blocks by planes intersecting the layer Parts of these planes which are inside the block structure or adjoin to it are called faults The block structure geometry is defined by the description of intersection lines of faults they will also be called faults below with the upper plane and by angles of dip for the fault planes The geometry on the lower plane is assumed to be similar to the one on the upper plane The notion vertex is used for the description of the system of faults Three or more faults cannot have a common point on the upper plane Vertex is a common point of two faults There are three types of vertices C corner vertex is a vertex which is an end point of a fault and at the same time an initial point of another one E end vertex is a vertex which is an initial or end point of a fault and
30. t is marked by lightblue color Information on the selected segment is outputted in the special window and contains the current time moment the parameters of the fault which this segment belongs to the coordinates of the cell with the maximum stress for this segment the percent and the additional remark if the stress reaches the maximum for the whole structure see Fig 6 CALCULATION OF MAXIMUM STRESS Selected segment LEFT RIGHT change segment Segment with maximum stress TAB change mode _ Other segments ESC return to main menu Fig 6 Maximum stress for structure from Fig 4 This mode helps to find the most active boundaries of the structure and to observe how the stress spreads through the structure Pressing lt ESC gt cancels both informational modes and returns you to the main menu III Image of Earthquake Flow If this item is selected then the subdirectories and the files with extension dpf this is the standard extension for files for catalog preparation from the current directory are screened in the special window You can choose a file If no file is selected the program returns to the main menu If the selected file corresponds to the current block structure then you have an opportunity to select some segment on the coordinate plane and to output the sequence of failures for it on the screen see Fig 7 Otherwise the error message is imaged It should be noted that the distribution of cell failures i
31. tersections with coordinates 5 2 5 3 5 4 There are 8 faults Their description is given in the table below number of fault initial point end point Dip angle 1 1 2 45 2 2 3 45 3 3 4 135 4 4 1 135 5 5 6 45 6 7 8 45 7 9 10 45 8 11 12 45 With the depth of the layer H 1 the faults and the vertices have on the lower plane the positions shown in Fig 3 4 Fig 3 The vertices and the faults on the lower plane The structure has 22 segments and 8 blocks these parts of the structure are detected by the program The definition of the boundary blocks is at user s discretion This simple block structure plays the role of the default structure for program EARTH PARAMETERS AND MOVEMENTS Block parameters The interaction between the block and the underlying medium at any point of the common part of the block and the lower plane the block bottom is described for the 2D model by the equation dAu Wafu 1 it 1 where the horizontal elastic force per unit area f is defined by the formula f K Ar Au 2 Here Ar is the vector of the total horizontal displacement between the block and the underlying medium at the point Au is the vector of the horizontal inelastic displacement at the point K and W are parameters that characterize the interaction between the block and the underlying medium The values of all coefficients may be different for different bloc
32. urn to the main menu Below there is the detailed description of the items listed above 1 Geometry of Block Structure This mode gives an opportunity to specify the geometry of a block structure which is defined by the description of intersection lines of the faults with the upper plane and by angles of dip for the fault planes The faults and vertices are defined directly on the coordinate plane the unit is equal to 10 km The dip angles and other numerical parameters are defined in the special menu system There are the following restrictions in program EARTH on the geometric parameters of a block structure the maximum values are listed Structure elements Max value Vertices 100 Faults 75 Segments 150 Blocks 30 Boundary blocks 20 Cells per a segment row 250 Rows per a segment 40 Cells per a bottom trapezium 1100 10 Trapeziums per a block bottom 7 When specification of the block structure geometry is finished the verification procedure is performed It should be noted that the block structure is inadmissible in the following cases a there is an intersection of more than two faults at one vertex b there is a vertex belonging to only one fault or not belonging to any fault c there is a multiply connected block structure d there is a segment which does not occur in any block e there is a segment which has intersection of its sides If the structure is re
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