NUMERICAL-METHODS FOR REFLECTION INVERSE PROBLEMS - CONVERGENCE AND NONIMPULSIVE SOURCES

We study numerical methods for a one-dimensional reflection inverse problem. A normally incident impulsive plane wave is sent into a stratified elastic half-space from an adjoining homogeneous elastic half-space, and the reflected wave (the reflectance) is measured. The characteristic impedance of the medium is to be recovered as a function of travel time. This inverse problem occurs in several applications, including reflection seismology and determining vocal tract shape for speech synthesis. We show that if the step reflectance or ramp reflectance (the first or second time integral of the reflectance) is sampled appropriately and the problem is discretized accordingly, then the solution of the discrete inverse problem converges uniformly to the impedance profile, and the convergence is second order in the mesh width.