Difference between revisions of "Guide to programming with madagascar"
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This page was created from the LaTeX source in book/rsf/rsf/demo.tex using latex2wiki
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− | <center><font size="-1">''This page was created from the LaTeX source in [ | + | <center><font size="-1">''This page was created from the LaTeX source in [https://github.com/ahay/src/blob/master/book/rsf/rsf/demo.tex book/rsf/rsf/demo.tex] using [[latex2wiki]]''</font></center> |
This guide demonstrates a simple time-domain | This guide demonstrates a simple time-domain | ||
Line 32: | Line 32: | ||
==C program== | ==C program== | ||
− | + | <syntaxhighlight lang="c"> | |
− | <c> | ||
/* time-domain acoustic FD modeling */ | /* time-domain acoustic FD modeling */ | ||
#include <rsf.h> | #include <rsf.h> | ||
Line 42: | Line 41: | ||
bool verb; /* verbose flag */ | bool verb; /* verbose flag */ | ||
− | sf_file Fw,Fv,Fr,Fo; /* I/O files */ | + | sf_file Fw=NULL,Fv=NULL,Fr=NULL,Fo=NULL; /* I/O files */ |
sf_axis at,az,ax; /* cube axes */ | sf_axis at,az,ax; /* cube axes */ | ||
int it,iz,ix; /* index variables */ | int it,iz,ix; /* index variables */ | ||
Line 141: | Line 140: | ||
} | } | ||
if(verb) fprintf(stderr,"\n"); | if(verb) fprintf(stderr,"\n"); | ||
− | + | sf_close() | |
exit (0); | exit (0); | ||
} | } | ||
− | </ | + | </syntaxhighlight> |
− | |||
− | |||
*Declare input, output and auxiliary file tags: <tt>Fw</tt> for input wavelet, <tt>Fv</tt> for velocity, <tt>Fr</tt> for reflectivity, and <tt>Fo</tt> for output wavefield. | *Declare input, output and auxiliary file tags: <tt>Fw</tt> for input wavelet, <tt>Fv</tt> for velocity, <tt>Fr</tt> for reflectivity, and <tt>Fo</tt> for output wavefield. | ||
− | <c> | + | <syntaxhighlight lang="c"> |
sf_file Fw,Fv,Fr,Fo; /* I/O files */ | sf_file Fw,Fv,Fr,Fo; /* I/O files */ | ||
− | </ | + | </syntaxhighlight> |
*Declare RSF cube axes: <tt>at</tt> time axis, <tt>ax</tt> space axis, <tt>az</tt> depth axis. | *Declare RSF cube axes: <tt>at</tt> time axis, <tt>ax</tt> space axis, <tt>az</tt> depth axis. | ||
− | <c> | + | <syntaxhighlight lang="c"> |
sf_axis at,az,ax; /* cube axes */ | sf_axis at,az,ax; /* cube axes */ | ||
− | </ | + | </syntaxhighlight> |
*Declare multi-dimensional arrays for input, output and computations. | *Declare multi-dimensional arrays for input, output and computations. | ||
− | <c> | + | <syntaxhighlight lang="c"> |
float *ww,**vv,**rr; /* I/O arrays*/ | float *ww,**vv,**rr; /* I/O arrays*/ | ||
− | </ | + | </syntaxhighlight> |
*Open files for input/output. | *Open files for input/output. | ||
− | <c> | + | <syntaxhighlight lang="c"> |
Fw = sf_input ("in" ); | Fw = sf_input ("in" ); | ||
Fo = sf_output("out"); | Fo = sf_output("out"); | ||
Fv = sf_input ("vel"); | Fv = sf_input ("vel"); | ||
Fr = sf_input ("ref"); | Fr = sf_input ("ref"); | ||
− | </ | + | </syntaxhighlight> |
*Read axes from input files; write axes to output file. | *Read axes from input files; write axes to output file. | ||
− | <c> | + | <syntaxhighlight lang="c"> |
at = sf_iaxa(Fw,1); nt = sf_n(at); dt = sf_d(at); | at = sf_iaxa(Fw,1); nt = sf_n(at); dt = sf_d(at); | ||
az = sf_iaxa(Fv,1); nz = sf_n(az); dz = sf_d(az); | az = sf_iaxa(Fv,1); nz = sf_n(az); dz = sf_d(az); | ||
Line 176: | Line 173: | ||
sf_oaxa(Fo,ax,2); | sf_oaxa(Fo,ax,2); | ||
sf_oaxa(Fo,at,3); | sf_oaxa(Fo,at,3); | ||
− | </ | + | </syntaxhighlight> |
