Application of Lifted Methods to Seismic Imaging
Eileen Martin, Stanford University
Geophysical imaging problems can be posed as optimization problems in which we try to find a velocity model to fit recorded data of seismic events subject to PDE constraints. Even using a simplified scalar velocity model, these are large-scale problems (easily on the order of kilometers in each spatial direction) and every iteration of the optimization method requires a pair of PDE-solves. Thus, improving the convergence rate of the optimization method can lead to large savings in the computational cost of these imaging problems. As one possibility to speed up the convergence rate, I am particularly interested in applying lifted methods to seismic imaging problems. In recent years, lifted methods have been proposed to improve the convergence time of optimization problems. The idea of such methods is to reformulate the optimization problem in a higher-dimensional space, where the augmented problem is then solved using a suitable iterative method (for example, a Newton-type method). Inspired by the methods already proposed, I am investigating whether it is possible to solve nonlinear PDE-constrained optimization problems in a similar way.
Abstract Author(s): Eileen Martin