IFOS2D.c 257 KB
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/*-----------------------------------------------------------------------------------------
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 * Copyright (C) 2016  For the list of authors, see file AUTHORS.
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 *
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 * This file is part of IFOS.
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 *
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 * IFOS is free software: you can redistribute it and/or modify
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 * 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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 * IFOS is distributed in the hope that it will be useful,
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 * 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
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 * along with IFOS. 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 IFOS Version 2.0.3
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 * Inversion of Full Observerd Seismograms
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 *
 *  ----------------------------------------------------------------------*/
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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 */
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    int ns, nseismograms=0, nt, nd, fdo3, j, i, iter, h, infoout, SHOTINC,  hin, hin1, do_stf=0;
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    int NTDTINV, nxny, nxnyi, imat, imat1, imat2, IDXI, IDYI, hi, NTST, NTSTI;
    int lsnap, nsnap=0, lsamp=0, buffsize,  swstestshot, snapseis, snapseis1;
    int ntr=0, ntr_loc=0, ntr_glob=0, nsrc=0, nsrc_loc=0, nsrc_glob=0, ishot, irec, nshots=0, nshots1, Lcount, itest, itestshot;
    
    float muss, lamss;
    float memdyn, memmodel, memseismograms, membuffer, memtotal, eps_scale;
    float fac1, fac2;
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    float opteps_vp, opteps_vs, opteps_rho, Vp_avg, C_vp, Vs_avg, C_vs, rho_avg, C_rho, vshor_avg, C_vshor;
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    float memfwt, memfwt1, memfwtdata;
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    char *buff_addr, ext[10], *fileinp;
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    char jac[225];
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    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;
    
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    float L2, L2sum, L2_all_shots, L2sum_all_shots, *L2t, alphanom, alphadenom;
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    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;
    
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    float energy, energy_sum, energy_all_shots, energy_sum_all_shots = 0.0;
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    float energy_SH, energy_sum_SH, energy_all_shots_SH, energy_sum_all_shots_SH;
    float L2_SH, L2sum_SH, L2_all_shots_SH, L2sum_all_shots_SH;
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    // Pointer for dynamic wavefields:
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    float  **  psxx, **  psxy, **  psyy, **  psxz, **  psyz, **psp, ** ux, ** uy, ** uxy, ** uyx, ** u, ** Vp0, ** uttx, ** utty, ** Vs0, ** Rho0;
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    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;
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    float **waveconv_c55_shot_z, **waveconv_c66_shot_z, **waveconv_c55_s_z, **waveconv_c66_s_z, **waveconv_vshor_shot_z, **waveconv_vshor_z;
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    float  **  pvxp1, **  pvyp1, **  pvzp1, **  pvxm1, **  pvym1, **  pvzm1;
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    float ** gradg, ** gradp,** gradg_rho, ** gradp_rho, ** gradg_u, ** gradp_u, ** gradp_u_z,** gradp_rho_z, **gradp_vshor_z;
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    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 ***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;
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    float  ** srcpos=NULL, **srcpos_loc=NULL, ** srcpos1=NULL, **srcpos_loc_back=NULL, ** signals=NULL,** signals_SH=NULL,  *hc=NULL;
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    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;
    
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    /* Variables for vertically transversely isotropic modeling */
    float **pc11=NULL, **pc13=NULL, **pc33=NULL, **pc55=NULL, **pc55ipjp=NULL, **pc66=NULL, **pc66ipjp=NULL;
    float **pdelta=NULL, **pepsilon=NULL, **pgamma=NULL, **pvshornp1=NULL, **pvshor=NULL;
    
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    /* 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;
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    float ***pt=NULL, ***po=NULL; // SH Simulation
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    /* Variables for step length calculation */
    int step1, step2, step3=0, itests, iteste, stepmax, countstep;
    float scalefac;
    
    int RECINC, ntr1;
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    int SOURCE_SHAPE_OLD=0;
    int SOURCE_SHAPE_OLD_SH=0;
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    /* Variables for conjungate gradient */
    int PCG_iter_start=1;
    
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    /* Variables for L-BFGS */
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    int LBFGS_NPAR=3;
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    int LBFGS_iter_start=1;
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    float **s_LBFGS,**y_LBFGS, *rho_LBFGS;
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    int l=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;
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    float ** waveconv_old,** waveconv_u_old,** waveconv_rho_old,** waveconv_vshor_old;
    float ** waveconv_up,** waveconv_u_up,** waveconv_rho_up,** waveconv_vshor_up;
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    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;
    
