void lh_direct_LS( float **G /* The Forward Operator */,
int Nr /* Row Of G */,
int Nc /* Column of G */,
float **Cd /* The Covariance Matrix of Data Cd[Nr][Nr] */,
float **Cm /* The Covariance Matrix of model Cm[Nc][Nc] */,
float *d /* Data */,
float *m_prior /* m prior */,
float *m_post /* m posterior */ )
/*< Solve the Least Square Optimization Problem directly Using Matrix Inverse >*/
{
float **Gt, **A, **B1, **B2, **B3, **B, *C1, *C, **AB;
Gt = alloc2float( Nr , Nc );
A = alloc2float( Nr , Nc );
B1 = alloc2float( Nc , Nr );
B2 = alloc2float( Nr , Nr );
B3 = alloc2float( Nr , Nr );
B = alloc2float( Nr , Nr );
C1 = alloc1float( Nr );
C = alloc1float( Nr );
AB = alloc2float( Nr , Nc );
zero2float( Gt , Nr , Nc );
zero2float( A , Nr , Nc );
zero2float( B1 , Nc , Nr );
zero2float( B2 , Nr , Nr );
zero2float( B3 , Nr , Nr );
zero2float( B , Nr , Nr );
zero1float( C1 , Nr );
zero1float( C , Nr );
zero2float( AB , Nr , Nc );
lh_matrix_transpose( G , Gt , Nr , Nc );
lh_matrix_mu_matrix( Cm , Gt , A , Nc , Nc , Nr );
lh_matrix_mu_matrix( G , Cm , B1 , Nr , Nc , Nc );
lh_matrix_mu_matrix( B1 , Gt , B2 , Nr , Nc , Nr );
lh_matrix_add_matrix( B2 , Cd , B3 , Nr , Nr );
lh_matrix_inverse( B3 , B , Nr );
lh_matrix_mu_vector( G , m_prior , C1 , Nr , Nc );
lh_vector_sub_vector( d , C1 , C , Nr );
lh_matrix_mu_matrix( A , B , AB , Nc , Nr , Nr );
lh_matrix_mu_vector( AB , C , m_post , Nc , Nr );
lh_vector_add_vector( m_prior , m_post , m_post , Nc );
free2float( Gt );
free2float( A );
free2float( B1 );
free2float( B2 );
free2float( B3 );
free2float( B );
free1float( C1 );
free1float( C );
free2float( AB );
}
int main(int argc, char* argv[])
{
int ix, iz, jx, jz,ixx,izz,ixf,izf,i,j,im, jm,nx,nz,nxf,nzf,nxpad,nzpad,it,ii,jj;
float kxmax,kzmax;
float f0, t, t0, dx, dz, dxf, dzf,dt, dkx, dkz, dt2;
int mm, nvx, nvz, ns;
int hnkx, hnkz, nkx, nkz, nxz, nkxz;
int hnkx1, hnkz1, nkx1, nkz1;
int isx, isz, isxm, iszm; /*source location */
int itaper; /* tapering or not for spectrum of oprtator*/
int nstep; /* every nstep in spatial grids to calculate filters sparsely*/
float *coeff_1dx, *coeff_1dz, *coeff_2dx, *coeff_2dz; /* finite-difference coefficient */
float **apx, **apz, **apxx, **apzz; /* polarization operator of P-wave for a location */
float **apxs, **apzs, **apxxs, **apzzs; /* polarization operator of SV-wave for a location */
float ****ex, ****ez; /* operator for whole model for P-wave*/
float ****exs, ****ezs; /* operator for whole model for SV-wave*/
float **exx, **ezz; /* operator for constant model for P-wave*/
float **exxs, **ezzs; /* operator for constant model for SV-wave*/
float **vp0, **vs0, **epsi, **del, **theta; /* velocity model */
float **p1, **p2, **p3, **q1, **q2, **q3, **p3c, **q3c, **sum; /* wavefield array */
float *kx, *kz, *kkx, *kkz, *kx2, *kz2, **taper;
clock_t t1, t2, t3, t4;
float timespent;
float A, fx, fz;
int isep=1;
int ihomo=1;
char *tapertype;
double vp2, vs2, ep2, de2, the;
sf_init(argc,argv);
sf_file Fo1, Fo2, Fo3, Fo4, Fo5, Fo6, Fo7, Fo8, Fo9, Fo10, Fo11, Fo12;
t1=clock();
/* wavelet parameter for source definition */
f0=30.0;
t0=0.04;
A=1.0;
/* time samping paramter */
if (!sf_getint("ns",&ns)) ns=301;
if (!sf_getfloat("dt",&dt)) dt=0.001;
if (!sf_getint("isep",&isep)) isep=0; /* if isep=1, separate wave-modes */
if (!sf_getint("ihomo",&ihomo)) ihomo=0; /* if ihomo=1, homogeneous medium */
if (NULL== (tapertype=sf_getstring("tapertype"))) tapertype="D"; /* taper type*/
if (!sf_getint("nstep",&nstep)) nstep=1; /* grid step to calculate operators: 1<=nstep<=5 */
sf_warning("isep=%d",isep);
sf_warning("ihomo=%d",ihomo);
sf_warning("tapertype=%s",tapertype);
sf_warning("nstep=%d",nstep);
sf_warning("ns=%d dt=%f",ns,dt);
sf_warning("read velocity model parameters");
/* setup I/O files */
sf_file Fvp0, Fvs0, Feps, Fdel, Fthe;
Fvp0 = sf_input ("in"); /* vp0 using standard input */
Fvs0 = sf_input ("vs0"); /* vs0 */
Feps = sf_input ("epsi"); /* epsi */
Fdel = sf_input ("del"); /* delta */
Fthe = sf_input ("the"); /* theta */
/* Read/Write axes */
sf_axis az, ax;
az = sf_iaxa(Fvp0,1); nvz = sf_n(az); dz = sf_d(az)*1000.0;
ax = sf_iaxa(Fvp0,2); nvx = sf_n(ax); dx = sf_d(ax)*1000.0;
fx=sf_o(ax)*1000.0;
fz=sf_o(az)*1000.0;
/* source definition */
isx=nvx/2;
isz=nvz/2;
//isz=nvz*2/5;
/* wave modeling space */
nx=nvx;
nz=nvz;
nxpad=nx+2*m;
nzpad=nz+2*m;
sf_warning("fx=%f fz=%f dx=%f dz=%f",fx,fz,dx,dz);
sf_warning("nx=%d nz=%d nxpad=%d nzpad=%d", nx,nz,nxpad,nzpad);
