Solving Low-rank Smoothly Constrained Problems With Applications to Surface-wave Data Interpolation
Robert Baraldi, University of Washington
Travel time tomography is used by the geophysical community to determine the Earth's underlying structure by aggregating information from seismic data and fitting it to a physical model. Available data are noisy and very sparse, as they are collected at specific locations (stations) on the surface.
In exploration seismology, data interpolation and denoising techniques are an important preprocessing step prior to inversion. These techniques often use prior knowledge about the data, including parsimony in the frequency and wavelet domains as well as low-rank structure of particular matricizations. These techniques are rarely used in travel time tomography, where local ideas about data smoothness are more important.
In this work we present a novel variable-projection/smoothing algorithm that can both incorporate smoothness and obtain parsimonious representations over a wide range of data-misfit constraints. This approach is used to couple local receiver information and global source information to rapidly interpolate missing stations and denoise observed stations. We compare this approach to available formulations and algorithms and show that the new approach is competitive and has expanded functionality, in particular for non-smooth and non-convex constraints.
Abstract Author(s): Robert Baraldi, Carl Ulberg, Rajiv Kumar, Ken Creager, Aleksandr Aravkin