denise.c 260 KB
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/*-----------------------------------------------------------------------------------------
 * Copyright (C) 2013  For the list of authors, see file AUTHORS.
 *
 * This file is part of DENISE.
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 *
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 * DENISE 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, version 2.0 of the License only.
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 *
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 * DENISE 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.
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 *
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 * You should have received a copy of the GNU General Public License
 * along with DENISE. See file COPYING and/or <http://www.gnu.org/licenses/gpl-2.0.html>.
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 -----------------------------------------------------------------------------------------*/
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/* ----------------------------------------------------------------------
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 * This is program DENISE.
 * subwavelength DEtail resolving Nonlinear Iterative SEismic inversion
 *
 * If you use this code for your own research please cite at least one article
 * written by the developers of the package, e.g.
 * D. K�hn. Time domain 2D elastic full waveform tomography. PhD Thesis, Kiel
 * University, 2011.
 *
 *  ----------------------------------------------------------------------*/
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#include "fd.h"           /* general include file for viscoelastic FD programs */

#include "globvar.h"      /* definition of global variables  */
#include "cseife.h"

#include "stfinv/stfinv.h" /* libstfinv - inversion for source time function */

int main(int argc, char **argv){
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    /* variables in main */
    int ns, nseismograms=0, nt, nd, fdo3, j, i, ii, jj, shotid, recid, k, nc, iter, h, infoout, SHOTINC, TIMEWIN, test_eps, lq, iq, jq, hin, hin1, s=0;
    int NTDTINV, nxny, nxnyi, imat, imat1, imat2, IDXI, IDYI, hi, NTST, NTSTI, partest;
    int lsnap, nsnap=0, lsamp=0, buffsize, invtime, invtimer, sws, swstestshot, snapseis, snapseis1, PML;
    int ntr=0, ntr_loc=0, ntr_glob=0, nsrc=0, nsrc_loc=0, nsrc_glob=0, ishot, irec, nshots=0, nshots1, Lcount, itest, Lcountsum, itestshot;
    
    float pum, ppim, ppim1, ppim2, thetaf, thetab, e33, e33b, e11, e11b, muss, lamss;
    float memdyn, memmodel, memseismograms, membuffer, memtotal, dngn, fphi, sum, avggrad, beta, betan, betaz, betaLog, betaVp, betaVs, betarho, eps_scale, L2old;
    float fac1, fac2, wavefor, waverecipro, dump, dump1, epsilon, gradsign, mun, eps1, gradplastiter, gradglastiter, gradclastiter, betar, sig_max, sig_max1;
    float signL1, RMS, opteps_vp, opteps_vs, opteps_rho, Vs, Vp, Vp_avg, C_vp, Vs_avg, C_vs, Cd, rho_avg, C_rho, Vs_sum, Vp_sum, rho_sum, Zp, Zs;
    float freqshift, dfreqshift, memfwt, memfwt1, memfwtdata;
    char *buff_addr, ext[10], *fileinp;
    char wave_forward[225], wave_recipro[225], wave_conv[225], jac[225], jac2[225], jacsum[225], dwavelet[225], vyf[STRING_SIZE];
    
    double time1, time2, time3, time4, time5, time6, time7, time8,
    time_av_v_update=0.0, time_av_s_update=0.0, time_av_v_exchange=0.0,
    time_av_s_exchange=0.0, time_av_timestep=0.0;
    
    float L2, L2sum, L2_all_shots, L2sum_all_shots, *L2t, alphanomsum, alphanom, alphadenomsum, alphadenom, scaleamp ,sdummy, lamr;
    int sum_killed_traces=0, sum_killed_traces_testshots=0, killed_traces=0, killed_traces_testshots=0;
    int *ptr_killed_traces=&killed_traces, *ptr_killed_traces_testshots=&killed_traces_testshots;
    
    float energy, energy_sum, energy_all_shots, energy_sum_all_shots;
    
    // Pointer for dynamic wavefields:
    float  **  psxx, **  psxy, **  psyy, **  psxz, **  psyz, **psp, ** ux, ** uy, ** uz, ** uxy, ** uyx, ** Vp0, ** uttx, ** utty, ** Vs0, ** Rho0;
    float  **  pvx, **  pvy, **  pvz, **waveconv, **waveconv_lam, **waveconv_mu, **waveconv_rho, **waveconv_rho_s, **waveconv_u, **waveconvtmp, **wcpart, **wavejac,**waveconv_rho_s_z,**waveconv_u_z,**waveconv_rho_z;
    float **waveconv_shot, **waveconv_u_shot, **waveconv_rho_shot, **waveconv_u_shot_z, **waveconv_rho_shot_z;
    float  **  pvxp1, **  pvyp1, **  pvzp1, **  pvxm1, **  pvym1, **  pvzm1;
    float ** gradg, ** gradp,** gradg_rho, ** gradp_rho, ** gradg_u, ** gradp_u, ** gradp_u_z,** gradp_rho_z;
    float  **  prho,**  prhonp1, **prip=NULL, **prjp=NULL, **pripnp1=NULL, **prjpnp1=NULL, **  ppi, **  pu, **  punp1, **  puipjp, **  ppinp1;
    float  **  vpmat, ***forward_prop_x, ***forward_prop_y, ***forward_prop_rho_x, ***forward_prop_u, ***forward_prop_rho_y, ***forward_prop_p;
    float ** puip,** pujp;
    
    float ***forward_prop_z_xz,***forward_prop_z_yz,***forward_prop_rho_z,**waveconv_mu_z;
    float ** uxz, ** uyz;
    
    float  ** sectionvx=NULL, ** sectionvy=NULL, ** sectionvz=NULL, ** sectionp=NULL, ** sectionpnp1=NULL,
    ** sectioncurl=NULL, ** sectiondiv=NULL, ** sectionvxdata=NULL, ** sectionvydata=NULL, ** sectionvzdata=NULL, ** sectionvxdiff=NULL, ** sectionvzdiff=NULL, ** sectionvxdiffold=NULL, ** sectionvydiffold=NULL, ** sectionvzdiffold=NULL,** sectionpdata=NULL, ** sectionpdiff=NULL, ** sectionpdiffold=NULL,
    ** sectionvydiff=NULL, ** sectionpn=NULL, ** sectionread=NULL, ** sectionvy_conv=NULL, ** sectionvy_obs=NULL, ** sectionvx_conv=NULL,** sectionvx_obs=NULL, ** sectionvz_conv=NULL,** sectionvz_obs=NULL,
    ** sectionp_conv=NULL,** sectionp_obs=NULL, * source_time_function=NULL;
    float  **  absorb_coeff, ** taper_coeff, * epst1, * epst2,  * epst3, * picked_times;
    float  ** srcpos=NULL, **srcpos_loc=NULL, ** srcpos1=NULL, **srcpos_loc_back=NULL, ** signals=NULL,** signals_SH=NULL, ** signals_rec=NULL, *hc=NULL, ** dsignals=NULL;
    int   ** recpos=NULL, ** recpos_loc=NULL;
    /*int   ** tracekill=NULL, TRKILL, DTRKILL;*/
    int * DTINV_help;
    
    float ** bufferlef_to_rig,  ** bufferrig_to_lef, ** buffertop_to_bot, ** bufferbot_to_top;
    
    /* PML variables */
    float * d_x, * K_x, * alpha_prime_x, * a_x, * b_x, * d_x_half, * K_x_half, * alpha_prime_x_half, * a_x_half, * b_x_half, * d_y, * K_y, * alpha_prime_y, * a_y, * b_y, * d_y_half, * K_y_half, * alpha_prime_y_half, * a_y_half, * b_y_half;
    float ** psi_sxx_x, ** psi_syy_y, ** psi_sxy_y, ** psi_sxy_x, ** psi_vxx, ** psi_vyy, ** psi_vxy, ** psi_vyx, ** psi_vxxs;
    float ** psi_sxz_x, ** psi_syz_y, ** psi_vzx, ** psi_vzy;
    
    /* Variables for viscoelastic modeling */
    float **ptaus=NULL, **ptaup=NULL, *etaip=NULL, *etajm=NULL, *peta=NULL, **ptausipjp=NULL, **fipjp=NULL, ***dip=NULL, *bip=NULL, *bjm=NULL;
    float *cip=NULL, *cjm=NULL, ***d=NULL, ***e=NULL, ***pr=NULL, ***pp=NULL, ***pq=NULL, **f=NULL, **g=NULL;
    float **tausjp, **tausip, ***pt=NULL, ***po=NULL; // SH Simulation
    
    /* Variables for step length calculation */
    int step1, step2, step3=0, itests, iteste, stepmax, countstep;
    float scalefac;
    
    /* Variables for Pseudo-Hessian calculation */
    int RECINC, ntr1;
    float * jac_rho, * jac_u, * jac_lam_x, * jac_lam_y;
    float * temp_TS, * temp_TS1, * temp_TS2, * temp_TS3, * temp_TS4, * temp_TS5, * temp_conv, * temp_conv1, * temp_conv2;
    float temp_hess, temp_hess_lambda, temp_hess_mu, mulamratio;
    float ** hessian, ** hessian_u, ** hessian_rho, **hessian_shot, **hessian_u_shot, **hessian_rho_shot;
    int QUELLART_OLD;
    
    /* Variables for L-BFGS */
    int LBFGS=0, bfgsnum=0,bfgspar=3;
    int LBFGS_iter_start=1;
    float LBFGS_L2_temp;
    float **bfgsmod1,**bfgsmod2,**bfgsmod3,**bfgsgrad1, **bfgsgrad2, **bfgsgrad3, *bfgsscale1,*bfgsscale2,*bfgsscale3;
    int l=0;
    int w=0;
    int m=0;
    
    /* Check wolfe */
    int steplength_search=0;
    int FWI_run=1;
    int gradient_optimization=1;
    float alpha_SL_min=0, alpha_SL_max=0, alpha_SL=1.0;
    float alpha_SL_old;
    float ** waveconv_old,** waveconv_u_old,** waveconv_rho_old;
    float ** waveconv_up,** waveconv_u_up,** waveconv_rho_up;
    float L2_SL_old=0, L2_SL_new=0;
    float c1_SL=1e-4, c2_SL=0.9;
    int wolfe_status;
    int wolfe_sum_FWI=0;
    int wolfe_found_lower_L2=0;
    float alpha_SL_FS;
    float L2_SL_FS;
    int use_wolfe_failsafe=0;
    int wolfe_SLS_failed=0;
    
    /* Variables for energy weighted gradient */
    float ** Ws, **Wr, **We;
    float ** Ws_SH, **Wr_SH, **We_SH;
    float ** We_sum,** We_sum_SH;
    float We_sum_max1;
    float We_max_SH,We_max;
    
    int * recswitch=NULL;
    float ** fulldata=NULL, ** fulldata_vx=NULL, ** fulldata_vy=NULL, ** fulldata_vz=NULL, ** fulldata_p=NULL, ** fulldata_curl=NULL, ** fulldata_div=NULL;
    
    /* different modelling types */
    int mod_type=0;
    
    /*vector for abort criterion*/
    float * L2_hist=NULL;
    
    /* help variable for MIN_ITER */
    int min_iter_help=0;
    
    float ** workflow=NULL;
    int workflow_line_current=1;
    int workflow_lines;
    int change_wavetype_iter=-10; /* Have to be inialized negative */
    int wavetype_start; /* We need this due to MPI Comm */
    
    /* variable for time domain filtering */
    float FC;
    float *FC_EXT=NULL;
    int nfrq=0;
    int FREQ_NR=1;
    /* declaration of variables for trace killing */
    int ** kill_tmp;
    FILE *ftracekill;
    
    FILE *fprec, *FP2, *FP3, *FP4, *FP5, *FPL2, *FP6, *FP7;
    
    /* General parameters */
    int nt_out;
    
    MPI_Request *req_send, *req_rec;
    MPI_Status  *send_statuses, *rec_statuses;
    
    /* Initialize MPI environment */
    MPI_Init(&argc,&argv);
    MPI_Comm_size(MPI_COMM_WORLD,&NP);
    MPI_Comm_rank(MPI_COMM_WORLD,&MYID);
    
    setvbuf(stdout, NULL, _IONBF, 0);
    
    if (MYID == 0){
        time1=MPI_Wtime();
        clock();
    }
    
    /* print program name, version etc to stdout*/
    if (MYID == 0) info(stdout);
    
