/
Mtti2delrdecomp.cc
executable file
·1080 lines (831 loc) · 26 KB
/
Mtti2delrdecomp.cc
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/* 2-D two-components wavefield modeling based on original elastic anisotropic displacement
wave equation and vector decomposition based on lowrank approximation in TTI media.
Authors: Jiubing Cheng
Copyright (C) 2012 Tongji University, Shanghai, China
This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*/
#include <rsf.hh>
#include <assert.h>
/* low rank decomposition */
#include "vecmatop.hh"
#include "serialize.hh"
using namespace std;
/* prepared head files by myself */
#include "_cjb.h"
/*#include "_fd.h"
* when _fd.h has declared "m", we met compiling error at "m2=mid.m()";
* "expected unqualified-id before numeric constant"
*/
#ifndef M
#define M 5 /* 10th-order finite-difference: accuracy is 2*M */
#endif
#ifndef Mix
#define Mix 5 /* order of finite-difference for mix-derivative (2*mix) */
#endif
/* head files aumatically produced from C programs */
extern "C"{
#include "zero.h"
#include "ricker.h"
#include "kykxkztaper.h"
#include "fdcoef.h"
#include "eigen2x2.h"
#include "fwpttielastic.h"
#include "decomplowrank.h"
}
static std::valarray<float> vp, vs, ep, de, th;
static std::valarray<double> sinx, cosx, rkk;
/* dual-domain wave-mode separation and wave vector decomposition operator based on low-rank decomp. */
static int samplexxp(vector<int>& rs, vector<int>& cs, DblNumMat& resx);
static int samplexzp(vector<int>& rs, vector<int>& cs, DblNumMat& resz);
static int samplezzp(vector<int>& rs, vector<int>& cs, DblNumMat& resz);
static int samplexxs(vector<int>& rs, vector<int>& cs, DblNumMat& resx);
static int samplexzs(vector<int>& rs, vector<int>& cs, DblNumMat& resz);
static int samplezzs(vector<int>& rs, vector<int>& cs, DblNumMat& resz);
static void map2d1d(float *d, DblNumMat mat, int m, int n);
/*****************************************************************************************/
int main(int argc, char* argv[])
{
sf_init(argc,argv);
clock_t t1, t2, t3, t4;
float timespent;
t1=clock();
iRSF par(0);
int seed;
par.get("seed",seed,time(NULL)); // seed for random number generator
srand48(seed);
float eps;
par.get("eps",eps,1.e-6); // tolerance
int npk;
par.get("npk",npk,20); // maximum rank
int ns;
float dt;
par.get("ns",ns);
par.get("dt",dt);
sf_warning("ns=%d dt=%f",ns,dt);
sf_warning("npk=%d ",npk);
sf_warning("eps=%f",eps);
sf_warning("read velocity model parameters");
/* setup I files */
iRSF vp0, vs0("vs0"), epsi("epsi"), del("del"), the("the");
/* Read/Write axes */
int nxv, nzv;
vp0.get("n1",nzv);
