Wave-Propagation Modeling and Inversion Using Frequency-Domain Integral Equation Methods

Abstract

Full waveform inverse methods describe the full physics of wave propagation and can potentially overcome the limitations of ray theoretic methods. This work explores the use of integral equation based methods for simulation and inversion and illustrates their potential for computationally demanding problems. A frequency-domain integral equation approach to simulate wave-propagation in heterogeneous media and solve the inverse wave-scattering problem will be presented for elastic, acoustic, and electromagnetic systems. The method will be illustrated for georadar (ground- or ice-penetrating radar) applications and compared to results obtained using ray theoretic methods. In order to tackle the non-linearity of the problem, the inversion incorporates a broad range of frequencies to stabilize the solution. As with most non-linear inversion methods, a starting model that reasonably approximates the true model is critical to convergence of the algorithm. To improve the starting model, a variable reference inversion technique is developed that allows the background reference medium to vary for each source-receiver data pair and is less restrictive than using a single reference medium for the entire dataset. The reference medium can be assumed homogeneous (although different for each data point) to provide a computationally efficient, single-step, frequency-domain inversion approach that incorporates finite frequency effects not captured by ray based methods. The inversion can then be iterated on to further refine the solution.