    /* read parameters from parameter-file (stdin) */
    fileinp=argv[1];
    FP=fopen(fileinp,"r");
    if(FP==NULL) {
        if (MYID == 0){
            printf("\n==================================================================\n");
            printf(" Cannot open Denise input file %s \n",fileinp);
            printf("\n==================================================================\n\n");
            err(" --- ");
        }
    }
    
    /* read json formatted input file */
    read_par_json(stdout,fileinp);
    
    exchange_par();
    
    wavetype_start=WAVETYPE;
    if (MYID == 0) note(stdout);
    
    
    /* open log-file (each PE is using different file) */
    /*	fp=stdout; */
    sprintf(ext,".%i",MYID);
    strcat(LOG_FILE,ext);
    
    /* If Verbose==0, no PE will write a log file */
    if(!VERBOSE) sprintf(LOG_FILE,"/dev/null");
    
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    if ((MYID==0)) FP=stdout;
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    else {
        FP=fopen(LOG_FILE,"w");
    }
    fprintf(FP," This is the log-file generated by PE %d \n\n",MYID);
    
    /* domain decomposition */
    initproc();
    
    NT=iround(TIME/DT);  	  /* number of timesteps */
    /*ns=iround(NT/NDT);*/           /* number of samples per trace */
    ns=NT;	/* in a FWI one has to keep all samples of the forward modeled data
             at the receiver positions to calculate the adjoint sources and to do
             the backpropagation; look at function saveseis_glob.c to see that every
             NDT sample for the forward modeled wavefield is written to su files*/
    lsnap=iround(TSNAP1/DT);      /* first snapshot at this timestep */
    lsamp=NDT;
    
    
    /* output of parameters to log-file or stdout */
    if (MYID==0) write_par(FP);
    
    
    /* NXG, NYG denote size of the entire (global) grid */
    NXG=NX;
    NYG=NY;
    
    /* In the following, NX and NY denote size of the local grid ! */
    NX = IENDX;
    NY = IENDY;
    
    
    if (SEISMO){
        recpos=receiver(FP, &ntr);
        recswitch = ivector(1,ntr);
        recpos_loc = splitrec(recpos,&ntr_loc, ntr, recswitch);
        ntr_glob=ntr;
        ntr=ntr_loc;
    }
    
    /* memory allocation for abort criterion*/
    L2_hist = vector(1,1000);
    
    if(INV_STF) fulldata = matrix(1,ntr_glob,1,NT);
    
    /* estimate memory requirement of the variables in megabytes*/
    
    switch (SEISMO){
        case 1 : /* particle velocities only */
            nseismograms=2;
            break;
        case 2 : /* pressure only */
            nseismograms=1;
            break;
        case 3 : /* curl and div only */
            nseismograms=2;
            break;
        case 4 : /* everything */
            nseismograms=5;
            break;
        case 5 : /* everything except curl and div */
            nseismograms=3;
            break;
    }
    
    /* use only every DTINV time sample for the inversion */
    /*DTINV=15;*/
    DTINV_help=ivector(1,NT);
    NTDTINV=ceil((float)NT/(float)DTINV);		/* round towards next higher integer value */
    
    /* save every IDXI and IDYI spatial point during the forward modelling */
    IDXI=1;
    IDYI=1;
    
    /*allocate memory for dynamic, static and buffer arrays */
    fac1=(NX+FDORDER)*(NY+FDORDER);
    fac2=sizeof(float)*pow(2.0,-20.0);
    
    nd = FDORDER/2 + 1;
    
    // decide how much space for exchange is needed
    switch (WAVETYPE) {
        case 1:
            fdo3 = 2*nd;
            break;
        case 2:
            fdo3 = 1*nd;
            break;
        case 3:
            fdo3 = 3*nd;
            break;
        default:
            fdo3 = 2*nd;
            break;
    }
    
    
    if (L){
        memdyn=(5.0+3.0*(float)L)*fac1*fac2;
        memmodel=(12.0+3.0*(float)L)*fac1*fac2;
        
    } else {
        memdyn=5.0*fac1*fac2;
        memmodel=6.0*fac1*fac2;
    }
    memseismograms=nseismograms*ntr*ns*fac2;
    
    memfwt=5.0*((NX/IDXI)+FDORDER)*((NY/IDYI)+FDORDER)*NTDTINV*fac2;
    memfwt1=20.0*NX*NY*fac2;
    memfwtdata=6.0*ntr*ns*fac2;
    
    membuffer=2.0*fdo3*(NY+NX)*fac2;
    buffsize=2.0*2.0*fdo3*(NX+NY)*sizeof(MPI_FLOAT);
    memtotal=memdyn+memmodel+memseismograms+memfwt+memfwt1+memfwtdata+membuffer+(buffsize*pow(2.0,-20.0));
    
    
    if (MYID==0 && WAVETYPE == 1){
        fprintf(FP,"\n **Message from main (printed by PE %d):\n",MYID);
        fprintf(FP," Size of local grids: NX=%d \t NY=%d\n",NX,NY);
        fprintf(FP," Each process is now trying to allocate memory for:\n");
        fprintf(FP," Dynamic variables: \t\t %6.2f MB\n", memdyn);
        fprintf(FP," Static variables: \t\t %6.2f MB\n", memmodel);
        fprintf(FP," Seismograms: \t\t\t %6.2f MB\n", memseismograms);
        fprintf(FP," Buffer arrays for grid exchange:%6.2f MB\n", membuffer);
        fprintf(FP," Network Buffer for MPI_Bsend: \t %6.2f MB\n", buffsize*pow(2.0,-20.0));
        fprintf(FP," ------------------------------------------------ \n");
        fprintf(FP," Total memory required: \t %6.2f MB.\n\n", memtotal);
    }
    
    
    /* allocate buffer for buffering messages */
    buff_addr=malloc(buffsize);
    if (!buff_addr) err("allocation failure for buffer for MPI_Bsend !");
    MPI_Buffer_attach(buff_addr,buffsize);
    
    /* allocation for request and status arrays */
    req_send=(MPI_Request *)malloc(REQUEST_COUNT*sizeof(MPI_Request));
    req_rec=(MPI_Request *)malloc(REQUEST_COUNT*sizeof(MPI_Request));
    send_statuses=(MPI_Status *)malloc(REQUEST_COUNT*sizeof(MPI_Status));
    rec_statuses=(MPI_Status *)malloc(REQUEST_COUNT*sizeof(MPI_Status));
    
    
    /* memory allocation for dynamic (wavefield) arrays */
    if(!ACOUSTIC){
        switch (WAVETYPE) {
            case 1: // P and SV Waves
                psxx =  matrix(-nd+1,NY+nd,-nd+1,NX+nd);
                psxy =  matrix(-nd+1,NY+nd,-nd+1,NX+nd);
                psyy =  matrix(-nd+1,NY+nd,-nd+1,NX+nd);
                break;
                
            case 2: // SH Waves
                psxz =  matrix(-nd+1,NY+nd,-nd+1,NX+nd);
                psyz =  matrix(-nd+1,NY+nd,-nd+1,NX+nd);
                break;
                
            case 3: // P, SH and SV Waves
                psxx =  matrix(-nd+1,NY+nd,-nd+1,NX+nd);
                psxy =  matrix(-nd+1,NY+nd,-nd+1,NX+nd);
                psyy =  matrix(-nd+1,NY+nd,-nd+1,NX+nd);
                psxz =  matrix(-nd+1,NY+nd,-nd+1,NX+nd);
                psyz =  matrix(-nd+1,NY+nd,-nd+1,NX+nd);
                break;
        }
    }else{
        psp  =  matrix(-nd+1,NY+nd,-nd+1,NX+nd);
    }
    
    if(GRAD_METHOD==2) {
        bfgsnum=N_LBFGS;
        
        if(WAVETYPE==2) bfgspar=2;
        
        bfgsmod1=fmatrix(1,bfgsnum,1,bfgspar*NX*NY);
        
        bfgsgrad1=fmatrix(1,bfgsnum,1,bfgspar*NX*NY);
        
        bfgsscale1=vector(1,bfgsnum);
        
        for(l=1;l<=bfgsnum;l++){
            for(m=1;m<=bfgspar*NX*NY;m++){
                bfgsmod1[l][m]=0.0;
                bfgsgrad1[l][m]=0.0;
            }
            bfgsscale1[l]=0.0;
        }
    }
    
    if(!ACOUSTIC){
        if(WAVETYPE==1||WAVETYPE==3){
            ux   =  matrix(-nd+1,NY+nd,-nd+1,NX+nd);
            uy   =  matrix(-nd+1,NY+nd,-nd+1,NX+nd);
            uxy  =  matrix(-nd+1,NY+nd,-nd+1,NX+nd);
            uyx  =  matrix(-nd+1,NY+nd,-nd+1,NX+nd);
            uttx   =  matrix(-nd+1,NY+nd,-nd+1,NX+nd);
            utty   =  matrix(-nd+1,NY+nd,-nd+1,NX+nd);
        }
        if(WAVETYPE==2||WAVETYPE==3){
            uxz   =  matrix(-nd+1,NY+nd,-nd+1,NX+nd);
            uyz   =  matrix(-nd+1,NY+nd,-nd+1,NX+nd);
        }
    }
    
    switch (WAVETYPE) {
        case 1: // P and SV Waves
            pvx  =  matrix(-nd+1,NY+nd,-nd+1,NX+nd);
            pvy  =  matrix(-nd+1,NY+nd,-nd+1,NX+nd);
            pvxp1  =  matrix(-nd+1,NY+nd,-nd+1,NX+nd);
            pvyp1  =  matrix(-nd+1,NY+nd,-nd+1,NX+nd);
            pvxm1  =  matrix(-nd+1,NY+nd,-nd+1,NX+nd);
            pvym1  =  matrix(-nd+1,NY+nd,-nd+1,NX+nd);
            break;
            
        case 2: // SH Waves
            pvz  =  matrix(-nd+1,NY+nd,-nd+1,NX+nd);
            pvzp1  =  matrix(-nd+1,NY+nd,-nd+1,NX+nd);
            pvzm1  =  matrix(-nd+1,NY+nd,-nd+1,NX+nd);
            break;
            
        case 3: // P and SV Waves
            pvx  =  matrix(-nd+1,NY+nd,-nd+1,NX+nd);
            pvy  =  matrix(-nd+1,NY+nd,-nd+1,NX+nd);
            pvxp1  =  matrix(-nd+1,NY+nd,-nd+1,NX+nd);
            pvyp1  =  matrix(-nd+1,NY+nd,-nd+1,NX+nd);
            pvxm1  =  matrix(-nd+1,NY+nd,-nd+1,NX+nd);
            pvym1  =  matrix(-nd+1,NY+nd,-nd+1,NX+nd);
            pvz  =  matrix(-nd+1,NY+nd,-nd+1,NX+nd);
            pvzp1  =  matrix(-nd+1,NY+nd,-nd+1,NX+nd);
            pvzm1  =  matrix(-nd+1,NY+nd,-nd+1,NX+nd);
            break;
    }
    
    Vp0  =  matrix(-nd+1,NY+nd,-nd+1,NX+nd);
    if(!ACOUSTIC)
        Vs0  =  matrix(-nd+1,NY+nd,-nd+1,NX+nd);
    Rho0  =  matrix(-nd+1,NY+nd,-nd+1,NX+nd);
    