vp0.get("n2",nxv);
float az, ax;
vp0.get("o1",az);
vp0.get("o2",ax);
float fx, fz;
fx=ax*1000.0;
fz=az*1000.0;
float dx, dz;
vp0.get("d1",az);
vp0.get("d2",ax);
dz = az*1000.0;
dx = ax*1000.0;
/* wave modeling space */
int nx, nz, nxz;
nx=nxv;
nz=nzv;
nxz=nx*nz;
vp.resize(nxz);
vs.resize(nxz);
ep.resize(nxz);
de.resize(nxz);
th.resize(nxz);
vp0>>vp;
vs0>>vs;
epsi>>ep;
del>>de;
the>>th;
for(int i=0;i<nxz;i++)
th[i] *= SF_PI/180.0;
/* Fourier spectra demension */
int nkz,nkx,nk;
nkx=nx;
nkz=nz;
nk = nkx*nkz;
float dkz,dkx,kz0,kx0;
dkx=2*SF_PI/dx/nx;
dkz=2*SF_PI/dz/nz;
kx0=-SF_PI/dx;
kz0=-SF_PI/dz;
sinx.resize(nk);
cosx.resize(nk);
rkk.resize(nk);
double kx, kz, k2, rk;
int i=0, j=0, k=0, ix, iz;
for(ix=0; ix < nkx; ix++)
{
kx = kx0+ix*dkx;
if(kx==0.0) kx=0.0000000001*dkx;
for (iz=0; iz < nkz; iz++)
{
kz = kz0+iz*dkz;
if(kz==0.0) kz=0.0000000001*dkz;
k2 = kx*kx+kz*kz;
rk = sqrt(k2);
sinx[i] = kx/rk;
cosx[i] = kz/rk;
rkk[i] = rk;
i++;
}
}
/*****************************************************************************
* Calculating vector decomposition operator for P-wave
* ***************************************************************************/
vector<int> md(nxz), nd(nk);
for (k=0; k < nxz; k++) md[k] = k;
for (k=0; k < nk; k++) nd[k] = k;
vector<int> lid, rid;
DblNumMat mid, mat;
int m2xxp, n2xxp, m2xzp, n2xzp, m2zzp, n2zzp;
float *ldataxxp, *fmidxxp, *rdataxxp;
float *ldataxzp, *fmidxzp, *rdataxzp;
float *ldatazzp, *fmidzzp, *rdatazzp;
/** Apx2 ****/
iC( ddlowrank(nxz,nk,samplexxp,eps,npk,lid,rid,mid) );
m2xxp=mid.m();
n2xxp=mid.n();
sf_warning("m2xxp=%d n2xxp=%d",m2xxp, n2xxp);
fmidxxp = sf_floatalloc(m2xxp*n2xxp);
ldataxxp = sf_floatalloc(nxz*m2xxp);
rdataxxp = sf_floatalloc(n2xxp*nk);
map2d1d(fmidxxp, mid, m2xxp, n2xxp);
iC ( samplexxp(md,lid,mat) );
map2d1d(ldataxxp, mat, nxz, m2xxp);
iC ( samplexxp(rid,nd,mat) );
map2d1d(rdataxxp, mat, n2xxp, nk);
/** ApxApz ****/
iC( ddlowrank(nxz,nk,samplexzp,eps,npk,lid,rid,mid) );
m2xzp=mid.m();
n2xzp=mid.n();
sf_warning("m2xzp=%d n2xzp=%d",m2xzp, n2xzp);
fmidxzp = sf_floatalloc(m2xzp*n2xzp);
ldataxzp = sf_floatalloc(nxz*m2xzp);
rdataxzp = sf_floatalloc(n2xzp*nk);
map2d1d(fmidxzp, mid, m2xzp, n2xzp);
iC ( samplexzp(md,lid,mat) );
map2d1d(ldataxzp, mat, nxz, m2xzp);
iC ( samplexzp(rid,nd,mat) );
map2d1d(rdataxzp, mat, n2xzp, nk);
/** Apz2 ****/
iC( ddlowrank(nxz,nk,samplezzp,eps,npk,lid,rid,mid) );
m2zzp=mid.m();
n2zzp=mid.n();
sf_warning("m2zzp=%d n2zzp=%d",m2zzp, n2zzp);
fmidzzp = sf_floatalloc(m2zzp*n2zzp);
ldatazzp = sf_floatalloc(nxz*m2zzp);
rdatazzp = sf_floatalloc(n2zzp*nk);
map2d1d(fmidzzp, mid, m2zzp, n2zzp);