    /*vector for abort criterion*/
    float * L2_hist=NULL;
    
    /* help variable for MIN_ITER */
    int min_iter_help=0;
    
    float ** workflow=NULL;
    int workflow_lines;
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    char workflow_header[STRING_SIZE];
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    int change_wavetype_iter=-10; /* Have to be inialized negative */
    int wavetype_start; /* We need this due to MPI Comm */
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    int buf1=0, buf2=0;
    WORKFLOW_STAGE=1;
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    /* variable for time domain filtering */
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    float F_LOW_PASS;
    float *F_LOW_PASS_EXT=NULL;
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    int nfrq=0;
    int FREQ_NR=1;
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    float JOINT_EQUAL_PSV=0.0, JOINT_EQUAL_SH=0.0;
    float JOINT_EQUAL_PSV_all=0.0, JOINT_EQUAL_SH_all=0.0;
    int JOINT_EQUAL_new_max=1;
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    FILE *fprec, *FPL2;
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    FILE *FPL2_JOINT;
    char L2_joint_log[STRING_SIZE];
    
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    /* 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");
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            printf(" Cannot open IFOS input file %s \n",fileinp);
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            printf("\n==================================================================\n\n");
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            declare_error(" --- ");
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        }
    }
    
    /* 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*/
    
    /* 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;
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    /* Reading source positions from SOURCE_FILE */
    srcpos=sources(&nsrc);
    nsrc_glob=nsrc;
    ishot=0;    
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    if (SEISMO){
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        recpos=receiver(&ntr, srcpos, ishot);
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        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);
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    if (!buff_addr) declare_error("allocation failure for buffer for MPI_Bsend !");
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    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) {
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        /* Allocate memory for L-BFGS */
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        if(WAVETYPE==2 && !VTI) LBFGS_NPAR=2;
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        s_LBFGS=fmatrix(1,N_LBFGS,1,LBFGS_NPAR*NX*NY);
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        y_LBFGS=fmatrix(1,N_LBFGS,1,LBFGS_NPAR*NX*NY);
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        rho_LBFGS=vector(1,N_LBFGS);
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        for(l=1;l<=N_LBFGS;l++){
            for(m=1;m<=LBFGS_NPAR*NX*NY;m++){
                s_LBFGS[l][m]=0.0;
                y_LBFGS[l][m]=0.0;
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            }
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            rho_LBFGS[l]=0.0;
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        }
    }
    
    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);
        }
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    }else{
        u = matrix(-nd+1,NY+nd,-nd+1,NX+nd);
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    }
    
    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);
    }
    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 */
        }
    }
    
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    if (VTI) {
	/* dynamic arrays for anisotropic modeling */
	pc11 = matrix(-nd+1,NY+nd,-nd+1,NX+nd);
	pc13 = matrix(-nd+1,NY+nd,-nd+1,NX+nd);
	pc33 = matrix(-nd+1,NY+nd,-nd+1,NX+nd);
	pc55 = matrix(-nd+1,NY+nd,-nd+1,NX+nd);
	pc55ipjp = matrix(-nd+1,NY+nd,-nd+1,NX+nd);
	pc66 = matrix(-nd+1,NY+nd,-nd+1,NX+nd);
	pc66ipjp = matrix(-nd+1,NY+nd,-nd+1,NX+nd);
	pdelta = matrix(-nd+1,NY+nd,-nd+1,NX+nd);
	pepsilon = matrix(-nd+1,NY+nd,-nd+1,NX+nd);
	if(WAVETYPE==2 || WAVETYPE==3) {
	    pgamma = matrix(-nd+1,NY+nd,-nd+1,NX+nd);
	    pvshornp1 = matrix(-nd+1,NY+nd,-nd+1,NX+nd);
	}
	pvshor = matrix(-nd+1,NY+nd,-nd+1,NX+nd);
    }
    
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    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) {
            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);
    }
    
