Lingyun Qiu, Institute for Mathematics and its Applications, University of Minnesota
520 Pao Yue-Kong Library
The main task in seismic inversion is to extract quantitative information of the interior of the Earth from the seismogram measured on the exterior surface.Mathematically, it is formulated as a data-fitting problem and is an ill-posed nonlinear inverse problem.
A conventional approach to Full Waveform Inversion (FWI) is to use a least-square objective function. The data misfit is measured in L2. To overcome the ill-posedness, different forms of regularization methods are also introduced. In this talk, two recent advances on choosing a more appropriate objective function for FWI will be presented.
The firstone is based on a generalized L1 Total Variation (TV) regularization method. L1-TV has become one of the most popular and successful methodology for image processing. It is widely used to restore images from blurry or noisy observations with the sharp interfaces, edges and discontinuities preserved. We apply a generalized TV regularization method to FWI with aid of the a priori information from other possible approaches. A steering field is introduced to guide the update using the wavefront information. The algorithm is efficiently implemented using the split Bregman method.
The second approach is to change how we measure the data difference by switching from L2 to the Wasserstein distance. The Wasserstein distance is a natural metric for comparing two histograms or probability distributions and becomes a very popular measure of similarity in computer vision. It bears the robustness to small shifts and noise in histograms and provides a larger convex zone compared to L2 distance. We employ the 2-Wasserstein space for mitigating the cycle-skipping problem. The approach is based on solving an optimal transport problem.