Fixed-point proximity algorithms solving an incomplete Fourier transform model for seismic wavefield modeling

Tingting Wu, Lixin Shen, Yuesheng Xu

Research output: Contribution to journalArticlepeer-review

Abstract

Seismic wavefield modeling is an important tool for the seismic interpretation. We consider modeling the wavefield in the frequency domain. This requires to solve a sequence of Helmholtz equations of wave numbers governed by the Nyquist sampling theorem. Inevitably, we have to solve Helmholtz equations of large wave numbers, which is a challenging task numerically. To address this issue, we develop two methods for modeling the wavefield in the frequency domain to obtain an alias-free result using lower frequencies of a number fewer than typically required by the Nyquist sampling theorem. Specifically, we introduce two ℓ1 regularization models to deal with incomplete Fourier transforms, which arise from seismic wavefield modeling in the frequency domain, and propose a new sampling technique to avoid solving the Helmholtz equations of large wave numbers. In terms of the fixed-point equation via the proximity operator of the ℓ1 norm, we characterize solutions of the two ℓ1 regularization models and develop fixed-point algorithms to solve these two models. Numerical experiments are conducted on seismic data to test the approximation accuracy and the computational efficiency of the proposed methods. Numerical results show that the proposed methods are accurate, robust and efficient in modeling seismic wavefield in the frequency domain with only a few low frequencies.

Original languageEnglish (US)
Article number113208
JournalJournal of Computational and Applied Mathematics
Volume385
DOIs
StatePublished - Mar 15 2021

Keywords

  • Compressed sensing
  • Incomplete Fourier transform
  • Proximity algorithms
  • Seismic wavefield modeling

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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