High Frequency Wave Propagation

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High Frequency Transmission Travel-time Tomography Based on Eikonal Equations

Jianliang Qian

Mathematics and Statistics at Wichita State University

Abstract:  The purpose of travel-time tomography is reconstructing acoustic, seismic or electromagnetic wave-speed distribution from travel-time data. Traditional travel-time tomography is based on Fermat's principle and hinges on the so-called ray tracing technique to compute ray paths; therefore, ray-path coverage can be irregular and limited aperture. Based on some recent development in high frequency wave propagation (Engquist-Runborg'2003), we apply PDE techniques to construct new numerical methods for travel-time tomography. For first-arrival based travel-time tomography, we use the eikonal equation as the model equation and minimize an energy functional by a limited memory BFGS method. The required gradient can be derived by an adjoint state technique, and its computation can be achieved by solving one forward and one adjoint problem of the eikonal equation. In turn, the forward and adjoint problem can be solved efficiently by some fast numerical methods. The overall method is very fast and shows quadratic convergence in terms of energy and iteration steps. 2-D and 3-D numerical examples demonstrate the efficiency and accuracy of the new methods. This is a joint work with Shingyu Leung at UCLA.