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compute_kernels.f90
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compute_kernels.f90
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!========================================================================
!
! S P E C F E M 2 D Version 7 . 0
! --------------------------------
!
! Main historical authors: Dimitri Komatitsch and Jeroen Tromp
! Princeton University, USA
! and CNRS / University of Marseille, France
! (there are currently many more authors!)
! (c) Princeton University and CNRS / University of Marseille, April 2014
!
! This software is a computer program whose purpose is to solve
! the two-dimensional viscoelastic anisotropic or poroelastic wave equation
! using a spectral-element method (SEM).
!
! This software is governed by the CeCILL license under French law and
! abiding by the rules of distribution of free software. You can use,
! modify and/or redistribute the software under the terms of the CeCILL
! license as circulated by CEA, CNRS and Inria at the following URL
! "http://www.cecill.info".
!
! As a counterpart to the access to the source code and rights to copy,
! modify and redistribute granted by the license, users are provided only
! with a limited warranty and the software's author, the holder of the
! economic rights, and the successive licensors have only limited
! liability.
!
! In this respect, the user's attention is drawn to the risks associated
! with loading, using, modifying and/or developing or reproducing the
! software by the user in light of its specific status of free software,
! that may mean that it is complicated to manipulate, and that also
! therefore means that it is reserved for developers and experienced
! professionals having in-depth computer knowledge. Users are therefore
! encouraged to load and test the software's suitability as regards their
! requirements in conditions enabling the security of their systems and/or
! data to be ensured and, more generally, to use and operate it in the
! same conditions as regards security.
!
! The full text of the license is available in file "LICENSE".
!
!=====================================================================
!
!-------------------------------------------------------------------------------------------------
!
subroutine compute_kernels_el()
! elastic kernel calculations
! see e.g. Tromp et al. (2005)
use specfem_par, only: elastic,rho_k,rhorho_el_hessian_temp1,rhorho_el_hessian_temp2, &
rho_kl,mu_kl,kappa_kl,rhop_kl,beta_kl,alpha_kl,bulk_c_kl,bulk_beta_kl, &
rhorho_el_hessian_final1,rhorho_el_hessian_final2, &
nglob,nspec,ibool,accel_elastic,b_displ_elastic,b_accel_elastic, &
rhol_global,mul_global,kappal_global, &
hti_c11l_global,hti_c13l_global,hti_c33l_global,hti_c55l_global,hti_rhol_global,&
hti_alphal_global,hti_betal_global,hti_epsilonl_global,hti_deltal_global,hti_rhopl_global,&
tti_alphal_global,tti_betal_global,tti_epsilonl_global,tti_deltal_global,tti_rhopl_global,&
hti_etal_global,hti_alphahl_global,hti_alphanl_global, &
ipl_global, isl_global, lambdal_global, sigmal_global, vpl_global, vsl_global, &
density,poroelastcoef,kmato,assign_external_model,rhoext,vsext,vpext,&
c11ext,c13ext,c33ext,c55ext,c15ext,c35ext,&
c11uext,c13uext,c33uext,c55uext,thetaext,&
m1ext,m2ext,m3ext,m4ext,m5ext,m6ext,&
deltat,p_sv,displ_elastic,&
mu_k,kappa_k,elastic,ibool,hprime_xx,hprime_zz,xix,xiz,gammax,gammaz,&
hti_ec_c11_k,hti_ec_c13_k,hti_ec_c33_k,hti_ec_c55_k,hti_ec_rho_k, &
hti_ec_c11_kl,hti_ec_c13_kl,hti_ec_c33_kl,hti_ec_c55_kl,hti_ec_rho_kl, &
hti_coeffl_global, tti_coeffl_global, &
hti_thom_alpha_kl,hti_thom_beta_kl,hti_thom_epsilon_kl,hti_thom_delta_kl, &
hti_thom_rhop_kl, ANISO,&
pdh_hti_ec_c11,pdh_hti_ec_c13,pdh_hti_ec_c33,pdh_hti_ec_c55,pdh_hti_ec_rho, &
pdh_hti_thom_alpha,pdh_hti_thom_beta,pdh_hti_thom_epsilon,pdh_hti_thom_delta,pdh_hti_thom_rhop, &
pdh_hti_ec_c11_temp,pdh_hti_ec_c13_temp,pdh_hti_ec_c33_temp,pdh_hti_ec_c55_temp,pdh_hti_ec_rho_temp, &
pdh_hti_ec_c11_temp1,pdh_hti_ec_c13_temp1,pdh_hti_ec_c33_temp1,pdh_hti_ec_c55_temp1,pdh_hti_ec_rho_temp1, &
pdh_hti_thom_alpha_temp,pdh_hti_thom_beta_temp,pdh_hti_thom_epsilon_temp,pdh_hti_thom_delta_temp, &
pdh_hti_thom_rhop_temp,&
Qalpha_k,Qbeta_k,Qkappa_k,Qmu_k,Qalpha_kl,Qbeta_kl,Qkappa_kl,Qmu_kl,&
Qalphal_global,Qbetal_global,Qkappal_global,Qmul_global,&
hti_thom2_alpha_kl,hti_thom2_beta_kl,hti_thom2_epsilon_kl,hti_thom2_delta_kl,hti_thom2_eta_kl,&
hti_thom2_rhop_kl,&
pdh_hti_thom2_alpha,pdh_hti_thom2_beta,pdh_hti_thom2_epsilon,pdh_hti_thom2_delta,pdh_hti_thom2_rhop,&
pdh_hti_thom2_eta,&
hti_vel_alpha_kl,hti_vel_beta_kl,hti_vel_alphah_kl,hti_vel_alphan_kl,hti_vel_rhop_kl,&
pdh_hti_vel_alpha,pdh_hti_vel_beta,pdh_hti_vel_alphah,pdh_hti_vel_alphan,pdh_hti_vel_rhop,&
tti_ec_c11_k,tti_ec_c13_k,tti_ec_c15_k,tti_ec_c33_k,tti_ec_c35_k,tti_ec_c55_k,tti_ec_rho_k,&
tti_ec_c11_kl,tti_ec_c13_kl,tti_ec_c15_kl,tti_ec_c33_kl,tti_ec_c35_kl,tti_ec_c55_kl,tti_ec_rho_kl,&
tti_ecu_c11_kl,tti_ecu_c13_kl,tti_ecu_c33_kl,tti_ecu_c55_kl,tti_ecu_theta_kl,tti_ecu_rho_kl,&
pdh_tti_ec_c11_temp,pdh_tti_ec_c13_temp,pdh_tti_ec_c15_temp,pdh_tti_ec_c33_temp,&
pdh_tti_ec_c35_temp,pdh_tti_ec_c55_temp,pdh_tti_ec_rho_temp,&
pdh_tti_ec_c11_temp1,pdh_tti_ec_c13_temp1,pdh_tti_ec_c15_temp1,pdh_tti_ec_c33_temp1,&
pdh_tti_ec_c35_temp1,pdh_tti_ec_c55_temp1,pdh_tti_ec_rho_temp1,&
pdh_tti_ec_c11,pdh_tti_ec_c13,pdh_tti_ec_c15,pdh_tti_ec_c33,&
pdh_tti_ec_c35,pdh_tti_ec_c55,pdh_tti_ec_rho,&
pdh_tti_ecu_c11_temp,pdh_tti_ecu_c13_temp,pdh_tti_ecu_c33_temp,pdh_tti_ecu_c55_temp, &
pdh_tti_ecu_theta_temp,pdh_tti_ecu_rho_temp,&
pdh_tti_ecu_c11,pdh_tti_ecu_c13,pdh_tti_ecu_c33,pdh_tti_ecu_c55,pdh_tti_ecu_theta,pdh_tti_ecu_rho, &
tti_c11l_global,tti_c13l_global,tti_c15l_global,tti_c33l_global,&
tti_c35l_global,tti_c55l_global,tti_rhol_global, &
tti_c11ul_global,tti_c13ul_global,tti_c33ul_global,tti_c55ul_global,tti_thetaul_global,tti_rhoul_global,&
dl_lambda_kl, dl_mu_kl, dl_rho_kl, dip_ip_kl, dip_is_kl, dip_rho_kl, vipi_vp_kl, vipi_vs_kl, vipi_ip_kl, &
vipii_vp_kl, vipii_vs_kl, vipii_is_kl, sigma_vp_kl, sigma_sigma_kl, sigma_rho_kl, &
dl_lambda_k, dl_mu_k, dl_rho_k, dip_ip_k, dip_is_k, dip_rho_k, vipi_vp_k, vipi_vs_k, vipi_ip_k, &
vipii_vp_k, vipii_vs_k, vipii_is_k, sigma_vp_k, sigma_sigma_k, sigma_rho_k, &
pdh_vp, pdh_vs, pdh_rhop, pdh_kappa, pdh_mu, pdh_rho, &
pdh_dl_lambda, pdh_dl_mu, pdh_dl_rho, pdh_dip_ip,pdh_dip_is,pdh_dip_rho,&
pdh_vipi_vp,pdh_vipi_vs,pdh_vipi_ip, pdh_vipii_vp,pdh_vipii_vs,pdh_vipii_is, &
pdh_sigma_vp,pdh_sigma_sigma,pdh_sigma_rho, &
pdh_vp_temp, pdh_vs_temp, pdh_rhop_temp, pdh_kappa_temp, pdh_mu_temp, pdh_rho_temp, &