    NTST=20;
    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 */
    
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    if(FORWARD_ONLY==0){
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        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);
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	    if (VTI) {
		waveconv_c55_shot_z = matrix(-nd+1,NY+nd,-nd+1,NX+nd);
		waveconv_c66_shot_z = matrix(-nd+1,NY+nd,-nd+1,NX+nd);
		waveconv_c55_s_z = matrix(-nd+1,NY+nd,-nd+1,NX+nd);
		waveconv_c66_s_z = matrix(-nd+1,NY+nd,-nd+1,NX+nd);
		waveconv_vshor_shot_z = matrix(-nd+1,NY+nd,-nd+1,NX+nd);
		waveconv_vshor_z = matrix(-nd+1,NY+nd,-nd+1,NX+nd);
		gradp_vshor_z = matrix(-nd+1,NY+nd,-nd+1,NX+nd);
	    }
	    waveconv_u_shot_z = matrix(-nd+1,NY+nd,-nd+1,NX+nd);
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            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){
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            c1_SL=WOLFE_C1_SL;
            c2_SL=WOLFE_C2_SL;
            
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            waveconv_old= matrix(-nd+1,NY+nd,-nd+1,NX+nd);
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            if(!ACOUSTIC){
		waveconv_u_old= matrix(-nd+1,NY+nd,-nd+1,NX+nd);
		waveconv_vshor_old= matrix(-nd+1,NY+nd,-nd+1,NX+nd);
	    }
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            waveconv_rho_old= matrix(-nd+1,NY+nd,-nd+1,NX+nd);
            
            waveconv_up= matrix(-nd+1,NY+nd,-nd+1,NX+nd);
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            if(!ACOUSTIC) {
		waveconv_u_up= matrix(-nd+1,NY+nd,-nd+1,NX+nd);
		waveconv_vshor_up= matrix(-nd+1,NY+nd,-nd+1,NX+nd);
	    }
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            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);
        }
        
    }
    
    /* 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){
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      alloc_sections(ntr,ns,&sectionvx,&sectionvy,&sectionvz,&sectionp,&sectionpnp1,&sectionpn,&sectioncurl,&sectiondiv,
	&sectionpdata,&sectionpdiff,&sectionpdiffold,&sectionvxdata,&sectionvxdiff,&sectionvxdiffold,&sectionvydata,
	&sectionvydiff,&sectionvydiffold,&sectionvzdata,&sectionvzdiff,&sectionvzdiffold);
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    }
    
    /* Memory for seismic data */
    sectionread=matrix(1,ntr_glob,1,ns);
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    /* 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);
    
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        read_workflow(FILE_WORKFLOW,&workflow, &workflow_lines,workflow_header);
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    }
    
    /* create model grids */
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    if(L){
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        if(!ACOUSTIC){
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            if (READMOD){
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		if(VTI){
		    readmod_vti(prho,ppi,pu,pdelta,pepsilon,pvshor,ptaus,ptaup,peta);
		}
		else {
		    readmod(prho,ppi,pu,ptaus,ptaup,peta);
		}
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            }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){
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		if (VTI) {
		    readmod_el_vti(prho,ppi,pu,pdelta,pepsilon,pvshor);
		}
		else {
		    readmod_elastic(prho,ppi,pu);
		}
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            }else{
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		if(VTI){
		    model_elastic_vti(prho,ppi,pu,pdelta,pepsilon,pvshor);
		}
		else {
		    model_elastic(prho,ppi,pu);
		}
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            }
        }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 */
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    checkfd(FP, prho, ppi, pu, ptaus, ptaup, peta, hc, srcpos, nsrc, recpos, ntr_glob, pepsilon, pdelta, pvshor);
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    /* 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);
    
    SHOTINC=1;
    RECINC=1;
    
    switch(TIME_FILT){
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        case 1: F_LOW_PASS=F_LOW_PASS_START; break;
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            /*read frequencies from file*/
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        case 2: F_LOW_PASS_EXT=filter_frequencies(&nfrq); F_LOW_PASS=F_LOW_PASS_EXT[FREQ_NR]; break;
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    }
    
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    /* Save old SOURCE_SHAPE, which is needed for STF */
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    SOURCE_SHAPE_OLD = SOURCE_SHAPE;
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    if(WAVETYPE==2 || WAVETYPE==3) SOURCE_SHAPE_OLD_SH=SOURCE_SHAPE_SH;
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    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
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        if(USE_WORKFLOW&&(FORWARD_ONLY==0)){
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            apply_workflow(workflow,workflow_lines,workflow_header,&iter,&F_LOW_PASS,wavetype_start,&change_wavetype_iter,&LBFGS_iter_start);
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        }
        