iC ( samplezzp(md,lid,mat) );
map2d1d(ldatazzp, mat, nxz, m2zzp);
iC ( samplezzp(rid,nd,mat) );
map2d1d(rdatazzp, mat, n2zzp, nk);
/*****************************************************************************
* Calculating vector decomposition operator for SV-wave
* ***************************************************************************/
int m2xxs, n2xxs, m2xzs, n2xzs, m2zzs, n2zzs;
float *ldataxxs, *fmidxxs, *rdataxxs;
float *ldataxzs, *fmidxzs, *rdataxzs;
float *ldatazzs, *fmidzzs, *rdatazzs;
/** Asx2 ****/
iC( ddlowrank(nxz,nk,samplexxs,eps,npk,lid,rid,mid) );
m2xxs=mid.m();
n2xxs=mid.n();
sf_warning("m2xxs=%d n2xxs=%d",m2xxs, n2xxs);
fmidxxs = sf_floatalloc(m2xxs*n2xxs);
ldataxxs = sf_floatalloc(nxz*m2xxs);
rdataxxs = sf_floatalloc(n2xxs*nk);
map2d1d(fmidxxs, mid, m2xxs, n2xxs);
iC ( samplexxs(md,lid,mat) );
map2d1d(ldataxxs, mat, nxz, m2xxs);
iC ( samplexxs(rid,nd,mat) );
map2d1d(rdataxxs, mat, n2xxs, nk);
/** AsxAsz ****/
iC( ddlowrank(nxz,nk,samplexzs,eps,npk,lid,rid,mid) );
m2xzs=mid.m();
n2xzs=mid.n();
sf_warning("m2xzs=%d n2xzs=%d",m2xzs, n2xzs);
fmidxzs = sf_floatalloc(m2xzs*n2xzs);
ldataxzs = sf_floatalloc(nxz*m2xzs);
rdataxzs = sf_floatalloc(n2xzs*nk);
map2d1d(fmidxzs, mid, m2xzs, n2xzs);
iC ( samplexzs(md,lid,mat) );
map2d1d(ldataxzs, mat, nxz, m2xzs);
iC ( samplexzs(rid,nd,mat) );
map2d1d(rdataxzs, mat, n2xzs, nk);
/** Asz2 ****/
iC( ddlowrank(nxz,nk,samplezzs,eps,npk,lid,rid,mid) );
m2zzs=mid.m();
n2zzs=mid.n();
sf_warning("m2zzs=%d n2zzs=%d",m2zzs, n2zzs);
fmidzzs = sf_floatalloc(m2zzs*n2zzs);
ldatazzs = sf_floatalloc(nxz*m2zzs);
rdatazzs = sf_floatalloc(n2zzs*nk);
map2d1d(fmidzzs, mid, m2zzs, n2zzs);
iC ( samplezzs(md,lid,mat) );
map2d1d(ldatazzs, mat, nxz, m2zzs);
iC ( samplezzs(rid,nd,mat) );
map2d1d(rdatazzs, mat, n2zzs, nk);
/****************End of Calculating vector Decomposition Operator****************/
t2=clock();
timespent=(float)(t2-t1)/CLOCKS_PER_SEC;
sf_warning("CPU time for operator matrix low-rank decomp: %f(second)",timespent);
/****************begin to calculate wavefield****************/
/****************begin to calculate wavefield****************/
/* wavelet parameter for source definition */
float A, f0, t0;
f0=30.0;
t0=0.04;
A=1.0;
int nxpad, nzpad;
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);
int mm=2*M+1;
float dt2=dt*dt;
/* source definition */
int ixs, izs, ixms, izms;
ixs=nxv/2;
izs=nzv/2;
ixms=ixs+M; /* source's x location */
izms=izs+M; /* source's z-location */
float xs, zs;
xs=fx+ixs*dx;
zs=fz+izs*dz;
sf_warning("source location: (%f, %f)",xs, zs);
/* setup I/O files */
oRSF Elasticx("out"),Elasticz("ElasticZ");
