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Abstract: Seismic Tomography is a method to image the Earth’s subsurface. In order to better interpret the resulting images, it is important to assess imaging uncertainties. This is hard to achieve. Monte Carlo random sampling methods are often used for this purpose but the ‘curse of dimensionality’ makes them computationally intractable for high-dimensional parameter spaces. To extend uncertainty analysis to larger systems we introduce variational inference methods for seismic tomography. In contrast to random sampling, variational methods solve an optimization problem yet still provide probabilistic results. We apply variational inference to solve two types of tomographic problems using synthetic and real data: travel time tomography and full waveform inversion. We test two different variational methods: automatic differential variational inference (ADVI) and Stein variational gradient descent (SVGD). We show that ADVI provides a robust mean velocity model but biased uncertainties, whereas SVGD produces an accurate match to the results of Monte Carlo analysis, but at fraction of the computational cost. In addition, SVGD is significantly easier to parallelize, and for very large problems can be run in minibatch mode; this is impossible for Monte Carlo methods without incurring probabilistic errors. We, therefore, contend that variational methods may have greater potential to extend probabilistic analysis to other Geophysical inverse problems and to higher dimensional tomographic systems than is currently thought possible.
Biography: Andrew Curtis is the Professor of Mathematical Geoscience at the University of Edinburgh, U.K. He has a B. Sc. Hons. in Mathematics (Edinburgh, 1990) and a D. Phil. (Ph.D.) in Geophysics (Oxford, 1994). He was a post-doctoral research fellow at Utrecht University 1994-1997, after which he researched seismic data processing and imaging during 8 years as a scientist in Schlumberger Cambridge Research. He left Schlumberger in 2005 to join the University of Edinburgh, first as a Reader, then as a Professor from 2009. While at the University of Edinburgh he was Head of the Institute of Earth and Planetary Sciences from 2011 to 2014. In 2017 he won the Society of Exploration Geophysics Reginald Fessenden Award for his work on seismic interferometry. His interests include imaging and monitoring the subsurface (or really, the inside of anything at all), inversion methods, wave theory, mathematical geology, experimental design, hazard and risk analysis, and elicitation theory.