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 failures 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, dpmi16bi.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 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: [email protected] 2) Dr. V.Rozenberg, Institute of Mathematics and Mechanics, Ural Branch, Russian Academy of Sciences, S.Kovalevskoi str., 16, Ekaterinburg 620990, RUSSIA; e-mail: [email protected] 2 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 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 (I) 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 intersections with coordinates (5,2), (5,3), (5,4). There are 8 faults. Their description is given in the table below. number of fault 1 2 3 4 5 6 7 8 initial point 1 2 3 4 5 7 9 11 end point 2 3 4 1 6 8 10 12 Dip angle 45q 45q 135q 135q 45q 45q 45q 45q 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 d'u = Wu fu, dt (1) where the horizontal elastic force per unit area fu is defined by the formula fu = Ku ('r - 'u). (2) 5 Here 'r is the vector of the total horizontal displacement between the block and the underlying medium at the point, 'u is the vector of the horizontal inelastic displacement at the point. Ku and Wu are parameters that characterize the interaction between the block and the underlying medium. The values of all coefficients may be different for different blocks. 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 d'w = Wf f, dt (3) where the elastic force per unit area f in the fault plane is defined by the formula f = Kf ('r - 'w). (4) Here 'r is the vector of the total displacement in the fault plane between the blocks at the point, 'w is the vector of the inelastic displacement in the fault plane at the point. Kf and Wf 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 N= |f | , P p0 (5) where P is the parameter which may be interpreted as the difference between lithostatic and hydrostatic pressure, p0 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 N at any part of a fault reaches the level B, a failure occurs. After that the components of the vector 'w are changed sharply to reduce the value of N to the level Hf (Hf < B). The parts of faults for which failure occurred are in the creep state. It means that in equation (3) the parameter Ws , Ws t Wf, is used instead of Wf. The creep continues while the value of N is higher than the level Hs (Hs < Hf ). When k d Hs the cell returns to the normal state and henceforth the parameter Wf is used in equation (3) for this cell. The values of parameters B, Hf , Hs, and Ws 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 Vx , 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 = (z1, 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 't. The states of the structure are calculated for the discrete time moments ti = t0 + i't (i = 1, 2, ...), where t0 is the initial moment. Space discretization is defined by a space step H and 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 H 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 ti (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 = (log10 S + 4.01)/1.02, (7) where S is the total area (in km2) of cells involved in the earthquake. MODES OF WORK Program EARTH has the following 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 N (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 dependence 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 records 1-4 5-6 7-8 9-10 11-12 13-20 Content time of the earthquake in minutes A.D. latitude100 longitude100 depth (km) magnitude100 Are not used (reserved) Type integer4 integer2 integer2 integer2 integer2 In addition, the following information has to be specified: the latitude and the longitude of the coordinate origin; the initial year of the catalog (00h 00m of the 1st 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 III. 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 <ENTER>. It is possible to terminate the program and to return to DOS command line by selecting the special item “Exit” and pressing <Y> 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 <ESC> to return 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 Vertices Faults Segments Blocks Boundary blocks Cells per a segment row Rows per a segment Cells per a bottom trapezium 10 Max value 100 75 150 30 20 250 40 1100 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 recognized 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. 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 Function and Comments <o>, <m>, To find a desired point on the coordinate plane in order to enter or delete a vertex. The direction of cursor moving <p>, <n> 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. <HOME>, <END> To place the cursor at the upper left corner and the lower right corner of the coordinate plane respectively. <SHIFT> + <o>, <m>, <p>, <n> To realize picture scrolling in the corresponding direction. <SHIFT> + <HOME> To return the coordinate origin to the point (0, 0). <ENTER> 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 <ENTER> at a screen point without inputted vertex (mode “Draw vertex”, the blue cursor). If you press <ENTER> 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 <ENTER> 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 possible to extend the existing fault by a natural way. 12 <DEL> To fulfil some deleting operations. If <DEL> 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. <INS> 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. <F1> To output help information on hot keys. <F2> To show the block structure on the bottom plane (the mode works only after successful verification). Repeated pressing switches off the bottom plane. <F3> To image on the screen the scheme of lineaments prepared for some seismic zone and stored in file “lineam.dat”. Repeated pressing cancels this mode and eliminates the scheme. Lineaments may be useful during the geometry specification. <F4> 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). <ESC> To return to the menu of “Dynamics of Block Structure”. Verification procedure. Functional key <F4> 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 definition 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 <ENTER>. Specify other segments of the first boundary block by use of <+> and <–>. Press <ENTER> to complete definition of the block and to start definition of a next one by analogy. Press <ESC> 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 <PgUp>, <PgDn>. 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 Kf in (4). The range of changing is [0, 100]. To specify for the fault the value (in cm/bars) of parameter Wf in (3). The range of changing is [0, 500]. To specify for the fault the value (in cm/bars) of parameter Ws which is used in (3) for the creep state. The range of changing is [0, 500]. Note that Ws t Wf. 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 Hf . The range of changing is [0, 100]. Level HS To specify for the fault the value of level Hs. The range of changing is [0, 100]. Note that B > Hf > Hs. Otherwise new values of these parameters will be abrogated. By pressing <Esc> 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 <PgUp>, <PgDn>. 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 Ku in (2). The range of changing is [0, 100]. Coef WU To specify for the block bottom the value (in cm/bars) of parameter Wu 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, 100]. U-velocity To specify for the block the value (in 10-6 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 <Esc> 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 <PgUp>, <PgDn>. 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 10-6 of a radian) of the angle velocity of its rotation around the coordinate origin. The range of changing is [-100, 100]. By pressing <Esc> 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 local 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 't 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 H (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 parameters will be abrogated. 16 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 N (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 <ESC> 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. 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 the 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 N (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 <TAB> 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 segment 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. 18 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 <ESC> 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 “.dpt” (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 in 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 Fig. 7. Image of earthquake flow for structure from Fig. 4 There are the following functional keys. Key <o>, <m> Function and Comments To select a segment for viewing. The selected segment is marked by lightblue color. <ENTER> 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 <ESC> to return to the base picture of the mode. <F1> To output help information on hot keys. <F2> 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 <ESC> to return to the base picture of the mode. <F3> 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 in the logarithmic scale. Press <ESC> to return to the base picture 20 of the mode. <ESC> 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 the number of such segments. If one of last two items is selected then the subdirectories and the files with extension “.dpt” (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 Fig. 8. Plots of dependencies for structure from Fig. 4 Pressing <ESC> 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 4. File with Initial Data 5. File for Text Information 6. File for Catalog Preparation 7. File for Catalog You can press <ESC> 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 <ESC> 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 save 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 “.ddt” 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 <ESC> 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 “.ddt” 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 calculations 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 <ESC> 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 “.dpt” 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 during previous executions of the program in mode “Simulation of Block Dynamics”. Pressing <ENTER> confirms your choice, <ESC> 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 <ENTER> confirms your choice, <ESC> 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 “.dpt” files. The main menu contains five items: File with Block Structure, View of Block Structure, Numerical Parameters, DPT-reading & Visualization, Exit. File with block 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 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 & visualization. If this item is selected then the subdirectories and the files with extension “.dpt” 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 “lineam.dat”. Specification of lineament vertices (their local coordinates x and y) is realized by means of the simplest 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 “lineam.dat”. 25

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