Analysis and Application of Optimal Transport For Challenging Seismic Inverse Problems
Abstract
In seismic exploration, sources and measurements of seismic waves on the surface are used to determine model parameters representing geophysical properties of the earth. Full-waveform inversion (FWI) is a nonlinear seismic inverse technique that inverts the model parameters by minimizing the difference between the synthetic data from the forward wave propagation and the observed true data in Partial Differential Equation (PDE)-constrained optimization. The traditional least-squares method of measuring this difference suffers from three main drawbacks including local minima trapping, sensitivity to noise, and difficulties in reconstruction below reflecting layers. Unlike the local amplitude comparison in the least-squares method, the quadratic Wasserstein distance from the optimal transport theory considers both the amplitude differences and the phase mismatches when measuring data misfit. The speaker will briefly review her research team’s earlier development and analysis of optimal transport-based inversion and include improvements, for example, a stronger convexity proof. The main focus will be on the third “challenge” with new results on sub-reflection recovery.
About the speaker
Dr. Yang Yunan obtained her BS in Mathematics and the Applied Mathematics from Zhejiang University in 2013 and her PhD in Mathematics from the University of Texas at Austin in 2018. She then joined New York University (NYU) and is currently the Courant Instructor at the Courant Institute of Mathematical Sciences of NYU.
Dr. Yang’s research interests are on numerical analysis, optimal transport and the applications, optimization, and machine learning. She is participating in the reviewing activities for journals including Journal of Computational Physics, Journal of Scientific Computing, Society for Industrial and Applied Mathematics (SIAM) Journal on Scientific Computing, Geophysics and Geophysical Journal International.
Dr. Yang is the recipient of the SIAM Travel Award in 2017-2019 and the finalist of the 19th Leslie Fox Prize for Numerical Analysis of the Institute of Mathematics and its Applications.
About the program
For more information, please refer to the program website at http://iasprogram.ust.hk/inverseproblems.