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        if(GRAD_METHOD==2&&(FORWARD_ONLY==0)){
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            /* 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) {
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                lbfgs_reset(iter,N_LBFGS,LBFGS_NPAR,s_LBFGS,y_LBFGS,rho_LBFGS);
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                /* set values */
                FWI_run=1;
                gradient_optimization=1;
            }
            
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            /* Reset fail status of parabolic step length search */
            step3=0;
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        }
        
        if (MYID==0){
            time2=MPI_Wtime();
            fprintf(FP,"\n\n\n ------------------------------------------------------------------\n");
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            if(FORWARD_ONLY==0) {
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                fprintf(FP,"\n\n\n                   TDFWI ITERATION %d \t of %d \n",iter,ITERMAX);
            } else {
                fprintf(FP,"\n\n\n                        FD-SIMULATION \n");
            }
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            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 (VTI){
		    change_parameterization_vti(prho, ppi, pu, pepsilon, pdelta, pvshor, pc11, pc13, pc33, pc55, pc66);
		}
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                if (L){
                    if(!ACOUSTIC){
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			if(VTI){
			    matcopy_vti(prho, pc11, pc13, pc33, pc55, pc66, ptaus, ptaup);
			}
			else {
			    matcopy(prho,ppi,pu,ptaus,ptaup);
			}
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                    } else {
                        matcopy_viscac(prho,ppi,ptaup);
                    }
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                }else{
                    if(!ACOUSTIC){
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			if (VTI) {
			    matcopy_elastic_vti(prho, pc11, pc13, pc33, pc55, pc66);
			}
			else {
			    matcopy_elastic(prho, ppi, pu);
			}
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                    }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 */
                
                
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                if(!ACOUSTIC) av_mue(pu,puipjp,prho);
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                av_rho(prho,prip,prjp);
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                if (!ACOUSTIC && L) av_tau(ptaus,ptausipjp);
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		if (VTI) av_c55c66(pc55,pc55ipjp, pc66,pc66ipjp);
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                /* Preparing memory variables for update_s (viscoelastic) */
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                if (L) {
                    if(!ACOUSTIC){
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			if(VTI){
			    prepare_update_s_vti(etajm,etaip,peta,fipjp,pc55,pc66ipjp,ppi,prho,ptaus,ptaup,ptausipjp,f,g,bip,bjm,cip,cjm,dip,d,e);
			}
			else {
			    prepare_update_s(etajm,etaip,peta,fipjp,pu,puipjp,ppi,prho,ptaus,ptaup,ptausipjp,f,g,bip,bjm,cip,cjm,dip,d,e);
			}
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                    } else {
                        prepare_update_p(etajm,peta,ppi,prho,ptaup,g,bjm,cjm,e);
                    }
                }
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                /* Do some initia calculations */
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                if(iter==1){
                    
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                    /* Calculationg material parameters according to PARAMETERIZATION */
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                    for (j=1;j<=NY;j=j+IDY){
                        for (i=1;i<=NX;i=i+IDX){
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                            if(PARAMETERIZATION==1){
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                                Vp0[j][i] = ppi[j][i];
                                if(!ACOUSTIC) Vs0[j][i] = pu[j][i];
                                Rho0[j][i] = prho[j][i];}
                            
                            
                            
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                            if(PARAMETERIZATION==2){
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                                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];
                                
                            }
                            
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                            if(PARAMETERIZATION==3){
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                                Vp0[j][i] = ppi[j][i];
                                Vs0[j][i] = pu[j][i];
                                Rho0[j][i] = prho[j][i];
                                
                            }
                            
                        }
                    }
                    
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                    /* Get average values from material parameters */
                    Vp_avg=average_matrix(ppi);
                    rho_avg=average_matrix(prho);
                    if(!ACOUSTIC) Vs_avg=average_matrix(pu);
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		    if (VTI) {
			vshor_avg=average_matrix(pvshor);
		    }
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                    if(!ACOUSTIC) {
			if (VTI) {
			    if (VERBOSE) printf("MYID = %d \t Vp_avg = %e \t Vs_avg = %e \t rho_avg = %e \t vshor_avg = %e \n ",MYID,Vp_avg,Vs_avg,rho_avg,vshor_avg);
			}
			else 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);
		    }
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                    else if(VERBOSE) printf("MYID = %d \t Vp_avg = %e \t rho_avg = %e \n ",MYID,Vp_avg,rho_avg);
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                    C_vp = Vp_avg*Vp_avg;
                    if(!ACOUSTIC) C_vs = Vs_avg*Vs_avg;
                    C_rho = rho_avg*rho_avg;
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		    if (VTI) {
			C_vshor = vshor_avg*vshor_avg;
		    }
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                }
                