oRSF ElasticPx("ElasticPx");
oRSF ElasticPz("ElasticPz");
oRSF ElasticSVx("ElasticSVx");
oRSF ElasticSVz("ElasticSVz");
Elasticx.put("n1",nkz);
Elasticx.put("n2",nkx);
Elasticx.put("d1",dz/1000);
Elasticx.put("d2",dx/1000);
Elasticx.put("o1",fz/1000);
Elasticx.put("o2",fx/1000);
Elasticz.put("n1",nkz);
Elasticz.put("n2",nkx);
Elasticz.put("d1",dz/1000);
Elasticz.put("d2",dx/1000);
Elasticz.put("o1",fz/1000);
Elasticz.put("o2",fx/1000);
ElasticPx.put("n1",nkz);
ElasticPx.put("n2",nkx);
ElasticPx.put("d1",dz/1000);
ElasticPx.put("d2",dx/1000);
ElasticPx.put("o1",fz/1000);
ElasticPx.put("o2",fx/1000);
ElasticPz.put("n1",nkz);
ElasticPz.put("n2",nkx);
ElasticPz.put("d1",dz/1000);
ElasticPz.put("d2",dx/1000);
ElasticPz.put("o1",fz/1000);
ElasticPz.put("o2",fx/1000);
ElasticSVx.put("n1",nkz);
ElasticSVx.put("n2",nkx);
ElasticSVx.put("d1",dz/1000);
ElasticSVx.put("d2",dx/1000);
ElasticSVx.put("o1",fz/1000);
ElasticSVx.put("o2",fx/1000);
ElasticSVz.put("n1",nkz);
ElasticSVz.put("n2",nkx);
ElasticSVz.put("d1",dz/1000);
ElasticSVz.put("d2",dx/1000);
ElasticSVz.put("o1",fz/1000);
ElasticSVz.put("o2",fx/1000);
float *coeff_2dx=sf_floatalloc(mm);
float *coeff_2dz=sf_floatalloc(mm);
float *coeff_1dx=sf_floatalloc(mm);
float *coeff_1dz=sf_floatalloc(mm);
coeff2d(coeff_2dx,dx);
coeff2d(coeff_2dz,dz);
coeff1dmix(coeff_1dx,dx);
coeff1dmix(coeff_1dz,dz);
float **p1=sf_floatalloc2(nzpad, nxpad);
float **p2=sf_floatalloc2(nzpad, nxpad);
float **p3=sf_floatalloc2(nzpad, nxpad);
float **q1=sf_floatalloc2(nzpad, nxpad);
float **q2=sf_floatalloc2(nzpad, nxpad);
float **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);
sf_warning("==================================================");
sf_warning("== Porpagation Using Elastic anisotropic Eq. ==");
sf_warning("==================================================");
float **vpp, **vss, **epp, **dee, **thee;
vpp=sf_floatalloc2(nz,nx);
vss=sf_floatalloc2(nz,nx);
epp=sf_floatalloc2(nz,nx);
dee=sf_floatalloc2(nz,nx);
thee=sf_floatalloc2(nz,nx);
k=0;
for(i=0;i<nx;i++)
for(j=0;j<nz;j++)
{
vpp[i][j]=vp[k];
vss[i][j]=vs[k];
epp[i][j]=ep[k];
dee[i][j]=de[k];
thee[i][j]=th[k];
k++;
}
std::valarray<float> x(nxz);
float *px, *pz;
px=sf_floatalloc(nxz);
pz=sf_floatalloc(nxz);
int ii, jj;
int *ijkx = sf_intalloc(nkx);
int *ijkz = sf_intalloc(nkz);
ikxikz(ijkx, ijkz, nkx, nkz);
for(int it=0;it<ns;it++)
{
float t=it*dt;
if(it%50==0)
sf_warning("Elastic: it= %d",it);
// 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[ixms+i][izms+j]+=i*Ricker(t, f0, t0, A);
q2[ixms+i][izms+j]+=j*Ricker(t, f0, t0, A);
}
}
/* fwpttielastic: forward-propagating using original elastic equation of displacement in TTI media*/
