Scientific Computation and Applied & Industrial Mathematics: Rongrong Wang

In this talk, we examine two methods for frequency extrapolation. Frequency extrapolation is the problem of utilizing data processing techniques to obtain the entire spectrum of an objective signal while only a middle band is sampled. This problem is well-posed for signals with special structures, such as those with a few non-zeros. The study is motivated by seismic inversion. Due to physical constraints, data obtained from a seismic survey is severely limiting in both the low and high frequency extent for the purposes of inversion. In particular, the missing low frequencies are known to be extremely essential, because when missing, most inversion algorithms are very likely to get stuck in local minima. In the numerical section, I will demonstrate the efficacy of the proposed methods in manufacturing low frequencies with real seismic examples and visualized inversion results.