Eran Treister (University of British Columbia, Vancouver, Canada)
Parameter estimation is performed by fitting data measurements to a model using Bayesian statistics, assuming additional prior information. The estimation requires a numerical solution of a large scale optimization problem, whose objective traditionally includes data fidelity and regularization terms.
In this talk we will concentrate on parameter estimation of physical models, obtained by solving optimization problems that are constrained by partial differential equations (PDEs). We will focus on the 3D Full Waveform Inversion, which arises in seismic exploration of oil and gas reservoirs, earth sub-surface mapping, ultrasound imaging and more. In the context of seismic exploration, FWI is highly computationally challenging: it includes large amounts of data that need to be fit using repeated expensive simulations of wave scatterings, where each of those simulations includes a numerical solution of the Helmholtz equation in several millions of variables. We will demonstrate how to computationally treat this inverse problem, and improve its solution by using travel time tomography in a joint inversion framework. We will present efficient algorithms for the solution of the Helmholtz and eikonal equations (the two associated PDEs). In addition, we will introduce jInv - our parallel open-source inversion package, which is written in Julia and is highly flexible and easy to manage for solving such inverse problems. In particular we will demonstrate how to use the PDE solvers in jInv for the parallel joint inversion using a Gauss Newton algorithm.
Eran Treister is currently a post-doctoral fellow in the Dept of Earth and Ocean Sciences at the University of British Columbia, Vancouver, Canada, and is about to join the Computer Science Dept. at Ben Gurion University of the Negev in Beer Sheba, Israel. He received his Ph.D. degree in Computer Science from the Technion — Israel Institute of Technology, Israel, in 2014. His primary research interest is scientific computing, focusing on multigrid methods, inverse problems, and optimization.