Notes on Layer Stripping Solutions of Higher Dimensional Inverse Seismic Problems,
MASSACHUSETTS INST OF TECH CAMBRIDGE LAB FOR INFORMATION AND DECISION SYSTEMS
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The subject of this paper is the inverse seismic problem in dimensions higher than one, in which local density and wave speed are function of more than one spatial variable. To clarify matters, some terminology is introduced. The dimension of and inverse problem is defined as the number of spatial variables on which the quantities of interest rho and c depend. Thus, the two-dimensional problem is the inverse problem of determining rhox,z and cx,z from surface measurements of the displacement ux, y, z0, t, and the three-dimensional problem is the inverse problem of determining rhox,y,z and cx,y,z from surface measurements of the displacement ux,y,zO,t. Note that the dimension of a problem need not be the same as the dimension of the medium for which it is defined--a problem of given dimension of the medium for which it is defined -- a problem of given dimension can be embedded in a medium of higher dimension. For example, the offset problem described in a previous work is a 1-D problem embedded in a 2-D medium, while the point-source problem of that same paper is a 1-D problem embedded in a 3-D medium. While a considerable amount of work has been done on the 1-D problem, much less has been done on the 2-D and 3-D problems.
- Numerical Mathematics