    /* memory allocation for static (model) arrays */
    prho =  matrix(-nd+1,NY+nd,-nd+1,NX+nd);
    prhonp1 =  matrix(-nd+1,NY+nd,-nd+1,NX+nd);
    prip =  matrix(-nd+1,NY+nd,-nd+1,NX+nd);
    prjp =  matrix(-nd+1,NY+nd,-nd+1,NX+nd);
    pripnp1 =  matrix(-nd+1,NY+nd,-nd+1,NX+nd);
    prjpnp1 =  matrix(-nd+1,NY+nd,-nd+1,NX+nd);
    ppi  =  matrix(-nd+1,NY+nd,-nd+1,NX+nd);
    ppinp1  =  matrix(-nd+1,NY+nd,-nd+1,NX+nd);
    if(!ACOUSTIC){
        pu   =  matrix(-nd+1,NY+nd,-nd+1,NX+nd);
        punp1   =  matrix(-nd+1,NY+nd,-nd+1,NX+nd);
        puipjp   =  matrix(-nd+1,NY+nd,-nd+1,NX+nd);
        if(WAVETYPE==2 || WAVETYPE==3) {
            puip =  matrix(-nd+1,NY+nd,-nd+1,NX+nd);
            pujp =  matrix(-nd+1,NY+nd,-nd+1,NX+nd);
        }
    }
    vpmat   =  matrix(-nd+1,NY+nd,-nd+1,NX+nd);
    
    
    if((EPRECOND==1)||(EPRECOND==3)){
        if(WAVETYPE==1 || WAVETYPE==3) {
            We_sum = matrix(-nd+1,NY+nd,-nd+1,NX+nd);
            Ws = matrix(-nd+1,NY+nd,-nd+1,NX+nd); /* total energy of the source wavefield */
            Wr = matrix(-nd+1,NY+nd,-nd+1,NX+nd); /* total energy of the receiver wavefield */
            We = matrix(-nd+1,NY+nd,-nd+1,NX+nd); /* total energy of source and receiver wavefield */
        }
        if(WAVETYPE==2 || WAVETYPE==3) {
            We_sum_SH = matrix(-nd+1,NY+nd,-nd+1,NX+nd);
            Ws_SH = matrix(-nd+1,NY+nd,-nd+1,NX+nd); /* total energy of the source wavefield */
            Wr_SH = matrix(-nd+1,NY+nd,-nd+1,NX+nd); /* total energy of the receiver wavefield */
            We_SH = matrix(-nd+1,NY+nd,-nd+1,NX+nd); /* total energy of source and receiver wavefield */
        }
    }
    
    if (L) {
        /* dynamic (wavefield) arrays for viscoelastic modeling */
        pr = f3tensor(-nd+1,NY+nd,-nd+1,NX+nd,1,L);
        pp = f3tensor(-nd+1,NY+nd,-nd+1,NX+nd,1,L);
        pq = f3tensor(-nd+1,NY+nd,-nd+1,NX+nd,1,L);
        /* memory allocation for static arrays for viscoelastic modeling */
        dip = f3tensor(-nd+1,NY+nd,-nd+1,NX+nd,1,L);
        d =  f3tensor(-nd+1,NY+nd,-nd+1,NX+nd,1,L);
        e =  f3tensor(-nd+1,NY+nd,-nd+1,NX+nd,1,L);
        ptaus =  matrix(-nd+1,NY+nd,-nd+1,NX+nd);
        ptausipjp =  matrix(-nd+1,NY+nd,-nd+1,NX+nd);
        if(WAVETYPE==2 || WAVETYPE==3) {
            tausip =  matrix(-nd+1,NY+nd,-nd+1,NX+nd);
            tausjp =  matrix(-nd+1,NY+nd,-nd+1,NX+nd);
            pt = f3tensor(-nd+1,NY+nd,-nd+1,NX+nd,1,L);
            po = f3tensor(-nd+1,NY+nd,-nd+1,NX+nd,1,L);
        }
        ptaup =  matrix(-nd+1,NY+nd,-nd+1,NX+nd);
        fipjp =  matrix(-nd+1,NY+nd,-nd+1,NX+nd);
        f =  matrix(-nd+1,NY+nd,-nd+1,NX+nd);
        g =  matrix(-nd+1,NY+nd,-nd+1,NX+nd);
        peta =  vector(1,L);
        etaip =  vector(1,L);
        etajm =  vector(1,L);
        bip =  vector(1,L);
        bjm =  vector(1,L);
        cip =  vector(1,L);
        cjm =  vector(1,L);
    }
    
    /*nf=4;
     nfstart=4;*/
    
    NTST=20;
    NTSTI=NTST/DTINV;
    
    nxny=NX*NY;
    nxnyi=(NX/IDXI)*(NY/IDYI);
    
    /* Parameters for step length calculations */
    stepmax = STEPMAX; /* number of maximum misfit calculations/steplength 2/3*/
    scalefac = SCALEFAC; /* scale factor for the step length */
    
    if(INVMAT==0){
        waveconv = matrix(-nd+1,NY+nd,-nd+1,NX+nd);
        waveconv_lam = matrix(-nd+1,NY+nd,-nd+1,NX+nd);
        waveconv_shot = matrix(-nd+1,NY+nd,-nd+1,NX+nd);
        
        waveconvtmp = matrix(-nd+1,NY+nd,-nd+1,NX+nd);
        wcpart = matrix(1,3,1,3);
        wavejac = matrix(-nd+1,NY+nd,-nd+1,NX+nd);
        
        if(!ACOUSTIC){
            forward_prop_x =  f3tensor(-nd+1,NY+nd,-nd+1,NX+nd,1,NT/DTINV);
            forward_prop_y =  f3tensor(-nd+1,NY+nd,-nd+1,NX+nd,1,NT/DTINV);
        }else{
            forward_prop_p =  f3tensor(-nd+1,NY+nd,-nd+1,NX+nd,1,NT/DTINV);
        }
        gradg = matrix(-nd+1,NY+nd,-nd+1,NX+nd);
        gradp = matrix(-nd+1,NY+nd,-nd+1,NX+nd);
        
        if(WAVETYPE==1 || WAVETYPE==3){
            forward_prop_rho_x =  f3tensor(-nd+1,NY+nd,-nd+1,NX+nd,1,NT/DTINV);
            forward_prop_rho_y =  f3tensor(-nd+1,NY+nd,-nd+1,NX+nd,1,NT/DTINV);
        }
        if(WAVETYPE==2 || WAVETYPE==3){
            forward_prop_rho_z =  f3tensor(-nd+1,NY+nd,-nd+1,NX+nd,1,NT/DTINV);
            forward_prop_z_xz =  f3tensor(-nd+1,NY+nd,-nd+1,NX+nd,1,NT/DTINV);
            forward_prop_z_yz =  f3tensor(-nd+1,NY+nd,-nd+1,NX+nd,1,NT/DTINV);
            waveconv_rho_shot_z = matrix(-nd+1,NY+nd,-nd+1,NX+nd);
            waveconv_u_shot_z = matrix(-nd+1,NY+nd,-nd+1,NX+nd);
            waveconv_mu_z = matrix(-nd+1,NY+nd,-nd+1,NX+nd);
            waveconv_rho_s_z = matrix(-nd+1,NY+nd,-nd+1,NX+nd);
            waveconv_u_z = matrix(-nd+1,NY+nd,-nd+1,NX+nd);
            waveconv_rho_z = matrix(-nd+1,NY+nd,-nd+1,NX+nd);
            gradp_u_z = matrix(-nd+1,NY+nd,-nd+1,NX+nd);
            gradp_rho_z = matrix(-nd+1,NY+nd,-nd+1,NX+nd);
        }
        
        gradg_rho = matrix(-nd+1,NY+nd,-nd+1,NX+nd);
        gradp_rho = matrix(-nd+1,NY+nd,-nd+1,NX+nd);
        waveconv_rho = matrix(-nd+1,NY+nd,-nd+1,NX+nd);
        waveconv_rho_s = matrix(-nd+1,NY+nd,-nd+1,NX+nd);
        waveconv_rho_shot = matrix(-nd+1,NY+nd,-nd+1,NX+nd);
        
        if(WOLFE_CONDITION){
            waveconv_old= matrix(-nd+1,NY+nd,-nd+1,NX+nd);
            waveconv_u_old= matrix(-nd+1,NY+nd,-nd+1,NX+nd);
            waveconv_rho_old= matrix(-nd+1,NY+nd,-nd+1,NX+nd);
            
            waveconv_up= matrix(-nd+1,NY+nd,-nd+1,NX+nd);
            waveconv_u_up= matrix(-nd+1,NY+nd,-nd+1,NX+nd);
            waveconv_rho_up= matrix(-nd+1,NY+nd,-nd+1,NX+nd);
        }
        
        if(!ACOUSTIC){
            forward_prop_u =  f3tensor(-nd+1,NY+nd,-nd+1,NX+nd,1,NT/DTINV);
            gradg_u = matrix(-nd+1,NY+nd,-nd+1,NX+nd);
            gradp_u = matrix(-nd+1,NY+nd,-nd+1,NX+nd);
            waveconv_u = matrix(-nd+1,NY+nd,-nd+1,NX+nd);
            waveconv_mu = matrix(-nd+1,NY+nd,-nd+1,NX+nd);
            waveconv_u_shot = matrix(-nd+1,NY+nd,-nd+1,NX+nd);
        }
        
        if(HESSIAN){
            jac_rho =  vector(1,nxnyi*(NTDTINV));
            jac_u =  vector(1,nxnyi*(NTDTINV));
            jac_lam_x =  vector(1,nxnyi*(NTDTINV));
            jac_lam_y =  vector(1,nxnyi*(NTDTINV));
            temp_TS =  vector(1,NTDTINV);
            temp_TS1 =  vector(1,NTDTINV);
            temp_TS2 =  vector(1,NTDTINV);
            temp_TS3 =  vector(1,NTDTINV);
            temp_TS4 =  vector(1,NTDTINV);
            temp_TS5 =  vector(1,NTDTINV);
            temp_conv =  vector(1,NTDTINV);
            temp_conv1 =  vector(1,NTDTINV);
            temp_conv2 =  vector(1,NTDTINV);
            hessian = matrix(-nd+1,NY+nd,-nd+1,NX+nd);
            hessian_u = matrix(-nd+1,NY+nd,-nd+1,NX+nd);
            hessian_rho = matrix(-nd+1,NY+nd,-nd+1,NX+nd);
            hessian_shot = matrix(-nd+1,NY+nd,-nd+1,NX+nd);
            hessian_u_shot = matrix(-nd+1,NY+nd,-nd+1,NX+nd);
            hessian_rho_shot = matrix(-nd+1,NY+nd,-nd+1,NX+nd);
        }
    }
    
    /* Allocate memory for boundary */
    if(FW>0){
        d_x = vector(1,2*FW);
        K_x = vector(1,2*FW);
        alpha_prime_x = vector(1,2*FW);
        a_x = vector(1,2*FW);
        b_x = vector(1,2*FW);
        
        d_x_half = vector(1,2*FW);
        K_x_half = vector(1,2*FW);
        alpha_prime_x_half = vector(1,2*FW);
        a_x_half = vector(1,2*FW);
        b_x_half = vector(1,2*FW);
        
        d_y = vector(1,2*FW);
        K_y = vector(1,2*FW);
        alpha_prime_y = vector(1,2*FW);
        a_y = vector(1,2*FW);
        b_y = vector(1,2*FW);
        
        d_y_half = vector(1,2*FW);
        K_y_half = vector(1,2*FW);
        alpha_prime_y_half = vector(1,2*FW);
        a_y_half = vector(1,2*FW);
        b_y_half = vector(1,2*FW);
        
        if (WAVETYPE==1||WAVETYPE==3){
            psi_sxx_x =  matrix(1,NY,1,2*FW);
            psi_syy_y =  matrix(1,2*FW,1,NX);
            psi_sxy_y =  matrix(1,2*FW,1,NX);
            psi_sxy_x =  matrix(1,NY,1,2*FW);
            psi_vxx   =  matrix(1,NY,1,2*FW);
            psi_vxxs  =  matrix(1,NY,1,2*FW);
            psi_vyy   =  matrix(1,2*FW,1,NX);
            psi_vxy   =  matrix(1,2*FW,1,NX);
            psi_vyx   =  matrix(1,NY,1,2*FW);
        }
        if(WAVETYPE==2||WAVETYPE == 3 ){
            psi_sxz_x =  matrix(1,NY,1,2*FW);
            psi_syz_y =  matrix(1,2*FW,1,NX);
            psi_vzx   =  matrix(1,NY,1,2*FW);
            psi_vzy   =  matrix(1,2*FW,1,NX);
        }
    }
    
    taper_coeff=  matrix(1,NY,1,NX);
    
    
    /* memory allocation for buffer arrays in which the wavefield
     information which is exchanged between neighbouring PEs is stored */
    bufferlef_to_rig = matrix(1,NY,1,fdo3);
    bufferrig_to_lef = matrix(1,NY,1,fdo3);
    buffertop_to_bot = matrix(1,NX,1,fdo3);
    bufferbot_to_top = matrix(1,NX,1,fdo3);
    