*Allocate arrays and read wavelet, velocity and reflectivity. | *Allocate arrays and read wavelet, velocity and reflectivity. | ||
− | <c> | + | <syntaxhighlight lang="c"> |
ww=sf_floatalloc(nt); sf_floatread(ww ,nt ,Fw); | ww=sf_floatalloc(nt); sf_floatread(ww ,nt ,Fw); | ||
vv=sf_floatalloc2(nz,nx); sf_floatread(vv[0],nz*nx,Fv); | vv=sf_floatalloc2(nz,nx); sf_floatread(vv[0],nz*nx,Fv); | ||
rr=sf_floatalloc2(nz,nx); sf_floatread(rr[0],nz*nx,Fr); | rr=sf_floatalloc2(nz,nx); sf_floatread(rr[0],nz*nx,Fr); | ||
− | </ | + | </syntaxhighlight> |
*Allocate temporary arrays. | *Allocate temporary arrays. | ||
− | <c> | + | <syntaxhighlight lang="c"> |
um=sf_floatalloc2(nz,nx); | um=sf_floatalloc2(nz,nx); | ||
uo=sf_floatalloc2(nz,nx); | uo=sf_floatalloc2(nz,nx); | ||
up=sf_floatalloc2(nz,nx); | up=sf_floatalloc2(nz,nx); | ||
ud=sf_floatalloc2(nz,nx); | ud=sf_floatalloc2(nz,nx); | ||
− | </ | + | </syntaxhighlight> |
*Loop over time. | *Loop over time. | ||
− | <c> | + | <syntaxhighlight lang="c"> |
for (it=0; it<nt; it++) { | for (it=0; it<nt; it++) { | ||
− | </ | + | </syntaxhighlight> |
*Compute Laplacian: <math>\Delta U</math>. | *Compute Laplacian: <math>\Delta U</math>. | ||
− | <c> | + | <syntaxhighlight lang="c"> |
for (iz=2; iz<nz-2; iz++) { | for (iz=2; iz<nz-2; iz++) { | ||
for (ix=2; ix<nx-2; ix++) { | for (ix=2; ix<nx-2; ix++) { | ||
Line 206: | Line 203: | ||
} | } | ||
} | } | ||
− | </ | + | </syntaxhighlight> |
*Inject source wavelet: <math>\left[ \Delta U - f(t) \right]</math> | *Inject source wavelet: <math>\left[ \Delta U - f(t) \right]</math> | ||
− | <c> | + | <syntaxhighlight lang="c"> |
for (iz=0; iz<nz; iz++) { | for (iz=0; iz<nz; iz++) { | ||
for (ix=0; ix<nx; ix++) { | for (ix=0; ix<nx; ix++) { | ||
Line 214: | Line 211: | ||
} | } | ||
} | } | ||
− | </ | + | </syntaxhighlight> |
*Scale by velocity: <math>\left[ \Delta U - f(t) \right] v^2</math> | *Scale by velocity: <math>\left[ \Delta U - f(t) \right] v^2</math> | ||
− | <c> | + | <syntaxhighlight lang="c"> |
for (iz=0; iz<nz; iz++) { | for (iz=0; iz<nz; iz++) { | ||
for (ix=0; ix<nx; ix++) { | for (ix=0; ix<nx; ix++) { | ||
Line 222: | Line 219: | ||
} | } | ||
} | } | ||
− | </ | + | </syntaxhighlight> |
*Time step: <math>U_{i+1} = \left[ \Delta U -f(t) \right] v^2 \Delta t^2 + 2 U_{i} - U_{i-1}</math> | *Time step: <math>U_{i+1} = \left[ \Delta U -f(t) \right] v^2 \Delta t^2 + 2 U_{i} - U_{i-1}</math> | ||
− | <c> | + | <syntaxhighlight lang="c"> |
for (iz=0; iz<nz; iz++) { | for (iz=0; iz<nz; iz++) { | ||
for (ix=0; ix<nx; ix++) { | for (ix=0; ix<nx; ix++) { | ||
Line 236: | Line 233: | ||
} | } | ||
} | } | ||
− | </ | + | </syntaxhighlight> |
==C++ program== | ==C++ program== | ||
− | + | <syntaxhighlight lang="cpp"> | |
− | <cpp> | ||
// time-domain acoustic FD modeling | // time-domain acoustic FD modeling | ||
#include <valarray> | #include <valarray> | ||
Line 296: | Line 292: | ||
if(verb) cerr << endl; | if(verb) cerr << endl; | ||
for (int it=0; it<nt; it++) { | for (int it=0; it<nt; it++) { | ||
− | if(verb) cerr << " | + | if(verb) cerr << "\b\b\b\b\b" << it; |
// 4th order laplacian | // 4th order laplacian | ||
Line 328: | Line 324: | ||
exit(0); | exit(0); | ||
} | } | ||
− | + | </syntaxhighlight> | |
− | </ | ||
*Declare input, output and auxiliary file cubes (of type <tt>CUB</tt>). | *Declare input, output and auxiliary file cubes (of type <tt>CUB</tt>). | ||
− | <cpp> | + | <syntaxhighlight lang="cpp"> |