vp0=sf_floatalloc2(nz,nx);
vs0=sf_floatalloc2(nz,nx);
epsi=sf_floatalloc2(nz,nx);
del=sf_floatalloc2(nz,nx);
theta=sf_floatalloc2(nz,nx);
nxz=nx*nz;
mm=2*m+1;
dt2=dt*dt;
isxm=isx+m; /* source's x location */
iszm=isz+m; /* source's z-location */
/* read velocity model */
sf_floatread(vp0[0],nxz,Fvp0);
sf_floatread(vs0[0],nxz,Fvs0);
sf_floatread(epsi[0],nxz,Feps);
sf_floatread(del[0],nxz,Fdel);
sf_floatread(theta[0],nxz,Fthe);
for(i=0;i<nx;i++)
for(j=0;j<nz;j++)
theta[i][j] *= PI/180.0;
t2=clock();
Fo1 = sf_output("out"); /* Elastic-wave x-component */
Fo2 = sf_output("Elasticz"); /* Elastic-wave z-component */
/* setup I/O files */
puthead3(Fo1, nz, nx, 1, dz/1000.0, dx/1000.0, dt, fz/1000.0, fx/1000.0, 0.0);
puthead3(Fo2, nz, nx, 1, dz/1000.0, dx/1000.0, dt, fz/1000.0, fx/1000.0, 0.0);
/*****************************************************************************
* Calculating polarization operator for wave-mode separation
* ***************************************************************************/
if(isep==1)
{
sf_warning("==================================================");
sf_warning("== Calculating Polarization Operator ==");
sf_warning("==================================================");
/* calculate spatial steps for operater in sparsely sampling grid point */
dxf=dx*nstep;
dzf=dz*nstep;
nxf=nx/nstep+1;
nzf=nz/nstep+1;
/* operators length for calculation */
hnkx=400.0/dx;
hnkz=400.0/dz;
nkx=2*hnkx+1; /* operator length in kx-direction */
nkz=2*hnkz+1; /* operator length in kz-direction */
/* truncated spatial operators length for filtering*/
hnkx1=200.0/dx;
hnkz1=200.0/dz;
nkx1=2*hnkx1+1;
nkz1=2*hnkz1+1;
sf_warning("nx=%d nz=%d nxf=%d nzf=%d", nx,nz,nxf,nzf);
sf_warning("dx=%f dz=%f dxf=%f dzf=%f", dx,dz,dxf,dzf);
sf_warning("hnkx=%d hnkz=%d nkx=%d nkz=%d", hnkx, hnkz, nkx, nkz);
sf_warning("hnkx1=%d hnkz1=%d nkx1=%d nkz1=%d", hnkx1, hnkz1, nkx1, nkz1);
dkx=2*PI/dx/nkx;
dkz=2*PI/dz/nkz;
kxmax=PI/dx;
kzmax=PI/dz;
kx=sf_floatalloc(nkx);
kz=sf_floatalloc(nkx);
kkx=sf_floatalloc(nkx);
kkz=sf_floatalloc(nkx);
kx2=sf_floatalloc(nkx);
kz2=sf_floatalloc(nkx);
taper=sf_floatalloc2(nkz, nkx);
// define axis samples and taper in wavenumber domain
kxkztaper(kx, kz, kkx, kkz, kx2, kz2, taper, nkx, nkz, hnkx, hnkz, dkx, dkz, kxmax, kzmax, tapertype);
nkxz=nkx*nkz;
/* truncation of spatial filter */
if(ihomo==1)
{
exx=sf_floatalloc2(nkz1, nkx1);
ezz=sf_floatalloc2(nkz1, nkx1);
exxs=sf_floatalloc2(nkz1, nkx1);
ezzs=sf_floatalloc2(nkz1, nkx1);
}else{
ex=sf_floatalloc4(nkz1, nkx1, nz, nx);
ez=sf_floatalloc4(nkz1, nkx1, nz, nx);
exs=sf_floatalloc4(nkz1, nkx1, nz, nx);
ezs=sf_floatalloc4(nkz1, nkx1, nz, nx);
}
/*****************************************************************************
* Calculating polarization operator for wave-mode separation
* ***************************************************************************/
apx=sf_floatalloc2(nkz, nkx);
apz=sf_floatalloc2(nkz, nkx);
apxs=sf_floatalloc2(nkz, nkx);
apzs=sf_floatalloc2(nkz, nkx);
apxx=sf_floatalloc2(nkz, nkx);
apzz=sf_floatalloc2(nkz, nkx);
apxxs=sf_floatalloc2(nkz, nkx);
apzzs=sf_floatalloc2(nkz, nkx);
/* setup I/O files for wavenumber-domain operators */
Fo3 = sf_output("apx"); /* P-wave's polarization x-comp */
Fo4 = sf_output("apz"); /* P-wave's polarization z-comp */
Fo5 = sf_output("apxs"); /* SV-wave's polarization x-comp */
Fo6 = sf_output("apzs"); /* SV-wave's polarization z-comp */
puthead1(Fo3, nkz, nkx, dkz, -kzmax, dkx, -kxmax);
puthead1(Fo4, nkz, nkx, dkz, -kzmax, dkx, -kxmax);
puthead1(Fo5, nkz, nkx, dkz, -kzmax, dkx, -kxmax);
puthead1(Fo6, nkz, nkx, dkz, -kzmax, dkx, -kxmax);
/* setup I/O files for space-domain operators */
Fo7 = sf_output("apxx"); /* P-wave's polarization x-comp in (x,z) domain */
Fo8 = sf_output("apzz"); /* P-wave's polarization z-comp in (x,z) domain */
Fo9 = sf_output("apxxs"); /* SV-wave's polarization x-comp in (x,z) domain */
Fo10 = sf_output("apzzs"); /* SV-wave's polarization z-comp in (x,z) domain */
puthead2(Fo7, nkz, nkx, dz/1000.0, 0.0, dx/1000.0, 0.0);
puthead2(Fo8, nkz, nkx, dz/1000.0, 0.0, dx/1000.0, 0.0);
puthead2(Fo9, nkz, nkx, dz/1000.0, 0.0, dx/1000.0, 0.0);
puthead2(Fo10, nkz, nkx, dz/1000.0, 0.0, dx/1000.0, 0.0);
/*************calculate projection deviation grid-point by grid-point **********/
for(ix=0,ixf=0;ix<nx;ix+=nstep,ixf++)
{
for(iz=0,izf=0;iz<nz;iz+=nstep,izf++)
{
vp2=vp0[ix][iz]*vp0[ix][iz];
vs2=vs0[ix][iz]*vs0[ix][iz];
ep2=1.0+2*epsi[ix][iz];
de2=1.0+2*del[ix][iz];