    /* Allocate memory to save full seismograms */
    switch (SEISMO){
        case 1 : /* particle velocities only */
            switch (WAVETYPE) {
                case 1:
                    fulldata_vx = matrix(1,ntr_glob,1,NT);
                    fulldata_vy = matrix(1,ntr_glob,1,NT);
                    break;
                    
                case 2:
                    fulldata_vz = matrix(1,ntr_glob,1,NT);
                    break;
                    
                case 3:
                    fulldata_vx = matrix(1,ntr_glob,1,NT);
                    fulldata_vy = matrix(1,ntr_glob,1,NT);
                    fulldata_vz = matrix(1,ntr_glob,1,NT);
                    break;
            }
            break;
        case 2 : /* pressure only */
            fulldata_p = matrix(1,ntr_glob,1,NT);
            break;
        case 3 : /* curl and div only */
            fulldata_div = matrix(1,ntr_glob,1,NT);
            fulldata_curl = matrix(1,ntr_glob,1,NT);
            break;
        case 4 : /* everything */
            switch (WAVETYPE) {
                case 1:
                    fulldata_vx = matrix(1,ntr_glob,1,NT);
                    fulldata_vy = matrix(1,ntr_glob,1,NT);
                    break;
                    
                case 2:
                    fulldata_vz = matrix(1,ntr_glob,1,NT);
                    break;
                    
                case 3:
                    fulldata_vx = matrix(1,ntr_glob,1,NT);
                    fulldata_vy = matrix(1,ntr_glob,1,NT);
                    fulldata_vz = matrix(1,ntr_glob,1,NT);
                    break;
            }
            fulldata_p = matrix(1,ntr_glob,1,NT);
            fulldata_div = matrix(1,ntr_glob,1,NT);
            fulldata_curl = matrix(1,ntr_glob,1,NT);
            break;
        case 5 : /* everything except curl and div*/
            switch (WAVETYPE) {
                case 1:
                    fulldata_vx = matrix(1,ntr_glob,1,NT);
                    fulldata_vy = matrix(1,ntr_glob,1,NT);
                    break;
                    
                case 2:
                    fulldata_vz = matrix(1,ntr_glob,1,NT);
                    break;
                    
                case 3:
                    fulldata_vx = matrix(1,ntr_glob,1,NT);
                    fulldata_vy = matrix(1,ntr_glob,1,NT);
                    fulldata_vz = matrix(1,ntr_glob,1,NT);
                    break;
            }
            fulldata_p = matrix(1,ntr_glob,1,NT);
            break;
            
    }
    if (ntr>0){
        switch (SEISMO){
            case 1 : /* particle velocities only */
                switch (WAVETYPE) {
                    case 1:
                        sectionvx=matrix(1,ntr,1,ns);
                        sectionvy=matrix(1,ntr,1,ns);
                        break;
                    case 2:
                        sectionvz=matrix(1,ntr,1,ns);
                        break;
                    case 3:
                        sectionvx=matrix(1,ntr,1,ns);
                        sectionvy=matrix(1,ntr,1,ns);
                        sectionvz=matrix(1,ntr,1,ns);
                        break;
                }
                break;
            case 2 : /* pressure only */
                sectionp=matrix(1,ntr,1,ns);
                sectionpnp1=matrix(1,ntr,1,ns);
                sectionpn=matrix(1,ntr,1,ns);
                break;
            case 3 : /* curl and div only */
                sectioncurl=matrix(1,ntr,1,ns);
                sectiondiv=matrix(1,ntr,1,ns);
                break;
            case 4 : /* everything */
                switch (WAVETYPE) {
                    case 1:
                        sectionvx=matrix(1,ntr,1,ns);
                        sectionvy=matrix(1,ntr,1,ns);
                        break;
                    case 2:
                        sectionvz=matrix(1,ntr,1,ns);
                        break;
                    case 3:
                        sectionvx=matrix(1,ntr,1,ns);
                        sectionvy=matrix(1,ntr,1,ns);
                        sectionvz=matrix(1,ntr,1,ns);
                        break;
                }
                sectioncurl=matrix(1,ntr,1,ns);
                sectiondiv=matrix(1,ntr,1,ns);
                sectionp=matrix(1,ntr,1,ns);
                break;
            case 5 : /* everything except curl and div*/
                switch (WAVETYPE) {
                    case 1:
                        sectionvx=matrix(1,ntr,1,ns);
                        sectionvy=matrix(1,ntr,1,ns);
                        break;
                    case 2:
                        sectionvz=matrix(1,ntr,1,ns);
                        break;
                    case 3:
                        sectionvx=matrix(1,ntr,1,ns);
                        sectionvy=matrix(1,ntr,1,ns);
                        sectionvz=matrix(1,ntr,1,ns);
                        break;
                }
                sectionp=matrix(1,ntr,1,ns);
                break;
        }
    }
    
    /* Memory for seismic data */
    sectionread=matrix(1,ntr_glob,1,ns);
    sectionpdata=matrix(1,ntr,1,ns);
    sectionpdiff=matrix(1,ntr,1,ns);
    sectionpdiffold=matrix(1,ntr,1,ns);
    switch (WAVETYPE) {
        case 1:
            sectionvxdata=matrix(1,ntr,1,ns);
            sectionvxdiff=matrix(1,ntr,1,ns);
            sectionvxdiffold=matrix(1,ntr,1,ns);
            sectionvydata=matrix(1,ntr,1,ns);
            sectionvydiff=matrix(1,ntr,1,ns);
            sectionvydiffold=matrix(1,ntr,1,ns);
            break;
            
        case 2:
            sectionvzdata=matrix(1,ntr,1,ns);
            sectionvzdiff=matrix(1,ntr,1,ns);
            sectionvzdiffold=matrix(1,ntr,1,ns);
            break;
            
        case 3:
            sectionvxdata=matrix(1,ntr,1,ns);
            sectionvxdiff=matrix(1,ntr,1,ns);
            sectionvxdiffold=matrix(1,ntr,1,ns);
            sectionvydata=matrix(1,ntr,1,ns);
            sectionvydiff=matrix(1,ntr,1,ns);
            sectionvydiffold=matrix(1,ntr,1,ns);
            sectionvzdata=matrix(1,ntr,1,ns);
            sectionvzdiff=matrix(1,ntr,1,ns);
            sectionvzdiffold=matrix(1,ntr,1,ns);
            break;
    }
    
    /* Memory for inversion for source time function */
    if((INV_STF==1)||(TIME_FILT==1) || (TIME_FILT==2)){
        sectionp_conv=matrix(1,ntr_glob,1,NT);
        sectionp_obs=matrix(1,ntr_glob,1,NT);
        source_time_function = vector(1,NT);
        switch (WAVETYPE) {
            case 1:
                sectionvy_conv=matrix(1,ntr_glob,1,NT);
                sectionvy_obs=matrix(1,ntr_glob,1,NT);
                sectionvx_conv=matrix(1,ntr_glob,1,NT);
                sectionvx_obs=matrix(1,ntr_glob,1,NT);
                break;
                
            case 2:
                sectionvz_conv=matrix(1,ntr_glob,1,NT);
                sectionvz_obs=matrix(1,ntr_glob,1,NT);
                break;
                
            case 3:
                sectionvy_conv=matrix(1,ntr_glob,1,NT);
                sectionvy_obs=matrix(1,ntr_glob,1,NT);
                sectionvx_conv=matrix(1,ntr_glob,1,NT);
                sectionvx_obs=matrix(1,ntr_glob,1,NT);
                sectionvz_conv=matrix(1,ntr_glob,1,NT);
                sectionvz_obs=matrix(1,ntr_glob,1,NT);
                break;
        }
    }
    
    /* memory for source position definition */
    srcpos1=fmatrix(1,8,1,1);
    
    /* memory of L2 norm */
    L2t = vector(1,4);
    epst1 = vector(1,3);
    epst2 = vector(1,3);
    epst3 = vector(1,3);
    picked_times = vector(1,ntr);
    
    fprintf(FP," ... memory allocation for PE %d was successfull.\n\n", MYID);
    
    
    /* Holberg coefficients for FD operators*/
    hc = holbergcoeff();
    
    MPI_Barrier(MPI_COMM_WORLD);
    
    /* Reading source positions from SOURCE_FILE */
    srcpos=sources(&nsrc);
    nsrc_glob=nsrc;
    
    if(INVMAT==0&&USE_WORKFLOW){
        read_workflow(FILE_WORKFLOW,&workflow, &workflow_lines);
    }
    
    /* create model grids */
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    if(L){
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        if(!ACOUSTIC){
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            if (READMOD){
                readmod(prho,ppi,pu,ptaus,ptaup,peta);
            }else{
                model(prho,ppi,pu,ptaus,ptaup,peta);
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            }
        }else{
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            if (READMOD){
                readmod_viscac(prho,ppi,ptaup,peta);
            }else{
                model_viscac(prho,ppi,ptaup,peta);
            }
        }
    }else{
        if(!ACOUSTIC){
            if (READMOD){
                readmod_elastic(prho,ppi,pu);
            }else{
                model_elastic(prho,ppi,pu);
            }
        }else{
            if (READMOD){
                readmod_acoustic(prho,ppi);
            }else{
                model_acoustic(prho,ppi);
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            }
        }
    }
    
    /* check if the FD run will be stable and free of numerical dispersion */
    checkfd(FP, prho, ppi, pu, ptaus, ptaup, peta, hc, srcpos, nsrc, recpos, ntr_glob);
    
    /* calculate damping coefficients for CPMLs*/
    if(FW>0)
        PML_pro(d_x, K_x, alpha_prime_x, a_x, b_x, d_x_half, K_x_half, alpha_prime_x_half, a_x_half, b_x_half, d_y, K_y, alpha_prime_y, a_y, b_y, d_y_half, K_y_half, alpha_prime_y_half, a_y_half, b_y_half);
    
    MPI_Barrier(MPI_COMM_WORLD);
    
    if (CHECKPTREAD){
        if (MYID==0){
            time3=MPI_Wtime();
            fprintf(FP," Reading wavefield from check-point file %s \n",CHECKPTFILE);
        }
        
        read_checkpoint(-1, NX+2, -1, NY+2, pvx, pvy, psxx, psyy, psxy);
        MPI_Barrier(MPI_COMM_WORLD);
        if (MYID==0){
            time4=MPI_Wtime();
            fprintf(FP," finished (real time: %4.2f s).\n",time4-time3);
        }
    }
    
    /* comunication initialisation for persistent communication */
    /*comm_ini(bufferlef_to_rig, bufferrig_to_lef, buffertop_to_bot, bufferbot_to_top, req_send, req_rec);*/
    
    snapseis=1;
    snapseis1=1;
    SHOTINC=1;
    RECINC=1;
    
    switch(TIME_FILT){
        case 1: FC=FC_START; break;
            /*read frequencies from file*/
        case 2: FC_EXT=filter_frequencies(&nfrq); FC=FC_EXT[FREQ_NR]; break;
    }
    
    QUELLART_OLD = QUELLART;
    
    nt_out=10000;
    if(!VERBOSE) nt_out=1e5;
    /*------------------------------------------------------------------------------*/
    /*----------- start fullwaveform iteration loop --------------------------------*/
    /*------------------------------------------------------------------------------*/
    
    for(iter=1;iter<=ITERMAX;iter++){  /* fullwaveform iteration loop */
        
        // At each iteration the workflow is applied
        if(USE_WORKFLOW&&(INVMAT==0)){
            
            apply_workflow(workflow,workflow_lines,workflow_line_current,&iter,&FC,wavetype_start,&change_wavetype_iter,&LBFGS_iter_start);
            
        }
        
        if(GRAD_METHOD==2&&(INVMAT==0)){
            
            /* detect a change in inversion process and restart L-BFGS */
            if(iter==INV_RHO_ITER||iter==INV_VP_ITER||iter==INV_VS_ITER){
                LBFGS_iter_start=iter;
                
                if(WOLFE_CONDITION) {
                    /* Restart Step Length search */
                    alpha_SL_old=1;
                }
                
                /* set values */
                FWI_run=1;
                gradient_optimization=1;
            }
            
            /* restart L-BFGS */
            if(iter==LBFGS_iter_start) {
                lbfgs_reset(iter,bfgsnum,bfgspar,bfgsmod1,bfgsgrad1,bfgsscale1);
                
                /* set values */
                FWI_run=1;
                gradient_optimization=1;
            }
            