pdh_dl_lambda_temp, pdh_dl_mu_temp, pdh_dl_rho_temp, pdh_dip_ip_temp,pdh_dip_is_temp,pdh_dip_rho_temp,&
pdh_vipi_vp_temp,pdh_vipi_vs_temp,pdh_vipi_ip_temp, pdh_vipii_vp_temp,pdh_vipii_vs_temp,pdh_vipii_is_temp, &
pdh_sigma_vp_temp,pdh_sigma_sigma_temp,pdh_sigma_rho_temp, &
pdh_vp_temp1, pdh_vs_temp1, pdh_rhop_temp1, pdh_kappa_temp1, pdh_mu_temp1, pdh_rho_temp1, &
pdh_dl_lambda_temp1, pdh_dl_mu_temp1, pdh_dl_rho_temp1, pdh_dip_ip_temp1,pdh_dip_is_temp1,pdh_dip_rho_temp1,&
pdh_vipi_vp_temp1,pdh_vipi_vs_temp1,pdh_vipi_ip_temp1, &
pdh_vipii_vp_temp1,pdh_vipii_vs_temp1,pdh_vipii_is_temp1, &
pdh_sigma_vp_temp1,pdh_sigma_sigma_temp1,pdh_sigma_rho_temp1,&
tti_ecu_c11_k,tti_ecu_c13_k,tti_ecu_c33_k,tti_ec_c55_k,tti_ecu_theta_k,tti_ecu_rho_k,&
m1l_global,m2l_global,m3l_global,m4l_global,m5l_global,m6l_global,p1l_global,p2l_global,M_PAR,&
tti_thom_alpha_kl,tti_thom_beta_kl,tti_thom_epsilon_kl,tti_thom_delta_kl,tti_thom_theta_kl,&
tti_thom_rhop_kl,pdh_tti_thom_alpha,pdh_tti_thom_beta,pdh_tti_thom_epsilon,pdh_tti_thom_delta,&
pdh_tti_thom_rhop,pdh_tti_thom_theta,pdh_tti_thom_alpha_temp,pdh_tti_thom_beta_temp,pdh_tti_thom_epsilon_temp,&
pdh_tti_thom_delta_temp,pdh_tti_thom_rhop_temp,pdh_tti_thom_theta_temp,ATTENUATION_VISCOELASTIC_SOLID,&
QKappa_attenuationext,Qmu_attenuationext,Qalpha_attenuationext,Qbeta_attenuationext,&
tti_vel_alpha_kl,tti_vel_beta_kl,tti_vel_alphah_kl,tti_vel_alphan_kl,&
tti_vel_theta_kl,tti_vel_rhop_kl,&
pdh_tti_vel_alpha,pdh_tti_vel_beta,pdh_tti_vel_alphah,pdh_tti_vel_alphan,pdh_tti_vel_rhop,pdh_tti_vel_theta,&
pdh_tti_vel_alpha_temp,pdh_tti_vel_beta_temp,pdh_tti_vel_alphah_temp,pdh_tti_vel_alphan_temp,pdh_tti_vel_rhop_temp,&
pdh_tti_vel_theta_temp,e1,e11,e13,e1_x,e1_z,b_e1,b_e11,b_e13,N_SLS,Q_KL_TROMP,Q_KL_CHAR,Q_KL_FICH,Q_KL
implicit none
include "constants.h"
!local variables
integer :: i,j,k,ispec,iglob
real(kind=CUSTOM_REAL) :: dux_dxi,dux_dgamma,duy_dxi,duy_dgamma,duz_dxi,duz_dgamma
real(kind=CUSTOM_REAL) :: dux_dxl,duy_dxl,duz_dxl,dux_dzl,duy_dzl,duz_dzl
real(kind=CUSTOM_REAL) :: b_dux_dxi,b_dux_dgamma,b_duy_dxi,b_duy_dgamma,b_duz_dxi,b_duz_dgamma
real(kind=CUSTOM_REAL) :: b_dux_dxl,b_duy_dxl,b_duz_dxl,b_dux_dzl,b_duy_dzl,b_duz_dzl
real(kind=CUSTOM_REAL) :: dsxx,dsxz,dszz
real(kind=CUSTOM_REAL) :: b_dsxx,b_dsxz,b_dszz
real(kind=CUSTOM_REAL) :: e1_sum,e11_sum,e13_sum,e1_x_sum,e1_z_sum
real(kind=CUSTOM_REAL) :: lambdaplus2mu_att,lambda_att,mu_att,lambdaplusmu_att
real(kind=CUSTOM_REAL) :: sigma_xx_att,sigma_zz_att,sigma_xz_att
integer :: i_sls
! Jacobian matrix and determinant
double precision :: xixl,xizl,gammaxl,gammazl
do ispec = 1,nspec
if( elastic(ispec) ) then
do j=1,NGLLZ; do i=1,NGLLX
! derivative along x and along z
dux_dxi = 0._CUSTOM_REAL; duy_dxi = 0._CUSTOM_REAL; duz_dxi = 0._CUSTOM_REAL
dux_dgamma = 0._CUSTOM_REAL; duy_dgamma = 0._CUSTOM_REAL; duz_dgamma = 0._CUSTOM_REAL
b_dux_dxi = 0._CUSTOM_REAL; b_duy_dxi = 0._CUSTOM_REAL; b_duz_dxi = 0._CUSTOM_REAL
b_dux_dgamma = 0._CUSTOM_REAL; b_duy_dgamma = 0._CUSTOM_REAL; b_duz_dgamma = 0._CUSTOM_REAL
! first double loop over GLL points to compute and store gradients
! we can merge the two loops because NGLLX == NGLLZ
do k = 1,NGLLX
dux_dxi = dux_dxi + displ_elastic(1,ibool(k,j,ispec))*hprime_xx(i,k)
duy_dxi = duy_dxi + displ_elastic(2,ibool(k,j,ispec))*hprime_xx(i,k)
duz_dxi = duz_dxi + displ_elastic(3,ibool(k,j,ispec))*hprime_xx(i,k)
dux_dgamma = dux_dgamma + displ_elastic(1,ibool(i,k,ispec))*hprime_zz(j,k)
duy_dgamma = duy_dgamma + displ_elastic(2,ibool(i,k,ispec))*hprime_zz(j,k)
duz_dgamma = duz_dgamma + displ_elastic(3,ibool(i,k,ispec))*hprime_zz(j,k)
b_dux_dxi = b_dux_dxi + b_displ_elastic(1,ibool(k,j,ispec))*hprime_xx(i,k)
b_duy_dxi = b_duy_dxi + b_displ_elastic(2,ibool(k,j,ispec))*hprime_xx(i,k)
b_duz_dxi = b_duz_dxi + b_displ_elastic(3,ibool(k,j,ispec))*hprime_xx(i,k)
b_dux_dgamma = b_dux_dgamma + b_displ_elastic(1,ibool(i,k,ispec))*hprime_zz(j,k)
b_duy_dgamma = b_duy_dgamma + b_displ_elastic(2,ibool(i,k,ispec))*hprime_zz(j,k)
b_duz_dgamma = b_duz_dgamma + b_displ_elastic(3,ibool(i,k,ispec))*hprime_zz(j,k)
enddo
xixl = xix(i,j,ispec)
xizl = xiz(i,j,ispec)
gammaxl = gammax(i,j,ispec)
gammazl = gammaz(i,j,ispec)
! derivatives of displacement
dux_dxl = dux_dxi*xixl + dux_dgamma*gammaxl
dux_dzl = dux_dxi*xizl + dux_dgamma*gammazl
duy_dxl = duy_dxi*xixl + duy_dgamma*gammaxl
duy_dzl = duy_dxi*xizl + duy_dgamma*gammazl
duz_dxl = duz_dxi*xixl + duz_dgamma*gammaxl
duz_dzl = duz_dxi*xizl + duz_dgamma*gammazl
b_dux_dxl = b_dux_dxi*xixl + b_dux_dgamma*gammaxl
b_dux_dzl = b_dux_dxi*xizl + b_dux_dgamma*gammazl
b_duy_dxl = b_duy_dxi*xixl + b_duy_dgamma*gammaxl
b_duy_dzl = b_duy_dxi*xizl + b_duy_dgamma*gammazl
b_duz_dxl = b_duz_dxi*xixl + b_duz_dgamma*gammaxl
b_duz_dzl = b_duz_dxi*xizl + b_duz_dgamma*gammazl
iglob = ibool(i,j,ispec)
if( p_sv ) then !P-SV waves
dsxx = dux_dxl
dsxz = HALF * (duz_dxl + dux_dzl)
dszz = duz_dzl
b_dsxx = b_dux_dxl
b_dsxz = HALF * (b_duz_dxl + b_dux_dzl)
b_dszz = b_duz_dzl
if (.not. ATTENUATION_VISCOELASTIC_SOLID) then
kappa_k(iglob) = (dux_dxl + duz_dzl) * (b_dux_dxl + b_duz_dzl)
mu_k(iglob) = dsxx * b_dsxx + dszz * b_dszz + &
2._CUSTOM_REAL * dsxz * b_dsxz - 1._CUSTOM_REAL/3._CUSTOM_REAL * kappa_k(iglob)
endif
!!! ATTENUATION
e1_sum=0._CUSTOM_REAL
e11_sum=0._CUSTOM_REAL
e13_sum=0._CUSTOM_REAL
e1_x_sum=0._CUSTOM_REAL
e1_z_sum=0._CUSTOM_REAL
lambdaplus2mu_att=0._CUSTOM_REAL
lambdaplusmu_att=0._CUSTOM_REAL
lambda_att=0._CUSTOM_REAL
mu_att=0._CUSTOM_REAL
sigma_xx_att=0._CUSTOM_REAL
sigma_zz_att=0._CUSTOM_REAL
sigma_xz_att=0._CUSTOM_REAL
if (ATTENUATION_VISCOELASTIC_SOLID) then
do i_sls = 1,N_SLS
e1_sum = e1_sum + e1(i,j,ispec,i_sls)
e11_sum = e11_sum + e11(i,j,ispec,i_sls)
e13_sum = e13_sum + e13(i,j,ispec,i_sls)
e1_x_sum = e1_x_sum + e1_x(i,j,ispec,i_sls)
e1_z_sum = e1_z_sum + e1_z(i,j,ispec,i_sls)
enddo
Qkappa_k(iglob) = - (b_dux_dxl + b_duz_dzl) * e1_sum
Qmu_k(iglob) = - b_dsxx * e1_x_sum - b_dszz * e1_z_sum - 2._CUSTOM_REAL * b_dsxz * e13_sum + &
1._CUSTOM_REAL/3._CUSTOM_REAL * Qkappa_k(iglob)
mu_att = rhoext(i,j,ispec)*vsext(i,j,ispec)*vsext(i,j,ispec)
lambdaplus2mu_att = rhoext(i,j,ispec)*vpext(i,j,ispec)*vpext(i,j,ispec)
lambda_att = lambdaplus2mu_att - 2._CUSTOM_REAL * mu_att
lambdaplusmu_att = lambdaplus2mu_att - mu_att
sigma_xx_att = (lambdaplus2mu_att*dux_dxl+lambda_att*duz_dzl)+&
+ lambdaplusmu_att*e1_sum+2._CUSTOM_REAL*mu_att*e11_sum
sigma_zz_att = (lambdaplus2mu_att*duz_dzl+lambda_att*dux_dxl)+&
+ lambdaplusmu_att*e1_sum-2._CUSTOM_REAL*mu_att*e11_sum
sigma_xz_att = mu_att * (duz_dxl + dux_dzl)
if ((trim(Q_KL) == 'tromp') .OR. (trim(Q_KL) == 'ficht')) then