the=theta[ix][iz];
if(ixf%10==0&&izf%100==0) sf_warning("Operator: nxf=%d ixf=%d izf=%d vp2=%f vs2=%f",nxf, ixf,izf,vp2,vs2);
/*************calculate projection operrate with tapering **********/
zero2float(apx, nkz, nkx);
zero2float(apz, nkz, nkx);
zero2float(apxs, nkz, nkx);
zero2float(apzs, nkz, nkx);
/* polvtipsv: P- and SV-wave polarization operators in VTI media */
itaper=1;
polttipsv(apx,apz,apxs,apzs,kx,kz,kkx,kkz,taper,hnkx,hnkz,dkx,dkz,
vp2,vs2,ep2,de2,the,itaper);
ikxkz2xz(apx, apxx, hnkx, hnkz, nkx, nkz);
ikxkz2xz(apz, apzz, hnkx, hnkz, nkx, nkz);
ikxkz2xz(apxs, apxxs, hnkx, hnkz, nkx, nkz);
ikxkz2xz(apzs, apzzs, hnkx, hnkz, nkx, nkz);
// truncation and saving of operator in space-domain
if(ihomo==1)
{
for(jx=-hnkx1,ixx=hnkx-hnkx1;jx<=hnkx1;jx++,ixx++)
for(jz=-hnkz1,izz=hnkz-hnkz1;jz<=hnkz1;jz++,izz++)
{
exx[jx+hnkx1][jz+hnkz1]=apxx[ixx][izz];
ezz[jx+hnkx1][jz+hnkz1]=apzz[ixx][izz];
exxs[jx+hnkx1][jz+hnkz1]=apxxs[ixx][izz];
ezzs[jx+hnkx1][jz+hnkz1]=apzzs[ixx][izz];
}
}else{
for(jx=-hnkx1,ixx=hnkx-hnkx1;jx<=hnkx1;jx++,ixx++)
for(jz=-hnkz1,izz=hnkz-hnkz1;jz<=hnkz1;jz++,izz++)
{
ex[ixf][izf][jx+hnkx1][jz+hnkz1]=apxx[ixx][izz];
ez[ixf][izf][jx+hnkx1][jz+hnkz1]=apzz[ixx][izz];
exs[ixf][izf][jx+hnkx1][jz+hnkz1]=apxxs[ixx][izz];
ezs[ixf][izf][jx+hnkx1][jz+hnkz1]=apzzs[ixx][izz];
}
}
if((ixf==nxf/2&&izf==nzf/2&&ihomo==0)||ihomo==1)
{
//write-disk operators in kx-kz domain
sf_floatwrite(apx[0], nkxz, Fo3);
sf_floatwrite(apz[0], nkxz, Fo4);
sf_floatwrite(apxs[0], nkxz, Fo5);
sf_floatwrite(apzs[0], nkxz, Fo6);
//write-disk operators in x-z domain
sf_floatwrite(apxx[0], nkxz, Fo7);
sf_floatwrite(apzz[0], nkxz, Fo8);
sf_floatwrite(apxxs[0], nkxz, Fo9);
sf_floatwrite(apzzs[0], nkxz, Fo10);
}
if(ihomo==1) goto loop;
}// iz loop
}//ix loop
loop:;
free(kx);
free(kz);
free(kx2);
free(kz2);
free(kkx);
free(kkz);
free(*taper);
free(*apx);
free(*apz);
free(*apxs);
free(*apzs);
free(*apxx);
free(*apzz);
free(*apxxs);
free(*apzzs);
}// isep loop
/****************End of Calculating Projection Deviation Operator****************/
t3=clock();
timespent=(float)(t3-t2)/CLOCKS_PER_SEC;
sf_warning("Computation time (operators): %f (second)",timespent);
/****************begin to calculate wavefield****************/
/****************begin to calculate wavefield****************/
sf_warning("==================================================");
sf_warning("== Propagation Using Elastic Wave Eq. ==");
sf_warning("==================================================");
coeff_2dx=sf_floatalloc(mm);
coeff_2dz=sf_floatalloc(mm);
coeff_1dx=sf_floatalloc(mm);
coeff_1dz=sf_floatalloc(mm);
coeff2d(coeff_2dx,dx);
coeff2d(coeff_2dz,dz);
p1=sf_floatalloc2(nzpad, nxpad);
p2=sf_floatalloc2(nzpad, nxpad);
p3=sf_floatalloc2(nzpad, nxpad);
q1=sf_floatalloc2(nzpad, nxpad);
q2=sf_floatalloc2(nzpad, nxpad);
q3=sf_floatalloc2(nzpad, nxpad);
zero2float(p1, nzpad, nxpad);
zero2float(p2, nzpad, nxpad);
zero2float(p3, nzpad, nxpad);
zero2float(q1, nzpad, nxpad);
zero2float(q2, nzpad, nxpad);
zero2float(q3, nzpad, nxpad);
coeff1dmix(coeff_1dx,dx);
coeff1dmix(coeff_1dz,dz);
if(isep==1)
{
Fo11 = sf_output("ElasticSepP"); /* scalar wavefield using P-wave's polarization projection oprtator*/
Fo12 = sf_output("ElasticSepSV"); /* scalar wavefield using SV-wave's polarization projection oprtator*/
puthead3(Fo11, nz, nx, 1, dz/1000.0, dx/1000.0, dt, fz/1000.0, fx/1000.0, 0.0);
puthead3(Fo12, nz, nx, 1, dz/1000.0, dx/1000.0, dt, fz/1000.0, fx/1000.0, 0.0);
p3c=sf_floatalloc2(nz,nx);
q3c=sf_floatalloc2(nz,nx);
sum=sf_floatalloc2(nz,nx);
}
for(it=0;it<ns;it++)
{
t=it*dt;
// 2D exploding force source (e.g., Wu's PhD
for(i=-1;i<=1;i++)
for(j=-1;j<=1;j++)
{
if(fabs(i)+fabs(j)==2)
{
p2[isxm+i][iszm+j]+=i*Ricker(t, f0, t0, A);
q2[isxm+i][iszm+j]+=j*Ricker(t, f0, t0, A);
}
}
// 2D equil-energy force source (e.g., Wu's PhD)
/*
for(i=-1;i<=1;i++)
for(j=-1;j<=1;j++)
{
if(fabs(i)+fabs(j)==2)
{
if(i==-1&&j==1)
q2[isxm+i][iszm+j]+=sqrt(2.0)*Ricker(t, f0, t0, A);
if(i==-1&&j==-1)
p2[isxm+i][iszm+j]+=-sqrt(2.0)*Ricker(t, f0, t0, A);
if(i==1&&j==1)
p2[isxm+i][iszm+j]+=sqrt(2.0)*Ricker(t, f0, t0, A);
if(i==1&&j==-1)
q2[isxm+i][iszm+j]+=-sqrt(2.0)*Ricker(t, f0, t0, A);
}
}
*/
/* fwpvtielastic: forward-propagating using original elastic equation of displacement in VTI media*/
fwpttielastic(dt2, p1, p2, p3, q1, q2, q3, coeff_2dx, coeff_2dz, coeff_1dx, coeff_1dz,
dx, dz, nx, nz, nxpad, nzpad, vp0, vs0, epsi, del, theta);
/******* output wavefields: component and divergence *******/