        }
        
        if (MYID==0){
            time2=MPI_Wtime();
            fprintf(FP,"\n\n\n ------------------------------------------------------------------\n");
            fprintf(FP,"\n\n\n                   TDFWI ITERATION %d \t of %d \n",iter,ITERMAX);
            fprintf(FP,"\n\n\n ------------------------------------------------------------------\n");
        }
        
        countstep=0;
        
        if(GRAD_METHOD==1) {FWI_run=1; steplength_search=0; gradient_optimization=1;}
        
        /*-----------------------------------------------------*/
        /*  While loop for Wolfe step length search            */
        /*-----------------------------------------------------*/
        while(FWI_run || steplength_search || gradient_optimization) {
            
            /*-----------------------------------------------------*/
            /*              Calculate Misfit and gradient          */
            /*-----------------------------------------------------*/
            if(FWI_run){
                /* For the calculation of the material parameters between gridpoints
                 they have to be averaged. For this, values lying at 0 and NX+1,
                 for example, are required on the local grid. These are now copied from the
                 neighbouring grids */
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                if (L){
                    if(!ACOUSTIC){
                        matcopy(prho,ppi,pu,ptaus,ptaup);
                    } else {
                        matcopy_viscac(prho,ppi,ptaup);
                    }
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                }else{
                    if(!ACOUSTIC){
                        matcopy_elastic(prho, ppi, pu);
                    }else{
                        matcopy_acoustic(prho, ppi);
                    }
                }
                
                MPI_Barrier(MPI_COMM_WORLD);
                
                /* MPI split for processors with ntr>0 */
                int myid_ntr, group_id=0, groupsize;
                MPI_Comm	MPI_COMM_NTR;
                
                if (ntr) group_id = 1;
                else group_id = 0;
                MPI_Comm_split(MPI_COMM_WORLD, group_id, MYID, &MPI_COMM_NTR);
                MPI_Comm_rank(MPI_COMM_NTR, &myid_ntr);
                /* end of MPI split for processors with ntr>0 */
                
                
                if(!ACOUSTIC) av_mue(pu,puipjp,puip,pujp,prho);
                av_rho(prho,prip,prjp);
                if (!ACOUSTIC && L) av_tau(ptaus,ptausipjp,tausip,tausjp);
                
                
                /* Preparing memory variables for update_s (viscoelastic) */
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                if (L) {
                    if(!ACOUSTIC){
                        prepare_update_s(etajm,etaip,peta,fipjp,pu,puipjp,ppi,prho,ptaus,ptaup,ptausipjp,f,g,bip,bjm,cip,cjm,dip,d,e);
                    } else {
                        prepare_update_p(etajm,peta,ppi,prho,ptaup,g,bjm,cjm,e);
                    }
                }
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                if(iter==1){
                    
                    /* Calculationg material parameters according to INVMAT1 */
                    for (i=1;i<=NX;i=i+IDX){
                        for (j=1;j<=NY;j=j+IDY){
                            
                            if(INVMAT1==1){
                                
                                Vp0[j][i] = ppi[j][i];
                                if(!ACOUSTIC) Vs0[j][i] = pu[j][i];
                                Rho0[j][i] = prho[j][i];}
                            
                            
                            
                            if(INVMAT1==2){
                                
                                Vp0[j][i] = sqrt((ppi[j][i]+2.0*pu[j][i])*prho[j][i]);
                                Vs0[j][i] = sqrt((pu[j][i])*prho[j][i]);
                                Rho0[j][i] = prho[j][i];
                                
                            }
                            
                            if(INVMAT1==3){
                                
                                Vp0[j][i] = ppi[j][i];
                                Vs0[j][i] = pu[j][i];
                                Rho0[j][i] = prho[j][i];
                                
                            }
                            
                        }
                    }
                    
                    /* ----------------------------- */
                    /* calculate Covariance matrices */
                    /* ----------------------------- */
                    
                    Lcount = 1;
                    Vp_avg = 0.0;
                    if(!ACOUSTIC) Vs_avg = 0.0;
                    rho_avg = 0.0;
                    
                    for (i=1;i<=NX;i=i+IDX){
                        for (j=1;j<=NY;j=j+IDY){
                            
                            /* calculate average Vp, Vs */
                            Vp_avg+=ppi[j][i];
                            if(!ACOUSTIC)  Vs_avg+=pu[j][i];
                            /* calculate average rho */
                            rho_avg+=prho[j][i];
                            
                            Lcount++;
                        }
                    }
                    
                    /* calculate average Vp, Vs and rho of all CPUs*/
                    Lcountsum = 0.0;
                    MPI_Allreduce(&Lcount,&Lcountsum,1,MPI_INT,MPI_SUM,MPI_COMM_WORLD);
                    Lcount=Lcountsum;
                    
                    Vp_sum = 0.0;
                    MPI_Allreduce(&Vp_avg,&Vp_sum,1,MPI_FLOAT,MPI_SUM,MPI_COMM_WORLD);
                    Vp_avg=Vp_sum;
                    
                    if(!ACOUSTIC){
                        Vs_sum = 0.0;
                        MPI_Allreduce(&Vs_avg,&Vs_sum,1,MPI_FLOAT,MPI_SUM,MPI_COMM_WORLD);
                        Vs_avg=Vs_sum;
                    }
                    
                    rho_sum = 0.0;
                    MPI_Allreduce(&rho_avg,&rho_sum,1,MPI_FLOAT,MPI_SUM,MPI_COMM_WORLD);
                    rho_avg=rho_sum;
                    
                    Vp_avg /=Lcount;
                    if(!ACOUSTIC) Vs_avg /=Lcount;
                    rho_avg /=Lcount;
                    
                    if(!ACOUSTIC) if(VERBOSE) printf("MYID = %d \t Vp_avg = %e \t Vs_avg = %e \t rho_avg = %e \n ",MYID,Vp_avg,Vs_avg,rho_avg);
                    else if(VERBOSE) printf("MYID = %d \t Vp_avg = %e \t rho_avg = %e \n ",MYID,Vp_avg,rho_avg);
                    
                    C_vp = Vp_avg*Vp_avg;
                    if(!ACOUSTIC) C_vs = Vs_avg*Vs_avg;
                    C_rho = rho_avg*rho_avg;
                }
                
                /* Open Log File for L2 norm */
                if(INVMAT!=10){
                    if(MYID==0){
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                        if(iter==1){
                            FPL2=fopen(MISFIT_LOG_FILE,"w");
                        }
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                        if(iter>1){FPL2=fopen(MISFIT_LOG_FILE,"a");}
                    }
                }
                
                /* initialization of L2 calculation */
                L2=0.0;
                Lcount=0;
                energy=0.0;
                L2_all_shots=0.0;
                energy_all_shots=0.0;
                killed_traces=0;
                killed_traces_testshots=0;
                
                
                EPSILON=0.0;  /* test step length */
                exchange_par();
                
                /* initialize waveconv matrix*/
                if(WAVETYPE==1||WAVETYPE==3){
                    if(INVMAT==0){
                        for (i=1;i<=NX;i=i+IDX){
                            for (j=1;j<=NY;j=j+IDY){
                                waveconv[j][i]=0.0;
                            }
                        }
                        
                        if(!ACOUSTIC){
                            for (i=1;i<=NX;i=i+IDX){
                                for (j=1;j<=NY;j=j+IDY){
                                    waveconv_u[j][i]=0.0;
                                }
                            }
                        }
                        
                        for (i=1;i<=NX;i=i+IDX){
                            for (j=1;j<=NY;j=j+IDY){
                                waveconv_rho[j][i]=0.0;
                                
                            }
                        }
                    }
                }
                /* initialize waveconv matrix*/
                if(WAVETYPE==2||WAVETYPE==3){
                    if(INVMAT==0){
                        for (i=1;i<=NX;i=i+IDX){
                            for (j=1;j<=NY;j=j+IDY){
                                waveconv_rho_z[j][i]=0.0;
                                waveconv_u_z[j][i]=0.0;
                                
                            }
                        }
                    }
                }
                if(HESSIAN){
                    for (i=1;i<=NX;i=i+IDX){
                        for (j=1;j<=NY;j=j+IDY){
                            hessian[j][i]=0.0;
                            hessian_u[j][i]=0.0;
                            hessian_rho[j][i]=0.0;
                        }
                    }
                }
                
                if((EPRECOND>0)&&(EPRECOND_ITER==iter||(EPRECOND_ITER==0))){
                    for(i=1;i<=NX;i=i+IDX){
                        for(j=1;j<=NY;j=j+IDY){
                            if(WAVETYPE==1||WAVETYPE==3) We_sum[j][i]=0.0;
                            if(WAVETYPE==2||WAVETYPE==3) We_sum_SH[j][i]=0.0;
                        }
                    }
                }
                
                if(HESSIAN && TRKILL){ /* reading trace kill information */
                    kill_tmp = imatrix(1,ntr_glob,1,nsrc_glob);
                    
                    ftracekill=fopen(TRKILL_FILE,"r");
                    if (ftracekill==NULL) err(" Trace kill file could not be opened!");
                    for(i=1;i<=ntr_glob;i++){
                        for(j=1;j<=nsrc_glob;j++){
                            fscanf(ftracekill,"%d",&kill_tmp[i][j]);
                        }
                    }
                    fclose(ftracekill);
                } /* end if(TRKILL)*/
                
                
                
                itestshot=TESTSHOT_START;
                swstestshot=0;
                
                if(INVTYPE==2){
                    if (RUN_MULTIPLE_SHOTS) nshots=nsrc; else nshots=1;
                    
                    /*------------------------------------------------------------------------------*/
                    /*----------- Start of loop over shots -----------------------------------------*/
                    /*------------------------------------------------------------------------------*/
                    
                    for (ishot=1;ishot<=nshots;ishot+=SHOTINC){
                        /*for (ishot=1;ishot<=1;ishot+=1){*/
                        QUELLART = QUELLART_OLD;
                        
                        if (INV_STF==1 && WAVETYPE !=1) {
                            fprintf(FP,"\n==================================================================================\n");
                            fprintf(FP,"\n====== Source time function inversion and WAVETYPE !=1 not supported    ==========\n");
                            fprintf(FP,"\n==================================================================================\n");
                            err(" NO STFI and WAVETYPE !=1 ");
                        }
                        
                        /*------------------------------------------------------------------------------*/
                        /*----------- Start of inversion of source time function -----------------------*/
                        /*------------------------------------------------------------------------------*/
                        
                        if((INV_STF==1)&&((iter==1)||(s==1))){
                            fprintf(FP,"\n==================================================================================\n");
                            fprintf(FP,"\n MYID=%d *****  Forward simulation for inversion of source time function ******** \n",MYID);
                            fprintf(FP,"\n MYID=%d * Starting simulation (forward model) for shot %d of %d. Iteration %d ** \n",MYID,ishot,nshots,iter);
                            fprintf(FP,"\n==================================================================================\n\n");
                            
                            for (nt=1;nt<=8;nt++) srcpos1[nt][1]=srcpos[nt][ishot];
                            
                            if (RUN_MULTIPLE_SHOTS){
                                /* find this single source positions on subdomains */
                                if (nsrc_loc>0) free_matrix(srcpos_loc,1,8,1,1);
                                srcpos_loc=splitsrc(srcpos1,&nsrc_loc, 1);
                            }else{
                                /* Distribute multiple source positions on subdomains */
                                srcpos_loc = splitsrc(srcpos,&nsrc_loc, nsrc);
                            }
                            
