Acoustic inverse scattering via Helmholtz operator factorization and optimization

Journal Article · Mon Nov 01 04:00:00 EDT 2010 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2010.07.027· OSTI ID:21418115

Hoop, Maarten V. de, ^[1]

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1. Center for Computational and Applied Mathematics, Purdue University, 150 N. University Street, West Lafayette, IN 47907 (United States)

We present a joint acoustic/seismic inverse scattering and finite-frequency (reflection) tomography program, formulated as a coupled set of optimization problems, in terms of inhomogeneous Helmholtz equations. We use a higher order finite difference scheme for these Helmholtz equations to guarantee sufficient accuracy. We adapt a structured approximate direct solver for the relevant systems of algebraic equations, which addresses storage requirements through compression, to yield a complexity for computing the gradients or images in the optimization problems that consists of two parts, viz., the cost for all the matrix factorizations which is roughly O(rN) (for example O(rNlogN) when d = 2) times the number of frequencies, and the cost for all solutions by substitution which is roughly O(N) (for example O(Nlog(rlogN)) when d = 2) times the number of frequencies times the number of sources (events), where N = n{sup d} if n is the number of grid samples in any direction, and r is a parameter depending on the preset accuracy and the problem at hand. With this complexity, the multi-frequency approach to inverse scattering and finite-frequency tomography becomes computationally feasible with large data sets, in dimensions d = 2 and 3.

• OSTI ID: 21418115
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: 22 Vol. 229; ISSN JCTPAH; ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
ACCURACY
APPROXIMATIONS
CALCULATION METHODS
DIAGNOSTIC TECHNIQUES
DIFFERENTIAL EQUATIONS
EQUATIONS
FACTORIZATION
HELMHOLTZ THEOREM
INVERSE SCATTERING PROBLEM
MATHEMATICAL SOLUTIONS
MATRICES
OPTIMIZATION
PARTIAL DIFFERENTIAL EQUATIONS
TOMOGRAPHY
WAVE EQUATIONS