Open AccessFrequency response modelling of seismic waves using finite difference time domain with phase sensitive detection (TD–PSD)
Author(s) -
Nihei Kurt T.,
Li Xiaoye
Publication year - 2007
Publication title -
geophysical journal international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0956-540X
DOI - 10.1111/j.1365-246x.2006.03262.x
Subject(s) - frequency domain , finite difference , time domain , fourier transform , harmonic , finite difference method , frequency response , algorithm , computer science , mathematics , mathematical analysis , acoustics , physics , engineering , computer vision , electrical engineering
SUMMARY This paper describes an efficient approach for computing the frequency response of seismic waves propagating in 2‐ and 3‐D earth models within which the magnitude and phase are required at many locations. The approach consists of running an explicit finite difference time domain (TD) code with a time harmonic source out to steady‐state. The magnitudes and phases at locations in the model are computed using phase sensitive detection (PSD). PSD does not require storage of time‐series (unlike a fast Fourier transform), reducing its memory requirements. Additionally, the response from multiple sources can be obtained from a single finite difference run by encoding each source with a different frequency. For 2‐D models with many sources, this time domain phase sensitive detection (TD–PSD) approach has a higher arithmetic complexity than direct solution of the finite difference frequency domain (FD) equations using nested dissection re‐ordering (FD–ND). The storage requirements for 2‐D finite difference TD–PSD are lower than FD–ND. For 3‐D finite difference models, TD–PSD has significantly lower arithmetic complexity and storage requirements than FD–ND, and therefore, may prove useful for computing the frequency response of large 3‐D earth models.