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Mzfraclr2.cc
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Mzfraclr2.cc
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// Complex lowrank decomposition for 2-D viscoacoustic isotropic wave propagation.
// Copyright (C) 2014 University of Texas at Austin
//
// 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 <time.h>
#include <rsf.hh>
#include "vecmatop.hh"
#include "serialize.hh"
using namespace std;
static std::valarray<float> vs,qs;
static std::valarray<double> kx, kz;
static std::valarray<double> lpass;
static float ct,cb,cl,cr;
static int nkz,nkx,nz,nx,nbt,nbb,nbl,nbr;
static float dt,w0,gama;
static bool rev,compen,avg;
static int mode,sign,abc;
int sample(vector<int>& rs, vector<int>& cs, ZpxNumMat& res)
{
int nr = rs.size();
int nc = cs.size();
res.resize(nr,nc);
setvalue(res,zpx(0.0,0.0));
for(int a=0; a<nr; a++) {
int i = rs[a];
int iz = i%nz;
int ix = (int) i/nz;
double c0 = vs[i];
double q = qs[i];
for(int b=0; b<nc; b++) {
int j = cs[b];
double k = hypot(kz[j],kx[j]);
double gamma = atan(1./q)/SF_PI;
double c = c0*cos(SF_PI*gamma/2.);
if (c<=0) sf_error("c negative!");
zpx phf;
if (mode == 0) { /*viscoacoustic*/
double eta = -pow(c0,2.*gamma)*pow(w0,-2.*gamma)*cos(SF_PI*gamma);
double tao = -pow(c0,2.*gamma-1.)*pow(w0,-2.*gamma)*sin(SF_PI*gamma);
if (avg) gamma = gama;
double p1 = tao*pow(c,2)*pow(k,2.*gamma+1.);
double p2 = -pow(p1,2) - 4*eta*pow(c,2)*pow(k,2.*gamma+2.);
if (p2 < 0) sf_error("Square root is imaginary!");
zpx phr = (compen) ? zpx(-p1*dt/2.*lpass[j],0) : zpx(p1*dt/2.,0);
zpx phi = (sign==0)? zpx(0,sqrt(p2)*dt/2.) : zpx(0,-1*sqrt(p2)*dt/2.);
zpx phase = phr + phi;
phf = exp(phase);
} else if (mode == 1) { /*loss dominated*/
double tao = -pow(c0,2.*gamma-1.)*pow(w0,-2.*gamma)*sin(SF_PI*gamma);
if (avg) gamma = gama;
double p1 = tao*pow(c,2)*pow(k,2.*gamma+1.);
double p2 = -pow(p1,2) + 4*pow(c,2)*pow(k,2);
if (p2 < 0) sf_warning("square root is imaginary!!!");
zpx phr = (compen) ? zpx(-p1*dt/2.*lpass[j],0) : zpx(p1*dt/2.,0);
zpx phi = (sign==0)? zpx(0,sqrt(p2)*dt/2.) : zpx(0,-1*sqrt(p2)*dt/2.);
zpx phase = phr + phi;
phf = exp(phase);
} else if (mode == 2) { /*dispersion-dominated*/
double eta = -pow(c0,2.*gamma)*pow(w0,-2.*gamma)*cos(SF_PI*gamma);
if (avg) gamma = gama;
double phase = sqrt(-eta*pow(c,2)*pow(k,2.*gamma+2.))*dt;
phf = zpx(cos(phase),sin(phase));
} else { /*acoustic*/
double phase = c0*k*dt;
phf = zpx(cos(phase),sin(phase));
}
/* absorbing boundary */
if (abc==0) {
if (iz < nbt)
phf *= exp(-pow(ct*(nbt-iz)*abs((kz[j]==0)?0:kz[j]/k),2));
else if (iz > nz-1-nbb)
phf *= exp(-pow(cb*(iz-nz+1+nbb)*abs((kz[j]==0)?0:kz[j]/k),2));
if (ix < nbl)
phf *= exp(-pow(cl*(nbl-ix)*abs((kx[j]==0)?0:kx[j]/k),2));
else if (ix > nx-1-nbr)
phf *= exp(-pow(cr*(ix-nx+1+nbr)*abs((kx[j]==0)?0:kx[j]/k),2));
} else {
if (iz < nbt)
phf *= exp(-pow(ct*(nbt-iz),2));
else if (iz > nz-1-nbb)
phf *= exp(-pow(cb*(iz-nz+1+nbb),2));
if (ix < nbl)
phf *= exp(-pow(cl*(nbl-ix),2));
else if (ix > nx-1-nbr)
phf *= exp(-pow(cr*(ix-nx+1+nbr),2));
}
res(a,b) = (rev) ? conj(phf) : phf;
}
}
return 0;
}
int tukey(float a, float cutoff, float vm, std::valarray<double>& tuk)
{
double kmax = hypot(kz[nkz-1],kx[nkx-1]);
double kbond;