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                /* Seperate PSV and SH logging in case of a joint inversion */
                if(WAVETYPE==3){
                    sprintf(L2_joint_log,"%s_JOINT",MISFIT_LOG_FILE);
                }
                
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                /* Open Log File for L2 norm */
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                if(!FORWARD_ONLY && MYID==0){
                    
                    if(iter==1){
                        
                        FPL2=fopen(MISFIT_LOG_FILE,"w");
                        
                        /* Write header for misfit log file */
                        if(GRAD_METHOD==1&&VERBOSE) {
                            if (TIME_FILT==0){
                                fprintf(FPL2,"opteps_vp \t epst1[1] \t epst1[2] \t epst1[3] \t L2t[1] \t L2t[2] \t L2t[3] \t L2t[4] \n");}
                            else{
                                fprintf(FPL2,"opteps_vp \t epst1[1] \t epst1[2] \t epst1[3] \t L2t[1] \t L2t[2] \t L2t[3] \t L2t[4] \t F_LOW_PASS \n");
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                            }
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                        }
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                        if(WAVETYPE==3) FPL2_JOINT=fopen(L2_joint_log,"w");
                        
                    } else {
                        
                        FPL2=fopen(MISFIT_LOG_FILE,"a");
                        
                        if(WAVETYPE==3) FPL2_JOINT=fopen(L2_joint_log,"a");
                        
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                    }
                }
                
                /* initialization of L2 calculation */
                L2=0.0;
                energy=0.0;
                L2_all_shots=0.0;
                energy_all_shots=0.0;
                killed_traces=0;
                killed_traces_testshots=0;
                
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                if(WAVETYPE==2||WAVETYPE==3){
                    L2_SH=0.0;
                    energy_SH=0.0;
                    L2_all_shots_SH=0.0;
                    energy_all_shots_SH=0.0;
                }
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                EPSILON=0.0;  /* test step length */
                exchange_par();
                
                /* initialize waveconv matrix*/
                if(WAVETYPE==1||WAVETYPE==3){
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                    if(FORWARD_ONLY==0){
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                        for (j=1;j<=NY;j=j+IDY){
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                            for (i=1;i<=NX;i=i+IDX){
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                                waveconv[j][i]=0.0;
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                                waveconv_rho[j][i]=0.0;
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                                if(!ACOUSTIC) waveconv_u[j][i]=0.0;
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                            }
                        }
                    }
                }
                /* initialize waveconv matrix*/
                if(WAVETYPE==2||WAVETYPE==3){
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                    if(FORWARD_ONLY==0){
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                        for (j=1;j<=NY;j=j+IDY){
                            for (i=1;i<=NX;i=i+IDX){
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                                waveconv_rho_z[j][i]=0.0;
                                waveconv_u_z[j][i]=0.0;
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				if (VTI) {
				    waveconv_vshor_z[j][i]=0.0;
				}
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                            }
                        }
                    }
                }
                
                if((EPRECOND>0)&&(EPRECOND_ITER==iter||(EPRECOND_ITER==0))){
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                    for (j=1;j<=NY;j=j+IDY){
                        for (i=1;i<=NX;i=i+IDX){
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                            if(WAVETYPE==1||WAVETYPE==3) We_sum[j][i]=0.0;
                            if(WAVETYPE==2||WAVETYPE==3) We_sum_SH[j][i]=0.0;
                        }
                    }
                }
                
                
                
