Propagation of Singularities and Some Inverse Problems in Wave Propagation

Abstract

We review a number of results relating the propagation of singularities for hyperbolic partial differential equations i.e. the persistence, or non-localization, of wave motion with well-posedness for some inverse problems of reflection type, such as arise for instance in seismology and ultrasonics. By far the most complete information is available for layered problems. We show how a simple but refined propagation-of-singularities theorem, with estimates, yields important functional properties of the model-data relationship for such problems, including regularity in various useful coefficient classes, separation of scales,....We explain the essential role of travel time in the study of these problems, and show how its function may be generalized to multidimensional (i.e. non-layered) problems.

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Document Details

Document Type
Technical Report
Publication Date
May 01, 1989
Accession Number
ADA455262

Entities

People

  • William W. Symes

Organizations

  • Rice University

Tags

DTIC Thesaurus Topics

  • Abstracts
  • Applied Mathematics
  • Differential Equations
  • Equations
  • Formulas (Mathematics)
  • Information Operations
  • Inverse Problems
  • Mathematical Analysis
  • Mathematics
  • Partial Differential Equations
  • Reflection
  • Travel Time
  • Wave Propagation

Fields of Study

  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Linear Algebra
  • Wave Propagation and Nonlinear Chaotic Dynamics.