kappa_k(iglob) = (sigma_xx_att + sigma_zz_att)*(b_dux_dxl+b_duz_dzl)
mu_k(iglob) = sigma_xx_att * b_dux_dxl + sigma_zz_att * b_duz_dzl + &
2._CUSTOM_REAL * sigma_xz_att * b_dsxz - &
1._CUSTOM_REAL/3._CUSTOM_REAL * kappa_k(iglob)
endif
if (trim(Q_KL) == 'chara') then
kappa_k(iglob) = (dux_dxl + duz_dzl) * (b_dux_dxl + b_duz_dzl)
mu_k(iglob) = dsxx * b_dsxx + dszz * b_dszz + &
2._CUSTOM_REAL * dsxz * b_dsxz - 1._CUSTOM_REAL/3._CUSTOM_REAL * kappa_k(iglob)
endif
endif
!Qkappa_k(iglob) = -kappa_k(iglob)
!Qmu_k(iglob) = -mu_k(iglob)
Qalpha_k(iglob) = Qkappa_k(iglob)
Qbeta_k(iglob) = Qmu_k(iglob)
! diagonal pseudo-Hessian
pdh_kappa_temp(iglob) = (b_dux_dxl + b_duz_dzl) * (b_dux_dxl + b_duz_dzl)
pdh_mu_temp(iglob) = b_dsxx * b_dsxx + b_dszz * b_dszz + SQRT(2._CUSTOM_REAL) * b_dsxz * b_dsxz - &
SQRT(1._CUSTOM_REAL/3._CUSTOM_REAL) * pdh_kappa_temp(iglob)
pdh_rho_temp(iglob) = b_displ_elastic(1,iglob)**2 + b_displ_elastic(2,iglob)**2 + b_displ_elastic(3,iglob)**2
!pdh_vp_temp(iglob) = 2 * (1._CUSTOM_REAL + 4._CUSTOM_REAL*mul_global(iglob)/(3._CUSTOM_REAL*kappal_global(iglob))) * &
! pdh_kappa_temp(iglob)
!pdh_vs_temp(iglob) = pdh_mu_temp(iglob) - 4._CUSTOM_REAL*mul_global(iglob)*pdh_kappa_temp(iglob)/ &
! (3._CUSTOM_REAL*kappal_global(iglob))
!pdh_rhop_temp(iglob) = pdh_rho_temp(iglob) + pdh_kappa_temp(iglob) + pdh_mu_temp(iglob)
!!! HTI elastic constants parameterization PWY
if (ANISO) then
hti_ec_c11_k(iglob) = dux_dxl * b_dux_dxl
hti_ec_c13_k(iglob) = (duz_dzl * b_dux_dxl) + (dux_dxl * b_duz_dzl)
hti_ec_c33_k(iglob) = duz_dzl * b_duz_dzl
hti_ec_c55_k(iglob) = (duz_dxl + dux_dzl) * (b_duz_dxl + b_dux_dzl)
tti_ec_c11_k(iglob) = dux_dxl * b_dux_dxl
tti_ec_c13_k(iglob) = (duz_dzl * b_dux_dxl) + (dux_dxl * b_duz_dzl)
tti_ec_c15_k(iglob) = 2._CUSTOM_REAL * (duz_dxl * b_dux_dxl) + 2._CUSTOM_REAL * (dux_dxl * b_duz_dxl)
tti_ec_c33_k(iglob) = duz_dzl * b_duz_dzl
tti_ec_c35_k(iglob) = 2._CUSTOM_REAL * (duz_dxl * b_duz_dzl) + 2._CUSTOM_REAL * (duz_dzl * b_duz_dxl)
tti_ec_c55_k(iglob) = 4._CUSTOM_REAL * (duz_dxl * b_duz_dxl)
!! diagonal pseudo Hessian
pdh_hti_ec_c11_temp(iglob) = b_dux_dxl * b_dux_dxl
pdh_hti_ec_c13_temp(iglob) = (b_duz_dzl + b_dux_dxl) * (b_duz_dzl + b_dux_dxl)
pdh_hti_ec_c33_temp(iglob) = b_duz_dzl * b_duz_dzl
pdh_hti_ec_c55_temp(iglob) = (b_duz_dxl + b_dux_dzl) * (b_duz_dxl + b_dux_dzl)
pdh_hti_ec_c11_temp1(iglob) = b_dux_dxl
pdh_hti_ec_c13_temp1(iglob) = (b_duz_dzl + b_dux_dxl)
pdh_hti_ec_c33_temp1(iglob) = b_duz_dzl
pdh_hti_ec_c55_temp1(iglob) = (b_duz_dxl + b_dux_dzl)
pdh_tti_ec_c11_temp(iglob) = b_dux_dxl * b_dux_dxl
pdh_tti_ec_c13_temp(iglob) = (b_duz_dzl + b_dux_dxl) * (b_duz_dzl + b_dux_dxl)
pdh_tti_ec_c15_temp(iglob) = 4._CUSTOM_REAL * (b_duz_dxl + b_dux_dxl) * (b_duz_dxl + b_dux_dxl)
pdh_tti_ec_c33_temp(iglob) = b_duz_dzl * b_duz_dzl
pdh_tti_ec_c35_temp(iglob) = 4._CUSTOM_REAL * (b_duz_dxl + b_duz_dzl) * (b_duz_dxl + b_duz_dzl)
pdh_tti_ec_c55_temp(iglob) = 4._CUSTOM_REAL * (b_duz_dxl * b_duz_dxl)
endif
else !SH (membrane) waves
mu_k(iglob) = duy_dxl * b_duy_dxl + duy_dzl * b_duy_dzl
endif
enddo; enddo
endif
enddo
do iglob = 1,nglob
rho_k(iglob) = accel_elastic(1,iglob)*b_displ_elastic(1,iglob) + &
accel_elastic(2,iglob)*b_displ_elastic(2,iglob) + &
accel_elastic(3,iglob)*b_displ_elastic(3,iglob)
hti_ec_rho_k(iglob) = rho_k(iglob) ! density kl hti elastic constant parameterization PWY
tti_ec_rho_k(iglob) = rho_k(iglob)
rhorho_el_hessian_temp1(iglob) = b_accel_elastic(1,iglob)*b_accel_elastic(1,iglob) + &
b_accel_elastic(2,iglob)*b_accel_elastic(2,iglob) + &
b_accel_elastic(3,iglob)*b_accel_elastic(3,iglob)
pdh_hti_ec_rho_temp(iglob) = rhorho_el_hessian_temp1(iglob)
pdh_tti_ec_rho_temp(iglob) = rhorho_el_hessian_temp1(iglob)
! pdh_rho_temp(iglob) = rhorho_el_hessian_temp1(iglob)
! pdh_vp_temp(iglob) = 2._CUSTOM_REAL * (1._CUSTOM_REAL + 4._CUSTOM_REAL*mul_global(iglob)/(3._CUSTOM_REAL*kappal_global(iglob))) * &
! pdh_kappa_temp(iglob)
! pdh_vs_temp(iglob) = pdh_mu_temp(iglob) - 4._CUSTOM_REAL*mul_global(iglob)*pdh_kappa_temp(iglob)/ &
! (3._CUSTOM_REAL*kappal_global(iglob))
! pdh_rhop_temp(iglob) = pdh_rho_temp(iglob) + pdh_kappa_temp(iglob) + pdh_mu_temp(iglob)
rhorho_el_hessian_temp2(iglob) = accel_elastic(1,iglob)*b_accel_elastic(1,iglob) + &
accel_elastic(2,iglob)*b_accel_elastic(2,iglob) + &
accel_elastic(3,iglob)*b_accel_elastic(3,iglob)
! pdh_rho_temp(iglob) = b_displ_elastic(1,iglob)**2 + b_displ_elastic(2,iglob)**2 + b_displ_elastic(3,iglob)**2
enddo
do ispec = 1, nspec
if( elastic(ispec) ) then
do j = 1, NGLLZ
do i = 1, NGLLX
iglob = ibool(i,j,ispec)
if( .not. assign_external_model ) then
rhol_global(iglob) = density(1,kmato(ispec))
mul_global(iglob) = poroelastcoef(2,1,kmato(ispec))
kappal_global(iglob) = poroelastcoef(3,1,kmato(ispec)) - &
4._CUSTOM_REAL*mul_global(iglob) / 3._CUSTOM_REAL
else
rhol_global(iglob) = rhoext(i,j,ispec)
mul_global(iglob) = rhoext(i,j,ispec)*vsext(i,j,ispec)*vsext(i,j,ispec)
kappal_global(iglob) = rhoext(i,j,ispec)*vpext(i,j,ispec)*vpext(i,j,ispec) - &
4._CUSTOM_REAL*mul_global(iglob) / 3._CUSTOM_REAL
lambdal_global(iglob) = kappal_global(iglob) - 2._CUSTOM_REAL*mul_global(iglob) / 3._CUSTOM_REAL
ipl_global(iglob) = rhoext(i,j,ispec)*vpext(i,j,ispec)
isl_global(iglob) = rhoext(i,j,ispec)*vsext(i,j,ispec)
sigmal_global(iglob) = vpext(i,j,ispec) / vsext(i,j,ispec)
vpl_global(iglob) = vpext(i,j,ispec)
vsl_global(iglob) = vsext(i,j,ispec)
!! Attenuation
Qkappal_global(iglob) = QKappa_attenuationext(i,j,ispec)
Qmul_global(iglob) = Qmu_attenuationext(i,j,ispec)
Qbetal_global(iglob) = Qbeta_attenuationext(i,j,ispec)
Qalphal_global(iglob) = Qalpha_attenuationext(i,j,ispec)
!tti_c11ul_global(iglob) = c11uext(i,j,ispec)
!tti_c13ul_global(iglob) = c13uext(i,j,ispec)
!tti_c33ul_global(iglob) = c33uext(i,j,ispec)
!tti_c55ul_global(iglob) = c55uext(i,j,ispec)
!tti_thetaul_global(iglob) = thetaext(i,j,ispec)
pdh_vp_temp(iglob) = SQRT(2 * (1._CUSTOM_REAL + 4._CUSTOM_REAL*mul_global(iglob)/(3._CUSTOM_REAL*kappal_global(iglob)))) * &
pdh_kappa_temp(iglob)
pdh_vs_temp(iglob) = SQRT(2._CUSTOM_REAL) * pdh_mu_temp(iglob) - SQRT(8._CUSTOM_REAL*mul_global(iglob)/&
(3._CUSTOM_REAL*kappal_global(iglob)))*pdh_kappa_temp(iglob)
pdh_rhop_temp(iglob) = pdh_rho_temp(iglob) + pdh_kappa_temp(iglob) + pdh_mu_temp(iglob)
pdh_dl_lambda_temp(iglob) = SQRT(2*(1 + 2*mul_global(iglob)/(3*kappal_global(iglob)))) * &
pdh_kappa_temp(iglob)
pdh_dl_mu_temp(iglob) = pdh_mu_temp(iglob) + SQRT(2*mul_global(iglob)/(3*kappal_global(iglob)))*&
pdh_kappa_temp(iglob)
pdh_dl_rho_temp(iglob) = pdh_rho_temp(iglob)
pdh_dip_ip_temp(iglob) = SQRT(2 * (1._CUSTOM_REAL + 4._CUSTOM_REAL*mul_global(iglob)/&