CUB Fw("in", "i"); Fw.headin(); //Fw.report(); | CUB Fw("in", "i"); Fw.headin(); //Fw.report(); | ||
CUB Fv("vel","i"); Fv.headin(); //Fv.report(); | CUB Fv("vel","i"); Fv.headin(); //Fv.report(); | ||
CUB Fr("ref","i"); Fr.headin(); //Fr.report(); | CUB Fr("ref","i"); Fr.headin(); //Fr.report(); | ||
CUB Fo("out","o"); Fo.setup(3,Fv.esize()); | CUB Fo("out","o"); Fo.setup(3,Fv.esize()); | ||
− | </ | + | </syntaxhighlight> |
*Declare, read and write RSF cube axes: <tt>at</tt> time axis, <tt>ax</tt> space axis, <tt>az</tt> depth axis. | *Declare, read and write RSF cube axes: <tt>at</tt> time axis, <tt>ax</tt> space axis, <tt>az</tt> depth axis. | ||
− | <cpp> | + | <syntaxhighlight lang="cpp"> |
sf_axis at = Fw.getax(0); int nt = sf_n(at); float dt = sf_d(at); | sf_axis at = Fw.getax(0); int nt = sf_n(at); float dt = sf_d(at); | ||
sf_axis az = Fv.getax(0); int nz = sf_n(az); float dz = sf_d(az); | sf_axis az = Fv.getax(0); int nz = sf_n(az); float dz = sf_d(az); | ||
Line 348: | Line 343: | ||
Fo.putax(2,at); | Fo.putax(2,at); | ||
Fo.headou(); | Fo.headou(); | ||
− | </ | + | </syntaxhighlight> |
*Declare multi-dimensional <tt>valarrays</tt> for input, output and read data. | *Declare multi-dimensional <tt>valarrays</tt> for input, output and read data. | ||
− | <cpp> | + | <syntaxhighlight lang="cpp"> |
valarray<float> ww( nt ); ww=0; Fw >> ww; | valarray<float> ww( nt ); ww=0; Fw >> ww; | ||
valarray<float> vv( nz*nx ); vv=0; Fv >> vv; | valarray<float> vv( nz*nx ); vv=0; Fv >> vv; | ||
valarray<float> rr( nz*nx ); rr=0; Fr >> rr; | valarray<float> rr( nz*nx ); rr=0; Fr >> rr; | ||
− | </ | + | </syntaxhighlight> |
*Declare multi-dimensional <tt>valarrays</tt> for temporary storage. | *Declare multi-dimensional <tt>valarrays</tt> for temporary storage. | ||
− | <cpp> | + | <syntaxhighlight lang="cpp"> |
valarray<float> um(nz*nx); um=0; | valarray<float> um(nz*nx); um=0; | ||
valarray<float> uo(nz*nx); uo=0; | valarray<float> uo(nz*nx); uo=0; | ||
valarray<float> up(nz*nx); up=0; | valarray<float> up(nz*nx); up=0; | ||
valarray<float> ud(nz*nx); ud=0; | valarray<float> ud(nz*nx); ud=0; | ||
− | </ | + | </syntaxhighlight> |
*Initialize multidimensional <tt>valarray</tt> index counter (of type <tt>VAI</tt>). | *Initialize multidimensional <tt>valarray</tt> index counter (of type <tt>VAI</tt>). | ||
− | <cpp> | + | <syntaxhighlight lang="cpp"> |
VAI k(nz,nx); | VAI k(nz,nx); | ||
− | </ | + | </syntaxhighlight> |
*Loop over time. | *Loop over time. | ||
− | <cpp> | + | <syntaxhighlight lang="cpp"> |
for (int it=0; it<nt; it++) { | for (int it=0; it<nt; it++) { | ||
− | </ | + | </syntaxhighlight> |
*Compute Laplacian: <math>\Delta U</math>. | *Compute Laplacian: <math>\Delta U</math>. | ||
− | <cpp> | + | <syntaxhighlight lang="cpp"> |
for (int iz=2; iz<nz-2; iz++) { | for (int iz=2; iz<nz-2; iz++) { | ||
for (int ix=2; ix<nx-2; ix++) { | for (int ix=2; ix<nx-2; ix++) { | ||
Line 382: | Line 377: | ||
} | } | ||
} | } | ||
− | </ | + | </syntaxhighlight> |
*Inject source wavelet: <math>\left[ \Delta U - f(t) \right]</math> | *Inject source wavelet: <math>\left[ \Delta U - f(t) \right]</math> | ||
− | <cpp> | + | <syntaxhighlight lang="cpp"> |
ud -= ww[it] * rr; | ud -= ww[it] * rr; | ||
− | </ | + | </syntaxhighlight> |
*Scale by velocity: <math>\left[ \Delta U - f(t) \right] v^2</math> | *Scale by velocity: <math>\left[ \Delta U - f(t) \right] v^2</math> | ||
− | <cpp> | + | <syntaxhighlight lang="cpp"> |
ud *= vv*vv; | ud *= vv*vv; | ||
− | </ | + | </syntaxhighlight> |
