TY - JOUR

T1 - Scattering techniques for a one dimensional inverse problem in geophysics

AU - Carroll, R.

AU - Santosa, F.

AU - Paynec, L.

PY - 1981

Y1 - 1981

N2 - 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, .

AB - 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, .

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U2 - 10.1002/mma.1670030112

DO - 10.1002/mma.1670030112

M3 - Article

AN - SCOPUS:0019686422

VL - 3

SP - 145

EP - 171

JO - Mathematical Methods in the Applied Sciences

JF - Mathematical Methods in the Applied Sciences

SN - 0170-4214

IS - 1

ER -