(3._CUSTOM_REAL*kappal_global(iglob)))) * pdh_kappa_temp(iglob)
pdh_dip_is_temp(iglob) = SQRT(2._CUSTOM_REAL) * pdh_mu_temp(iglob) - SQRT(8._CUSTOM_REAL*mul_global(iglob)/&
(3._CUSTOM_REAL*kappal_global(iglob)))*pdh_kappa_temp(iglob)
pdh_dip_rho_temp(iglob) = pdh_rho_temp(iglob) - pdh_kappa_temp(iglob) - pdh_mu_temp(iglob)
pdh_vipi_vp_temp(iglob) = SQRT(2 * (1._CUSTOM_REAL + 8._CUSTOM_REAL*mul_global(iglob)/&
(3._CUSTOM_REAL*kappal_global(iglob)))) * pdh_kappa_temp(iglob) - pdh_mu_temp(iglob) -pdh_rho_temp(iglob)
pdh_vipi_vs_temp(iglob) = SQRT(2._CUSTOM_REAL) * pdh_mu_temp(iglob) - SQRT(8._CUSTOM_REAL*mul_global(iglob)/&
(3._CUSTOM_REAL*kappal_global(iglob)))*pdh_kappa_temp(iglob)
pdh_vipi_ip_temp(iglob) = pdh_rho_temp(iglob) + pdh_kappa_temp(iglob) + pdh_mu_temp(iglob)
pdh_vipii_vp_temp(iglob) = SQRT(2 * (1._CUSTOM_REAL + 8._CUSTOM_REAL*mul_global(iglob)/&
(3._CUSTOM_REAL*kappal_global(iglob)))) * pdh_kappa_temp(iglob)
pdh_vipii_vs_temp(iglob) = pdh_mu_temp(iglob) - SQRT(11._CUSTOM_REAL*mul_global(iglob)/&
(3._CUSTOM_REAL*kappal_global(iglob)))*pdh_kappa_temp(iglob)-pdh_rho_temp(iglob)
pdh_vipii_is_temp(iglob) = pdh_rho_temp(iglob) + pdh_kappa_temp(iglob) + pdh_mu_temp(iglob)
pdh_sigma_vp_temp(iglob) = SQRT(2._CUSTOM_REAL) * (pdh_mu_temp(iglob) + pdh_kappa_temp(iglob))
pdh_sigma_sigma_temp(iglob) = SQRT(2._CUSTOM_REAL) * pdh_mu_temp(iglob) - SQRT(8._CUSTOM_REAL*mul_global(iglob)/&
(3._CUSTOM_REAL*kappal_global(iglob)))*pdh_kappa_temp(iglob)
pdh_sigma_rho_temp(iglob) = pdh_rho_temp(iglob) + pdh_kappa_temp(iglob) + pdh_mu_temp(iglob)
!! HTI parameters global
if (ANISO) then
hti_rhol_global(iglob) = rhoext(i,j,ispec)
hti_c11l_global(iglob) = c11ext(i,j,ispec)
hti_c13l_global(iglob) = c13ext(i,j,ispec)
hti_c33l_global(iglob) = c33ext(i,j,ispec)
hti_c55l_global(iglob) = c55ext(i,j,ispec)
tti_rhol_global(iglob) = rhoext(i,j,ispec)
tti_c11l_global(iglob) = c11ext(i,j,ispec)
tti_c13l_global(iglob) = c13ext(i,j,ispec)
tti_c33l_global(iglob) = c33ext(i,j,ispec)
tti_c55l_global(iglob) = c55ext(i,j,ispec)
tti_c15l_global(iglob) = c15ext(i,j,ispec)
tti_c35l_global(iglob) = c35ext(i,j,ispec)
tti_c11ul_global(iglob) = c11uext(i,j,ispec)
tti_c13ul_global(iglob) = c13uext(i,j,ispec)
tti_c33ul_global(iglob) = c33uext(i,j,ispec)
tti_c55ul_global(iglob) = c55uext(i,j,ispec)
tti_thetaul_global(iglob) = thetaext(i,j,ispec)
tti_rhoul_global(iglob) = rhoext(i,j,ispec)
m1l_global(iglob) = m1ext(i,j,ispec)
m2l_global(iglob) = m2ext(i,j,ispec)
m3l_global(iglob) = m3ext(i,j,ispec)
m4l_global(iglob) = m4ext(i,j,ispec)
m5l_global(iglob) = m5ext(i,j,ispec)
m6l_global(iglob) = m6ext(i,j,ispec)
p1l_global(iglob) = c11uext(i,j,ispec) - 2._CUSTOM_REAL * c13uext(i,j,ispec) + &
c33uext(i,j,ispec) - 4._CUSTOM_REAL * c55uext(i,j,ispec)
p2l_global(iglob) = c11uext(i,j,ispec) - c13uext(i,j,ispec)
hti_rhopl_global(iglob) = rhoext(i,j,ispec)
hti_alphal_global(iglob) = SQRT(c33ext(i,j,ispec)/rhoext(i,j,ispec))
hti_betal_global(iglob) = SQRT(c55ext(i,j,ispec)/rhoext(i,j,ispec))
hti_deltal_global(iglob) = (hti_c13l_global(iglob) + hti_c55l_global(iglob))**2/(2._CUSTOM_REAL*&
hti_c33l_global(iglob)*(hti_c33l_global(iglob)-hti_c55l_global(iglob)))-&
(hti_c33l_global(iglob) - hti_c55l_global(iglob))/(2._CUSTOM_REAL * hti_c33l_global(iglob))
hti_epsilonl_global(iglob) = (hti_c11l_global(iglob)-hti_c33l_global(iglob))/&
(2._CUSTOM_REAL * hti_c33l_global(iglob))
hti_etal_global(iglob) = (hti_epsilonl_global(iglob) - hti_deltal_global(iglob))/&
(1._CUSTOM_REAL + 2._CUSTOM_REAL * hti_deltal_global(iglob))
hti_alphahl_global(iglob) = hti_alphal_global(iglob) * SQRT(1._CUSTOM_REAL+2*hti_epsilonl_global(iglob))
hti_alphanl_global(iglob) = hti_alphal_global(iglob) * SQRT(1._CUSTOM_REAL+2*hti_deltal_global(iglob))
hti_coeffl_global(nglob) = SQRT(2._CUSTOM_REAL*hti_deltal_global(iglob)*hti_alphal_global(iglob)*&
hti_alphal_global(iglob)*(hti_alphal_global(iglob)*hti_alphal_global(iglob)-&
hti_betal_global(iglob)*hti_betal_global(iglob))+&
(hti_alphal_global(iglob)*hti_alphal_global(iglob)-&
hti_betal_global(iglob)*hti_betal_global(iglob))**2)
!tti_rhopl_global(iglob) = rhoext(i,j,ispec)
!tti_alphal_global(iglob) = SQRT(c33uext(i,j,ispec)/rhoext(i,j,ispec))
!tti_betal_global(iglob) = SQRT(c55uext(i,j,ispec)/rhoext(i,j,ispec))
!tti_deltal_global(iglob) = (tti_c13ul_global(iglob) + tti_c55ul_global(iglob))**2/(2._CUSTOM_REAL*&
! tti_c33ul_global(iglob)*(tti_c33ul_global(iglob)-tti_c55ul_global(iglob)))-&
! (tti_c33ul_global(iglob) - tti_c55ul_global(iglob))/(2._CUSTOM_REAL * tti_c33ul_global(iglob))
!tti_epsilonl_global(iglob) = (tti_c11ul_global(iglob)-tti_c33ul_global(iglob))/&
! (2._CUSTOM_REAL * tti_c33ul_global(iglob))
!tti_coeffl_global(nglob) = SQRT(2._CUSTOM_REAL*tti_deltal_global(iglob)*tti_alphal_global(iglob)*&
! tti_alphal_global(iglob)*(tti_alphal_global(iglob)*tti_alphal_global(iglob)-&
! tti_betal_global(iglob)*tti_betal_global(iglob))+&
! (tti_alphal_global(iglob)*tti_alphal_global(iglob)-&
! tti_betal_global(iglob)*tti_betal_global(iglob))**2)
!!! Kernels in TTI unrotated elastic-constant parameterization
!tti_ecu_c11_k(iglob) = tti_ec_c11_k(iglob)*tti_c11ul_global(iglob)*m1ext(i,j,ispec)/(tti_c11l_global(iglob) * 8) + &
! tti_ec_c13_k(iglob)*tti_c11ul_global(iglob)*m2ext(i,j,ispec)/(tti_c13l_global(iglob)*8) + &
! tti_ec_c15_k(iglob)*tti_c11ul_global(iglob)*m5ext(i,j,ispec)/(tti_c15l_global(iglob)*4) + &
! tti_ec_c33_k(iglob)*tti_c11ul_global(iglob)*m3ext(i,j,ispec)/(tti_c33l_global(iglob)*8) + &
! tti_ec_c35_k(iglob)*tti_c11ul_global(iglob)*m5ext(i,j,ispec)/(tti_c35l_global(iglob)*4) - &
! tti_ec_c35_k(iglob)*tti_c11ul_global(iglob)*2*m4ext(i,j,ispec)/(tti_c35l_global(iglob)*4) + &
! tti_ec_c55_k(iglob)*tti_c11ul_global(iglob)*m2ext(i,j,ispec)/(tti_c55l_global(iglob)*8)
!!! diagonal pseudo Hessian
pdh_hti_thom_alpha_temp(iglob) = 2._CUSTOM_REAL * hti_rhopl_global(iglob) * hti_alphal_global(iglob) * &
pdh_hti_ec_c33_temp1(iglob) + 2._CUSTOM_REAL * hti_rhopl_global(iglob) * hti_alphal_global(iglob) * &
(2._CUSTOM_REAL * hti_epsilonl_global(iglob) + 1._CUSTOM_REAL) * pdh_hti_ec_c11_temp1(iglob) + &
4._CUSTOM_REAL*hti_rhopl_global(iglob)*hti_deltal_global(iglob)*hti_alphal_global(iglob)* &
hti_alphal_global(iglob)*hti_alphal_global(iglob)*pdh_hti_ec_c13_temp1(iglob)/hti_coeffl_global(nglob)-&
2._CUSTOM_REAL*hti_rhopl_global(iglob)*hti_deltal_global(iglob)*hti_alphal_global(iglob)*&
hti_betal_global(iglob)*hti_betal_global(iglob)*pdh_hti_ec_c13_temp1(iglob)/hti_coeffl_global(nglob)+&
2._CUSTOM_REAL*hti_rhopl_global(iglob)*hti_alphal_global(iglob)*&