*Time step: <math>U_{i+1} = \left[ \Delta U -f(t) \right] v^2 \Delta t^2 + 2 U_{i} - U_{i-1}</math> | *Time step: <math>U_{i+1} = \left[ \Delta U -f(t) \right] v^2 \Delta t^2 + 2 U_{i} - U_{i-1}</math> | ||
− | <cpp> | + | <syntaxhighlight lang="cpp"> |
up=(float)2 * uo - um + ud * dt2; | up=(float)2 * uo - um + ud * dt2; | ||
um = uo; | um = uo; | ||
uo = up; | uo = up; | ||
− | </ | + | </syntaxhighlight> |
==Fortran 90 program== | ==Fortran 90 program== | ||
− | + | <syntaxhighlight lang="fortran"> | |
− | <fortran> | ||
! time-domain acoustic FD modeling | ! time-domain acoustic FD modeling | ||
program AFDMf90 | program AFDMf90 | ||
Line 481: | Line 475: | ||
call exit(0) | call exit(0) | ||
end program AFDMf90 | end program AFDMf90 | ||
− | </ | + | </syntaxhighlight> |
*Declare input, output and auxiliary file tags. | *Declare input, output and auxiliary file tags. | ||
− | <fortran> | + | <syntaxhighlight lang="fortran"> |
type(file) :: Fw,Fv,Fr,Fo ! I/O files | type(file) :: Fw,Fv,Fr,Fo ! I/O files | ||
− | </ | + | </syntaxhighlight> |
*Declare RSF cube axes: <tt>at</tt> time axis, <tt>ax</tt> space axis, <tt>az</tt> depth axis. | *Declare RSF cube axes: <tt>at</tt> time axis, <tt>ax</tt> space axis, <tt>az</tt> depth axis. | ||
− | <fortran> | + | <syntaxhighlight lang="fortran"> |
type(axa) :: at,az,ax ! cube axes | type(axa) :: at,az,ax ! cube axes | ||
− | </ | + | </syntaxhighlight> |
*Declare multi-dimensional arrays for input, output and computations. | *Declare multi-dimensional arrays for input, output and computations. | ||
− | <fortran> | + | <syntaxhighlight lang="fortran"> |
real, allocatable :: vv(:,:),rr(:,:),ww(:) ! I/O arrays | real, allocatable :: vv(:,:),rr(:,:),ww(:) ! I/O arrays | ||
real, allocatable :: um(:,:),uo(:,:),up(:,:),ud(:,:) ! tmp arrays | real, allocatable :: um(:,:),uo(:,:),up(:,:),ud(:,:) ! tmp arrays | ||
− | </ | + | </syntaxhighlight> |
*Open files for input/output. | *Open files for input/output. | ||
− | <fortran> | + | <syntaxhighlight lang="fortran"> |
Fw=rsf_input ("in") | Fw=rsf_input ("in") | ||
Fv=rsf_input ("vel") | Fv=rsf_input ("vel") | ||
Fr=rsf_input ("ref") | Fr=rsf_input ("ref") | ||
Fo=rsf_output("out") | Fo=rsf_output("out") | ||
− | </ | + | </syntaxhighlight> |
*Read axes from input files; write axes to output file. | *Read axes from input files; write axes to output file. | ||
− | <fortran> | + | <syntaxhighlight lang="fortran"> |
call iaxa(Fw,at,1); call iaxa(Fv,az,1); call iaxa(Fv,ax,2) | call iaxa(Fw,at,1); call iaxa(Fv,az,1); call iaxa(Fv,ax,2) | ||
call oaxa(Fo,az,1); call oaxa(Fo,ax,2); call oaxa(Fo,at,3) | call oaxa(Fo,az,1); call oaxa(Fo,ax,2); call oaxa(Fo,at,3) | ||
− | </ | + | </syntaxhighlight> |
*Allocate arrays and read wavelet, velocity and reflectivity. | *Allocate arrays and read wavelet, velocity and reflectivity. | ||
− | <fortran> | + | <syntaxhighlight lang="fortran"> |
allocate(ww(at%n )); ww=0.; call rsf_read(Fw,ww) | allocate(ww(at%n )); ww=0.; call rsf_read(Fw,ww) | ||
allocate(vv(az%n,ax%n)); vv=0.; call rsf_read(Fv,vv) | allocate(vv(az%n,ax%n)); vv=0.; call rsf_read(Fv,vv) | ||
allocate(rr(az%n,ax%n)); rr=0.; call rsf_read(Fr,rr) | allocate(rr(az%n,ax%n)); rr=0.; call rsf_read(Fr,rr) | ||
− | </ | + | </syntaxhighlight> |
*Allocate temporary arrays. | *Allocate temporary arrays. | ||
− | <fortran> | + | <syntaxhighlight lang="fortran"> |
allocate(um(az%n,ax%n)); um=0. | allocate(um(az%n,ax%n)); um=0. | ||