                            if((QUELLART==7)||(QUELLART==3))err("QUELLART==7 or QUELLART==3 isn't possible with INV_STF==1");
                            MPI_Barrier(MPI_COMM_WORLD);
                            /* calculate wavelet for each source point */
                            signals=NULL;
                            signals=wavelet(srcpos_loc,nsrc_loc,ishot,0);
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                            /* initialize wavefield with zero */
                            if (L){
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                                if(!ACOUSTIC) {
                                    zero_fdveps_visc(-nd+1,NY+nd,-nd+1,NX+nd,pvx,pvy,pvz,psxx,psyy,psxy,psxz,psyz,ux,uy,uxy,pvxp1,pvyp1,psi_sxx_x,psi_sxy_x,psi_sxz_x,psi_vxx,psi_vyx,psi_vzx,psi_syy_y,psi_sxy_y,psi_syz_y,psi_vyy,psi_vxy,psi_vzy,psi_vxxs,pr,pp,pq,pt,po);
                                } else {
                                    zero_fdveps_viscac(-nd+1, NY+nd, -nd+1, NX+nd, pvx, pvy, psp, pvxp1, pvyp1, psi_sxx_x, psi_sxy_x, psi_vxx, psi_vyx, psi_syy_y, psi_sxy_y, psi_vyy, psi_vxy, psi_vxxs, pp);
                                }
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                            }else{
                                if(!ACOUSTIC)
                                    zero_fdveps(-nd+1,NY+nd,-nd+1,NX+nd,pvx,pvy,pvz,psxx,psyy,psxy,psxz,psyz,ux,uy,uxy,pvxp1,pvyp1,psi_sxx_x,psi_sxy_x,psi_sxz_x,psi_vxx,psi_vyx,psi_vzx,psi_syy_y,psi_sxy_y,psi_syz_y,psi_vyy,psi_vxy,psi_vzy,psi_vxxs);
                                else
                                    zero_fdveps_ac(-nd+1,NY+nd,-nd+1,NX+nd,pvx,pvy,psp,pvxp1,pvyp1,psi_sxx_x,psi_sxy_x,psi_vxx,psi_vyx,psi_syy_y,psi_sxy_y,psi_vyy,psi_vxy,psi_vxxs);
                            }
                            
                            
                            /*----------------------  loop over timesteps (forward model) ------------------*/
                            
                            lsnap=iround(TSNAP1/DT);
                            lsamp=NDT;
                            nsnap=0;
                            
                            hin=1;
                            hin1=1;
                            
                            imat=1;
                            imat1=1;
                            imat2=1;
                            hi=1;
                            
                            for (nt=1;nt<=NT;nt++){
                                
                                infoout = !(nt%nt_out);
                                /* Check if simulation is still stable */
                                if (isnan(pvy[NY/2][NX/2])) {
                                    fprintf(FP,"\n Time step: %d; pvy: %f \n",nt,pvy[NY/2][NX/2]);
                                    err(" Simulation is unstable !");}
                                
                                
                                if (MYID==0){
                                    if (infoout)  fprintf(FP,"\n Computing timestep %d of %d \n",nt,NT);
                                    time3=MPI_Wtime();
                                }
                                
                                if(!ACOUSTIC)
                                    update_v_PML(1, NX, 1, NY, nt, pvx, pvxp1, pvxm1, pvy, pvyp1, pvym1, uttx, utty, psxx, psyy, psxy, prip, prjp, srcpos_loc,signals,signals,nsrc_loc,absorb_coeff,hc,infoout,0, K_x, a_x,b_x, K_x_half, a_x_half, b_x_half, K_y, a_y, b_y, K_y_half, a_y_half, b_y_half, psi_sxx_x, psi_syy_y, psi_sxy_y, psi_sxy_x);
                                else
                                    update_v_acoustic_PML(1, NX, 1, NY, nt, pvx, pvxp1, pvxm1, pvy, pvyp1, pvym1, psp, prip, prjp, srcpos_loc,signals,signals,nsrc_loc,absorb_coeff,hc,infoout,0, K_x_half, a_x_half, b_x_half, K_y_half, a_y_half, b_y_half, psi_sxx_x, psi_syy_y);
                                
                                if (MYID==0){
                                    time4=MPI_Wtime();
                                    time_av_v_update+=(time4-time3);
                                    if (infoout)  fprintf(FP," particle velocity exchange between PEs ...");
                                }
                                
                                /* exchange of particle velocities between PEs */
                                exchange_v(pvx,pvy,pvz, bufferlef_to_rig, bufferrig_to_lef, buffertop_to_bot, bufferbot_to_top, req_send, req_rec,wavetype_start);
                                
                                if (MYID==0){
                                    time5=MPI_Wtime();
                                    time_av_v_exchange+=(time5-time4);
                                    if (infoout)  fprintf(FP," finished (real time: %4.2f s).\n",time5-time4);
                                }
                                
                                if (L) {   /* viscoelastic */
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                                    if(!ACOUSTIC) {
                                        update_s_visc_PML(1, NX, 1, NY, pvx, pvy, ux, uy, uxy, uyx, psxx, psyy, psxy, ppi, pu, puipjp, prho, hc, infoout,pr, pp, pq, fipjp, f, g, bip, bjm, cip, cjm, d, e, dip,K_x, a_x, b_x, K_x_half, a_x_half, b_x_half, K_y, a_y, b_y, K_y_half, a_y_half, b_y_half, psi_vxx, psi_vyy, psi_vxy, psi_vyx);
                                    }else{
                                        update_p_visc_PML(1, NX, 1, NY, pvx, pvy, psp, ppi, prho, hc, infoout, pp, g, bjm, cjm, e, K_x, a_x, b_x, K_x_half, a_x_half, b_x_half, K_y, a_y, b_y, K_y_half, a_y_half, b_y_half, psi_vxx, psi_vyy, psi_vxy, psi_vyx);
                                    }
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                                }else{
                                    if(!ACOUSTIC)
                                        update_s_elastic_PML(1, NX, 1, NY, pvx, pvy, ux, uy, uxy, uyx, psxx, psyy, psxy, ppi, pu, puipjp, absorb_coeff, prho, hc, infoout,K_x, a_x, b_x, K_x_half, a_x_half, b_x_half, K_y, a_y, b_y, K_y_half, a_y_half, b_y_half, psi_vxx, psi_vyy, psi_vxy, psi_vyx);
                                    else
                                        update_p_PML(1, NX, 1, NY, pvx, pvy, psp, ppi, absorb_coeff, prho, hc, infoout, K_x, a_x, b_x, K_x_half, a_x_half, b_x_half, K_y, a_y, b_y, K_y_half, a_y_half, b_y_half, psi_vxx, psi_vyy, psi_vxy, psi_vyx);
                                }
                                
                                /* explosive source */
                                if ((!CHECKPTREAD)&&(QUELLTYP==1))
                                    psource(nt,psxx,psyy,psp,srcpos_loc,signals,nsrc_loc,0);
                                
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                                if ((FREE_SURF) && (POS[2]==0)){
                                    if (!ACOUSTIC){
                                        if (L){    /* viscoelastic */
                                            surface_PML(1, pvx, pvy, psxx, psyy, psxy,psyz, pp, pq, ppi, pu, prho, ptaup, ptaus, etajm, peta, hc, K_x, a_x, b_x, psi_vxxs, ux, uy, uxy);
                                        }else{      /* elastic */
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                                            surface_elastic_PML(1, pvx, pvy, psxx, psyy, psxy,psyz, ppi, pu, prho, hc, K_x, a_x, b_x, psi_vxxs, ux, uy, uxy,uyz,psxz,uxz);
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                                        }
                                    } else { /* viscoelastic and elastic ACOUSTIC */
                                        surface_acoustic_PML(1, psp);
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                                    }
                                }
                                
                                
                                if (MYID==0){
                                    time6=MPI_Wtime();
                                    time_av_s_update+=(time6-time5);
                                    if (infoout)  fprintf(FP," stress exchange between PEs ...");
                                }
                                
                                
                                /* stress exchange between PEs */
                                if(!ACOUSTIC)
                                    exchange_s(psxx,psyy,psxy,psxz,psyz,bufferlef_to_rig, bufferrig_to_lef,buffertop_to_bot, bufferbot_to_top,req_send, req_rec,wavetype_start);
                                else
                                    exchange_p(psp,bufferlef_to_rig, bufferrig_to_lef,buffertop_to_bot, bufferbot_to_top,req_send, req_rec);
                                
                                if (MYID==0){
                                    time7=MPI_Wtime();
                                    time_av_s_exchange+=(time7-time6);
                                    if (infoout)  fprintf(FP," finished (real time: %4.2f s).\n",time7-time6);
                                }
                                
                                /* store amplitudes at receivers in section-arrays */
                                if (SEISMO){
                                    seismo_ssg(nt, ntr, recpos_loc, sectionvx, sectionvy,sectionvz,sectionp, sectioncurl, sectiondiv,pvx, pvy,pvz, psxx, psyy, psp, ppi, pu, hc);
                                    /*lsamp+=NDT;*/
                                }
                                
                                
                                if(nt==hin1){
                                    
                                    if(INVMAT==0){
                                        for (i=1;i<=NX;i=i+IDXI){
                                            for (j=1;j<=NY;j=j+IDYI){
                                                forward_prop_rho_x[j][i][hin]=pvxp1[j][i];
                                                forward_prop_rho_y[j][i][hin]=pvyp1[j][i];
                                            }
                                        }
                                        
                                        /* save snapshots from forward model */
                                        if(!ACOUSTIC){
                                            for (i=1;i<=NX;i=i+IDXI){
                                                for (j=1;j<=NY;j=j+IDYI){
                                                    if(VELOCITY==0){
                                                        forward_prop_x[j][i][hin]=psxx[j][i];
                                                        forward_prop_y[j][i][hin]=psyy[j][i];
                                                    } else {
                                                        forward_prop_x[j][i][hin]=ux[j][i];
                                                        forward_prop_y[j][i][hin]=uy[j][i];}
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                                                    // 	    				forward_prop_x[imat]=ux[j][i];
                                                    // 	    				forward_prop_y[imat]=uy[j][i];}
                                                    
                                                    // 	    		imat++;
                                                }
                                            }
                                        }else{
                                            for (i=1;i<=NX;i=i+IDXI){
                                                for (j=1;j<=NY;j=j+IDYI){
                                                    forward_prop_p[j][i][hin]=psp[j][i];
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                                                }
                                            }
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                                        }
                                        if(!ACOUSTIC){
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                                            for (i=1;i<=NX;i=i+IDXI){
                                                for (j=1;j<=NY;j=j+IDYI){
                                                    if(VELOCITY==0){
                                                        forward_prop_u[j][i][hin]=psxy[j][i];}
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                                                    // 	    				forward_prop_u[imat2]=psxy[j][i];}
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                                                    else{
                                                        forward_prop_u[j][i][hin]=uxy[j][i];}
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                                                    // 	    				forward_prop_u[imat2]=uxy[j][i];}
                                                    // 	    imat2++;
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                                                }
                                            }
                                        }
                                        
                                        hin++;
                                        hin1=hin1+DTINV;
                                        
                                    }
                                    DTINV_help[nt]=1;
                                    
                                }
                                
                                /* WRITE SNAPSHOTS TO DISK */
                                if ((SNAP) && (nt==lsnap) && (nt<=TSNAP2/DT)){
                                    snap(FP,nt,++nsnap,pvx,pvy,psxx,psyy,psp,pu,ppi,hc,ishot);
                                    lsnap=lsnap+iround(TSNAPINC/DT);
                                }
                                
                                
                                if (MYID==0){
                                    time8=MPI_Wtime();
                                    time_av_timestep+=(time8-time3);
                                    if (infoout)  fprintf(FP," total real time for timestep %d : %4.2f s.\n",nt,time8-time3);
                                }
                                
                                
                            }/*--------------------  End  of loop over timesteps (forward model) ----------*/
                            
                            switch (SEISMO){
                                    
                                case 1 : 	/* particle velocities only */
                                    catseis(sectionvx, fulldata_vx, recswitch, ntr_glob, MPI_COMM_WORLD);
                                    catseis(sectionvy, fulldata_vy, recswitch, ntr_glob, MPI_COMM_WORLD);
                                    if(WAVETYPE==2 || WAVETYPE==3) {
                                        catseis(sectionvz, fulldata_vz, recswitch, ntr_glob, MPI_COMM_WORLD);
                                    }
                                    if (MYID==0){
                                        saveseis_glob(FP,fulldata_vx,fulldata_vy,fulldata_vz,fulldata_p,fulldata_curl,fulldata_div,recpos,recpos_loc,ntr_glob,srcpos,ishot,ns,iter);}
                                    break;
                                    
                                case 2 :	/* pressure only */
                                    catseis(sectionp, fulldata_p, recswitch, ntr_glob, MPI_COMM_WORLD);
                                    if (MYID==0) saveseis_glob(FP,fulldata_vx,fulldata_vy,fulldata_vz,fulldata_p,fulldata_curl,fulldata_div,recpos,recpos_loc,ntr_glob,srcpos,ishot,ns,iter);
                                    break;
                                    