if(it==ns-1)
{
for(i=0;i<nx;i++)
{
im=i+m;
for(j=0;j<nz;j++)
{
jm=j+m;
sf_floatwrite(&p3[im][jm],1,Fo1);
sf_floatwrite(&q3[im][jm],1,Fo2);
}
}/* i loop*/
if(isep==1)
{
//////////////////////////////////////////////////////////////////////////////////////////
/* applying P-wave polarization projection operator in spatial domain */
zero2float(p3c,nz,nx);
zero2float(q3c,nz,nx);
zero2float(sum, nz, nx);
if(ihomo==1)
filter2dsepglobal(p3, q3, p3c, q3c, exx, ezz, nx, nz, hnkx1, hnkz1);
else
filter2dsep(p3, q3, p3c, q3c, ex, ez, nx, nz, nstep, hnkx1, hnkz1);
for(i=0;i<nx;i++)
for(j=0;j<nz;j++)
sum[i][j]=p3c[i][j]+q3c[i][j];
sf_floatwrite(sum[0],nx*nz, Fo11);
//////////////////////////////////////////////////////////////////////////////////////////
/* applying SV-wave polarization projection operator in spatial domain */
zero2float(p3c,nz,nx);
zero2float(q3c,nz,nx);
zero2float(sum, nz, nx);
if(ihomo==1)
filter2dsepglobal(p3, q3, p3c, q3c, exxs, ezzs, nx, nz, hnkx1, hnkz1);
else
filter2dsep(p3, q3, p3c, q3c, exs, ezs, nx, nz, nstep, hnkx1, hnkz1);
for(i=0;i<nx;i++)
for(j=0;j<nz;j++)
sum[i][j]=p3c[i][j]+q3c[i][j];
sf_floatwrite(sum[0],nx*nz, Fo12);
}// isep==1
}/* (it+1)%ntstep==0 */
/**************************************/
for(i=0,ii=m;i<nx;i++,ii++)
for(j=0,jj=m;j<nz;j++,jj++)
{
p1[ii][jj]=p2[ii][jj];
p2[ii][jj]=p3[ii][jj];
q1[ii][jj]=q2[ii][jj];
q2[ii][jj]=q3[ii][jj];
}
if(it%100==0)
sf_warning("Elastic: it= %d",it);
}/* it loop */
t4=clock();
timespent=(float)(t4-t3)/CLOCKS_PER_SEC;
sf_warning("Computation time (propagation + separation): %f (second)",timespent);
if(isep==1)
{
free(*p3c);
free(*q3c);
free(*sum);
if(ihomo==1)
{
free(*exx);
free(*ezz);
free(*exxs);
free(*ezzs);
}else{
free(***ex);
free(***ez);
free(***exs);
free(***ezs);
}
}
free(*p1);
free(*p2);
free(*p3);
free(*q1);
free(*q2);
free(*q3);
free(*vp0);
free(*vs0);
free(*epsi);
free(*del);
free(*theta);
exit(0);
}
int main(int argc, char* argv[])
{
int i,j,im,jm,nx,nz,nxpad,nzpad,it,ii,jj;
float f0, t, t0, dx, dz,dt, dt2;
int mm, nvx, nvz, ns;
int isx, isz, isxm, iszm; /*source location */
float *coeff_1dx, *coeff_1dz, *coeff_2dx, *coeff_2dz; /* finite-difference coefficient */
float **vp0, **vs0, **epsi, **del, **theta; /* velocity model */
float **p1, **p2, **p3, **q1, **q2, **q3; /* wavefield array */
float A, fx, fz;
clock_t t1, t2, t3;
sf_init(argc,argv);
sf_file Fo1, Fo2;
float timespent;
t1 = clock();
/* wavelet parameter for source definition */
f0=30.0;
t0=0.04;
A=1.0;
/* time samping paramter */
if (!sf_getint("ns",&ns)) ns=301;
if (!sf_getfloat("dt",&dt)) dt=0.001;
sf_warning("ns=%d dt=%f",ns,dt);
sf_warning("read velocity model parameters");
/* setup I/O files */
sf_file Fvp0, Fvs0, Feps, Fdel, Fthe;
Fvp0 = sf_input ("in"); /* vp0 using standard input */
Fvs0 = sf_input ("vs0"); /* vs0 */
Feps = sf_input ("epsi"); /* epsi */
Fdel = sf_input ("del"); /* delta */
Fthe = sf_input ("the"); /* theta */
/* Read/Write axes */
sf_axis az, ax;
az = sf_iaxa(Fvp0,1); nvz = sf_n(az); dz = sf_d(az)*1000.0;
ax = sf_iaxa(Fvp0,2); nvx = sf_n(ax); dx = sf_d(ax)*1000.0;
fx=sf_o(ax)*1000.0;
fz=sf_o(az)*1000.0;
/* source definition */
isx=nvx/2;
isz=nvz/2;
//isz=nvz*2/5;
/* wave modeling space */
nx=nvx;
nz=nvz;
nxpad=nx+2*_m;
nzpad=nz+2*_m;
sf_warning("fx=%f fz=%f dx=%f dz=%f",fx,fz,dx,dz);
sf_warning("nx=%d nz=%d nxpad=%d nzpad=%d", nx,nz,nxpad,nzpad);
vp0=sf_floatalloc2(nz,nx);
vs0=sf_floatalloc2(nz,nx);
epsi=sf_floatalloc2(nz,nx);
del=sf_floatalloc2(nz,nx);
theta=sf_floatalloc2(nz,nx);
int nxz=nx*nz;
mm=2*_m+1;
dt2=dt*dt;
isxm=isx+_m; /* source's x location */
iszm=isz+_m; /* source's z-location */
/* read velocity model */
sf_floatread(vp0[0],nxz,Fvp0);
sf_floatread(vs0[0],nxz,Fvs0);
sf_floatread(epsi[0],nxz,Feps);
sf_floatread(del[0],nxz,Fdel);
sf_floatread(theta[0],nxz,Fthe);
for(i=0;i<nx;i++)
for(j=0;j<nz;j++)
theta[i][j] *= SF_PI/180.0;
Fo1 = sf_output("out"); /* Elastic-wave x-component */
Fo2 = sf_output("Elasticz"); /* Elastic-wave z-component */
/* setup I/O files */
puthead3(Fo1, nz, nx, 1, dz/1000.0, dx/1000.0, dt, fz/1000.0, fx/1000.0, 0.0);
puthead3(Fo2, nz, nx, 1, dz/1000.0, dx/1000.0, dt, fz/1000.0, fx/1000.0, 0.0);
/****************begin to calculate wavefield****************/
/****************begin to calculate wavefield****************/
sf_warning("==================================================");
sf_warning("== Porpagation Using Elastic Wave Eq. ==");
sf_warning("==================================================");
