Numerical simulation of attenuated wavefields using a Padé approximant method
Realistic anelastic attenuation laws are usually formulated as convolution operators, but this representation is intractable for time-domain synthetic seismogram methods such as the finite difference method. An approach based on Padé approximants provides a convenient, accurate reformulation of gene...
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Published in | Geophysical Journal International Vol. 78; no. 1; pp. 105 - 118 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Oxford, UK
Blackwell Publishing Ltd
01.07.1984
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Subjects | |
Online Access | Get full text |
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Summary: | Realistic anelastic attenuation laws are usually formulated as convolution operators, but this representation is intractable for time-domain synthetic seismogram methods such as the finite difference method. An approach based on Padé approximants provides a convenient, accurate reformulation of general anelastic laws in differential form. The resulting differential operators form a uniformly convergent sequence of increasing order in the time derivative, and all are shown to be causal, stable and dissipative. In the special case of frequency-independent Q, all required coefficients for the operators are obtained in closed form in terms of Legendre polynomials. Low-order approximants are surprisingly accurate. Finite-difference impulse responses for a plane wave in a constant-Q medium, calculated with the fifth-order convergent, are virtually indistinguishable from the exact solution. The formulation is easily generalized to non-scalar waves. Moreover, this method provides a framework for incorporating amplitude-dependent attenuation into numerical simulations. |
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Bibliography: | istex:9F1DB7962681B0611BEF59ABF7807A840D4732B9 Now at: Science Horizons Inc., 710 Encinitas Blvd, Suite 101, Encinitas, CA 92024, USA. ark:/67375/HXZ-R22R5JWS-F ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23 |
ISSN: | 0956-540X 0016-8009 1365-246X |
DOI: | 10.1111/j.1365-246X.1984.tb06474.x |