User's Guide for Program EARTH

User's Guide for Program EARTH
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]
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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
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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.
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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)
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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.
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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
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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
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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
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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);
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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.
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<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
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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.
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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;
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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.
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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.
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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.
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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”.
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