Seismic wave extrapolation using lowrank symbol approximation

Geophysical Prospecting - Tập 61 Số 3 - Trang 526-536 - 2013
Sergey Fomel1, Lexing Ying2, Xiaolei Song1
1Bureau of Economic Geology, John A. and Katherine G. Jackson School of Geosciences, The University of Texas at Austin, University Station, Box X Austin, TX 78713-8924, USA
2Department of Mathematics, The University of Texas at Austin, 1 University Station, Austin, TX 78712, USA

Tóm tắt

ABSTRACTWe consider the problem of constructing a wave extrapolation operator in a variable and possibly anisotropic medium. Our construction involves Fourier transforms in space combined with the help of a lowrank approximation of the space‐wavenumber wave‐propagator matrix. A lowrank approximation implies selecting a small set of representative spatial locations and a small set of representative wavenumbers. We present a mathematical derivation of this method, a description of the lowrank approximation algorithm and numerical examples that confirm the validity of the proposed approach. Wave extrapolation using lowrank approximation can be applied to seismic imaging by reverse‐time migration in 3D heterogeneous isotropic or anisotropic media.

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Tài liệu tham khảo

10.1190/1.1444361

10.1190/1.1444815

Alkhalifah T., 2010, 80th Annual International Meeting, Society of Exploration Geophicists, 2950

10.1190/1.1443888

Aminzadeh F., 1997, 3D salt and overthrust models

BilletteF.J.andBrandsberg‐DahlS.2004.The 2004 BP velocity benchmark.67th Annual EAGE Meeting EAGE Expanded Abstracts B305.

ChuC.andStoffaP.2008.A pseudospectral‐finite difference hybrid approach for large‐scale seismic modelling and RTM on parallel computers.78th Annual International Meeting Society of Exploration Geophicists 2087–2091.

DuX. FletcherR.P.andFowlerP.J.2010.Pure P‐wave propagators versus pseudo acoustic propagators for RTM in VTI media.72nd Annual EAGE Meeting EAGE Expanded Abstracts Accepted.

10.4310/CMS.2009.v7.n2.a3

Etgen J., 1986, SEP‐48. Stanford Exploration Project, 133

EtgenJ.andBrandsberg‐DahlS.2009.The pseudo analytical method: Application of pseudo Laplacians to acoustic and acoustic anisotropic wave propagation.79th Annual International Meeting Society of Exploration Geophysicists 2552–2556.

10.1190/1.1567242

10.1190/1.1620639

10.1111/j.1365-2478.2004.00413.x

FowlerP. DuX.andFletcherR.P.2010.Recursive integral time extrapolation methods for scalar waves.80th Annual International Meeting Society of Exploration Geophysicists 3210–3215.

Golub G.H., 1996, Matrix Computations

10.1016/S0024-3795(96)00301-1

10.1137/0917055

JohnsonW.B.andLindenstraussJ.1984.Extensions of Lipschitz mappings into a Hilbert space. In: Conference in modern analysis and probability (New Haven Connecticut 1982) American Mathmatical Society volume26 ofContemporary Mathmatics 189–206.

MagenA.2002.Dimensionality reductions that preserve volumes and distance to affine spaces and their algorithmic applications. In: Randomization and approximation techniques in computer science.Springer volume2483ofLecture Notes in Computer Science 239–253.

10.1190/1.3587217

10.1190/1.1442557

Song J., 2001, The optimized expression of a high dimensional function/manifold in a lower dimensional space, Chinese Scientific Bulletin, 46, 977

10.1190/geo2010-0287.1

SongX. FomelS. YingL.andDingT.2011.Lowrank finite‐differences for wave extrapolation.81st Annual International Meeting Society of Exploration Geophysicists 3372–3376.

10.1111/j.1365-2478.1987.tb00830.x

WardsB.D. MargraveG.F.andLamoureuxM.P.2008.Phase‐shift time‐stepping for reverse‐time migration.78th Annual International Meeting Society of Exploration Geophysicists 2262–2266.

10.1190/1.3123476

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Geophysical Prospecting

Tập 61 Số 3

526-536

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