allocate(uo(az%n,ax%n)); uo=0. | allocate(uo(az%n,ax%n)); uo=0. | ||
allocate(up(az%n,ax%n)); up=0. | allocate(up(az%n,ax%n)); up=0. | ||
allocate(ud(az%n,ax%n)); ud=0. | allocate(ud(az%n,ax%n)); ud=0. | ||
− | </ | + | </syntaxhighlight> |
*Loop over time. | *Loop over time. | ||
− | <fortran> | + | <syntaxhighlight lang="fortran"> |
do it=1,at%n | do it=1,at%n | ||
− | </ | + | </syntaxhighlight> |
*Compute Laplacian: <math>\Delta U</math>. | *Compute Laplacian: <math>\Delta U</math>. | ||
− | <fortran> | + | <syntaxhighlight lang="fortran"> |
do iz=2,az%n-2 | do iz=2,az%n-2 | ||
do ix=2,ax%n-2 | do ix=2,ax%n-2 | ||
Line 537: | Line 531: | ||
end do | end do | ||
end do | end do | ||
− | </ | + | </syntaxhighlight> |
*Inject source wavelet: <math>\left[ \Delta U - f(t) \right]</math> | *Inject source wavelet: <math>\left[ \Delta U - f(t) \right]</math> | ||
− | <fortran> | + | <syntaxhighlight lang="fortran"> |
ud = ud - ww(it) * rr | ud = ud - ww(it) * rr | ||
− | </ | + | </syntaxhighlight> |
*Scale by velocity: <math>\left[ \Delta U - f(t) \right] v^2</math> | *Scale by velocity: <math>\left[ \Delta U - f(t) \right] v^2</math> | ||
− | <fortran> | + | <syntaxhighlight lang="fortran"> |
ud= ud *vv*vv | ud= ud *vv*vv | ||
− | </ | + | </syntaxhighlight> |
*Time step: <math>U_{i+1} = \left[ \Delta U -f(t) \right] v^2 \Delta t^2 + 2 U_{i} - U_{i-1}</math> | *Time step: <math>U_{i+1} = \left[ \Delta U -f(t) \right] v^2 \Delta t^2 + 2 U_{i} - U_{i-1}</math> | ||
− | <fortran> | + | <syntaxhighlight lang="fortran"> |
up = 2*uo - um + ud * dt2 | up = 2*uo - um + ud * dt2 | ||
um = uo | um = uo | ||
uo = up | uo = up | ||
− | </ | + | </syntaxhighlight> |
==References== | ==References== | ||
<references/> | <references/> |
Revision as of 14:05, 9 August 2018
This guide demonstrates a simple time-domain finite-differences modeling code in RSF.
Introduction
This section presents time-domain finite-difference modeling [1] written with the RSF library. The program is demonstrated with the C, C++ and Fortran 90 interfaces. The acoustic wave-equation
can be written as
is the Laplacian symbol, is the source wavelet, is the velocity, and is a scalar wavefield. A discrete time-step involves the following computations:
where , and represent the propagating wavefield at various time steps.
C program
/* time-domain acoustic FD modeling */
#include <rsf.h>
int main(int argc, char* argv[])
{
/* Laplacian coefficients */
float c0=-30./12.,c1=+16./12.,c2=- 1./12.;
bool verb; /* verbose flag */
sf_file Fw=NULL,Fv=NULL,Fr=NULL,Fo=NULL; /* I/O files */
sf_axis at,az,ax; /* cube axes */
int it,iz,ix; /* index variables */
int nt,nz,nx;
float dt,dz,dx,idx,idz,dt2;
float *ww,**vv,**rr; /* I/O arrays*/
float **um,**uo,**up,**ud;/* tmp arrays */
sf_init(argc,argv);
if(! sf_getbool("verb",&verb)) verb=0;
/* setup I/O files */
Fw = sf_input ("in" );
Fo = sf_output("out");
Fv = sf_input ("vel");
Fr = sf_input ("ref");
/* Read/Write axes */
at = sf_iaxa(Fw,1); nt = sf_n(at); dt = sf_d(at);
az = sf_iaxa(Fv,1); nz = sf_n(az); dz = sf_d(az);
ax = sf_iaxa(Fv,2); nx = sf_n(ax); dx = sf_d(ax);
sf_oaxa(Fo,az,1);
sf_oaxa(Fo,ax,2);
sf_oaxa(Fo,at,3);
dt2 = dt*dt;
idz = 1/(dz*dz);
idx = 1/(dx*dx);
/* read wavelet, velocity & reflectivity */
ww=sf_floatalloc(nt); sf_floatread(ww ,nt ,Fw);
vv=sf_floatalloc2(nz,nx); sf_floatread(vv[0],nz*nx,Fv);
rr=sf_floatalloc2(nz,nx); sf_floatread(rr[0],nz*nx,Fr);
/* allocate temporary arrays */
um=sf_floatalloc2(nz,nx);
uo=sf_floatalloc2(nz,nx);
