Scattering techniques for a one dimensional inverse problem in geophysics

R. Carroll, F. Santosa, L. Paynec

Research output: Contribution to journalArticlepeer-review

38 Scopus citations

Abstract

A one dimensional problem for SH waves in an elastic medium is treated which can be written as vtt = A−1 (Avy)y, A = (ϱμ)1/2, ϱ = density, and μ = shear modulus. Assume A ϵ C1 and A′/A ϵ L1; from an input vy(t, 0) = ∂(t) let the response v(t, 0) = g(t) be measured (v(t, y) = 0 for t < 0). Inverse scattering techniques are generalized to recover A(y) for y > 0 in terms of the solution K of a Gelfand‐Levitan type equation, .

Original languageEnglish (US)
Pages (from-to)145-171
Number of pages27
JournalMathematical Methods in the Applied Sciences
Volume3
Issue number1
DOIs
StatePublished - 1981

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