fwpttielastic(dt2, p1, p2, p3, q1, q2, q3, coeff_2dx, coeff_2dz, coeff_1dx, coeff_1dz,
dx, dz, nx, nz, nxpad, nzpad, vpp, vss, epp, dee, thee);
/******* output wavefields: component and divergence *******/
if(it==ns-1)
{
k=0;
for(i=0;i<nx;i++){
int im=i+M;
for(j=0;j<nz;j++){
int jm=j+M;
x[k] = px[k] = p3[im][jm];
k++;
}
}
Elasticx<<x;
k=0;
for(i=0;i<nx;i++){
int im=i+M;
for(j=0;j<nz;j++){
int jm=j+M;
x[k] = pz[k] = q3[im][jm];
k++;
}
}
Elasticz<<x;
t3=clock();
timespent=(float)(t3-t2)/CLOCKS_PER_SEC;
sf_warning("CPU time for wavefield modeling: %f(second)",timespent);
/* separate qP wave */
sf_warning("vector decomposition of P-wave based on lowrank decomp.");
decomplowrank2d(ldataxxp, rdataxxp, fmidxxp,
ldataxzp, rdataxzp, fmidxzp,
ldatazzp, rdatazzp, fmidzzp,
px, pz, ijkx, ijkz,
nx, nz, nxz, nk, M, m2xxp, n2xxp, m2xzp, n2xzp, m2zzp, n2zzp);
for(i=0;i<nxz;i++)
x[i] = px[i];
ElasticPx<<x;
for(i=0;i<nxz;i++)
x[i] = pz[i];
ElasticPz<<x;
k=0;
for(i=0;i<nx;i++){
int im=i+M;
for(j=0;j<nz;j++){
int jm=j+M;
px[k] = p3[im][jm];
pz[k] = q3[im][jm];
k++;
}
}
/* separate qSV wave */
sf_warning("vector decomposition of SV-wave based on lowrank decomp.");
decomplowrank2d(ldataxxs, rdataxxs, fmidxxs,
ldataxzs, rdataxzs, fmidxzs,
ldatazzs, rdatazzs, fmidzzs,
px, pz, ijkx, ijkz,
nx, nz, nxz, nk, M, m2xxs, n2xxs, m2xzs, n2xzs, m2zzs, n2zzs);
for(i=0;i<nxz;i++)
x[i] = px[i];
ElasticSVx<<x;
for(i=0;i<nxz;i++)
x[i] = pz[i];
ElasticSVz<<x;
t4=clock();
timespent=(float)(t4-t3)/CLOCKS_PER_SEC;
sf_warning("CPU time for vector decomposition: %f(second)",timespent);
}/* (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];
}
}/* it loop */
free(ldataxxp);
free(ldatazzp);
free(ldataxzp);
free(rdataxxp);
free(rdataxzp);
free(rdatazzp);
free(fmidxxp);
free(fmidxzp);
free(fmidzzp);
free(ldataxxs);
free(ldatazzs);
free(ldataxzs);
free(rdataxxs);
free(rdataxzs);
free(rdatazzs);
free(fmidxxs);
free(fmidxzs);
free(fmidzzs);
free(px);
free(pz);
free(*p1);
free(*p2);
free(*p3);
free(*q1);
free(*q2);
free(*q3);
free(*vpp);
free(*vss);
free(*epp);
free(*dee);
free(*thee);
free(coeff_2dx);
free(coeff_2dz);
free(coeff_1dx);
free(coeff_1dz);
free(ijkx);
free(ijkz);
exit(0);
}
/* Apx2 */
static int samplexxp(vector<int>& rs, vector<int>& cs, DblNumMat& res)
{
int nr = rs.size();
int nc = cs.size();
res.resize(nr,nc);
setvalue(res,0.0);
double aa[2][2],ve[2][2],va[2]; /*matrix, eigeinvector and eigeinvalues*/
double c33, c44, c11, c13c44, a11, a12, a22;
double sx, cx;
for(int a=0; a<nr; a++)
{
int i=rs[a];
double vp2 = vp[i]*vp[i];
double vs2 = vs[i]*vs[i];
double ep2 = 1.0+2*ep[i];
