Skip to Main Content
Skip Nav Destination
GEOREF RECORD

Iterative finite-difference solution analysis of acoustic wave equation in the Laplace-Fourier domain

Evan Schankee Um, Michael Commer and Gregory A. Newman
Iterative finite-difference solution analysis of acoustic wave equation in the Laplace-Fourier domain
Geophysics (April 2012) 77 (2): T29-T36

Abstract

We have investigated numerical characteristics of iterative solutions to the acoustic wave equation in the Laplace-Fourier (LF) domain. We transformed the time-domain acoustic wave equation into the LF domain; the transformed equation was discretized with finite differences and was solved with iterative methods. Finite-difference modeling experiments demonstrate that iterative methods require an infinitesimal stopping tolerance to accurately compute the pressure field especially at long offsets. To understand the requirement for such infinitesimal tolerance values, we analyzed the evolution of intermediate solution vectors, residual vectors, and search direction vectors during the iteration. The analysis showed that the requirement arises from the fact that in the solution space, the amplitude of the pressure field varies more than sixty orders of magnitude on the common log scale. Accordingly, we propose a rule of thumb for choosing a proper stopping tolerance value. We also examined numerical dispersion errors in terms of the grid sampling resolutions per skin depth and wavelength. We found that despite the similarity of the form of the acoustic wave and electromagnetic diffusion equations, the former is different from the latter due to the fact that in the LF domain, the skin depth of the acoustic wave equation is decoupled from its wavelength. This aspect requires that in the LF domain, its grid size be determined by considering the minimum grid sampling resolutions based not only the wavelength but also the skin depth.


ISSN: 0016-8033
EISSN: 1942-2156
Coden: GPYSA7
Serial Title: Geophysics
Serial Volume: 77
Serial Issue: 2
Title: Iterative finite-difference solution analysis of acoustic wave equation in the Laplace-Fourier domain
Affiliation: Lawrence Berkeley National Laboratory, Geophysics Department, Berkeley, CA, United States
Pages: T29-T36
Published: 201204
Text Language: English
Publisher: Society of Exploration Geophysicists, Tulsa, OK, United States
References: 24
Accession Number: 2012-059469
Categories: Applied geophysics
Document Type: Serial
Bibliographic Level: Analytic
Illustration Description: illus. incl. 2 tables
Country of Publication: United States
Secondary Affiliation: GeoRef, Copyright 2018, American Geosciences Institute. Reference includes data from GeoScienceWorld, Alexandria, VA, United States. Reference includes data supplied by Society of Exploration Geophysicists, Tulsa, OK, United States
Update Code: 201231
Close Modal

or Create an Account

Close Modal
Close Modal