(hti_alphal_global(iglob)**2-hti_betal_global(iglob)**2)*pdh_hti_ec_c13_temp1(iglob)/hti_coeffl_global(nglob)
pdh_hti_thom_beta_temp(iglob) = 2._CUSTOM_REAL*hti_rhopl_global(iglob)*hti_betal_global(iglob)*&
pdh_hti_ec_c55_temp1(iglob)-2._CUSTOM_REAL*hti_rhopl_global(iglob)*hti_deltal_global(iglob)*hti_alphal_global(iglob)*&
hti_alphal_global(iglob)*hti_betal_global(iglob)*pdh_hti_ec_c13_temp1(iglob)/hti_coeffl_global(nglob) - &
2._CUSTOM_REAL*hti_rhopl_global(iglob)*hti_betal_global(iglob)*&
(hti_alphal_global(iglob)**2-hti_betal_global(iglob)**2)*pdh_hti_ec_c13_temp1(iglob)/hti_coeffl_global(nglob)-&
2._CUSTOM_REAL*hti_rhopl_global(iglob)*hti_betal_global(iglob)*pdh_hti_ec_c13_temp1(iglob)
pdh_hti_thom_epsilon_temp(iglob) = 2._CUSTOM_REAL*hti_rhopl_global(iglob)*pdh_hti_ec_c13_temp1(iglob)*&
hti_alphal_global(iglob)**2
pdh_hti_thom_delta_temp(iglob) = hti_rhopl_global(iglob)*pdh_hti_ec_c13_temp1(iglob)*&
(hti_alphal_global(iglob)**2-hti_betal_global(iglob)**2)*hti_alphal_global(iglob)**2/hti_coeffl_global(nglob)
pdh_hti_thom_rhop_temp(iglob) = pdh_hti_ec_rho_temp(iglob)+pdh_hti_ec_c33_temp1(iglob)*hti_alphal_global(iglob)**2 +&
pdh_hti_ec_c55_temp1(iglob)*hti_betal_global(iglob)**2+pdh_hti_ec_c13_temp1(iglob)*hti_coeffl_global(nglob)-&
pdh_hti_ec_c13_temp1(iglob)*hti_betal_global(iglob)**2+pdh_hti_ec_c11_temp1(iglob)*&
(2._CUSTOM_REAL * hti_epsilonl_global(iglob)+1._CUSTOM_REAL)*hti_alphal_global(iglob)**2
endif
endif
rho_kl(i,j,ispec) = rho_kl(i,j,ispec) - rhol_global(iglob) * rho_k(iglob) * deltat
if (ATTENUATION_VISCOELASTIC_SOLID) then
if((trim(Q_KL) == 'tromp') .OR. (trim(Q_KL) == 'ficht')) then
mu_kl(i,j,ispec) = mu_kl(i,j,ispec) - TWO * mu_k(iglob) * deltat
kappa_kl(i,j,ispec) = kappa_kl(i,j,ispec) - kappa_k(iglob) * deltat
endif
if (trim(Q_KL) == 'chara') then
mu_kl(i,j,ispec) = mu_kl(i,j,ispec) - TWO * mul_global(iglob) * mu_k(iglob) * deltat
kappa_kl(i,j,ispec) = kappa_kl(i,j,ispec) - kappal_global(iglob) * kappa_k(iglob) * deltat
endif
endif
if (.not. ATTENUATION_VISCOELASTIC_SOLID) then
mu_kl(i,j,ispec) = mu_kl(i,j,ispec) - TWO * mul_global(iglob) * mu_k(iglob) * deltat
kappa_kl(i,j,ispec) = kappa_kl(i,j,ispec) - kappal_global(iglob) * kappa_k(iglob) * deltat
endif
! attenuation
! Qkappa_kl(i,j,ispec) = -1._CUSTOM_REAL * kappa_kl(i,j,ispec)/Qkappal_global(iglob)
! Qmu_kl(i,j,ispec) = -1._CUSTOM_REAL * mu_kl(i,j,ispec)/Qmul_global(iglob)
!Qalpha_kl(i,j,ispec) = -1._CUSTOM_REAL * kappa_kl(i,j,ispec)*(3.0*kappal_global(iglob)+4.0*mul_global(iglob))/ &
! (3.0*kappal_global(iglob)+mul_global(iglob))
!Qalpha_kl(i,j,ispec) = 0.5 * Qalpha_kl(i,j,ispec) - 0.5 * kappa_kl(i,j,ispec)*(3.0*mul_global(iglob)*Qkappal_global(iglob))/ &
! ((3.0*kappal_global(iglob)+4.0*mul_global(iglob))*Qmul_global(iglob) - &
! 3.0*mul_global(iglob)*Qkappal_global(iglob)) + 0.5 * Qmu_kl(i,j,ispec)
!Qkappa_kl(i,j,ispec) = 0.5*Qalpha_kl(i,j,ispec) + 0.5* Qmu_kl(i,j,ispec)
!
rhop_kl(i,j,ispec) = rho_kl(i,j,ispec) + kappa_kl(i,j,ispec) + mu_kl(i,j,ispec)
! not attenuation
if ( .not. ATTENUATION_VISCOELASTIC_SOLID) then
beta_kl(i,j,ispec) = TWO * (mu_kl(i,j,ispec) - 4._CUSTOM_REAL * mul_global(iglob)/&
(3._CUSTOM_REAL * kappal_global(iglob)) * kappa_kl(i,j,ispec))
alpha_kl(i,j,ispec) = TWO * (1._CUSTOM_REAL + 4._CUSTOM_REAL * mul_global(iglob)/&
(3._CUSTOM_REAL * kappal_global(iglob))) * kappa_kl(i,j,ispec)
endif
! attenuation
if (ATTENUATION_VISCOELASTIC_SOLID) then
if (trim(Q_KL) == 'tromp') then
!Qkappa_kl(i,j,ispec) = -1._CUSTOM_REAL * kappa_kl(i,j,ispec)/Qkappal_global(iglob)
Qkappa_kl(i,j,ispec) = -1._CUSTOM_REAL * kappa_kl(i,j,ispec)
!Qmu_kl(i,j,ispec) = -1._CUSTOM_REAL * mu_kl(i,j,ispec)/Qmul_global(iglob)
Qmu_kl(i,j,ispec) = -1._CUSTOM_REAL * mu_kl(i,j,ispec)
endif
if (trim(Q_KL) == 'chara') then
Qkappa_kl(i,j,ispec) = Qkappa_kl(i,j,ispec) + kappal_global(iglob) * Qkappal_global(iglob) * Qkappa_k(iglob) * deltat
! (1._CUSTOM_REAL + Qkappal_global(iglob))
Qmu_kl(i,j,ispec) = Qmu_kl(i,j,ispec) + mul_global(iglob) * Qmul_global(iglob) * Qmu_k(iglob) * deltat
! (1._CUSTOM_REAL + Qmul_global(iglob))
endif
if (trim(Q_KL) == 'ficht') then
Qkappa_kl(i,j,ispec) = Qkappa_kl(i,j,ispec) + Qkappal_global(iglob)*kappal_global(iglob) * Qkappa_k(iglob) * deltat
Qmu_kl(i,j,ispec) = Qmu_kl(i,j,ispec) + 2._CUSTOM_REAL*Qmul_global(iglob)*mul_global(iglob)*Qmu_k(iglob)*deltat
endif
!Qkappa_kl(i,j,ispec) = 0.5_CUSTOM_REAL * Qkappa_kl(i,j,ispec) + 0.5_CUSTOM_REAL * Qmu_kl(i,j,ispec)
Qalpha_kl(i,j,ispec) = (Qbetal_global(iglob) * vpl_global(iglob)*vpl_global(iglob))*Qkappa_kl(i,j,ispec)/&
(Qbetal_global(iglob) * vpl_global(iglob)*vpl_global(iglob) - &
Qalphal_global(iglob) * vsl_global(iglob)*vsl_global(iglob))
Qbeta_kl(i,j,ispec) = Qmu_kl(i,j,ispec) - &
(Qalphal_global(iglob) * vsl_global(iglob)**2)*Qkappa_kl(i,j,ispec)/&
(Qbetal_global(iglob) * vpl_global(iglob)**2 - Qalphal_global(iglob) * vsl_global(iglob)**2)
!Qbeta_kl(i,j,ispec) = Qmu_kl(i,j,ispec)
beta_kl(i,j,ispec) = TWO * (mu_kl(i,j,ispec) - 4._CUSTOM_REAL * mul_global(iglob)/&
(3._CUSTOM_REAL * kappal_global(iglob)) * kappa_kl(i,j,ispec)) + &
(2._CUSTOM_REAL * Qalphal_global(iglob) * vsl_global(iglob)**2)*Qkappa_kl(i,j,ispec)/&
(Qbetal_global(iglob) * vpl_global(iglob)**2 - Qalphal_global(iglob) * vsl_global(iglob)**2)-&
(2._CUSTOM_REAL * vsl_global(iglob)**2)*Qkappa_kl(i,j,ispec)/&
(vpl_global(iglob)**2 - vsl_global(iglob)**2)
alpha_kl(i,j,ispec) = TWO * (1._CUSTOM_REAL + 4._CUSTOM_REAL * mul_global(iglob)/&
(3._CUSTOM_REAL * kappal_global(iglob))) * kappa_kl(i,j,ispec) + &
(2._CUSTOM_REAL * vpl_global(iglob)**2)*Qkappa_kl(i,j,ispec)/&
(vpl_global(iglob)**2 - vsl_global(iglob)**2) - &
(2._CUSTOM_REAL * Qbetal_global(iglob) * vpl_global(iglob)**2)*Qkappa_kl(i,j,ispec)/&
(Qbetal_global(iglob) * vpl_global(iglob)**2 - Qalphal_global(iglob) * vsl_global(iglob)**2)
endif
dl_lambda_kl(i,j,ispec) = (1._CUSTOM_REAL - 2._CUSTOM_REAL*mul_global(iglob)/(3._CUSTOM_REAL*kappal_global(iglob)))*&
kappa_kl(i,j,ispec)
dl_mu_kl(i,j,ispec) = mu_kl(i,j,ispec) + 2._CUSTOM_REAL*mul_global(iglob)*kappa_kl(i,j,ispec)/&
(3._CUSTOM_REAL*kappal_global(iglob))
dl_rho_kl(i,j,ispec) = rho_kl(i,j,ispec)
dip_ip_kl(i,j,ispec) = alpha_kl(i,j,ispec)
dip_is_kl(i,j,ispec) = beta_kl(i,j,ispec)
dip_rho_kl(i,j,ispec) = rho_kl(i,j,ispec) - kappa_kl(i,j,ispec) - mu_kl(i,j,ispec)
vipi_vp_kl(i,j,ispec) = alpha_kl(i,j,ispec) - rhop_kl(i,j,ispec)
vipi_vs_kl(i,j,ispec) = beta_kl(i,j,ispec)
vipi_ip_kl(i,j,ispec) = rhop_kl(i,j,ispec)
vipii_vp_kl(i,j,ispec) = alpha_kl(i,j,ispec)
vipii_vs_kl(i,j,ispec) = beta_kl(i,j,ispec) - rhop_kl(i,j,ispec)
vipii_is_kl(i,j,ispec) = rhop_kl(i,j,ispec)
sigma_vp_kl(i,j,ispec) = alpha_kl(i,j,ispec) + beta_kl(i,j,ispec)