                                case 3 : 	/* curl and div only */
                                    catseis(sectiondiv, fulldata_div, recswitch, ntr_glob, MPI_COMM_WORLD);
                                    catseis(sectioncurl, fulldata_curl, recswitch, ntr_glob, MPI_COMM_WORLD);
                                    if (MYID==0) saveseis_glob(FP,fulldata_vx,fulldata_vy,fulldata_vz,fulldata_p,fulldata_curl,fulldata_div,recpos,recpos_loc,ntr_glob,srcpos,ishot,ns,iter);
                                    break;
                                    
                                case 4 :	/* everything */
                                    catseis(sectionvx, fulldata_vx, recswitch, ntr_glob, MPI_COMM_WORLD);
                                    catseis(sectionvy, fulldata_vy, recswitch, ntr_glob, MPI_COMM_WORLD);
                                    catseis(sectionp, fulldata_p, recswitch, ntr_glob, MPI_COMM_WORLD);
                                    if(WAVETYPE==2 || WAVETYPE==3) {
                                        catseis(sectionvz, fulldata_vz, recswitch, ntr_glob, MPI_COMM_WORLD);
                                    }
                                    catseis(sectiondiv, fulldata_div, recswitch, ntr_glob, MPI_COMM_WORLD);
                                    catseis(sectioncurl, fulldata_curl, recswitch, ntr_glob, MPI_COMM_WORLD);
                                    if (MYID==0) saveseis_glob(FP,fulldata_vx,fulldata_vy,fulldata_vz,fulldata_p,fulldata_curl,fulldata_div,recpos,recpos_loc,ntr_glob,srcpos,ishot,ns,iter);
                                    break;
                                    
                                case 5 :	/* everything except curl and div*/
                                    catseis(sectionvx, fulldata_vx, recswitch, ntr_glob, MPI_COMM_WORLD);
                                    catseis(sectionvy, fulldata_vy, recswitch, ntr_glob, MPI_COMM_WORLD);
                                    if(WAVETYPE==2 || WAVETYPE==3) {
                                        catseis(sectionvz, fulldata_vz, recswitch, ntr_glob, MPI_COMM_WORLD);
                                    }
                                    catseis(sectionp, fulldata_p, recswitch, ntr_glob, MPI_COMM_WORLD);
                                    if (MYID==0) saveseis_glob(FP,fulldata_vx,fulldata_vy,fulldata_vz,fulldata_p,fulldata_curl,fulldata_div,recpos,recpos_loc,ntr_glob,srcpos,ishot,ns,iter);
                                    break;
                                    
                            } /* end of switch (SEISMO) */
                            
                            /* end of Forward simulation for inversion of source time function */
                            
                            /*----------- Start of inversion of source time function -------------*/
                            if((TIME_FILT==1) ||(TIME_FILT==2)){
                                
                                if (INVMAT==0){
                                    if((INV_STF==1)&&((iter==1)||(s==1))){
                                        
                                        if (nsrc_loc>0){
                                            
                                            /*time domain filtering of the observed data sectionvy_obs */
                                            if ((QUELLTYPB==1)|| (QUELLTYPB==2)){
                                                inseis(fprec,ishot,sectionvy_obs,ntr_glob,ns,2,iter);
                                                timedomain_filt(sectionvy_obs,FC,ORDER,ntr_glob,ns,1);
                                            }
                                            if (QUELLTYPB==4){
                                                inseis(fprec,ishot,sectionp_obs,ntr_glob,ns,9,iter);
                                                timedomain_filt(sectionp_obs,FC,ORDER,ntr_glob,ns,1);
                                            }
                                            
                                            printf("\n ====================================================================================================== \n");
                                            printf("\n Time Domain Filter is used for the inversion: lowpass filter, corner frequency of %.2f Hz, order %d\n",FC,ORDER);
                                            printf("\n ====================================================================================================== \n");
                                            
                                            if(iter==1){
                                                printf("\n ====================================================== \n");
                                                printf("\n MYID = %d: STF inversion at first iteration \n",MYID);
                                            }
                                            else{
                                                printf("\n ================================================================================================ \n");
                                                printf("\n MYID = %d: STF inversion because of frequency step at the end of the last iteration \n",MYID);
                                            }
                                            
                                            if ((QUELLTYPB==1)|| (QUELLTYPB==2)){
                                                stf(FP,fulldata_vy,sectionvy_obs,sectionvy_conv,source_time_function,recpos,recpos_loc,ntr_glob,ntr,srcpos,ishot,ns,iter,nsrc_glob,FC);
                                            }
                                            if (QUELLTYPB==4){
                                                stf(FP,fulldata_p,sectionp_obs,sectionp_conv,source_time_function,recpos,recpos_loc,ntr_glob,ntr,srcpos,ishot,ns,iter,nsrc_glob,FC);
                                            }
                                        }
                                    }
                                }
                            }
                            
                            else{
                                if (INVMAT==0){
                                    if((INV_STF==1)&&(iter==N_STF_START)){
                                        
                                        if(ishot==nshots){
                                            N_STF_START=N_STF_START+N_STF;
                                        }
                                        
                                        if (nsrc_loc>0){
                                            printf("\n ====================================================== \n");
                                            printf("\n MYID = %d: STF inversion due to the increment N_STF \n",MYID);
                                            
                                            if ((QUELLTYPB==1)|| (QUELLTYPB==2)){
                                                inseis(fprec,ishot,sectionvy_obs,ntr_glob,ns,2,iter);
                                            }
                                            if (QUELLTYPB==4){
                                                inseis(fprec,ishot,sectionp_obs,ntr_glob,ns,9,iter);
                                            }
                                            
                                            if ((QUELLTYPB==1)|| (QUELLTYPB==2)){
                                                stf(FP,fulldata_vy,sectionvy_obs,sectionvy_conv,source_time_function,recpos,recpos_loc,ntr_glob,ntr,srcpos,ishot,ns,iter,nsrc_glob,FC);
                                            }
                                            if (QUELLTYPB==4){
                                                stf(FP,fulldata_p,sectionp_obs,sectionp_conv,source_time_function,recpos,recpos_loc,ntr_glob,ntr,srcpos,ishot,ns,iter,nsrc_glob,FC);
                                            }
                                        }
                                    }
                                }
                            }
                            
                            
                            MPI_Barrier(MPI_COMM_WORLD);
                            
                            
                        }
                        
                        /*------------------------------------------------------------------------------*/
                        /*----------- End of inversion of source time function -------------------------*/
                        /*------------------------------------------------------------------------------*/
                        
                        fprintf(FP,"\n==================================================================================\n");
                        fprintf(FP,"\n MYID=%d * Starting simulation (forward model) for shot %d of %d. Iteration %d ** \n",MYID,ishot,nshots,iter);
                        fprintf(FP,"\n==================================================================================\n\n");
                        
                        for (nt=1;nt<=8;nt++) srcpos1[nt][1]=srcpos[nt][ishot];
                        
                        /*-----------------------------------*/
                        /* determine source position on grid */
                        /*-----------------------------------*/
                        if (RUN_MULTIPLE_SHOTS){
                            /* find this single source positions on subdomains */
                            if (nsrc_loc>0) free_matrix(srcpos_loc,1,8,1,1);
                            srcpos_loc=splitsrc(srcpos1,&nsrc_loc, 1);
                        }else{
                            /* Distribute multiple source positions on subdomains */
                            srcpos_loc = splitsrc(srcpos,&nsrc_loc, nsrc);
                        }
                        
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                        if(INV_STF){
                            QUELLART=7;
                            fprintf(FP,"\n MYID=%d *****  Due to inversion of source time function QUELLART is switched to 7  ********** \n",MYID);
                            fprintf(FP,"\n MYID=%d *****  Using optimized source time function located in %s.shot%d  ********** \n\n\n",MYID,SIGNAL_FILE,ishot);
                        }
                        
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                        MPI_Barrier(MPI_COMM_WORLD);
                        
                        /*-------------------*/
                        /* calculate wavelet */
                        /*-------------------*/
                        /* calculate wavelet for each source point P SV */
                        if(WAVETYPE==1||WAVETYPE==3){
                            signals=NULL;
                            signals=wavelet(srcpos_loc,nsrc_loc,ishot,0);
                        }
                        /* calculate wavelet for each source point SH */
                        if(WAVETYPE==2||WAVETYPE==3){
                            signals_SH=NULL;
                            signals_SH=wavelet(srcpos_loc,nsrc_loc,ishot,1);
                        }
                        
                        /*------------------------------------------------------------------------------*/
                        /*----------- Start of Time Domain Filtering -----------------------------------*/
                        /*------------------------------------------------------------------------------*/
                        
                        if (((TIME_FILT==1) || (TIME_FILT==2)) && (HESSIAN==0) && (QUELLART!=6) && (INV_STF==0)){
                            fprintf(FP," Time Domain Filter applied: lowpass filter, corner frequency of %.2f Hz, order %d\n",FC,ORDER);
                            
                            /*time domain filtering of the source signal */
                            if(WAVETYPE==1||WAVETYPE==3) timedomain_filt(signals,FC,ORDER,nsrc_loc,ns,1);
                            if(WAVETYPE==2||WAVETYPE==3) timedomain_filt(signals_SH,FC,ORDER,nsrc_loc,ns,1);
                            
                            
                            if(WAVETYPE==1||WAVETYPE==3){
                                if ((QUELLTYPB==1)|| (QUELLTYPB==2)){
                                    /*time domain filtering of the observed data sectionvy_obs */
                                    inseis(fprec,ishot,sectionvy_obs,ntr_glob,ns,2,iter);
                                    timedomain_filt(sectionvy_obs,FC,ORDER,ntr_glob,ns,1);
                                }
                                
                                if ((QUELLTYPB==1)|| (QUELLTYPB==3)){
                                    /*time domain filtering of the observed data sectionvx_obs */
                                    inseis(fprec,ishot,sectionvx_obs,ntr_glob,ns,1,iter);
                                    timedomain_filt(sectionvx_obs,FC,ORDER,ntr_glob,ns,1);
                                }
                                
                                if (QUELLTYPB==4){
                                    /*time domain filtering of the observed data sectionp_obs */
                                    inseis(fprec,ishot,sectionp_obs,ntr_glob,ns,9,iter);
                                    timedomain_filt(sectionp_obs,FC,ORDER,ntr_glob,ns,1);
                                }
                            }
                            
                            if(WAVETYPE==2||WAVETYPE==3){
                                /*time domain filtering of the observed data sectionvx_obs */
                                inseis(fprec,ishot,sectionvz_obs,ntr_glob,ns,10,iter);
                                timedomain_filt(sectionvz_obs,FC,ORDER,ntr_glob,ns,1);
                            }
                            
                        }
                        
                        if(nsrc_loc>0){
                            /* source type is delta pulse */
                            if(QUELLART==6){/*FFT_filt(signals,1.0,1,ns,1);}*/
                                if(WAVETYPE==1||WAVETYPE==3) timedomain_filt(signals,FC_HESSIAN,ORDER_HESSIAN,nsrc_loc,ns,1);
                                if(WAVETYPE==2||WAVETYPE==3) timedomain_filt(signals_SH,FC_HESSIAN,ORDER_HESSIAN,nsrc_loc,ns,1);
                                
                            }
                            
                            if(HESSIAN==1){	/*calculation of Hessian matrix; in this case also the forward modelled wavefields
                                             must be filtered with the Butterworth filter applied to the delta impulse during
                                             the backpropagation*/
                                timedomain_filt(signals,FC_HESSIAN,ORDER_HESSIAN,nsrc_loc,ns,1);}
                            
                            /*char  source_signal_file[STRING_SIZE];
                             sprintf(source_signal_file,"%s_source_signal.%d.su.shot%d", MFILE, MYID,ishot);
                             fprintf(stdout,"\n PE %d outputs source time function in SU format to %s \n ", MYID, source_signal_file);
                             output_source_signal(fopen(source_signal_file,"w"),signals,NT,1);*/
                            
                        }
                        /*------------------------------------------------------------------------------*/
                        /*----------- End of Time Domain Filtering -------------------------------------*/
                        /*------------------------------------------------------------------------------*/
                        
                        MPI_Barrier(MPI_COMM_WORLD);
                        
