Notes on Layer Stripping Solutions of Higher Dimensional Inverse Seismic Problems,

Abstract

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 rho(x,z) and c(x,z) from surface measurements of the displacement u(x, y, z=0, t), and the three-dimensional problem is the inverse problem of determining rho(x,y,z) and c(x,y,z) from surface measurements of the displacement u(x,y,z=O,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.

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Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1983
Accession Number
ADA158641

Entities

People

  • A. E. Yagle

Organizations

  • Massachusetts Institute of Technology

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Acoustic Waves
  • Computational Science
  • Differential Equations
  • Displacement
  • Equations
  • Inverse Problems
  • Inverse Scattering
  • Inversion
  • Measurement
  • Partial Differential Equations
  • Plane Waves
  • Scattering
  • Schrodinger Equation
  • Three Dimensional
  • Two Dimensional
  • Wave Equations
  • Wave Propagation

Fields of Study

  • Mathematics

Readers

  • Electromagnetic Wave Scattering and Antenna Radiation Engineering
  • Systems Analysis and Design
  • Wave Propagation and Nonlinear Chaotic Dynamics.