sigma_sigma_kl(i,j,ispec) = - beta_kl(i,j,ispec)
sigma_rho_kl(i,j,ispec) = rhop_kl(i,j,ispec)
!! Diagonal pseudo-Hessian in isotropic-elastic media
pdh_vp(i,j,ispec) = pdh_vp(i,j,ispec) + pdh_vp_temp(iglob)*pdh_vp_temp(iglob)*deltat
pdh_vs(i,j,ispec) = pdh_vs(i,j,ispec) + pdh_vs_temp(iglob)*pdh_vs_temp(iglob)*deltat
pdh_rhop(i,j,ispec) = pdh_rhop(i,j,ispec) + 0.2 * pdh_vs_temp(iglob)*pdh_vs_temp(iglob)*deltat
pdh_kappa(i,j,ispec) = pdh_kappa(i,j,ispec) +kappal_global(iglob)* pdh_kappa_temp(iglob)*&
pdh_kappa_temp(iglob)*deltat
pdh_mu(i,j,ispec) = pdh_mu(i,j,ispec) + mul_global(iglob)*pdh_mu_temp(iglob)*&
pdh_mu_temp(iglob)*deltat
pdh_rho(i,j,ispec) = pdh_rho(i,j,ispec) + rhol_global(iglob)*pdh_rho_temp(iglob)*&
pdh_rho_temp(iglob)*deltat
pdh_dl_lambda(i,j,ispec) = pdh_dl_lambda(i,j,ispec) + lambdal_global(iglob)*pdh_dl_lambda_temp(iglob)*&
pdh_dl_lambda_temp(iglob)*deltat
pdh_dl_mu(i,j,ispec) = pdh_dl_mu(i,j,ispec) + mul_global(iglob)*pdh_dl_mu_temp(iglob)*&
pdh_dl_mu_temp(iglob)*deltat
pdh_dl_rho(i,j,ispec) = pdh_dl_rho(i,j,ispec) + rhol_global(iglob)*pdh_dl_rho_temp(iglob)*&
pdh_dl_rho_temp(iglob)*deltat
pdh_dip_ip(i,j,ispec) = pdh_dip_ip(i,j,ispec) + ipl_global(iglob)*pdh_dip_ip_temp(iglob)*&
pdh_dip_ip_temp(iglob)*deltat
pdh_dip_is(i,j,ispec) = pdh_dip_is(i,j,ispec) + isl_global(iglob)*pdh_dip_is_temp(iglob)*&
pdh_dip_is_temp(iglob)*deltat
pdh_dip_rho(i,j,ispec) = pdh_dip_rho(i,j,ispec) + pdh_dip_rho_temp(iglob)*&
pdh_dip_rho_temp(iglob)*deltat
pdh_vipi_vp(i,j,ispec) = pdh_vipi_vp(i,j,ispec) + vsl_global(iglob)*pdh_vipi_vs_temp(iglob)*&
pdh_vipi_vs_temp(iglob)*deltat
pdh_vipi_vs(i,j,ispec) = pdh_vipi_vs(i,j,ispec) + vsl_global(iglob)*pdh_vipi_vs_temp(iglob)*&
pdh_vipi_vs_temp(iglob)*deltat
pdh_vipi_ip(i,j,ispec) = pdh_vipi_ip(i,j,ispec) + vsl_global(iglob)*pdh_vipi_vs_temp(iglob)*&
pdh_vipi_vs_temp(iglob)*deltat
pdh_vipii_vp(i,j,ispec) = pdh_vipii_vp(i,j,ispec) + vsl_global(iglob)*pdh_vipii_vs_temp(iglob)*&
pdh_vipii_vs_temp(iglob)*deltat
pdh_vipii_vs(i,j,ispec) = pdh_vipii_vs(i,j,ispec) + vsl_global(iglob)*pdh_vipii_vs_temp(iglob)*&
pdh_vipii_vs_temp(iglob)*deltat
pdh_vipii_is(i,j,ispec) = pdh_vipii_is(i,j,ispec) + vsl_global(iglob)*pdh_vipii_vs_temp(iglob)*&
pdh_vipii_vs_temp(iglob)*deltat
pdh_sigma_vp(i,j,ispec) = pdh_sigma_vp(i,j,ispec) + rhol_global(iglob)*pdh_sigma_rho_temp(iglob)*&
pdh_sigma_rho_temp(iglob)*deltat
pdh_sigma_sigma(i,j,ispec) = pdh_sigma_sigma(i,j,ispec) + rhol_global(iglob)*pdh_sigma_rho_temp(iglob)*&
pdh_sigma_rho_temp(iglob)*deltat
pdh_sigma_rho(i,j,ispec) = pdh_sigma_rho(i,j,ispec) + rhol_global(iglob)*pdh_sigma_rho_temp(iglob)*&
pdh_sigma_rho_temp(iglob)*deltat
!pdh_vp(i,j,ispec) = 2 * (1._CUSTOM_REAL + 4._CUSTOM_REAL*mul_global(iglob)/(3._CUSTOM_REAL*kappal_global(iglob)))*&
! pdh_kappa(i,j,ispec)
!pdh_vs(i,j,ispec) = pdh_mu(i,j,ispec) - (4._CUSTOM_REAL*mul_global(iglob)/(3._CUSTOM_REAL*kappal_global(iglob)))*&
! pdh_kappa(i,j,ispec)
!pdh_rhop(i,j,ispec) = pdh_kappa(i,j,ispec) + pdh_mu(i,j,ispec) + pdh_rho(i,j,ispec)
!
bulk_c_kl(i,j,ispec) = TWO * kappa_kl(i,j,ispec)
bulk_beta_kl(i,j,ispec) = TWO * mu_kl(i,j,ispec)
rhorho_el_hessian_final1(i,j,ispec) = rhorho_el_hessian_final1(i,j,ispec) + &
rhorho_el_hessian_temp1(iglob) * deltat
rhorho_el_hessian_final2(i,j,ispec) = rhorho_el_hessian_final2(i,j,ispec) + &
rhorho_el_hessian_temp2(iglob) * deltat
! Kernels in HTI media with elastic constants parameterization
if (ANISO) then
hti_ec_rho_kl(i,j,ispec) = hti_ec_rho_kl(i,j,ispec) - hti_rhol_global(iglob) * &
hti_ec_rho_k(iglob) * deltat
hti_ec_c11_kl(i,j,ispec) = hti_ec_c11_kl(i,j,ispec) - hti_c11l_global(iglob) * &
hti_ec_c11_k(iglob) * deltat
hti_ec_c13_kl(i,j,ispec) = hti_ec_c13_kl(i,j,ispec) - hti_c13l_global(iglob) * &
hti_ec_c13_k(iglob) * deltat
hti_ec_c33_kl(i,j,ispec) = hti_ec_c33_kl(i,j,ispec) - hti_c33l_global(iglob) * &
hti_ec_c33_k(iglob) * deltat
hti_ec_c55_kl(i,j,ispec) = hti_ec_c55_kl(i,j,ispec) - hti_c55l_global(iglob) * &
hti_ec_c55_k(iglob) * deltat
tti_ec_rho_kl(i,j,ispec) = tti_ec_rho_kl(i,j,ispec) - tti_rhol_global(iglob) * &
tti_ec_rho_k(iglob) * deltat
tti_ec_c11_kl(i,j,ispec) = tti_ec_c11_kl(i,j,ispec) - tti_c11l_global(iglob) * &
tti_ec_c11_k(iglob) * deltat
tti_ec_c13_kl(i,j,ispec) = tti_ec_c13_kl(i,j,ispec) - tti_c13l_global(iglob) * &
tti_ec_c13_k(iglob) * deltat
tti_ec_c33_kl(i,j,ispec) = tti_ec_c33_kl(i,j,ispec) - tti_c33l_global(iglob) * &
tti_ec_c33_k(iglob) * deltat
tti_ec_c55_kl(i,j,ispec) = tti_ec_c55_kl(i,j,ispec) - tti_c55l_global(iglob) * &
tti_ec_c55_k(iglob) * deltat
tti_ec_c15_kl(i,j,ispec) = tti_ec_c15_kl(i,j,ispec) - tti_c15l_global(iglob) * &
tti_ec_c15_k(iglob) * deltat
tti_ec_c35_kl(i,j,ispec) = tti_ec_c35_kl(i,j,ispec) - tti_c35l_global(iglob) * &
tti_ec_c35_k(iglob) * deltat
tti_ecu_c11_kl(i,j,ispec) = tti_ecu_c11_kl(i,j,ispec) - tti_c11ul_global(iglob) * &
tti_ecu_c11_k(iglob) * deltat
!! Diagonal Hessian
pdh_hti_ec_c11(i,j,ispec) = pdh_hti_ec_c11(i,j,ispec) + &
pdh_hti_ec_c11_temp(iglob) * deltat
pdh_hti_ec_c13(i,j,ispec) = pdh_hti_ec_c13(i,j,ispec) + &
pdh_hti_ec_c13_temp(iglob) * deltat
pdh_hti_ec_c33(i,j,ispec) = pdh_hti_ec_c33(i,j,ispec) + &
pdh_hti_ec_c33_temp(iglob) * deltat
pdh_hti_ec_c55(i,j,ispec) = pdh_hti_ec_c55(i,j,ispec) + &
pdh_hti_ec_c55_temp(iglob) * deltat
pdh_hti_ec_rho(i,j,ispec) = pdh_hti_ec_rho(i,j,ispec) + &
pdh_hti_ec_rho_temp(iglob) * deltat
!! Diagonal Hessian
pdh_tti_ec_c11(i,j,ispec) = pdh_tti_ec_c11(i,j,ispec) + &
pdh_tti_ec_c11_temp(iglob) * deltat
pdh_tti_ec_c13(i,j,ispec) = pdh_tti_ec_c13(i,j,ispec) + &
pdh_tti_ec_c13_temp(iglob) * deltat
pdh_tti_ec_c33(i,j,ispec) = pdh_tti_ec_c33(i,j,ispec) + &
pdh_tti_ec_c33_temp(iglob) * deltat
pdh_tti_ec_c55(i,j,ispec) = pdh_tti_ec_c55(i,j,ispec) + &
pdh_tti_ec_c55_temp(iglob) * deltat
pdh_tti_ec_c15(i,j,ispec) = pdh_tti_ec_c15(i,j,ispec) + &
pdh_tti_ec_c15_temp(iglob) * deltat
pdh_tti_ec_c35(i,j,ispec) = pdh_tti_ec_c35(i,j,ispec) + &
pdh_tti_ec_c35_temp(iglob) * deltat
pdh_tti_ec_rho(i,j,ispec) = pdh_tti_ec_rho(i,j,ispec) + &
pdh_hti_ec_rho_temp(iglob) * deltat
pdh_hti_thom_alpha(i,j,ispec) = pdh_hti_thom_alpha(i,j,ispec)+&
pdh_hti_thom_alpha_temp(iglob) * pdh_hti_thom_alpha_temp(iglob) * deltat *&
hti_alphal_global(iglob)
pdh_hti_thom_beta(i,j,ispec) = pdh_hti_thom_beta(i,j,ispec)+&
pdh_hti_thom_beta_temp(iglob) * pdh_hti_thom_beta_temp(iglob) * deltat * &
hti_betal_global(iglob)
pdh_hti_thom_epsilon(i,j,ispec) = pdh_hti_thom_epsilon(i,j,ispec)+&
pdh_hti_thom_epsilon_temp(iglob) * pdh_hti_thom_epsilon_temp(iglob) * deltat * &
hti_epsilonl_global(iglob)
pdh_hti_thom_delta(i,j,ispec) = pdh_hti_thom_delta(i,j,ispec)+&