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                        /* initialize wavefield with zero */
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                        if (L){
                            if(!ACOUSTIC) {
                                zero_fdveps_visc(-nd+1,NY+nd,-nd+1,NX+nd,pvx,pvy,pvz,psxx,psyy,psxy,psxz,psyz,ux,uy,uxy,pvxp1,pvyp1,psi_sxx_x,psi_sxy_x,psi_sxz_x,psi_vxx,psi_vyx,psi_vzx,psi_syy_y,psi_sxy_y,psi_syz_y,psi_vyy,psi_vxy,psi_vzy,psi_vxxs,pr,pp,pq,pt,po);
                            } else {
                                zero_fdveps_viscac(-nd+1, NY+nd, -nd+1, NX+nd, pvx, pvy, psp, pvxp1, pvyp1, psi_sxx_x, psi_sxy_x, psi_vxx, psi_vyx, psi_syy_y, psi_sxy_y, psi_vyy, psi_vxy, psi_vxxs, pp); }
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                        }else{
                            if(!ACOUSTIC)
                                zero_fdveps(-nd+1,NY+nd,-nd+1,NX+nd,pvx,pvy,pvz,psxx,psyy,psxy,psxz,psyz,ux,uy,uxy,pvxp1,pvyp1,psi_sxx_x,psi_sxy_x,psi_sxz_x,psi_vxx,psi_vyx,psi_vzx,psi_syy_y,psi_sxy_y,psi_syz_y,psi_vyy,psi_vxy,psi_vzy,psi_vxxs);
                            else
                                zero_fdveps_ac(-nd+1,NY+nd,-nd+1,NX+nd,pvx,pvy,psp,pvxp1,pvyp1,psi_sxx_x,psi_sxy_x,psi_vxx,psi_vyx,psi_syy_y,psi_sxy_y,psi_vyy,psi_vxy,psi_vxxs);
                        }
                        
                        /*initialize gradient matrices for each shot with zeros PSV*/
                        if(WAVETYPE==1 || WAVETYPE==3) {
                            if(INVMAT==0){
                                for(i=1;i<=NX;i=i+IDX){
                                    for(j=1;j<=NY;j=j+IDY){
                                        waveconv_shot[j][i]=0.0;
                                        waveconv_rho_shot[j][i]=0.0;
                                    }
                                }
                                if(!ACOUSTIC){
                                    for(i=1;i<=NX;i=i+IDX){
                                        for(j=1;j<=NY;j=j+IDY){
                                            waveconv_u_shot[j][i]=0.0;
                                        }
                                    }
                                }
                            }
                        }
                        /*initialize gradient matrices for each shot with zeros SH*/
                        if(WAVETYPE==2 || WAVETYPE==3){
                            if(INVMAT==0){
                                for(i=1;i<=NX;i=i+IDX){
                                    for(j=1;j<=NY;j=j+IDY){
                                        waveconv_rho_shot_z[j][i]=0.0;
                                        waveconv_u_shot_z[j][i]=0.0;
                                    }
                                }
                                
                            }
                        }
                        
                        if((EPRECOND==1)||(EPRECOND==3)&&(EPRECOND_ITER==iter||(EPRECOND_ITER==0))){
                            for(i=1;i<=NX;i=i+IDX){
                                for(j=1;j<=NY;j=j+IDY){
                                    if(WAVETYPE==1 || WAVETYPE==3){
                                        Ws[j][i]=0.0;
                                        Wr[j][i]=0.0;
                                        We[j][i]=0.0;
                                    }
                                    if(WAVETYPE==2 || WAVETYPE==3){
                                        Ws_SH[j][i]=0.0;
                                        Wr_SH[j][i]=0.0;
                                        We_SH[j][i]=0.0;
                                    }
                                }
                            }
                        }
                        
                        
                        if(HESSIAN){
                            h=1;
                            for (nt=1;nt<=NT;nt=nt+DTINV){
                                for (i=1;i<=NX;i=i+IDX){
                                    for (j=1;j<=NY;j=j+IDY){
                                        jac_lam_x[h]=0.0;
                                        jac_lam_y[h]=0.0;
                                        jac_u[h]=0.0;
                                        jac_rho[h]=0.0;
                                        h++;
                                    }
                                }
                            }
                            
                            for(i=1;i<=NX;i=i+IDX){
                                for(j=1;j<=NY;j=j+IDY){
                                    hessian_shot[j][i]=0.0;
                                    hessian_u_shot[j][i]=0.0;
                                    hessian_rho_shot[j][i]=0.0;
                                }
                            }
                        }
                        
                        lsnap=iround(TSNAP1/DT); lsamp=NDT; nsnap=0;
                        hin=1; hin1=1;
                        imat=1; imat1=1; imat2=1; hi=1;
                        
                        if((!VERBOSE)&&(MYID==0)) fprintf(FP,"\n ****************************************\n ");
                        
                        /*------------------------------------------------------------------------------*/
                        /*----------------------  start loop over timesteps (forward model) ------------*/
                        /*------------------------------------------------------------------------------*/
                        for (nt=1;nt<=NT;nt++){
                            
                            // Ratio to give output to stout
                            infoout = !(nt%nt_out);
                            
                            if((!VERBOSE)&&(MYID==0)) if(!(nt%(NT/40))) fprintf(FP,"*");
                            
                            /* Check if simulation is still stable P and SV */
                            if (WAVETYPE==1 || WAVETYPE==3) {
                                if (isnan(pvy[NY/2][NX/2])) {
                                    fprintf(FP,"\n Time step: %d; pvy: %f \n",nt,pvy[NY/2][NX/2]);
                                    err(" Simulation is unstable !");
                                }
                            }
                            
                            /* Check if simulation is still stable SH */
                            if (WAVETYPE==2 || WAVETYPE==3) {
                                if (isnan(pvz[NY/2][NX/2])) {
                                    fprintf(FP,"\n Time step: %d; pvy: %f \n",nt,pvy[NY/2][NX/2]);
                                    err(" Simulation is unstable !");
                                }
                            }
                            
                            
                            
                            if (MYID==0){
                                if (infoout)  fprintf(FP,"\n Computing timestep %d of %d \n",nt,NT);
                                time3=MPI_Wtime();
                            }
                            
                            
                            /* update of particle velocities */
                            if(!ACOUSTIC) {
                                if (WAVETYPE==1 || WAVETYPE==3) {
                                    update_v_PML(1, NX, 1, NY, nt, pvx, pvxp1, pvxm1, pvy, pvyp1, pvym1, uttx, utty, psxx, psyy, psxy, prip, prjp, srcpos_loc,signals,signals,nsrc_loc,absorb_coeff,hc,infoout,0, K_x, a_x, b_x, K_x_half, a_x_half, b_x_half, K_y, a_y, b_y, K_y_half, a_y_half, b_y_half, psi_sxx_x, psi_syy_y, psi_sxy_y, psi_sxy_x);
                                }
                                
                                if (WAVETYPE==2 || WAVETYPE==3) {
                                    update_v_PML_SH(1, NX, 1, NY, nt, pvz, pvzp1, pvzm1, psxz, psyz,prjp, srcpos_loc, signals, signals_SH, nsrc_loc, absorb_coeff,hc,infoout,0, K_x, a_x, b_x, K_x_half, a_x_half, b_x_half, K_y, a_y, b_y, K_y_half, a_y_half, b_y_half, psi_sxz_x, psi_syz_y);
                                }
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                            } else {
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                                update_v_acoustic_PML(1, NX, 1, NY, nt, pvx, pvxp1, pvxm1, pvy, pvyp1, pvym1, psp, prip, prjp, srcpos_loc,signals,signals,nsrc_loc,absorb_coeff,hc,infoout,0, K_x_half, a_x_half, b_x_half, K_y_half, a_y_half, b_y_half, psi_sxx_x, psi_syy_y);
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                            }
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                            if (MYID==0){
                                time4=MPI_Wtime();
                                time_av_v_update+=(time4-time3);
                                if (infoout)  fprintf(FP," particle velocity exchange between PEs ...");
                            }
                            
                            /* exchange of particle velocities between PEs */
                            exchange_v(pvx,pvy,pvz, bufferlef_to_rig, bufferrig_to_lef, buffertop_to_bot, bufferbot_to_top, req_send, req_rec,wavetype_start);
                            
                            if (MYID==0){
                                time5=MPI_Wtime();
                                time_av_v_exchange+=(time5-time4);
                                if (infoout)  fprintf(FP," finished (real time: %4.2f s).\n",time5-time4);
                            }
                            
                            if (L) {   /* viscoelastic */
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                                if (WAVETYPE==1 || WAVETYPE==3) {
                                    if(!ACOUSTIC) {
                                        update_s_visc_PML(1, NX, 1, NY, pvx, pvy, ux, uy, uxy, uyx, psxx, psyy, psxy, ppi, pu, puipjp, prho, hc, infoout, pr, pp, pq, fipjp, f, g, bip, bjm, cip, cjm, d, e, dip, K_x, a_x, b_x, K_x_half, a_x_half, b_x_half, K_y, a_y, b_y, K_y_half, a_y_half, b_y_half, psi_vxx, psi_vyy, psi_vxy, psi_vyx);
                                    }else{
                                        update_p_visc_PML(1, NX, 1, NY, pvx, pvy, psp, ppi, prho, hc, infoout, pp, g, bjm, cjm, e, K_x, a_x, b_x, K_x_half, a_x_half, b_x_half, K_y, a_y, b_y, K_y_half, a_y_half, b_y_half, psi_vxx, psi_vyy, psi_vxy, psi_vyx);
                                    }
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                                }
                                if (WAVETYPE==2 || WAVETYPE==3) {
                                    update_s_visc_PML_SH(1, NX, 1, NY, pvz, psxz, psyz, pt, po, puip, pujp, tausip, tausjp, bip, bjm, cip, cjm, etajm, etaip, hc,infoout, K_x, a_x, b_x, K_x_half, a_x_half, b_x_half, K_y, a_y, b_y, K_y_half, a_y_half, b_y_half,psi_vzx, psi_vzy);
                                }
                            } else {   /* elastic */
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                                if (WAVETYPE==1 || WAVETYPE==3) {
                                    if(!ACOUSTIC) {
                                        update_s_elastic_PML(1, NX, 1, NY, pvx, pvy, ux, uy, uxy, uyx, psxx, psyy, psxy, ppi, pu, puipjp, absorb_coeff, prho, hc, infoout, K_x, a_x, b_x, K_x_half, a_x_half, b_x_half, K_y, a_y, b_y, K_y_half, a_y_half, b_y_half, psi_vxx, psi_vyy, psi_vxy, psi_vyx);
                                    } else {
                                        update_p_PML(1, NX, 1, NY, pvx, pvy, psp, ppi, absorb_coeff, prho, hc, infoout, K_x, a_x, b_x, K_x_half, a_x_half, b_x_half, K_y, a_y, b_y, K_y_half, a_y_half, b_y_half, psi_vxx, psi_vyy, psi_vxy, psi_vyx);
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                                    }
                                }
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                                if (WAVETYPE==2 || WAVETYPE==3) {
                                    update_s_elastic_PML_SH(1, NX, 1, NY, pvz,psxz,psyz,uxz,uyz,hc,infoout, K_x, a_x, b_x, K_x_half, a_x_half, b_x_half, K_y, a_y, b_y, K_y_half, a_y_half, b_y_half,psi_vzx, psi_vzy,puipjp,pu,prho);
                                }
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                            }
                            
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                            /* explosive source */
                            if ((!CHECKPTREAD)&&(QUELLTYP==1)&&(WAVETYPE==1||WAVETYPE==3))
                                psource(nt,psxx,psyy,psp,srcpos_loc,signals,nsrc_loc,0);
                            
                            /* apply free surface */
                            if ((FREE_SURF) && (POS[2]==0)){
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                                if (L) {
                                    /* viscoelastic */
                                    if(!ACOUSTIC) {
                                        surface_PML(1, pvx, pvy, psxx, psyy, psxy,psyz, pp, pq, ppi, pu, prho, ptaup, ptaus, etajm, peta, hc, K_x, a_x, b_x, psi_vxxs, ux, uy, uxy);
                                    }else{
                                        surface_acoustic_PML(1, psp);
                                    }
                                }else{
                                    /* elastic */
                                    if(!ACOUSTIC) {
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                                        surface_elastic_PML(1, pvx, pvy, psxx, psyy, psxy,psyz, ppi, pu, prho, hc, K_x, a_x, b_x, psi_vxxs, ux, uy, uxy,uyz, psxz,uxz);
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                                    }else{
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                                        surface_acoustic_PML(1, psp);
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                                    }
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