coeff_2dx=sf_floatalloc(mm);
coeff_2dz=sf_floatalloc(mm);
coeff_1dx=sf_floatalloc(mm);
coeff_1dz=sf_floatalloc(mm);
coeff2d(coeff_2dx,dx);
coeff2d(coeff_2dz,dz);
p1=sf_floatalloc2(nzpad, nxpad);
p2=sf_floatalloc2(nzpad, nxpad);
p3=sf_floatalloc2(nzpad, nxpad);
q1=sf_floatalloc2(nzpad, nxpad);
q2=sf_floatalloc2(nzpad, nxpad);
q3=sf_floatalloc2(nzpad, nxpad);
zero2float(p1, nzpad, nxpad);
zero2float(p2, nzpad, nxpad);
zero2float(p3, nzpad, nxpad);
zero2float(q1, nzpad, nxpad);
zero2float(q2, nzpad, nxpad);
zero2float(q3, nzpad, nxpad);
coeff1dmix(coeff_1dx,dx);
coeff1dmix(coeff_1dz,dz);
t2 = clock();
for(it=0;it<ns;it++)
{
t=it*dt;
// 2D exploding force source (e.g., Wu's PhD
for(i=-1;i<=1;i++)
for(j=-1;j<=1;j++)
{
if(fabs(i)+fabs(j)==2)
{
p2[isxm+i][iszm+j]+=sqrt(2.0)*i*Ricker(t, f0, t0, A);
q2[isxm+i][iszm+j]+=sqrt(2.0)*j*Ricker(t, f0, t0, A);
}
}
// 2D equil-energy force source (e.g., Wu's PhD)
/*
for(i=-1;i<=1;i++)
for(j=-1;j<=1;j++)
{
if(fabs(i)+fabs(j)==2)
{
if(i==-1&&j==1)
q2[isxm+i][iszm+j]+=sqrt(2.0)*Ricker(t, f0, t0, A);
if(i==-1&&j==-1)
p2[isxm+i][iszm+j]+=-sqrt(2.0)*Ricker(t, f0, t0, A);
if(i==1&&j==1)
p2[isxm+i][iszm+j]+=sqrt(2.0)*Ricker(t, f0, t0, A);
if(i==1&&j==-1)
q2[isxm+i][iszm+j]+=-sqrt(2.0)*Ricker(t, f0, t0, A);
}
}
*/
/* fwpvtielastic: forward-propagating using original elastic equation of displacement in VTI media*/
fwpttielastic(dt2, p1, p2, p3, q1, q2, q3, coeff_2dx, coeff_2dz, coeff_1dx, coeff_1dz,
dx, dz, nx, nz, nxpad, nzpad, vp0, vs0, epsi, del, theta);
/******* output wavefields: component and divergence *******/
if(it==ns-1)
{
for(i=0;i<nx;i++)
{
im=i+_m;
for(j=0;j<nz;j++)
{
jm=j+_m;
sf_floatwrite(&p3[im][jm],1,Fo1);
sf_floatwrite(&q3[im][jm],1,Fo2);
}
}/* i loop*/
}/* (it+1)%ntstep==0 */
/**************************************/
for(i=0,ii=_m;i<nx;i++,ii++)
for(j=0,jj=_m;j<nz;j++,jj++)
{
p1[ii][jj]=p2[ii][jj];
p2[ii][jj]=p3[ii][jj];
q1[ii][jj]=q2[ii][jj];
q2[ii][jj]=q3[ii][jj];
}
if(it%100==0)
sf_warning("Elastic: it= %d",it);
}/* it loop */
t3=clock();
timespent=(float)(t3-t2)/CLOCKS_PER_SEC;
sf_warning("CPU time for wavefield extrapolation.: %f(second)",timespent);
timespent=(float)(t3-t1)/(ns*CLOCKS_PER_SEC);
sf_warning("All CPU time: %f(second)",timespent);
free(*p1);
free(*p2);
free(*p3);
free(*q1);
free(*q2);
free(*q3);
free(*vp0);
free(*vs0);
free(*epsi);
free(*del);
free(*theta);
exit(0);
}
void fwpttielastic(float dt2, float** p1,float** p2,float** p3, float** q1,float** q2,float** q3,
float* coeff_2dx,float* coeff_2dz, float* coeff_1dx,float* coeff_1dz,
float dx, float dz, int nx, int nz, int nxpad, int nzpad,
float **vp0,float **vs0, float **epsilon,float **delta, float **theta)
/*< fwpttielastic: forward-propagating using original elastic equation of displacement in 2D TTI media>*/
{
int i,j,l;
float vp2,vs2,ep,de,vpx2,vpn2, the;
float sinthe,costhe,cos2,sin2,sin2a,cos_sin;
float px,pxz,qxz,qx,px1, qxz1, qx1, pxz1,hpx,hqx,hpz,hqz;
float **px_tmp;
float **qx_tmp;
int im, jm;
px_tmp=sf_floatalloc2(nzpad,nxpad);
qx_tmp=sf_floatalloc2(nzpad,nxpad);
zero2float(px_tmp,nzpad,nxpad);
zero2float(qx_tmp,nzpad,nxpad);
#ifdef _OPENMP
#pragma omp parallel for private(i,j,l) \
schedule(dynamic) \
shared(p2,q2,px_tmp,qx_tmp,coeff_1dx,dx)
#endif
for(i=_m;i<nx+_m;i++)
for(j=_m;j<nz+_m;j++)
{
for(l=-_mix;l<=_mix;l++)
{
int lm=l+_mix;
px_tmp[i][j]+=coeff_1dx[lm]*p2[i+l][j]/2.0/dx;
qx_tmp[i][j]+=coeff_1dx[lm]*q2[i+l][j]/2.0/dx;
}
}
#ifdef _OPENMP
#pragma omp parallel for private(i,j,l,im,jm,vp2,vs2,ep,de,vpx2,vpn2, the, sinthe,costhe,cos2,sin2,sin2a,cos_sin, px,pxz,qxz,qx,px1, qxz1, qx1, pxz1,hpx,hqx,hpz,hqz) \
schedule(dynamic) \
shared(p1,p2,p3,q1,q2,q3, \
px_tmp,qx_tmp, \
coeff_1dx,coeff_1dz,coeff_2dx,coeff_2dz, \
vp0,vs0,epsilon,delta,theta,dt2)
#endif
for(i=_m;i<nx+_m;i++)
{
im=i-_m;
for(j=_m;j<nz+_m;j++)
{
jm=j-_m;
vp2=vp0[im][jm]*vp0[im][jm];
vs2=vs0[im][jm]*vs0[im][jm];
ep=1+2*epsilon[im][jm];
de=1+2*delta[im][jm];
the=theta[im][jm];
costhe=cos(the);
sinthe=sin(the);
cos2=costhe*costhe;
sin2=sinthe*sinthe;
cos_sin=costhe*sinthe;
sin2a=2*cos_sin;
vpx2=vp2*ep;
vpn2=vp2*de;
/* coef=sqrt((vp2-vs2)*(vpn2-vs2)); */
pxz=0;
qxz=0;
for(l=-_mix;l<=_mix;l++)
{
int lm=l+_mix;
pxz+=coeff_1dz[lm]*px_tmp[i][j+l]/2.0/dz;
qxz+=coeff_1dz[lm]*qx_tmp[i][j+l]/2.0/dz;
}
hpx=0;
hpz=0;
hqx=0;
hqz=0;
for(l=-_m;l<=_m;l++)
{
int lm=l+_m;
hpx+=coeff_2dx[lm]*p2[i+l][j];
hqx+=coeff_2dx[lm]*q2[i+l][j];
hpz+=coeff_2dz[lm]*p2[i][j+l];
hqz+=coeff_2dz[lm]*q2[i][j+l];