up=sf_floatalloc2(nz,nx);
ud=sf_floatalloc2(nz,nx);
for (iz=0; iz<nz; iz++) {
for (ix=0; ix<nx; ix++) {
um[ix][iz]=0;
uo[ix][iz]=0;
up[ix][iz]=0;
ud[ix][iz]=0;
}
}
/* MAIN LOOP */
if(verb) fprintf(stderr,"\n");
for (it=0; it<nt; it++) {
if(verb) fprintf(stderr,"\b\b\b\b\b%d",it);
/* 4th order laplacian */
for (iz=2; iz<nz-2; iz++) {
for (ix=2; ix<nx-2; ix++) {
ud[ix][iz] =
c0* uo[ix ][iz ] * (idx+idz) +
c1*(uo[ix-1][iz ] + uo[ix+1][iz ])*idx +
c2*(uo[ix-2][iz ] + uo[ix+2][iz ])*idx +
c1*(uo[ix ][iz-1] + uo[ix ][iz+1])*idz +
c2*(uo[ix ][iz-2] + uo[ix ][iz+2])*idz;
}
}
/* inject wavelet */
for (iz=0; iz<nz; iz++) {
for (ix=0; ix<nx; ix++) {
ud[ix][iz] -= ww[it] * rr[ix][iz];
}
}
/* scale by velocity */
for (iz=0; iz<nz; iz++) {
for (ix=0; ix<nx; ix++) {
ud[ix][iz] *= vv[ix][iz]*vv[ix][iz];
}
}
/* time step */
for (iz=0; iz<nz; iz++) {
for (ix=0; ix<nx; ix++) {
up[ix][iz] =
2*uo[ix][iz]
- um[ix][iz]
+ ud[ix][iz] * dt2;
um[ix][iz] = uo[ix][iz];
uo[ix][iz] = up[ix][iz];
}
}
/* write wavefield to output */
sf_floatwrite(uo[0],nz*nx,Fo);
}
if(verb) fprintf(stderr,"\n");
sf_close()
exit (0);
}
- Declare input, output and auxiliary file tags: Fw for input wavelet, Fv for velocity, Fr for reflectivity, and Fo for output wavefield.
sf_file Fw,Fv,Fr,Fo; /* I/O files */
- Declare RSF cube axes: at time axis, ax space axis, az depth axis.
sf_axis at,az,ax; /* cube axes */
- Declare multi-dimensional arrays for input, output and computations.
float *ww,**vv,**rr; /* I/O arrays*/
- Open files for input/output.
Fw = sf_input ("in" );
Fo = sf_output("out");
Fv = sf_input ("vel");
Fr = sf_input ("ref");
- Read axes from input files; write axes to output file.
at = sf_iaxa(Fw,1); nt = sf_n(at); dt = sf_d(at);
az = sf_iaxa(Fv,1); nz = sf_n(az); dz = sf_d(az);
ax = sf_iaxa(Fv,2); nx = sf_n(ax); dx = sf_d(ax);
sf_oaxa(Fo,az,1);
sf_oaxa(Fo,ax,2);
sf_oaxa(Fo,at,3);
- Allocate arrays and read wavelet, velocity and reflectivity.
ww=sf_floatalloc(nt); sf_floatread(ww ,nt ,Fw);
vv=sf_floatalloc2(nz,nx); sf_floatread(vv[0],nz*nx,Fv);
rr=sf_floatalloc2(nz,nx); sf_floatread(rr[0],nz*nx,Fr);
- Allocate temporary arrays.
um=sf_floatalloc2(nz,nx);
uo=sf_floatalloc2(nz,nx);
up=sf_floatalloc2(nz,nx);
ud=sf_floatalloc2(nz,nx);
- Loop over time.
for (it=0; it<nt; it++) {
- Compute Laplacian: .
for (iz=2; iz<nz-2; iz++) {
for (ix=2; ix<nx-2; ix++) {
ud[ix][iz] =
c0* uo[ix ][iz ] * (idx+idz) +
c1*(uo[ix-1][iz ] + uo[ix+1][iz ])*idx +
c2*(uo[ix-2][iz ] + uo[ix+2][iz ])*idx +
c1*(uo[ix ][iz-1] + uo[ix ][iz+1])*idz +
c2*(uo[ix ][iz-2] + uo[ix ][iz+2])*idz;
}
}
- Inject source wavelet:
for (iz=0; iz<nz; iz++) {
for (ix=0; ix<nx; ix++) {
ud[ix][iz] -= ww[it] * rr[ix][iz];
}
}
- Scale by velocity:
for (iz=0; iz<nz; iz++) {
for (ix=0; ix<nx; ix++) {
ud[ix][iz] *= vv[ix][iz]*vv[ix][iz];
}
}
- Time step:
for (iz=0; iz<nz; iz++) {
for (ix=0; ix<nx; ix++) {
up[ix][iz] =
2*uo[ix][iz]
- um[ix][iz]
+ ud[ix][iz] * dt2;
um[ix][iz] = uo[ix][iz];
uo[ix][iz] = up[ix][iz];
}
}
C++ program
// time-domain acoustic FD modeling
#include <valarray>
#include <iostream>
#include <rsf.hh>
#include <cub.hh>
#include <vai.hh>
using namespace std;
int main(int argc, char* argv[])
{
// Laplacian coefficients
float c0=-30./12.,c1=+16./12.,c2=- 1./12.;
sf_init(argc,argv);// init RSF
bool verb; // vebose flag
if(! sf_getbool("verb",&verb)) verb=0;
// setup I/O files
CUB Fw("in", "i"); Fw.headin(); //Fw.report();
CUB Fv("vel","i"); Fv.headin(); //Fv.report();
CUB Fr("ref","i"); Fr.headin(); //Fr.report();
