Quantifying Uncertainty Across an Array of Seismic Applications

Over the past decade, global seismologists have imaged the bottom of tectonic plates, traced subducting slabs along their descent through the mantle, and detected a menagerie of structures in the core-mantle boundary region. These advances were made possible by vastly expanded computational resources and a staggering amount of high-quality, three-component, broadband data. Yet, the uncertainty of seismic images, tomograms and other geophysical inferences remains poorly quantified. Fortunately, improved computational capabilities and methods now make possible major advances in quantifying uncertainty. Transdimensional and hierarchical methods, which treat the parameterization and noise characteristics as unknowns to be inferred from the data, are particularly powerful tools for studying uncertainty across geophysical applications. Here, we a reversible-jump Markov chain Monte Carlo implementation of transdimensional, hierarchical Bayesian inference and present an array of case studies of uncertainty that tackle a range of challenges. We start by characterizing noise on seismograms and illustrate the importance of noise on receiver function estimates. Then, we quantify tradeoffs among physical parameters to which seismic waves are sensitive, in an application of joint inversion of surface wave dispersion, ellipticity, and receiver functions. Finally, we present estimates of errors and smearing in phase velocity maps and travel time tomography, emphasizing the limitations of traditional assumptions of normally-distributed errors in tomography.