double de2 = 1.0+2*de[i];
double coss=cos(th[i]);
double sins=sin(th[i]);
for(int b=0; b<nc; b++)
{
double s = sinx[cs[b]];
double c = cosx[cs[b]];
if(s==0&&c==0)
{
res(a,b) = 0.0;
continue;
}
c33=vp2;
c44=vs2;
c11=ep2*c33;
c13c44=sqrt((de2*c33-c44)*(c33-c44));
// rotatiing according to tilted symmetry axis
sx=s*coss+c*sins;
cx=c*coss-s*sins;
a11= c11*sx*sx+c44*cx*cx;
a12= c13c44*sx*cx;
a22= c44*sx*sx+c33*cx*cx;
aa[0][0] = a11;
aa[0][1] = a12;
aa[1][0] = a12;
aa[1][1] = a22;
dsolveSymmetric22(aa, ve, va);
double u1=ve[0][0];
double u2=ve[0][1];
/* get the closest direction to k */
if(u1*sx + u2*cx <0) {
u1 = -u1;
u2 = -u2;
}
res(a,b) = u1*u1;
}// b loop
}// a loop
return 0;
}
/* ApxApz*/
static int samplexzp(vector<int>& rs, vector<int>& cs, DblNumMat& res)
{
int nr = rs.size();
int nc = cs.size();
res.resize(nr,nc);
setvalue(res,0.0);
double aa[2][2],ve[2][2],va[2]; /*matrix, eigeinvector and eigeinvalues*/
double c33, c44, c11, c13c44, a11, a12, a22;
double sx, cx;
for(int a=0; a<nr; a++)
{
int i=rs[a];
double vp2 = vp[i]*vp[i];
double vs2 = vs[i]*vs[i];
double ep2 = 1.0+2*ep[i];
double de2 = 1.0+2*de[i];
double coss=cos(th[i]);
double sins=sin(th[i]);
for(int b=0; b<nc; b++)
{
double s = sinx[cs[b]];
double c = cosx[cs[b]];
if(s==0&&c==0)
{
res(a,b) = 0.0;
continue;
}
c33=vp2;
c44=vs2;
c11=ep2*c33;
c13c44=sqrt((de2*c33-c44)*(c33-c44));
// rotatiing according to tilted symmetry axis
sx=s*coss+c*sins;
cx=c*coss-s*sins;
a11= c11*sx*sx+c44*cx*cx;
a12= c13c44*sx*cx;
a22= c44*sx*sx+c33*cx*cx;
aa[0][0] = a11;
aa[0][1] = a12;
aa[1][0] = a12;
aa[1][1] = a22;
dsolveSymmetric22(aa, ve, va);
double u1=ve[0][0];
double u2=ve[0][1];
/* get the closest direction to k */
if(u1*sx + u2*cx <0) {
u1 = -u1;
u2 = -u2;
}
res(a,b) = u1*u2;
}// b loop
}// a loop
return 0;
}
/* Apz2 */
static int samplezzp(vector<int>& rs, vector<int>& cs, DblNumMat& res)
{
int nr = rs.size();
int nc = cs.size();
res.resize(nr,nc);
setvalue(res,0.0);
double aa[2][2],ve[2][2],va[2]; /*matrix, eigeinvector and eigeinvalues*/
double c33, c44, c11, c13c44, a11, a12, a22;
double sx, cx;
for(int a=0; a<nr; a++)
{
int i=rs[a];
double vp2 = vp[i]*vp[i];
double vs2 = vs[i]*vs[i];
double ep2 = 1.0+2*ep[i];
double de2 = 1.0+2*de[i];
double coss=cos(th[i]);
double sins=sin(th[i]);
for(int b=0; b<nc; b++)
{
double s = sinx[cs[b]];
double c = cosx[cs[b]];
if(s==0&&c==0)
{
res(a,b) = 0.0;
continue;
}
c33=vp2;
c44=vs2;
c11=ep2*c33;
c13c44=sqrt((de2*c33-c44)*(c33-c44));
// rotatiing according to tilted symmetry axis
sx=s*coss+c*sins;
cx=c*coss-s*sins;
a11= c11*sx*sx+c44*cx*cx;
a12= c13c44*sx*cx;
a22= c44*sx*sx+c33*cx*cx;
