Plane strain problem

[MengYuanzhuo]

Hello:

I'm doing some viscoelastic Q-FWI with specfem, but something bothered me:

• At present in isotropic media, it seems that only AXISYM conditions use 3D consistent modulus relationships in forward simulation operations, but 3D relationships have always been used in sensitivity kernel calculations. Should an option be added to allow people to freely control whether it is a plane strain condition?
• In parameter reading file:

if (AXISYM) then ! CHECK kappa
   kappal = rhol * vp * vp - FOUR_THIRDS * mul   ! kappa derived from vp,vs
else
   kappal = rhol * vp * vp - mul

if (AXISYM) then ! CHECK kappa
  kappal = lambdal + TWO_THIRDS * mul           ! kappa derived from lame parameters lambda,mu
  vp = sqrt((kappal + FOUR_THIRDS * mul)/rhol)
else
  kappal = lambdal + mul
  vp = sqrt((kappal + mul)/rhol)
endif

• and in save_adjoint_kernel.f90:

! Vs kernel
! ABAB !! Warning !! This is possibly false for plane strain (look for: bulk modulus plane strain) CHECK Kappa
beta_kl(i,j,ispec) = TWO * (mu_kl(i,j,ispec) - FOUR_THIRDS * mul/kappal * kappa_kl(i,j,ispec))
! Vp kernel
! ABAB !! Warning !! This is possibly false for plane strain (look for: bulk modulus plane strain) Check Kappa
alpha_kl(i,j,ispec) = TWO * (1._CUSTOM_REAL + FOUR_THIRDS * mul/kappal) * kappa_kl(i,j,ispec)