CUB Fo("out","o"); Fo.setup(3,Fv.esize());
// Read/Write axes
sf_axis at = Fw.getax(0); int nt = sf_n(at); float dt = sf_d(at);
sf_axis az = Fv.getax(0); int nz = sf_n(az); float dz = sf_d(az);
sf_axis ax = Fv.getax(1); int nx = sf_n(ax); float dx = sf_d(ax);
Fo.putax(0,az);
Fo.putax(1,ax);
Fo.putax(2,at);
Fo.headou();
float dt2 = dt*dt;
float idz = 1/(dz*dz);
float idx = 1/(dx*dx);
// read wavelet, velocity and reflectivity
valarray<float> ww( nt ); ww=0; Fw >> ww;
valarray<float> vv( nz*nx ); vv=0; Fv >> vv;
valarray<float> rr( nz*nx ); rr=0; Fr >> rr;
// allocate temporary arrays
valarray<float> um(nz*nx); um=0;
valarray<float> uo(nz*nx); uo=0;
valarray<float> up(nz*nx); up=0;
valarray<float> ud(nz*nx); ud=0;
// init ValArray Index counter
VAI k(nz,nx);
// MAIN LOOP
if(verb) cerr << endl;
for (int it=0; it<nt; it++) {
if(verb) cerr << "\b\b\b\b\b" << it;
// 4th order laplacian
for (int iz=2; iz<nz-2; iz++) {
for (int ix=2; ix<nx-2; ix++) {
ud[k(iz,ix)] =
c0* uo[ k(iz ,ix )] * (idx+idz) +
c1*(uo[ k(iz ,ix-1)]+uo[ k(iz ,ix+1)]) * idx +
c1*(uo[ k(iz-1,ix )]+uo[ k(iz+1,ix )]) * idz +
c2*(uo[ k(iz ,ix-2)]+uo[ k(iz ,ix+2)]) * idx +
c2*(uo[ k(iz-2,ix )]+uo[ k(iz+2,ix )]) * idz;
}
}
// inject wavelet
ud -= ww[it] * rr;
// scale by velocity
ud *= vv*vv;
// time step
up=(float)2 * uo - um + ud * dt2;
um = uo;
uo = up;
// write wavefield to output output
Fo << uo;
}
if(verb) cerr << endl;
exit(0);
}
- Declare input, output and auxiliary file cubes (of type CUB).
CUB Fw("in", "i"); Fw.headin(); //Fw.report();
CUB Fv("vel","i"); Fv.headin(); //Fv.report();
CUB Fr("ref","i"); Fr.headin(); //Fr.report();
CUB Fo("out","o"); Fo.setup(3,Fv.esize());
- Declare, read and write RSF cube axes: at time axis, ax space axis, az depth axis.
sf_axis at = Fw.getax(0); int nt = sf_n(at); float dt = sf_d(at);
sf_axis az = Fv.getax(0); int nz = sf_n(az); float dz = sf_d(az);
sf_axis ax = Fv.getax(1); int nx = sf_n(ax); float dx = sf_d(ax);
Fo.putax(0,az);
Fo.putax(1,ax);
Fo.putax(2,at);
Fo.headou();
- Declare multi-dimensional valarrays for input, output and read data.
valarray<float> ww( nt ); ww=0; Fw >> ww;
valarray<float> vv( nz*nx ); vv=0; Fv >> vv;
valarray<float> rr( nz*nx ); rr=0; Fr >> rr;
- Declare multi-dimensional valarrays for temporary storage.
valarray<float> um(nz*nx); um=0;
valarray<float> uo(nz*nx); uo=0;
valarray<float> up(nz*nx); up=0;
valarray<float> ud(nz*nx); ud=0;
- Initialize multidimensional valarray index counter (of type VAI).
VAI k(nz,nx);
- Loop over time.
for (int it=0; it<nt; it++) {
- Compute Laplacian: .
for (int iz=2; iz<nz-2; iz++) {
for (int ix=2; ix<nx-2; ix++) {
ud[k(iz,ix)] =
c0* uo[ k(iz ,ix )] * (idx+idz) +
c1*(uo[ k(iz ,ix-1)]+uo[ k(iz ,ix+1)]) * idx +
c1*(uo[ k(iz-1,ix )]+uo[ k(iz+1,ix )]) * idz +
c2*(uo[ k(iz ,ix-2)]+uo[ k(iz ,ix+2)]) * idx +
c2*(uo[ k(iz-2,ix )]+uo[ k(iz+2,ix )]) * idz;
}
}
- Inject source wavelet:
ud -= ww[it] * rr;
- Scale by velocity:
ud *= vv*vv;
- Time step:
up=(float)2 * uo - um + ud * dt2;
um = uo;
uo = up;
Fortran 90 program
! time-domain acoustic FD modeling
program AFDMf90
use rsf
implicit none
! Laplacian coefficients
real :: c0=-30./12.,c1=+16./12.,c2=- 1./12.
logical :: verb ! verbose flag
type(file) :: Fw,Fv,Fr,Fo ! I/O files
type(axa) :: at,az,ax ! cube axes
integer :: it,iz,ix ! index variables
real :: idx,idz,dt2
real, allocatable :: vv(:,:),rr(:,:),ww(:) ! I/O arrays
real, allocatable :: um(:,:),uo(:,:),up(:,:),ud(:,:) ! tmp arrays
call sf_init() ! init RSF
call from_par("verb",verb,.false.)
