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Helmholtz Decomposition of Seismic Wavefields with SPECFEM3D

Session: Numerical Modeling of Earthquake Motion, Rupture Dynamics, Seismic Noise, Wave Propagation and Inverse Problems I

Type: Oral

Date: 4/23/2021

Presentation Time: 10:30 AM Pacific

Description: 

The construction of seismic imaging conditions in elastic reverse time migration (RTM) often requires breaking down the seismic wavefield into its constituent P and S components. This is done by means of the Helmholtz decomposition, which involves taking the curl of the curl of the vector wavefield to obtain the S wavefield and the gradient of the divergence to obtain the P wavefield. These second spatial derivatives present certain challenges which make it difficult to perform this operation efficiently.

Here, we present a method for performing the Helmholtz decomposition of seismic wavefields in the time domain using SPECFEM3D, a spectral element elastic wave propagation code. Our technique is able to perform the decomposition of either forward or adjoint wavefields at any time step of a SPECFEM3D wavefield simulation. We show a few examples of decomposed wavefields and discuss some of the challenges associated with decomposition. Because the second spatial derivatives of the wavefield, particularly the gradient of the divergence, require a very high degree of spatial resolution, artifacts can arise when the Helmholtz decomposition is performed. This problem may be alleviated by filtering the data to remove high frequency information and by using a mesh with finer spatial resolution. We also present converted-wave elastic RTM images based on vector imaging conditions for a synthetic model that have been obtained using the decomposed P and S wavefields and discuss our plans to implement our imaging technique using adjoint wavefields produced from real seismic data.

Presenting Author: Leah Langer

Student Presenter: No

Authors