kbond = 2*SF_PI*cutoff/vm;
if (kbond > kmax) {
sf_warning("cutoff wavenumber %f larger than maximum wavenumber %f! Setting kbond = kmax...",kbond,kmax);
kbond = kmax;
}
for (int ikx=0; ikx<nkx; ikx++) {
for (int ikz=0; ikz<nkz; ikz++) {
int ik = ikz+ikx*nkz;
double k = hypot(kz[ik],kx[ik]);
if (k > kbond)
tuk[ik] = 0.;
else if (k >= kbond*(1.-0.5*a))
tuk[ik] = 0.5*(1.+cos(SF_PI*(2.*k/(a*kbond)-2./a+1.)));
else
tuk[ik] = 1.;
}
}
return 0;
}
int main(int argc, char** argv)
{
sf_init(argc,argv); // Initialize RSF
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-4); // tolerance
int npk;
par.get("npk",npk,20); // maximum rank
par.get("dt",dt); // time step
par.get("w0",w0); // reference frequency
w0 *= 2*SF_PI;
par.get("rev",rev,false); // reverse propagation
par.get("mode",mode,0); // mode of propagation: 0 is viscoacoustic (default); 1 is loss-dominated; 2 is dispersion dominated; 3 is acoustic
float aa,cut,vmax;
par.get("compen",compen,false); // compensate attenuation, only works if mode=0,1 (viscoacoustic)
if (mode==0 || mode==1)
if (compen) {
par.get("taper",aa,0.2); // taper ratio for tukey window
par.get("cutoff",cut,250.); // cutoff frequency
par.get("vmax",vmax,6000.); // maximum velocity
sf_warning("Compensating for attenuation!");
}
par.get("sign",sign,0); // sign of solution: 0 is positive, 1 is negative
par.get("avg",avg,false); // whether use average value of gamma
if (avg) {
par.get("gamma",gama);
sf_warning("Gamma_avg = %f",gama);
}
par.get("abc",abc,0); /*absorbing mode: 0-> direction dependent; 1-> direction independent.*/
par.get("nbt",nbt,0);
par.get("nbb",nbb,0);
par.get("nbl",nbl,0);
par.get("nbr",nbr,0);
par.get("ct",ct,0.0);
par.get("cb",cb,0.0);
par.get("cl",cl,0.0);
par.get("cr",cr,0.0);
iRSF vel, q("q");
vel.get("n1",nz);
vel.get("n2",nx);
int m = nx*nz;
vs.resize(m);
qs.resize(m);
vel >> vs;
q >> qs;
iRSF fft("fft");
fft.get("n1",nkz);
fft.get("n2",nkx);
float dkz,dkx;
fft.get("d1",dkz);
fft.get("d2",dkx);
float kz0,kx0;
fft.get("o1",kz0);
fft.get("o2",kx0);
int n = nkx*nkz;
kx.resize(n);
kz.resize(n);
for (int ikx=0; ikx < nkx; ikx++) {
for (int ikz=0; ikz < nkz; ikz++) {
int ik = ikz+ikx*nkz;
kx[ik] = 2*SF_PI*(kx0+ikx*dkx);
kz[ik] = 2*SF_PI*(kz0+ikz*dkz);
}
}
// set up tapering array
if ((mode==0 || mode==1) && compen) {
lpass.resize(n);
tukey(aa, cut, vmax, lpass);
}
vector<int> lidx, ridx;
ZpxNumMat mid;
iC( ddlowrank(m,n,sample,(double)eps,npk,lidx,ridx,mid) );
int n2=mid.n();
int m2=mid.m();
vector<int> midx(m), nidx(n);
for (int k=0; k < m; k++)
midx[k] = k;
for (int k=0; k < n; k++)
nidx[k] = k;
ZpxNumMat lmat(m,m2);
iC ( sample(midx,lidx,lmat) );
ZpxNumMat lmat2(m,n2);
iC( zzgemm(1.0, lmat, mid, 0.0, lmat2) );
zpx *ldat = lmat2.data();
std::valarray<sf_complex> ldata(m*n2);
for (int k=0; k < m*n2; k++) {
ldata[k] = sf_cmplx(real(ldat[k]),imag(ldat[k]));
}
oRSF left("left");
left.type(SF_COMPLEX);
left.put("n1",m);
left.put("n2",n2);
left << ldata;
ZpxNumMat rmat(n2,n);
iC ( sample(ridx,nidx,rmat) );
zpx *rdat = rmat.data();
std::valarray<sf_complex> rdata(n2*n);
for (int k=0; k < n2*n; k++) {
rdata[k] = sf_cmplx(real(rdat[k]),imag(rdat[k]));
}
oRSF right;
right.type(SF_COMPLEX);
right.put("n1",n2);
right.put("n2",n);
right << rdata;
exit(0);
}