I am currently using the SPECFEM2D, and I have enabled the APPROXIMATE_HESS_KL mode during my simulations. After computing the adjoint sources, I noticed that two Hessian Kernels are generated: Hessian1_kernel and Hessian2_kernel. However, the documentation for SPECFEM2D does not provide detailed descriptions of these kernels, and I am unsure about their specific meanings.
From what I can gather based on the SPECFEM3D documentation in the "Summing kernels" section (section 8.2.1), there typically appears to be only one kernel discussed. After plotting these two kernels, it seems that Hessian1_kernel might correspond to the P-wave velocity (Vp) and Hessian2_kernel might correspond to the S-wave velocity (Vs), but I am unable to find any kernel for the density parameter.
Could you please help clarify the following:
What exactly do Hessian1_kernel and Hessian2_kernel represent in the context of APPROXIMATE_HESS_KL?
Should there be a kernel representing the density, and if so, how can I generate or locate it?
Thank you for your assistance and for the ongoing development of this powerful tool.
Affected SPECFEM2D version
e70c9c88e5f0a1edc64870c514ef52d08e5d1ef0
Your software and hardware environment
Intel(R) Fortran Intel(R) 64 Compiler Classic for applications running on Intel(R) 64, Version 2021.12.0 Build 20240222_000000;Ubuntu22.04
Reproduction steps
1. set APPROXIMATE_HESS_KL = .true. # outputs approximate Hessian for preconditioning
2. run adjoint simulation
About the Hessian approximation, the first approximation Hessian1 only considers the forward seismic field, and the second approximation Hessian2 considers the forward and adjoint field.
armandoespindola
commented
2 weeks ago
Description
Hello,
I am currently using the SPECFEM2D, and I have enabled the
APPROXIMATE_HESS_KLmode during my simulations. After computing the adjoint sources, I noticed that two Hessian Kernels are generated:Hessian1_kernelandHessian2_kernel. However, the documentation for SPECFEM2D does not provide detailed descriptions of these kernels, and I am unsure about their specific meanings.From what I can gather based on the SPECFEM3D documentation in the "Summing kernels" section (section 8.2.1), there typically appears to be only one kernel discussed. After plotting these two kernels, it seems that
Hessian1_kernelmight correspond to the P-wave velocity (Vp) andHessian2_kernelmight correspond to the S-wave velocity (Vs), but I am unable to find any kernel for the density parameter.Could you please help clarify the following:
Hessian1_kernelandHessian2_kernelrepresent in the context of APPROXIMATE_HESS_KL?Thank you for your assistance and for the ongoing development of this powerful tool.
Affected SPECFEM2D version
e70c9c88e5f0a1edc64870c514ef52d08e5d1ef0
Your software and hardware environment
Intel(R) Fortran Intel(R) 64 Compiler Classic for applications running on Intel(R) 64, Version 2021.12.0 Build 20240222_000000;Ubuntu22.04
Reproduction steps
Screenshots
Logs
No response
OS
Linux