                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){
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       			if (SEISMO && READREC==2){
			  if (ntr>0) {
			    dealloc_sections(ntr,ns,recpos_loc,sectionvx,sectionvy,sectionvz,sectionp,sectionpnp1,sectionpn,sectioncurl,sectiondiv,
					     sectionpdata,sectionpdiff,sectionpdiffold,sectionvxdata,sectionvxdiff,sectionvxdiffold,sectionvydata,
					     sectionvydiff,sectionvydiffold,sectionvzdata,sectionvzdiff,sectionvzdiffold);
			  }
			  free_imatrix(recpos,1,3,1,ntr_glob);
			  recpos=receiver(&ntr, srcpos, ishot);
			  recpos_loc = splitrec(recpos,&ntr_loc, ntr, recswitch);
			  ntr_glob=ntr;
			  ntr=ntr_loc;
			  if (ntr>0){
				alloc_sections(ntr,ns,&sectionvx,&sectionvy,&sectionvz,&sectionp,&sectionpnp1,&sectionpn,&sectioncurl,&sectiondiv,
					      &sectionpdata,&sectionpdiff,&sectionpdiffold,&sectionvxdata,&sectionvxdiff,&sectionvxdiffold,&sectionvydata,
					      &sectionvydiff,&sectionvydiffold,&sectionvzdata,&sectionvzdiff,&sectionvzdiffold);
			  }
			  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);
			}
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                        SOURCE_SHAPE = SOURCE_SHAPE_OLD;
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                        if(WAVETYPE==2 || WAVETYPE==3) SOURCE_SHAPE_SH=SOURCE_SHAPE_OLD_SH;
                        
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                        /*------------------------------------------------------------------------------*/
                        /*----------- Start of inversion of source time function -----------------------*/
                        /*------------------------------------------------------------------------------*/
                        
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                        /* Do not Excute STF if this is a step length search run for Wolfe condition
                         * Therefore (gradient_optimization==1) is added.
                         */
                        
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                        if(((INV_STF==1)&&( (iter==1) || (do_stf==1) )) && (gradient_optimization==1) ){
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                            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);
                            }
                            
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                            if(SOURCE_SHAPE==3) declare_error("SOURCE_SHAPE==3 isn't possible with INV_STF==1");
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                            MPI_Barrier(MPI_COMM_WORLD);
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                            /*-------------------*/
                            /* calculate wavelet */
                            /*-------------------*/
                            /* calculate wavelet for each source point P SV */
                            if(WAVETYPE==1||WAVETYPE==3){
                                signals=NULL;
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                                signals=wavelet(srcpos_loc,nsrc_loc,ishot,0,1);
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                            }
                            /* calculate wavelet for each source point SH */
                            if(WAVETYPE==2||WAVETYPE==3){
                                signals_SH=NULL;
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                                signals_SH=wavelet(srcpos_loc,nsrc_loc,ishot,1,1);
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                            }
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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);
                            }
                            
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                            if((!VERBOSE)&&(MYID==0)) fprintf(FP,"\n ****************************************\n ");
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                            /*------------------------------------------------------------------------------*/
                            /*----------------------  start loop over timesteps ( STF ) --------------------*/
                            /*------------------------------------------------------------------------------*/
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                            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);
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                                if((!VERBOSE)&&(MYID==0)) if(!(nt%(NT/40))) fprintf(FP,"*");
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                                /* 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]);
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                                        declare_error(" Simulation is unstable !");
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                                    }
                                }
                                
                                /* 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]);
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                                        declare_error(" Simulation is unstable !");
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                                    }
                                }
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                                if (MYID==0){
                                    if (infoout)  fprintf(FP,"\n Computing timestep %d of %d \n",nt,NT);
                                    time3=MPI_Wtime();
                                }
                                
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                                /* 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);
                                    }
                                } 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);
                                        }
                                    }
                                    if (WAVETYPE==2 || WAVETYPE==3) {
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					if(VTI){
					    update_s_visc_vti_PML_SH(1, NX, 1, NY, pvz, uxz, uyz, psxz, psyz, pt, po, bip, bjm, cip, cjm, d, dip,fipjp, f, 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, pc55,pc66ipjp,prho);
					}
					else {
					    update_s_visc_PML_SH(1, NX, 1, NY, pvz, uxz, uyz, psxz, psyz, pt, po, bip, bjm, cip, cjm, d, dip,fipjp, f, 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);
					}
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                                    }
                                } else {   /* elastic */
                                    if (WAVETYPE==1 || WAVETYPE==3) {
                                        if(!ACOUSTIC) {
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					    if (VTI) {
						update_s_el_vti_PML(1, NX, 1, NY, pvx, pvy, ux, uy, uxy, uyx, psxx, psyy, psxy, pc11, pc13, pc33, pc55ipjp, 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_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);
					    }
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                                        } else {
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                                            update_p_PML(1, NX, 1, NY, pvx, pvy, psp, u, 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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                                        }
                                    }
                                    if (WAVETYPE==2 || WAVETYPE==3) {
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					if (VTI) {
					    update_s_el_vti_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,pc55,pc66ipjp,prho);
					}
					else {
					    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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                                }