}
px = cos2*hpx + sin2*hpz + sin2a*pxz;
px1 = sin2*hpx + cos2*hpz - sin2a*pxz;
qxz1 = -cos_sin*hqx + cos_sin*hqz + (cos2-sin2)*qxz;
p3[i][j]=2*p2[i][j] - p1[i][j] + dt2*( vpx2*px + vs2*px1 + sqrt((vp2-vs2)*(vpn2-vs2))*qxz1);
qx = cos2*hqx + sin2*hqz + sin2a*qxz;
qx1 = sin2*hqx + cos2*hqz - sin2a*qxz;
pxz1 = -cos_sin*hpx + cos_sin*hpz + (cos2-sin2)*pxz;
q3[i][j]=2*q2[i][j] - q1[i][j] + dt2*( vs2*qx + vp2*qx1 + sqrt((vp2-vs2)*(vpn2-vs2))*pxz1);
}
}
free(*px_tmp);
free(*qx_tmp);
}
int main( int argc , char* argv[] )
{
sf_init( argc , argv );
sf_file FI1, FI2, FI3, FO1;
sf_axis aa;
int dim, num_dim[SF_MAX_DIM], NTRACE, NT, nw, nwave, wsft, itrace, idim;
float dt, **ref, **Q, *wave, **gather, **TVM;
if(!sf_getint( "wsft" , &wsft )) sf_error( "MISSING wave_shift PARAMETER!!\n" );
/* The wave shift should be set up! */
FI1 = sf_input( "ref" );
FI2 = sf_input( "Q" );
FI3 = sf_input( "wave" );
FO1 = sf_output( "gather" );
NTRACE = sf_leftsize( FI1 , 1 );
dim = sf_filedims( FI1 , num_dim );
/* define the LEFTSIZE bigger than the first
* dimension, so we can treat the data as two
* dimensional-data,
*/
NT = sf_n( sf_iaxa( FI1 , 1 ) );
dt = sf_d( sf_iaxa( FI1 , 1 ) );
nw = sf_n( sf_iaxa( FI3 , 1 ) );
/* extract the information about the first
* dimension, which is needed by the function
* of calculating the attenuated wavelet
*/
nwave = lh_powerof2( nw );
/* compute the suitable length for the FFT
*/
ref = alloc2float( NT , NTRACE );
Q = alloc2float( NT , NTRACE );
gather = alloc2float( NT , NTRACE );
wave = alloc1float( nwave );
TVM = alloc2float( NT , NT );
zero2float( ref , NT , NTRACE );
zero2float( Q , NT , NTRACE );
zero2float( gather, NT , NTRACE );
zero1float( wave , nwave );
/* alloc and setup */
sf_floatread( &ref[0][0] , NT*NTRACE , FI1 );
sf_floatread( &Q[0][0] , NT*NTRACE , FI2 );
sf_floatread( &wave[0] , nw , FI3 );
for( itrace=0 ; itrace<NTRACE ; itrace++ )
{
zero2float( TVM , NT , NT );
lh_time_variant_matrix( wave , wsft , nwave , dt , &Q[itrace][0], NT , TVM );
lh_matrix_mu_vector( TVM , &ref[itrace][0] , &gather[itrace][0], NT , NT );
}
/*
float **spec_real, **spec_imag, **spec_amp;
int nwave1 = lh_powerof2( NT );
spec_real = alloc2float( nwave1 , NT );
spec_imag = alloc2float( nwave1 , NT );
spec_amp = alloc2float( 200 , NT );
zero2float( spec_real , nwave1 , NT );
zero2float( spec_imag , nwave1 , NT );
zero2float( spec_amp , 200 , NT );
int i,j;
for( i=0 ; i<NT ; i++ )
{
for( j=0 ; j<NT ; j++ )
spec_real[i][j] = TVM[j][i];
lh_fft( &spec_real[i][0] , &spec_imag[i][0], nwave1 , 1 );
for( j=0 ; j<200 ; j++ )
spec_amp[i][j] = sqrt( spec_real[i][j]*spec_real[i][j]+spec_imag[i][j]*spec_imag[i][j] );
}
lh_write_2d_float_bin_row( spec_amp , NT , 200 , "spec_amp_qwave.bin" );
*/
for( idim=1 ; idim<=dim ; idim++ )
{
aa = sf_iaxa( FI1 , idim );
sf_oaxa( FO1 , aa , idim );
}
sf_floatwrite( &gather[0][0] , NT*NTRACE , FO1 );
exit( 0 );
}
int main(int argc, char* argv[])
{
int ix, iz, jx, jz, ixf, izf, ixx, izz, i,j,im, jm,nx,nz,nxf,nzf,nxpad,nzpad,it,ii,jj;
float kxmax,kzmax;
float A, f0, t, t0, dx, dz, dxf, dzf, dt, dkx, dkz, dt2, div;
int mm, nvx, nvz, ns;
int hnkx, hnkz, nkx, nkz, nxz, nkxz;
int hnkx1=1, hnkz1=1, nkx1, nkz1;
int isx, isz, isxm, iszm; /*source location */
int itaper; /* tapering or not for spectrum of oprtator*/
int nstep; /* every nstep in spatial grids to calculate filters sparsely*/
float *coeff_1dx, *coeff_1dz, *coeff_2dx, *coeff_2dz; /* finite-difference coefficient */
float **apvx, **apvz, **apvxx, **apvzz; /* projection deviation operator of P-wave for a location */
float ****ex=NULL, ****ez=NULL; /* operator for whole model for P-wave*/
float **exx=NULL, **ezz=NULL; /* operator for constant model for P-wave*/
float **vp0, **vs0, **epsi, **del, **theta; /* velocity model */
float **p1, **p2, **p3, **q1, **q2, **q3, **p3c=NULL, **q3c=NULL, **sum=NULL; /* wavefield array */
float *kx, *kz, *kkx, *kkz, *kx2, *kz2, **taper;
clock_t t2, t3, t4, t5;
float timespent, fx,fz;
char *tapertype;
int isep=1;
int ihomo=1;
double vp2, vs2, ep2, de2, the;
sf_file Fo1, Fo2, Fo3, Fo4, Fo5, Fo6, Fo7, Fo8;
sf_file Fvp0, Fvs0, Feps, Fdel, Fthe;
sf_axis az, ax;
sf_init(argc,argv);
/* t1=clock(); */
/* wavelet parameter for source definition */
f0=30.0;
t0=0.04;
A=1.0;
/* time samping paramter */
if (!sf_getint("ns",&ns)) ns=301;
if (!sf_getfloat("dt",&dt)) dt=0.001;
if (!sf_getint("isep",&isep)) isep=0; /* if isep=1, separate wave-modes */
