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/*------------------------------------------------------------------------
 * Copyright (C) 2011 For the list of authors, see file AUTHORS.
 *
 * This file is part of SOFI2D.
 * 
 * SOFI2D 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.
 * 
 * SOFI2D is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 * 
 * You should have received a copy of the GNU General Public License
 * along with SOFI2D. See file COPYING and/or 
  * <http://www.gnu.org/licenses/gpl-2.0.html>.
--------------------------------------------------------------------------*/
/*------------------------------------------------------------------------
 *   stress free surface condition
 *
 *  ----------------------------------------------------------------------*/

#include "fd.h"

void surface(int ndepth, float ** vx, float ** vy, float ** sxx, float ** syy,
float ** sxy, float *** p, float *** q,
float  **  pi, float  **  u, float ** taup,
float ** taus, float * etajm, float * peta, float *hc, float * K_x, float * a_x, float * b_x, float ** psi_vxx){


	int i,j,l,m,h,h1,fdoh;
	float bjm, djm, e, fjm, g, dhi;
	float  vxx, vyy, sump=0.0;
	float  dthalbe;	
	extern float DT, DH;
	extern int NX, L, FDORDER;
	extern int FW, BOUNDARY;
	extern int NPROCX, NPROCY, POS[3], MYID; 
	extern int ABS_TYPE;	
	fdoh = FDORDER/2;
	dhi = 1.0/DH;
	dthalbe=DT/2.0;

	j=ndepth;     /* The free surface is located exactly in y=dh !! */
	for (i=1;i<=NX;i++){

		/* Compute values for shearmodulus u[j][i], P-wave modulus pi[j][i],
		tau for S-waves and P-waves taus[j][i], taup[j][i] at half indizes: */

		
/*		for (l=1;l<=L;l++){
			etajm[l]=0.5*(eta(i,j-1,l)+eta[j][i][l]);
		}
*/
		for (l=1;l<=L;l++){
			etajm[l]=peta[l];
		}

		/*Mirroring the components of the stress tensor to make
			a stress free surface (method of imaging)*/
		syy[j][i]=0.0;

		/* since syy is zero on the free surface also the
		corresponding memory-variables must set to zero */
		for (l=1;l<=L;l++) q[j][i][l]=0.0;


		/* now updating the stress component sxx and the memory-
		variables p[j][i][l] at the free surface */

		/* first calculate spatial derivatives of components
			of particle velocities */
		vxx = 0.0;
		vyy = 0.0;
		for (m=1; m<=fdoh; m++) {
			/*Mirroring the components of the stress tensor to make
			a stress free surface (method of imaging)*/
			syy[j-m][i]=-syy[j+m][i];
			sxy[j-m][i]=-sxy[j+m-1][i];

			vxx += hc[m]*(vx[j][i+m-1] -vx[j][i-m]);
			vyy += hc[m]*(vy[j+m-1][i] -vy[j-m][i]);
		}
		vxx *= dhi;
		vyy *= dhi;
		
		if (ABS_TYPE==1){
	      	/* apply PML boundary */    
             		/* left boundary */
             		if((!BOUNDARY) && (POS[1]==0) && (i<=FW)){
                        
                        	psi_vxx[j][i] = b_x[i] * psi_vxx[j][i] + a_x[i] * vxx;
                        	vxx = vxx / K_x[i] + psi_vxx[j][i];                 
             		}

             		/* right boundary */
             		if((!BOUNDARY) && (POS[1]==NPROCX-1) && (i>=NX-FW+1)){
                
                        	h1 = (i-NX+2*FW);
                        	h = i;
                        
                       	 	psi_vxx[j][h1] = b_x[h1] * psi_vxx[j][h1] + a_x[h1] * vxx;
                        	vxx = vxx / K_x[h1] + psi_vxx[j][h1];                                            
             		} 
		}

		/* sums used in updating sxx */
		sump=0.0;
		for (l=1;l<=L;l++) sump+=p[j][i][l];

		fjm=u[j][i]*2.0*(1.0+L*taus[j][i]);
		g=pi[j][i]*(1.0+L*taup[j][i]);

		/* partially updating sxx */
		sxx[j][i]+= -(DT*(g-fjm)*(g-fjm)*vxx/g)-(DT*(g-fjm)*vyy)-(dthalbe*sump);

		/* updating the memory-variable p[j][i][l] at the free surface */
		sump=0.0;
		for (l=1;l<=L;l++){
			bjm=etajm[l]/(1.0+(etajm[l]*0.5));
			djm=2.0*u[j][i]*taus[j][i];
			e=pi[j][i]*taup[j][i];
			p[j][i][l]+=bjm*(((djm-e)*((fjm/g)-1.0)*vxx)-((djm-e)*vyy));
			sump+=p[j][i][l];
		}
		/*completely updating the stress sxx */
		sxx[j][i]+=(dthalbe*sump);
	}
}