aa[0][0] = a11;
aa[0][1] = a12;
aa[1][0] = a12;
aa[1][1] = a22;
dsolveSymmetric22(aa, ve, va);
double u1=ve[0][0];
double u2=ve[0][1];
/* get the closest direction to k */
if(u1*sx + u2*cx <0) {
u1 = -u1;
u2 = -u2;
}
res(a,b) = u2*u2;
}// b loop
}// a loop
return 0;
}
/* Asx2 */
static int samplexxs(vector<int>& rs, vector<int>& cs, DblNumMat& res)
{
int nr = rs.size();
int nc = cs.size();
res.resize(nr,nc);
setvalue(res,0.0);
double aa[2][2],ve[2][2],va[2]; /*matrix, eigeinvector and eigeinvalues*/
double c33, c44, c11, c13c44, a11, a12, a22;
double sx, cx;
for(int a=0; a<nr; a++)
{
int i=rs[a];
double vp2 = vp[i]*vp[i];
double vs2 = vs[i]*vs[i];
double ep2 = 1.0+2*ep[i];
double de2 = 1.0+2*de[i];
double coss=cos(th[i]);
double sins=sin(th[i]);
for(int b=0; b<nc; b++)
{
double s = sinx[cs[b]];
double c = cosx[cs[b]];
if(s==0&&c==0)
{
res(a,b) = 0.0;
continue;
}
c33=vp2;
c44=vs2;
c11=ep2*c33;
c13c44=sqrt((de2*c33-c44)*(c33-c44));
// rotatiing according to tilted symmetry axis
sx=s*coss+c*sins;
cx=c*coss-s*sins;
a11= c11*sx*sx+c44*cx*cx;
a12= c13c44*sx*cx;
a22= c44*sx*sx+c33*cx*cx;
aa[0][0] = a11;
aa[0][1] = a12;
aa[1][0] = a12;
aa[1][1] = a22;
dsolveSymmetric22(aa, ve, va);
double u1=ve[1][0];
double u2=ve[1][1];
/* get the closest direction to k */
if(u1*cx - u2*sx <0) {
u1 = -u1;
u2 = -u2;
}
res(a,b) = u1*u1;
}// b loop
}// a loop
return 0;
}
/* AsxAsz*/
static int samplexzs(vector<int>& rs, vector<int>& cs, DblNumMat& res)
{
int nr = rs.size();
int nc = cs.size();
res.resize(nr,nc);
setvalue(res,0.0);
double aa[2][2],ve[2][2],va[2]; /*matrix, eigeinvector and eigeinvalues*/
double c33, c44, c11, c13c44, a11, a12, a22;
double sx, cx;
for(int a=0; a<nr; a++)
{
int i=rs[a];
double vp2 = vp[i]*vp[i];
double vs2 = vs[i]*vs[i];
double ep2 = 1.0+2*ep[i];
double de2 = 1.0+2*de[i];
double coss=cos(th[i]);
double sins=sin(th[i]);
for(int b=0; b<nc; b++)
{
double s = sinx[cs[b]];
double c = cosx[cs[b]];
if(s==0&&c==0)
{
res(a,b) = 0.0;
continue;
}
c33=vp2;
c44=vs2;
c11=ep2*c33;
c13c44=sqrt((de2*c33-c44)*(c33-c44));
// rotatiing according to tilted symmetry axis
sx=s*coss+c*sins;
cx=c*coss-s*sins;
a11= c11*sx*sx+c44*cx*cx;
a12= c13c44*sx*cx;
a22= c44*sx*sx+c33*cx*cx;
aa[0][0] = a11;
aa[0][1] = a12;
aa[1][0] = a12;
aa[1][1] = a22;
dsolveSymmetric22(aa, ve, va);
double u1=ve[1][0];
double u2=ve[1][1];
/* get the closest direction to k */
if(u1*cx - u2*sx <0) {
u1 = -u1;
u2 = -u2;
}
res(a,b) = u1*u2;
}// b loop
}// a loop
return 0;
}
/* Asz2 */
static int samplezzs(vector<int>& rs, vector<int>& cs, DblNumMat& res)
{
int nr = rs.size();
int nc = cs.size();
res.resize(nr,nc);