if (!sf_getint("ihomo",&ihomo)) ihomo=0; /* if ihomo=1, homogeneous medium */
if (NULL== (tapertype=sf_getstring("tapertype"))) tapertype="D"; /* taper type*/
if (!sf_getint("nstep",&nstep)) nstep=1; /* grid step to calculate operators: 1<=nstep<=5 */
sf_warning("isep=%d",isep);
sf_warning("ihomo=%d",ihomo);
sf_warning("tapertype=%s",tapertype);
sf_warning("nstep=%d",nstep);
sf_warning("ns=%d dt=%f",ns,dt);
sf_warning("read velocity model parameters");
/* setup I/O files */
Fvp0 = sf_input ("in"); /* vp0 using standard input */
Fvs0 = sf_input ("vs0"); /* vs0 */
Feps = sf_input ("epsi"); /* epsi */
Fdel = sf_input ("del"); /* delta */
Fthe = sf_input ("the"); /* theta */
/* Read/Write axes */
az = sf_iaxa(Fvp0,1); nvz = sf_n(az); dz = sf_d(az)*1000.0;
ax = sf_iaxa(Fvp0,2); nvx = sf_n(ax); dx = sf_d(ax)*1000.0;
fx=sf_o(ax);
fz=sf_o(az);
/* source definition */
isx=nvx/2;
isz=nvz/2;
/* isz=nvz*2/5; */
/* wave modeling space */
nx=nvx;
nz=nvz;
nxpad=nx+2*_m;
nzpad=nz+2*_m;
sf_warning("dx=%f dz=%f",dx,dz);
sf_warning("nx=%d nz=%d nxpad=%d nzpad=%d", nx,nz,nxpad,nzpad);
vp0=sf_floatalloc2(nz,nx);
vs0=sf_floatalloc2(nz,nx);
epsi=sf_floatalloc2(nz,nx);
del=sf_floatalloc2(nz,nx);
theta=sf_floatalloc2(nz,nx);
nxz=nx*nz;
mm=2*_m+1;
dt2=dt*dt;
isxm=isx+_m; /* source's x location */
iszm=isz+_m; /* source's z-location */
/* read velocity model */
sf_floatread(vp0[0],nxz,Fvp0);
sf_floatread(vs0[0],nxz,Fvs0);
sf_floatread(epsi[0],nxz,Feps);
sf_floatread(del[0],nxz,Fdel);
sf_floatread(theta[0],nxz,Fthe);
for(i=0;i<nx;i++)
for(j=0;j<nz;j++)
theta[i][j] *= SF_PI/180.0;
t2=clock();
/* setup I/O files */
Fo1 = sf_output("out"); /* pseudo-pure P-wave x-component */
Fo2 = sf_output("PseudoPurePz"); /* pseudo-pure P-wave z-component */
Fo3 = sf_output("PseudoPureP"); /* scalar P-wave field using divergence operator */
puthead3(Fo1, nz, nx, 1, dz/1000.0, dx/1000.0, dt, fz, fx, 0.0);
puthead3(Fo2, nz, nx, 1, dz/1000.0, dx/1000.0, dt, fz, fx, 0.0);
puthead3(Fo3, nz, nx, 1, dz/1000.0, dx/1000.0, dt, fz, fx, 0.0);
/*****************************************************************************
* Calculating polarization deviation operator for wave-mode separation
* ***************************************************************************/
if(isep==1)
{
/* calculate spatial steps for operater in sparsely sampling grid point */
dxf=dx*nstep;
dzf=dz*nstep;
nxf=nx/nstep+1;
nzf=nz/nstep+1;
/* operators length for calculation */
hnkx=400.0/dx;
hnkz=400.0/dz;
nkx=2*hnkx+1; /* operator length in kx-direction */
nkz=2*hnkz+1; /* operator length in kz-direction */
/* truncated spatial operators length for filtering*/
hnkx1=200.0/dx;
hnkz1=200.0/dz;
nkx1=2*hnkx1+1;
nkz1=2*hnkz1+1;
sf_warning("nx=%d nz=%d nxf=%d nzf=%d", nx,nz,nxf,nzf);
sf_warning("dx=%f dz=%f dxf=%f dzf=%f", dx,dz,dxf,dzf);
sf_warning("hnkx=%d hnkz=%d nkx=%d nkz=%d", hnkx, hnkz, nkx, nkz);
sf_warning("hnkx1=%d hnkz1=%d nkx1=%d nkz1=%d", hnkx1, hnkz1, nkx1, nkz1);
dkx=2*SF_PI/dx/nkx;
dkz=2*SF_PI/dz/nkz;
kxmax=SF_PI/dx;
kzmax=SF_PI/dz;
kx=sf_floatalloc(nkx);
kz=sf_floatalloc(nkx);
kkx=sf_floatalloc(nkx);
kkz=sf_floatalloc(nkx);
kx2=sf_floatalloc(nkx);
kz2=sf_floatalloc(nkx);
taper=sf_floatalloc2(nkz, nkx);
/* define axis samples and taper in wavenumber domain */
kxkztaper(kx, kz, kkx, kkz, kx2, kz2, taper, nkx, nkz, hnkx, hnkz, dkx, dkz, kxmax, kzmax, tapertype);
/* truncation of spatial filter */
p3c=sf_floatalloc2(nz,nx);
q3c=sf_floatalloc2(nz,nx);
sum=sf_floatalloc2(nz,nx);
if(ihomo==1)
{
exx=sf_floatalloc2(nkz1, nkx1);
ezz=sf_floatalloc2(nkz1, nkx1);
}
else{ /* to store spatail varaied operators */
ex=sf_floatalloc4(nkz1, nkx1, nzf, nxf);
ez=sf_floatalloc4(nkz1, nkx1, nzf, nxf);
}
nkxz=nkx*nkz;
apvx=sf_floatalloc2(nkz, nkx);
apvz=sf_floatalloc2(nkz, nkx);
apvxx=sf_floatalloc2(nkz, nkx);
apvzz=sf_floatalloc2(nkz, nkx);
/* setup I/O files */
Fo4 = sf_output("apvx"); /* P-wave projection deviation x-comp */
Fo5 = sf_output("apvz"); /* P-wave projection deviation z-comp */
Fo6 = sf_output("apvxx"); /* P-wave projection deviation x-comp in (x,z) domain */
Fo7 = sf_output("apvzz"); /* P-wave projection deviation z-comp in (x,z) domain */
puthead1(Fo4, nkz, nkx, dkz, -kzmax, dkx, -kxmax);
puthead1(Fo5, nkz, nkx, dkz, -kzmax, dkx, -kxmax);
puthead2(Fo6, nkz, nkx, dz/1000.0, 0.0, dx/1000.0, 0.0);
puthead2(Fo7, nkz, nkx, dz/1000.0, 0.0, dx/1000.0, 0.0);
/*************calculate projection deviation grid-point by grid-point **********/
for(ix=0,ixf=0;ix<nx;ix+=nstep,ixf++)
{
