Graves, R. W. and Clayton, R. W.
Modeling acoustic waves with paraxial extrapolators.
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Modeling by paraxial extrapolators is applicable to wave-propagation problems in which most of the energy is traveling within a restricted angular cone about a principal axis of the problem. Using this technique, frequency-domain finite-difference solutions accurate for propagation angles out to 60° are readily generated for both two-dimensional (2-D) and three-dimensional (3-D) models. Solutions for 3-D problems are computed by applying the 2-D paraxial operators twice, once along the x-axis and once along the y-axis, at each extrapolation step. The azimuthal anisotropy inherent to this splitting technique is essentially eliminated by adding a phase-correction operator to the extrapolation system. For heterogeneous models, scattering effects are incorporated by determining transmission and reflection coefficients at structural boundaries within the media. The direct forward-scattered waves are modeled with a single pass of the extrapolation operator in the paraxial direction for each frequency. The first-order backscattered energy is then modeled by extrapolation (in the opposite direction) of the reflected field determined on the first pass. Higher order scattering can be included by sweeping through the model with more passes. The chief advantages of the paraxial approach are (1) active storage is reduced by one dimension compared to solutions which must track both forward-scattered and backscattered waves simultaneously; thus, realistic 3-D problems can fit on today's computers, (2) the decomposition in frequency allows the technique to be implemented on highly parallel machines, (3) attenuation can be modeled as an arbitrary function of frequency, and (4) only a small number of frequencies are needed to produce movie-like time slices.
|Additional Information:||© 1990 Society of Exploration Geophysicists.
Presented at the 57th Annual International Meeting, Society of Exploration Geophysicists; Received March 3, 1989; revised September 22, 1989; Issue Date March 1990.
We would like to thank Amoco Foundation Inc. for the
generous fellowship support of R. W. G. during this study.
Some of the computations were done on a Convex C1/XP
purchased under NSF grant EAR-8721205. Cindy Arvesen
assisted with the drafting of figures.
Contribution 4746, Division of Geological and Planetary
Sciences, California Institute of Technology, Pasadena, California.|
|Funding Agency||Grant Number|
|Amoco Foundation Inc.||UNSPECIFIED|
|Other Numbering System:|
|Other Numbering System Name||Other Numbering System ID|
|Caltech Division of Geological and Planetary Sciences||4746|
|Official Citation:||Modeling acoustic waves with paraxial extrapolators
R. W. Graves and R. W. Clayton, Geophysics 55, 306 (1990), DOI:10.1190/1.1442838|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited On:||18 Oct 2012 15:54|
|Last Modified:||31 Jan 2017 21:31|
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