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Scattering techniques for a one dimensional inverse problem in geophysics
Author(s) -
Carroll R.,
Santosa F.,
Paynec L.
Publication year - 1981
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670030112
Subject(s) - mathematics , inverse , inverse problem , inverse scattering problem , shear modulus , mathematical physics , mathematical analysis , scattering , type (biology) , shear waves , generalized inverse , combinatorics , shear (geology) , physics , geometry , quantum mechanics , thermodynamics , materials science , geology , paleontology , composite material
A one dimensional problem for SH waves in an elastic medium is treated which can be written as v tt = A −1 ( Av y ) y , A = (ϱμ) 1/2 , ϱ = density, and μ = shear modulus. Assume A ϵ C 1 and A ′/ A ϵ L 1 ; from an input v y ( 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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