The Quarterly Journal of Mechanics and Applied Mathematics · 1988 · 210 citations · 0 references
Natural SciencesMathematicsPhysicsAcousticsPropagationTheoretical PhysicsAcoustic Inverse ProblemsAcoustic ScatteringAcoustic Wave PropagationInverse Problems In MechanicsScattering ProblemsScattering TheoryAcoustic Inverse ScatteringFrequency-domain Inverse ProblemsInverse ScatteringScattering Inverse Problems
We consider the inverse scattering problem of determining the speed of sound in an inhomogeneous medium of compact support from a knowledge of the far-field patterns of the scattered fields corresponding to many incident time-harmonic plane waves. Based on the investigation of a new class of boundary-value problems for the reduced wave equation, we show that the far-field patterns are all clustered around a hyperplane in L2(δΩ), where δΩ is the unit sphere. This result leads to two distinct optimization schemes for solving the inverse scattering problem. For the case of many incident plane waves, the second of these schemes is numerically more economical and using this scheme we provide numerical examples for the case of a spherically stratified medium.