! setup I/O files
Fw=rsf_input ("in")
Fv=rsf_input ("vel")
Fr=rsf_input ("ref")
Fo=rsf_output("out")
! Read/Write axes
call iaxa(Fw,at,1); call iaxa(Fv,az,1); call iaxa(Fv,ax,2)
call oaxa(Fo,az,1); call oaxa(Fo,ax,2); call oaxa(Fo,at,3)
dt2 = at%d*at%d
idz = 1/(az%d*az%d)
idx = 1/(ax%d*ax%d)
! read wavelet, velocity & reflectivity
allocate(ww(at%n )); ww=0.; call rsf_read(Fw,ww)
allocate(vv(az%n,ax%n)); vv=0.; call rsf_read(Fv,vv)
allocate(rr(az%n,ax%n)); rr=0.; call rsf_read(Fr,rr)
! allocate temporary arrays
allocate(um(az%n,ax%n)); um=0.
allocate(uo(az%n,ax%n)); uo=0.
allocate(up(az%n,ax%n)); up=0.
allocate(ud(az%n,ax%n)); ud=0.
! MAIN LOOP
do it=1,at%n
if(verb) write (0,*) it
! 4th order laplacian
do iz=2,az%n-2
do ix=2,ax%n-2
ud(iz,ix) = &
c0* uo(iz, ix ) * (idx + idz) + &
c1*(uo(iz ,ix-1) + uo(iz ,ix+1))*idx + &
c2*(uo(iz ,ix-2) + uo(iz ,ix+2))*idx + &
c1*(uo(iz-1,ix ) + uo(iz+1,ix ))*idz + &
c2*(uo(iz-2,ix ) + uo(iz+2,ix ))*idz
end do
end do
! inject wavelet
ud = ud - ww(it) * rr
! scale by velocity
ud= ud *vv*vv
! time step
up = 2*uo - um + ud * dt2
um = uo
uo = up
! write wavefield to output
call rsf_write(Fo,uo)
end do
call exit(0)
end program AFDMf90
- Declare input, output and auxiliary file tags.
type(file) :: Fw,Fv,Fr,Fo ! I/O files
- Declare RSF cube axes: at time axis, ax space axis, az depth axis.
type(axa) :: at,az,ax ! cube axes
- Declare multi-dimensional arrays for input, output and computations.
real, allocatable :: vv(:,:),rr(:,:),ww(:) ! I/O arrays
real, allocatable :: um(:,:),uo(:,:),up(:,:),ud(:,:) ! tmp arrays
- Open files for input/output.
Fw=rsf_input ("in")
Fv=rsf_input ("vel")
Fr=rsf_input ("ref")
Fo=rsf_output("out")
- Read axes from input files; write axes to output file.
call iaxa(Fw,at,1); call iaxa(Fv,az,1); call iaxa(Fv,ax,2)
call oaxa(Fo,az,1); call oaxa(Fo,ax,2); call oaxa(Fo,at,3)
- Allocate arrays and read wavelet, velocity and reflectivity.
allocate(ww(at%n )); ww=0.; call rsf_read(Fw,ww)
allocate(vv(az%n,ax%n)); vv=0.; call rsf_read(Fv,vv)
allocate(rr(az%n,ax%n)); rr=0.; call rsf_read(Fr,rr)
- Allocate temporary arrays.
allocate(um(az%n,ax%n)); um=0.
allocate(uo(az%n,ax%n)); uo=0.
allocate(up(az%n,ax%n)); up=0.
allocate(ud(az%n,ax%n)); ud=0.
- Loop over time.
do it=1,at%n
- Compute Laplacian: .
do iz=2,az%n-2
do ix=2,ax%n-2
ud(iz,ix) = &
c0* uo(iz, ix ) * (idx + idz) + &
c1*(uo(iz ,ix-1) + uo(iz ,ix+1))*idx + &
c2*(uo(iz ,ix-2) + uo(iz ,ix+2))*idx + &
c1*(uo(iz-1,ix ) + uo(iz+1,ix ))*idz + &
c2*(uo(iz-2,ix ) + uo(iz+2,ix ))*idz
end do
end do
- Inject source wavelet:
ud = ud - ww(it) * rr
- Scale by velocity:
ud= ud *vv*vv
- Time step:
up = 2*uo - um + ud * dt2
um = uo
uo = up
References
- ↑ "Hello world" of seismic imaging.