Characterisation of the low-frequency scattering data in the inverse problem of geophysics
- 1 May 1987
- journal article
- Published by IOP Publishing in Inverse Problems
- Vol. 3 (2) , L33-L35
- https://doi.org/10.1088/0266-5611/3/2/002
Abstract
Let ( Del 2+k2+k2v(x))u(x,y,k)=- delta (x-y),x in R3. Here u is the acoustic field generated by the point source located at the point y in an inhomogeneous medium with refraction coefficient 1+v(x). Assume that (*)(v(x) in L2(R3),v(x)=0 if x3>or=0 or mod xj mod >R, 11,y1):=16 pi 2limk to 0k-2us(x1,y1,k) for all x1,y1 in P=(x:x3=0) and 0s(x1,y1,k) is the scattered field. Necessary and sufficient conditions are given for a function f(x1,y1) to be the low-frequency scattering data corresponding to v(x) which satisfies conditions (*). Here x1=(x1,x2,0).Keywords
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