A Time-Domain Finite-Difference Method With Attenuation By A Recursive Algorithm
Name
1996.12 Cheng_Cheng_Toksoz.pdf
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232.48 KB
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Checksum (MD5)
c52dd722066bbe96f283ba524617efe1
Author(s)
Cheng, Ningya
Cheng, Arthur C. H.
Toksoz, M. Nafi
Date Issued
1996
Publisher
Massachusetts Institute of Technology. Earth Resources Laboratory
Series/Report no.
Earth Resources Laboratory Industry Consortia Annual Report;1996-12
Abstract
A recursive algorithm to incorporate attenuation into a time-domain finite-difference
calculation is developed. First, a rheological model of the generalized Maxwell body
is chosen. The discrete relaxation frequency and the peak strength of these Maxwell
bodies are jointly determined by fitting to an arbitrary Q law in the frequency band of
the interest. A conjugate gradient technique and a randomly chosen starting model are
used to determine optimum fitting. Examples of constant and frequency dependent Q
models are shown. Second, in order to include the attenuation into a finite-difference
staggered-grid scheme, the convolution integral of stress and strain is evaluated directly. The convolution integral can be expressed recursively. This is possible because the time-domain viscoelastic modulus function is exponential. The implementation of 1-D wave propagation in a constant Q medium is shown as a example. At the distance of 50 wavelengths and with three relaxation frequencies, the finite-difference results are in very good agreement with the analytic solutions.
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