ABSTRACT

Geophysics has provided a rich source of problems for mathematicians to work on, starting from Hadamard's Cauchy problem of Laplace's equation to the famous Calderon problem of electrical impedance tomography. Since geophysical exploration is a multibillion dollar industry, the geophysical community has always been open to new ideas, new tools, and new people. I will provide a bird's eye view of some problems arising from mathematical geophysics from the perspective of a computational mathematician. I will mainly cover some state-of-the-art fast algorithms for both direct and inverse problems of wave and potential fields, such as acoustic wave, elastic wave, gravity field, magnetic field, and electromagnetic field. I will illustrate these problems with computational results of both synthetic and field data.