pdh_hti_thom_delta_temp(iglob) * pdh_hti_thom_delta_temp(iglob) * deltat * &
hti_deltal_global(iglob)
pdh_hti_thom_rhop(i,j,ispec) = pdh_hti_thom_rhop(i,j,ispec)+&
pdh_hti_thom_rhop_temp(iglob) * pdh_hti_thom_rhop_temp(iglob) * deltat * &
hti_rhopl_global(iglob)
pdh_hti_thom2_alpha(i,j,ispec) = pdh_hti_thom2_alpha(i,j,ispec)+&
pdh_hti_thom_alpha_temp(iglob) * pdh_hti_thom_alpha_temp(iglob) * deltat *&
hti_alphal_global(iglob)
pdh_hti_thom2_beta(i,j,ispec) = pdh_hti_thom2_beta(i,j,ispec)+&
pdh_hti_thom_beta_temp(iglob) * pdh_hti_thom_beta_temp(iglob) * deltat * &
hti_betal_global(iglob)
pdh_hti_thom2_epsilon(i,j,ispec) = pdh_hti_thom2_epsilon(i,j,ispec)+&
pdh_hti_thom_epsilon_temp(iglob) * pdh_hti_thom_epsilon_temp(iglob) * deltat * &
hti_epsilonl_global(iglob)
pdh_hti_thom2_delta(i,j,ispec) = pdh_hti_thom2_delta(i,j,ispec)+&
pdh_hti_thom_delta_temp(iglob) * pdh_hti_thom_delta_temp(iglob) * deltat * &
hti_deltal_global(iglob)
pdh_hti_thom2_rhop(i,j,ispec) = pdh_hti_thom2_rhop(i,j,ispec)+&
pdh_hti_thom_rhop_temp(iglob) * pdh_hti_thom_rhop_temp(iglob) * deltat * &
hti_rhopl_global(iglob)
pdh_hti_thom2_eta(i,j,ispec) = pdh_hti_thom2_eta(i,j,ispec)+&
pdh_hti_thom_delta_temp(iglob) * pdh_hti_thom_delta_temp(iglob) * deltat * &
hti_deltal_global(iglob)
pdh_hti_vel_alpha(i,j,ispec) = pdh_hti_vel_alpha(i,j,ispec)+&
pdh_hti_thom_alpha_temp(iglob) * pdh_hti_thom_alpha_temp(iglob) * deltat *&
hti_alphal_global(iglob)
pdh_hti_vel_beta(i,j,ispec) = pdh_hti_vel_beta(i,j,ispec)+&
pdh_hti_thom_beta_temp(iglob) * pdh_hti_thom_beta_temp(iglob) * deltat * &
hti_betal_global(iglob)
pdh_hti_vel_alphah(i,j,ispec) = pdh_hti_vel_alphah(i,j,ispec)+&
pdh_hti_thom_alpha_temp(iglob) * pdh_hti_thom_alpha_temp(iglob) * deltat *&
hti_alphal_global(iglob)
pdh_hti_vel_alphan(i,j,ispec) = pdh_hti_vel_alphan(i,j,ispec)+&
pdh_hti_thom_alpha_temp(iglob) * pdh_hti_thom_alpha_temp(iglob) * deltat *&
hti_alphal_global(iglob)
pdh_hti_vel_rhop(i,j,ispec) = pdh_hti_vel_rhop(i,j,ispec)+&
pdh_hti_thom_rhop_temp(iglob) * pdh_hti_thom_rhop_temp(iglob) * deltat * &
hti_rhopl_global(iglob)
! Kernels in HTI media with Thomsen parameterization
hti_thom_rhop_kl(i,j,ispec) = hti_thom_rhop_kl(i,j,ispec) - hti_rhopl_global(iglob) * &
hti_ec_rho_k(iglob)*deltat - hti_rhopl_global(iglob) * hti_alphal_global(iglob)*hti_alphal_global(iglob)*&
hti_ec_c33_k(iglob)*deltat - hti_rhopl_global(iglob) * hti_betal_global(iglob)*hti_betal_global(iglob)*&
hti_ec_c55_k(iglob)*deltat - hti_rhopl_global(iglob) * (hti_coeffl_global(nglob)-hti_betal_global(iglob)*&
hti_betal_global(iglob))*hti_ec_c13_k(iglob)*deltat+hti_alphal_global(iglob)*hti_alphal_global(iglob)*&
(2._CUSTOM_REAL*hti_epsilonl_global(iglob)+1._CUSTOM_REAL)*hti_ec_c11_k(iglob)*deltat
hti_thom_alpha_kl(i,j,ispec) = hti_thom_alpha_kl(i,j,ispec) - 2._CUSTOM_REAL*hti_alphal_global(iglob)*&
hti_alphal_global(iglob)*hti_rhopl_global(iglob)*hti_ec_c33_k(iglob)*deltat-&
2._CUSTOM_REAL*hti_alphal_global(iglob)*hti_alphal_global(iglob)*hti_rhopl_global(iglob)*&
(2._CUSTOM_REAL*hti_epsilonl_global(iglob)+1._CUSTOM_REAL)*hti_ec_c11_k(iglob)*deltat-&
4._CUSTOM_REAL*hti_rhopl_global(iglob)*hti_deltal_global(iglob)*hti_alphal_global(iglob)*&
hti_alphal_global(iglob)*hti_alphal_global(iglob)*hti_alphal_global(iglob)*hti_ec_c13_k(iglob)*deltat/&
hti_coeffl_global(nglob)+2._CUSTOM_REAL*hti_rhopl_global(iglob)*hti_deltal_global(iglob)*hti_alphal_global(iglob)*&
hti_alphal_global(iglob)*hti_betal_global(iglob)*hti_betal_global(iglob)*hti_ec_c13_k(iglob)*deltat/&
hti_coeffl_global(nglob)-2._CUSTOM_REAL*hti_rhopl_global(iglob)*hti_alphal_global(iglob)*&
hti_alphal_global(iglob)*(hti_alphal_global(iglob)**2-hti_betal_global(iglob)**2)*&
hti_ec_c13_k(iglob)*deltat/hti_coeffl_global(nglob)
hti_thom_beta_kl(i,j,ispec) = hti_thom_beta_kl(i,j,ispec) - 2._CUSTOM_REAL*hti_rhopl_global(iglob)*&
hti_betal_global(iglob)*hti_betal_global(iglob)*hti_ec_c55_k(iglob)*deltat+&
2._CUSTOM_REAL*hti_rhopl_global(iglob)*hti_deltal_global(iglob)*hti_alphal_global(iglob)*&
hti_alphal_global(iglob)*hti_betal_global(iglob)*hti_betal_global(iglob)*hti_ec_c13_k(iglob)*deltat/&
hti_coeffl_global(nglob) + 2._CUSTOM_REAL*hti_rhopl_global(iglob)*hti_betal_global(iglob)*&
hti_betal_global(iglob)*(hti_alphal_global(iglob)**2-hti_betal_global(iglob)**2)*hti_ec_c13_k(iglob)*deltat/&
hti_coeffl_global(nglob) + 2._CUSTOM_REAL*hti_rhopl_global(iglob)*hti_betal_global(iglob)*&
hti_betal_global(iglob)*hti_ec_c13_k(iglob)*deltat
hti_thom_epsilon_kl(i,j,ispec) = hti_thom_epsilon_kl(i,j,ispec) - 2._CUSTOM_REAL*hti_rhopl_global(iglob)*&
hti_alphal_global(iglob)*hti_alphal_global(iglob)*hti_epsilonl_global(iglob)*hti_ec_c11_k(iglob)*deltat
hti_thom_delta_kl(i,j,ispec) = hti_thom_delta_kl(i,j,ispec) - hti_rhopl_global(iglob)*&
hti_alphal_global(iglob)*hti_alphal_global(iglob)*(hti_alphal_global(iglob)**2-hti_betal_global(iglob)**2)*&
hti_deltal_global(iglob)*hti_ec_c13_k(iglob)*deltat/hti_coeffl_global(nglob)
! Horizontal velocity and thomsen parameter parameterization
hti_thom2_rhop_kl(i,j,ispec) = hti_thom_rhop_kl(i,j,ispec)
hti_thom2_alpha_kl(i,j,ispec) = hti_thom_alpha_kl(i,j,ispec)
hti_thom2_beta_kl(i,j,ispec) = hti_thom_beta_kl(i,j,ispec)
hti_thom2_epsilon_kl(i,j,ispec)= hti_thom_epsilon_kl(i,j,ispec)+ &
hti_thom_delta_kl(i,j,ispec)*hti_epsilonl_global(iglob)/&
(hti_epsilonl_global(iglob)-hti_etal_global(iglob)) - hti_thom_alpha_kl(i,j,ispec)*hti_epsilonl_global(iglob)/&
(1._CUSTOM_REAL + 2._CUSTOM_REAL * hti_epsilonl_global(iglob))
hti_thom2_delta_kl(i,j,ispec) = hti_thom_delta_kl(i,j,ispec)
hti_thom2_eta_kl(i,j,ispec) = - 1._CUSTOM_REAL * hti_thom_delta_kl(i,j,ispec)*2._CUSTOM_REAL*hti_etal_global(iglob)/&
(1._CUSTOM_REAL + 2._CUSTOM_REAL * hti_etal_global(iglob))-&
hti_thom_delta_kl(i,j,ispec) * hti_etal_global(iglob)/(hti_epsilonl_global(iglob) - hti_etal_global(iglob))
! Velocity parameter parameterization
hti_vel_rhop_kl(i,j,ispec) = hti_thom_rhop_kl(i,j,ispec)
hti_vel_beta_kl(i,j,ispec) = hti_thom_beta_kl(i,j,ispec)
! hti_vel_alpha_kl(i,j,ispec) = hti_thom_alpha_kl(i,j,ispec)
! hti_vel_alpha_kl(i,j,ispec) = alpha_kl(i,j,ispec)
! hti_vel_alphah_kl(i,j,ispec) = hti_thom_alpha_kl(i,j,ispec)
! hti_vel_alphan_kl(i,j,ispec) = hti_thom_alpha_kl(i,j,ispec)
hti_vel_alpha_kl(i,j,ispec) = hti_thom_alpha_kl(i,j,ispec)-2._CUSTOM_REAL*hti_thom_epsilon_kl(i,j,ispec)* &
hti_alphahl_global(iglob)**2/(hti_alphahl_global(iglob)**2-hti_alphal_global(iglob)**2) - &
2._CUSTOM_REAL*hti_thom_delta_kl(i,j,ispec)*hti_alphanl_global(iglob)**2/&
(hti_alphanl_global(iglob)**2-hti_alphal_global(iglob)**2)
