SUFDMOD2_PML - Finite-Difference MODeling (2nd order) for acoustic wave
equation with PML absorbing boundary conditions.
Caveat: experimental PML absorbing boundary condition version,
may be buggy!
sufdmod2_pml wfile nx= nz= tmax= xs= zs= [optional parameters]
Required Parameters:
wfile file containing waves[nx][nz] for time steps
nx= number of x samples (2nd dimension)
nz= number of z samples (1st dimension)
xs= x coordinates of source
zs= z coordinates of source
tmax= maximum time
Optional Parameters:
nt=1+tmax/dt number of time samples (dt determined for stability)
mt=1 number of time steps (dt) per output time step
dx=1.0 x sampling interval
fx=0.0 first x sample
dz=1.0 z sampling interval
fz=0.0 first z sample
fmax = vmin/(10.0*h) maximum frequency in source wavelet
fpeak=0.5*fmax peak frequency in ricker wavelet
dfile= input file containing density[nx][nz]
vsx= x coordinate of vertical line of seismograms
hsz= z coordinate of horizontal line of seismograms
vsfile= output file for vertical line of seismograms[nz][nt]
hsfile= output file for horizontal line of seismograms[nx][nt]
ssfile= output file for source point seismograms[nt]
verbose=0 =1 for diagnostic messages, =2 for more
abs=1,1,1,1 Absorbing boundary conditions on top,left,bottom,right
sides of the model.
=0,1,1,1 for free surface condition on the top
...PML parameters....
pml_max=1000.0 PML absorption parameter
pml_thick=0 half-thickness of pml layer (0 = do not use PML)
Notes:
This program uses the traditional explicit second order differencing
method.
Two different absorbing boundary condition schemes are available. The
first is a traditional absorbing boundary condition scheme created by
Hale, 1990. The second is based on the perfectly matched layer (PML)
method of Berenger, 1995.
Authors: CWP:Dave Hale
CWP:modified for SU by John Stockwell, 1993.
CWP:added frequency specification of wavelet: Craig Artley, 1993
TAMU:added PML absorbing boundary condition:
Michael Holzrichter, 1998
References: (Hale's absobing boundary conditions)
Clayton, R. W., and Engquist, B., 1977, Absorbing boundary conditions
for acoustic and elastic wave equations, Bull. Seism. Soc. Am., 6,
1529-1540.
Clayton, R. W., and Engquist, B., 1980, Absorbing boundary conditions
for wave equation migration, Geophysics, 45, 895-904.
Hale, D., 1990, Adaptive absorbing boundaries for finite-difference
modeling of the wave equation migration, unpublished report from the
Center for Wave Phenomena, Colorado School of Mines.
Richtmyer, R. D., and Morton, K. W., 1967, Difference methods for
initial-value problems, John Wiley & Sons, Inc, New York.
Thomee, V., 1962, A stable difference scheme for the mixed boundary problem
for a hyperbolic, first-order system in two dimensions, J. Soc. Indust.
Appl. Math., 10, 229-245.
Toldi, J. L., and Hale, D., 1982, Data-dependent absorbing side boundaries,
Stanford Exploration Project Report SEP-30, 111-121.
References: (PML boundary conditions)
Jean-Pierre Berenger, ``A Perfectly Matched Layer for the Absorption of
Electromagnetic Waves,'' Journal of Computational Physics, vol. 114,
pp. 185-200.
Hastings, Schneider, and Broschat, ``Application of the perfectly
matched layer (PML) absorbing boundary condition to elastic wave
propogation,'' Journal of the Accoustical Society of America,
November, 1996.
Allen Taflove, ``Electromagnetic Modeling: Finite Difference Time
Domain Methods'', Baltimore, Maryland: Johns Hopkins University Press,
1995, chap. 7, pp. 181-195.
Trace header fields set: ns, delrt, tracl, tracr, offset, d1, d2,
sdepth, trid