Inverse geophysical problems for some noncompactly supported inhomogeneities

✍ Scribed by A.G. Ramm; D.N. Ghosh Roy

• Publisher: Elsevier Science
• Year: 1993
• Tongue: English
• Weight: 197 KB
• Volume: 6
• Category: Article
• ISSN: 0893-9659
• DOI: 10.1016/0893-9659(93)90070-4

✦ Synopsis

Let[V2 + k2n(x~,23)]u(x1,x2,x3) = -6(x1 -y1)6(x2 -y2)6(~3 -ys) in R"+. Assume that U(XI,X~,X~ = 0, yl,y2 = 0, y3 = 0, k) is measured at the plane P := {x : 23 = 0) for all positions of the source on the line y = (yi, y2 = 0, ys = 0), -oo < yr < 00, and receiver on the plane (~1, x2, x3 = 0), -oo < xl, 22 < 00, and for low-frequencies 0 < Ic < Ice, Ice > 0 is an arbitrary small wave number. Assume that n(zi,xs) is an arbitrary bounded piecewise-continuous function. The basic result is: the above low-frequency surface data determine n(zi , x3) uniquely.