hti_vel_alphah_kl(i,j,ispec) = 2._CUSTOM_REAL*hti_thom_epsilon_kl(i,j,ispec)*hti_alphahl_global(iglob)**2/&
(hti_alphahl_global(iglob)**2-hti_alphal_global(iglob)**2)
hti_vel_alphan_kl(i,j,ispec) = 2._CUSTOM_REAL*hti_thom_delta_kl(i,j,ispec)*hti_alphanl_global(iglob)**2/&
(hti_alphanl_global(iglob)**2-hti_alphal_global(iglob)**2)
!hti_thom_epsilon_kl(i,j,ispec) = hti_thom_epsilon_kl(i,j,ispec)-2._CUSTOM_REAL*hti_rhopl_global(iglob)*&
!hti_alphal_global(iglob)*hti_alphal_global(iglob)*hti_ec_c11_k(iglob)*deltat
!hti_thom_delta_kl(i,j,ispec) = hti_thom_delta_kl(i,j,ispec) - hti_rhopl_global(iglob)*&
!hti_alphal_global(iglob)*hti_alphal_global(iglob)*(hti_alphal_global(iglob)**2-hti_betal_global(iglob)**2)*&
!hti_ec_c13_k(iglob)*deltat/hti_coeffl_global(nglob)
if ((trim(M_PAR) == 'ttiecu') .OR. (trim(M_PAR) == 'ttithom' .OR. trim(M_PAR) == 'ttivel')) then
tti_ecu_c11_kl(i,j,ispec) = tti_ec_c11_kl(i,j,ispec) * tti_c11ul_global(iglob) * m1l_global(iglob) / &
(tti_c11l_global(iglob) * 8._CUSTOM_REAL) + &
tti_ec_c13_kl(i,j,ispec) * tti_c11ul_global(iglob) * m2l_global(iglob) / (tti_c13l_global(iglob) * 8._CUSTOM_REAL) + &
tti_ec_c15_kl(i,j,ispec) * tti_c11ul_global(iglob) * m5l_global(iglob) / (tti_c15l_global(iglob) * 4._CUSTOM_REAL) + &
tti_ec_c33_kl(i,j,ispec) * tti_c11ul_global(iglob) * m3l_global(iglob) / (tti_c33l_global(iglob) * 8._CUSTOM_REAL) + &
tti_ec_c35_kl(i,j,ispec) * tti_c11ul_global(iglob) * m5l_global(iglob) / (tti_c35l_global(iglob) * 4._CUSTOM_REAL) - &
tti_ec_c35_kl(i,j,ispec) * tti_c11ul_global(iglob) * 2._CUSTOM_REAL * m4l_global(iglob) / &
(tti_c35l_global(iglob) * 4._CUSTOM_REAL) + &
tti_ec_c55_kl(i,j,ispec) * tti_c11ul_global(iglob) * m2l_global(iglob)/(tti_c55l_global(iglob) * 8._CUSTOM_REAL)
tti_ecu_c13_kl(i,j,ispec) = tti_ec_c11_kl(i,j,ispec) * tti_c13ul_global(iglob) * m2l_global(iglob) / &
(tti_c11l_global(iglob) * 4._CUSTOM_REAL) + &
tti_ec_c13_kl(i,j,ispec) * tti_c13ul_global(iglob) * m6l_global(iglob) / (tti_c13l_global(iglob) * 8._CUSTOM_REAL) - &
tti_ec_c15_kl(i,j,ispec) * tti_c13ul_global(iglob) * m4l_global(iglob) / (tti_c15l_global(iglob) * 2._CUSTOM_REAL) + &
tti_ec_c33_kl(i,j,ispec) * tti_c13ul_global(iglob) * m2l_global(iglob) / (tti_c33l_global(iglob) * 4._CUSTOM_REAL) + &
tti_ec_c35_kl(i,j,ispec) * tti_c13ul_global(iglob) * m4l_global(iglob) / (tti_c35l_global(iglob) * 2._CUSTOM_REAL) - &
tti_ec_c55_kl(i,j,ispec) * tti_c13ul_global(iglob) * m2l_global(iglob)/(tti_c55l_global(iglob) * 4._CUSTOM_REAL)
tti_ecu_c33_kl(i,j,ispec) = tti_ec_c11_kl(i,j,ispec) * tti_c33ul_global(iglob) * m3l_global(iglob) / &
(tti_c11l_global(iglob) * 8._CUSTOM_REAL) + &
tti_ec_c13_kl(i,j,ispec) * tti_c33ul_global(iglob) * m2l_global(iglob) / (tti_c13l_global(iglob) * 8._CUSTOM_REAL) + &
tti_ec_c15_kl(i,j,ispec) * tti_c33ul_global(iglob) * m4l_global(iglob) / (tti_c15l_global(iglob) * 2._CUSTOM_REAL) - &
tti_ec_c15_kl(i,j,ispec) * tti_c33ul_global(iglob) * m5l_global(iglob) / (tti_c15l_global(iglob) * 4._CUSTOM_REAL) + &
tti_ec_c33_kl(i,j,ispec) * tti_c33ul_global(iglob) * m1l_global(iglob) / (tti_c33l_global(iglob) * 8._CUSTOM_REAL) - &
tti_ec_c35_kl(i,j,ispec) * tti_c33ul_global(iglob) * m5l_global(iglob) / (tti_c35l_global(iglob) * 4._CUSTOM_REAL) + &
tti_ec_c55_kl(i,j,ispec) * tti_c33ul_global(iglob) * m2l_global(iglob)/(tti_c55l_global(iglob) * 8._CUSTOM_REAL)
tti_ecu_c55_kl(i,j,ispec) = tti_ec_c11_kl(i,j,ispec) * tti_c55ul_global(iglob) * m2l_global(iglob) / &
(tti_c11l_global(iglob) * 2._CUSTOM_REAL) - &
tti_ec_c13_kl(i,j,ispec) * tti_c55ul_global(iglob) * m2l_global(iglob) / (tti_c13l_global(iglob) * 2._CUSTOM_REAL) - &
tti_ec_c15_kl(i,j,ispec) * tti_c55ul_global(iglob) * m4l_global(iglob) / (tti_c15l_global(iglob) * 1._CUSTOM_REAL) + &
tti_ec_c33_kl(i,j,ispec) * tti_c55ul_global(iglob) * m2l_global(iglob) / (tti_c33l_global(iglob) * 2._CUSTOM_REAL) + &
tti_ec_c35_kl(i,j,ispec) * tti_c55ul_global(iglob) * m4l_global(iglob) / (tti_c35l_global(iglob) * 1._CUSTOM_REAL) + &
tti_ec_c55_kl(i,j,ispec) * tti_c55ul_global(iglob) /(tti_c55l_global(iglob) * 1._CUSTOM_REAL) - &
tti_ec_c55_kl(i,j,ispec) * tti_c55ul_global(iglob) * m2l_global(iglob)/(tti_c55l_global(iglob) * 2._CUSTOM_REAL)
tti_ecu_theta_kl(i,j,ispec) = - tti_ec_c11_kl(i,j,ispec) * tti_thetaul_global(iglob) * p2l_global(iglob) * &
SIN(2._CUSTOM_REAL * tti_thetaul_global(iglob)) / (tti_c11l_global(iglob) * 1._CUSTOM_REAL) - &
tti_ec_c11_kl(i,j,ispec) * tti_thetaul_global(iglob) * p1l_global(iglob) * &
SIN(4._CUSTOM_REAL * tti_thetaul_global(iglob))/(tti_c11l_global(iglob) * 2._CUSTOM_REAL) + &
tti_ec_c13_kl(i,j,ispec) * tti_thetaul_global(iglob) * p1l_global(iglob) * &
SIN(4._CUSTOM_REAL * tti_thetaul_global(iglob))/(tti_c13l_global(iglob) * 2._CUSTOM_REAL) + &
tti_ec_c15_kl(i,j,ispec) * tti_thetaul_global(iglob) * p2l_global(iglob) * &
COS(2._CUSTOM_REAL * tti_thetaul_global(iglob))/(tti_c15l_global(iglob) * 1._CUSTOM_REAL) + &
tti_ec_c15_kl(i,j,ispec) * tti_thetaul_global(iglob) * p1l_global(iglob) * &
COS(4._CUSTOM_REAL * tti_thetaul_global(iglob))/(tti_c15l_global(iglob) * 2._CUSTOM_REAL) + &
tti_ec_c33_kl(i,j,ispec) * tti_thetaul_global(iglob) * p2l_global(iglob) * &
SIN(2._CUSTOM_REAL * tti_thetaul_global(iglob))/(tti_c33l_global(iglob) * 1._CUSTOM_REAL) - &
tti_ec_c33_kl(i,j,ispec) * tti_thetaul_global(iglob) * p1l_global(iglob) * &
SIN(4._CUSTOM_REAL * tti_thetaul_global(iglob))/(tti_c33l_global(iglob) * 2._CUSTOM_REAL) + &
tti_ec_c35_kl(i,j,ispec) * tti_thetaul_global(iglob) * p2l_global(iglob) * &
COS(2._CUSTOM_REAL * tti_thetaul_global(iglob))/(tti_c35l_global(iglob) * 1._CUSTOM_REAL) - &
tti_ec_c35_kl(i,j,ispec) * tti_thetaul_global(iglob) * p1l_global(iglob) * &
COS(4._CUSTOM_REAL * tti_thetaul_global(iglob))/(tti_c35l_global(iglob) * 2._CUSTOM_REAL) + &
tti_ec_c55_kl(i,j,ispec) * tti_thetaul_global(iglob) * p1l_global(iglob) * &
SIN(4._CUSTOM_REAL * tti_thetaul_global(iglob))/(tti_c55l_global(iglob) * 2._CUSTOM_REAL)
tti_ecu_rho_kl(i,j,ispec) = tti_ec_rho_kl(i,j,ispec)
!tti_ecu_c11_kl(i,j,ispec) = tti_ecu_c11_kl(i,j,ispec) - tti_c11l_global(iglob) * &
! tti_ec_c11_k(iglob) * deltat
!tti_ecu_c13_kl(i,j,ispec) = tti_ec_c13_kl(i,j,ispec)
!tti_ecu_c33_kl(i,j,ispec) = tti_ec_c33_kl(i,j,ispec)
!tti_ecu_c55_kl(i,j,ispec) = tti_ec_c55_kl(i,j,ispec)
!tti_ecu_theta_kl(i,j,ispec) = tti_ec_c15_kl(i,j,ispec)
!tti_ecu_rho_kl(i,j,ispec) = tti_ec_rho_kl(i,j,ispec)
pdh_tti_ecu_c11(i,j,ispec) = pdh_tti_ecu_c11(i,j,ispec) + &
pdh_tti_ec_c11_temp(iglob) * deltat
pdh_tti_ecu_c13(i,j,ispec) = pdh_tti_ecu_c13(i,j,ispec) + &
pdh_tti_ec_c13_temp(iglob) * deltat
pdh_tti_ecu_c33(i,j,ispec) = pdh_tti_ecu_c33(i,j,ispec) + &
pdh_tti_ec_c33_temp(iglob) * deltat