for(iz=0,izf=0;iz<nz;iz+=nstep,izf++)
{
vp2=vp0[ix][iz]*vp0[ix][iz];
vs2=vs0[ix][iz]*vs0[ix][iz];
ep2=1.0+2*epsi[ix][iz];
de2=1.0+2*del[ix][iz];
the=theta[ix][iz];
if(ixf%10==0&&izf%100==0) sf_warning("Operator: nxf=%d ixf=%d izf=%d vp2=%f vs2=%f",nxf, ixf,izf,vp2,vs2);
/*************calculate projection deviation without tapering **********/
itaper=0;
/* devvtip: projection deviation operators for P-wave in TTI media */
devttip(apvx,apvz,kx,kz,kkx,kkz,taper,hnkx,hnkz,dkx,dkz,vp2,vs2,ep2,de2,the,itaper);
/* inverse Fourier transform */
kxkz2xz(apvx, apvxx, hnkx, hnkz, nkx, nkz);
kxkz2xz(apvz, apvzz, hnkx, hnkz, nkx, nkz);
/* truncation and saving of operator in space-domain */
if(ihomo==1)
{
for(jx=-hnkx1,ixx=hnkx-hnkx1;jx<=hnkx1;jx++,ixx++)
for(jz=-hnkz1,izz=hnkz-hnkz1;jz<=hnkz1;jz++,izz++)
{
exx[jx+hnkx1][jz+hnkz1]=apvxx[ixx][izz];
ezz[jx+hnkx1][jz+hnkz1]=apvzz[ixx][izz];
}
}else{
for(jx=-hnkx1,ixx=hnkx-hnkx1;jx<=hnkx1;jx++,ixx++)
for(jz=-hnkz1,izz=hnkz-hnkz1;jz<=hnkz1;jz++,izz++)
{
ex[ixf][izf][jx+hnkx1][jz+hnkz1]=apvxx[ixx][izz];
ez[ixf][izf][jx+hnkx1][jz+hnkz1]=apvzz[ixx][izz];
}
}
if((ix==nx/2&&iz==nz/2&&ihomo==0)||ihomo==1)
{
sf_floatwrite(apvx[0], nkxz, Fo4);
sf_floatwrite(apvz[0], nkxz, Fo5);
sf_floatwrite(apvxx[0], nkxz, Fo6);
sf_floatwrite(apvzz[0], nkxz, Fo7);
}
if(ihomo==1) goto loop;
}/* iz loop */
}/* ix loop */
loop:;
free(kx);
free(kz);
free(kx2);
free(kz2);
free(kkx);
free(kkz);
free(*taper);
free(*apvx);
free(*apvz);
free(*apvxx);
free(*apvzz);
}/* isep */
/****************End of Calculating Projection Deviation Operator****************/
t3=clock();
timespent=(float)(t3-t2)/CLOCKS_PER_SEC;
sf_warning("Computation time (operators): %f (second)",timespent);
/****************begin to calculate wavefield****************/
coeff_2dx=sf_floatalloc(mm);
coeff_2dz=sf_floatalloc(mm);
coeff_1dx=sf_floatalloc(mm);
coeff_1dz=sf_floatalloc(mm);
coeff2d(coeff_2dx,dx);
coeff2d(coeff_2dz,dz);
coeff1d(coeff_1dx,dx);
coeff1d(coeff_1dz,dz);
p1=sf_floatalloc2(nzpad, nxpad);
p2=sf_floatalloc2(nzpad, nxpad);
p3=sf_floatalloc2(nzpad, nxpad);
q1=sf_floatalloc2(nzpad, nxpad);
q2=sf_floatalloc2(nzpad, nxpad);
q3=sf_floatalloc2(nzpad, nxpad);
zero2float(p1, nzpad, nxpad);
zero2float(p2, nzpad, nxpad);
zero2float(p3, nzpad, nxpad);
zero2float(q1, nzpad, nxpad);
zero2float(q2, nzpad, nxpad);
zero2float(q3, nzpad, nxpad);
if(isep==1)
{
/* setup I/O files */
Fo8 = sf_output("PseudoPureSepP"); /* scalar P-wave field using polarization projection oprtator*/
puthead3(Fo8, nz, nx, 1, dz/1000.0, dx/1000.0, dt, fz, fx, 0.0);
} else {
Fo8 = NULL;
}
sf_warning("==================================================");
sf_warning("== Propagation Using Pseudo-Pure P-Wave Eq. ==");
sf_warning("==================================================");
t4=clock();
for(it=0;it<ns;it++)
{
t=it*dt;
p2[isxm][iszm]+=Ricker(t, f0, t0, A);
q2[isxm][iszm]+=Ricker(t, f0, t0, A);
/* fwpttipseudop: forward-propagating in TTI media with pseudo-pure P-wave equation */
fwpttipseudop(dt2, p1, p2, p3, q1, q2, q3, coeff_2dx, coeff_2dz,
dx, dz, nx, nz, nxpad, nzpad, vp0, vs0, epsi, del, theta);
/******* output wavefields: component and divergence *******/
if(it==ns-1)
{
for(i=0;i<nx;i++)
{
im=i+_m;
for(j=0;j<nz;j++)
{
jm=j+_m;
sf_floatwrite(&p3[im][jm],1,Fo1);
sf_floatwrite(&q3[im][jm],1,Fo2);
div=p3[im][jm]+q3[im][jm];
sf_floatwrite(&div,1,Fo3);
}
}/* i loop*/
/* correct projection error for accurate separate qP wave in spatial domain */
if(isep==1)
{
zero2float(p3c,nz,nx);
zero2float(q3c,nz,nx);
zero2float(sum, nz, nx);
if(ihomo==1)
filter2dsepglobal(p3, q3, p3c, q3c, exx, ezz, nx, nz, hnkx1, hnkz1);
else
filter2dsep(p3, q3, p3c, q3c, ex, ez, nx, nz, nstep, hnkx1, hnkz1);
for(i=0;i<nx;i++)
for(j=0;j<nz;j++)
sum[i][j]=p3c[i][j]+q3c[i][j];
sf_floatwrite(sum[0],nx*nz, Fo8);
}
}/* (it+1)%ntstep==0 */
/**************************************/
for(i=0,ii=_m;i<nx;i++,ii++)
for(j=0,jj=_m;j<nz;j++,jj++)
{
p1[ii][jj]=p2[ii][jj];
p2[ii][jj]=p3[ii][jj];
q1[ii][jj]=q2[ii][jj];
q2[ii][jj]=q3[ii][jj];
}
if(it%50==0)
sf_warning("Pseudo: it= %d",it);
}/* it loop */
t5=clock();
timespent=(float)(t5-t4)/CLOCKS_PER_SEC;
sf_warning("Computation time (propagation + separation): %f (second)",timespent);
if(isep==1)
{
free(*p3c);
free(*q3c);
free(*sum);
if(ihomo==1)
{
free(*exx);
free(*ezz);
}else{
free(***ex);
free(***ez);
}
}
free(*p1);
free(*p2);
free(*p3);
free(*q1);
free(*q2);
free(*q3);
free(*vp0);
free(*vs0);
free(*epsi);
free(*del);
free(*theta);
exit(0);
}