A three-dimensional semianalytic viscoelastic model for time-dependent analysis of the earthquake cycle
MAXWELL V2.2 - December, 2017
Instructions for using the maxwell program. The
mathematical formulation is provided in the references.
RREFERENCES:
Smith, B. and D. Sandwell, A three-dimensional semianalytic viscoelastic
model for time-dependent analysis of the earthquake cycle,
J. Geophys. Res., v. 109, B12401, 2004.
Sandwell, D. and B. Smith-Konter, 2018. Maxwell: A Semi-analytic 4-D Code
for Earthquake Cycle Modeling of Transform Fault Systems,
Computers & Geosciences, 114, pp.84-97.
INSTALLATION: Get the complete tar distribution with test cases at: http://topex.ucsd.edu/body_force/viscoelastic/maxwellV2.4.tar or use this GITHUB repository https://github.com/dsandwell/fftfault
After unpacking the tar file one should compile and test the code.
Instructions are provided in INSTALL_TEST.txt. You will need C and Fortran compilers. Also the reading and writing
of grid files uses the GMT library. There are two FORTRAN callable
subroutines lib/readgrd.c and lib/writegrd.c with versions for GMT6, GMT5, and GMT4. You may need to modify all the makefiles to have the correct paths to the
GMT distribution. Also you could replace these routines with your favorite
grid file format. After running the test one can redo all the benchmarks provided
in this manuscript although you will need Matlab and GMT5 to make all the figures.
USAGE OF MAIN PROGRAM MAXWELL:
The main program calculates 3-D surface displacements or stress due to slip across a vertical fault consisting of many elements - slip varies on each element. The model consists of an elastic plate of thickness H overlying a viscoelastic half- space. All fault elements slip between depths D1 and D2 above the base of the elastic plate. The model simulates both single-couple and double couple dislocations for either deep continuous slip (secular models) or shallow coseismic slip (episodic models).
The program has 11 required and 4 optional command line arguments as follows:
Usage: maxwell F D1 D2 Z T dble ele.dat istr U.grd V.grd W.grd [H eta pois fd]
F - Factor to multiply output files used primarily for computing
displacement taking place over multiple years.
D1 D2 - Depth to bottom (D1) and top of fault (D2). Both
values should be negative, since z is positive upward in the model.
(H < D1 < D2 < 0).
Z - Depth of observation plane (negative). The observation plane
must also be above the bottom of the fault (D1 < Z). Thus stress
and displacement can be computed from the base of the fault to the
surface of the earth.
T - Time since earthquake (yrs). For secular models, T=9999 (infinity).
For episodic models that simulate earthquake events, this parameter
should be set to the number of years that have passed since that
event.
dble - Double or single couple option: 0-single couple,
1-double couple. For secular models representing deep slip,
a single couple can be used. For episodic or coseismic
models, a double couple should be used. (Note: if a single-couple
is used then a "mirror" fault segment is inserted in the model
grid to balance the overall moment of the model.)
ele.dat - Element file containing two header records followed by any
number of fault element records. Execution time is largely
independent of the number of fault elements. Elements must be
longer than 4 times the grid spacing (dx).
Header records:
# dx sig fault_orient (note slip is in mm)
1. 1. 90
where dx = grid spacing (default = 1km)
sig = source width in pixels (default = 1)
fault_orient = general fault orientation
(degrees from x-axis) Used only for Coulomb
stress calculation.
Fault element records: x1 x2 y1 y2 F1 F2 F3
x1 x2 = start stop fault element grid location in km
y1 y2 = start stop fault element grid location in km
F1 F2 F3 = strike-slip, dip-slip, and opening in mm
(left-lateral strike-slip is positive.)
Header records for maxwell_v
# dx sig fault_orient itermx shear_grid
1. 1. 90 10 rmu.grd
itermx = number of iterations used for variability calculation
rmu.grd - name of the file containing the shear modulus grid
Example ele.dat file:
dx sig fault_orient (note slip is in mm) #iter rigidity_grid
1 1 82.05 0 rigidity.grd
549.36 549.36 0.00 128.53 -40.00 0.00 0.00
549.36 549.62 128.53 132.51 -40.00 0.00 0.00
549.62 549.88 132.51 136.48 -40.00 0.00 0.00
549.88 550.26 136.48 142.45 -40.00 0.00 0.00
550.26 551.43 142.45 149.49 -40.00 0.00 0.00
551.43 552.47 149.49 154.55 -40.00 0.00 0.00
552.47 552.85 154.55 160.52 -40.00 0.00 0.00
552.85 553.23 160.52 166.48 -40.00 0.00 0.00
553.23 554.26 166.48 171.54 -40.00 0.00 0.00
554.26 555.95 171.54 175.70 -40.00 0.00 0.00
istress - Displacement/stress output option:
(0)-displacement U,V,W
(1)-stress Txx,Tyy,Txy
(2)-stress Tnormal,Tshear,Tcoulomb
x,y,z.grd - Names for output files of displacement or stress.
The following are optional parameters to override the default values set in the source code:
H - Elastic plate thickness (default: H=-50km)
eta - Half-space viscosity (default: eta=1.e19 Pas)
pois - Poisson ratio (default: pois=0.25)
fd - Locking depth factor (default: fd=1)
This parameter only applies for double couple
models and is used for easy manipulation of a set
of locking depths for multiple faults. For fd > 1,
all locking depths will be multiplied by fd and
thus become deeper.
LIMITATIONS OF MODEL:
Vertical Fault Plane: The present model only accommodates a purely vertical fault plane, as the mathematical formulation uses a vertically-integrated point- source Green's function to simulate a fault plane. For the general case of dipping faults, this integration could be numerically performed, although we have not incorporated this feature into our code.
Uniform observation depth: The output generated by the model is in the form of 3 grd grids representing one of three output options:
(0)-displacement U,V,W (1)-Stress Txx,Tyy,Txy (2)-Stress Tnormal,Tshear,Tcoulomb
All three grids are results of deformation occurring at a specified observation depth (Z). The model should be run at a variety of output depths to create a full 3-D image of displacement or stress above the base of the fault plane.