Title: Seismic imaging and uncertainty assessment using variational methods
Authors: Xin Zhang - University of Edinburgh (United Kingdom) [presenting]
Andrew Curtis - University of Edinburgh (United Kingdom)
Abstract: In a variety of geoscientic applications, maps of subsurface properties together with the corresponding maps of uncertainties to assess their reliability are required. Seismic tomography is a method that is widely used to generate those maps. Since tomography is significantly nonlinear, Monte Carlo sampling methods are often used for this purpose, but they are generally computationally intractable for large data sets and high-dimensionality parameter spaces. Variational methods solve the Bayesian inference problem as an optimization problem, yet still provide fully probabilistic results. We test two variational methods: automatic differential variational inference (ADVI) and Stein variational gradient descent (SVGD). We use them to solve both travel time tomography and full waveform inversion problems. The results show that variational inference methods can produce accurate approximations to the results of Monte Carlo sampling methods at significantly lower computational cost, provided that gradients of parameters with respect to data can be calculated efficiently. We therefore contend that variational methods may have greater potential to extend probabilistic analysis to higher dimensional tomographic systems than current Monte Carlo methods.