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SPECFEM / specfem3d

SPECFEM3D_Cartesian simulates acoustic (fluid), elastic (solid), coupled acoustic/elastic, poroelastic or seismic wave propagation in any type of conforming mesh of hexahedra (structured or not).
GNU General Public License v3.0
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On the calculation of the steepest descent direction in src/tomography/get_sd_direction.f90 #1495

Closed ZQiwen closed 2 years ago

ZQiwen commented 2 years ago

Hi,

I'm trying to do some waveform tomography studies using the specfem3d package, especially using the codes under src/tomography/. I am wondering that: As a discrete version of the formulas (e.g. eq. (16)) in Tromp et al. (2005), should the steepest descent direction in the code get_sd_direction.f90 be model_dbeta(i,j,k,ispec) = - kernel_beta(i,j,k,ispec) * volumel instead of model_dbeta(i,j,k,ispec) = - kernel_beta(i,j,k,ispec) whereas the volume is the volume associated with GLL point of the index (i,j,k,ispec)?

Here is the eq. (16) from Tromp et al. (2005) image

Qiwen

danielpeter commented 2 years ago

that's not the same. equation (16) relates to the misfit, not the model update.

please see the comment here in your PR: https://github.com/geodynamics/specfem3d/pull/1494#issuecomment-1085985870

ZQiwen commented 2 years ago

Hi Daniel!

Thanks for the response! Yes, you are right. The kernel is already the gradient, it doesn't make any sense to multiply a volume. Thank you for the explanation!

Qiwen