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
SN - 0170-4214
VL - 3
SP - 145
EP - 171
JO - Mathematical Methods in the Applied Sciences
JF - Mathematical Methods in the Applied Sciences
IS - 1
ER -