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The asymptotic local finite-difference method of the fractional wave equation and its viscous seismic wavefield simulation

Song Guojie, Zhang Xinmin, Wang Zhiliang, Chen Yali and Chen Puchun
The asymptotic local finite-difference method of the fractional wave equation and its viscous seismic wavefield simulation
Geophysics (April 2020) 85 (3): T179-T189

Abstract

Viscous seismic wave propagation simulation using the fractional order equation has attracted much recent attention. However, conventional finite-difference (FD) methods of the fractional partial difference equation adopt a global difference operator to approximate the fractional derivatives, which reduces the computational efficiency dramatically. To improve the efficiency of the FD method, we have developed a reasonable truncated stencil pattern by strict mathematical derivation and adopted an asymptotic local FD (ALFD) method. Theoretical analysis and numerical results indicate that the ALFD method is accurate and efficient. In fact, our numerical results illustrate that the numerical solution solved by the ALFD method has a maximum relative error not exceeding 0.014% compared to the reference solution (applied to a finely meshed computational domain). The computation speed of ALFD is also significantly faster than that of the original FD method. The computational time of the three ALFD methods satisfying a different preset accuracy is only approximately 2.71%, 1.26%, and 0.78% of that of the original fractional wave equation FD method. The ALFD method provides a useful tool for viscoelastic seismic wavefield propagation simulation.


ISSN: 0016-8033
EISSN: 1942-2156
Coden: GPYSA7
Serial Title: Geophysics
Serial Volume: 85
Serial Issue: 3
Title: The asymptotic local finite-difference method of the fractional wave equation and its viscous seismic wavefield simulation
Affiliation: Southwest Petroleum University, School of Sciences, Chengdu, China
Pages: T179-T189
Published: 20200416
Text Language: English
Publisher: Society of Exploration Geophysicists, Tulsa, OK, United States
References: 48
Accession Number: 2020-041663
Categories: Applied geophysics
Document Type: Serial
Bibliographic Level: Analytic
Illustration Description: illus. incl. 3 tables
Country of Publication: United States
Secondary Affiliation: GeoRef, Copyright 2020, 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: 2020
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