This proposal focuses on application of full Bayesian analysis techniques to large ill-posed inverse problems in earthquake physics and earthquake engineering specifically the kinematics and dynamics of large earthquakes, and monitoring the structural health of the built environment. Both geophysics and earthquake engineering are experiencing an explosion of observations. Using this wealth of data typically involves solving large ill-conditioned inverse problems requiring large numbers of uncertain parameters necessary for realistic forward models. The core of this project centers on the necessary algorithmic and software developments required for application of Bayesian approaches to problems much larger than are currently tractable. In particular, the project targets problems involving very fast forward models but with many hundreds of free parameters as well as problems with fewer parameters but more expensive forward models. The researchers will develop and apply efficient, general, and robust techniques for sampling posterior distributions of model parameters that are suited for large parallel computing architectures. While this project is motivated by specific disciplinary goals. The geophysical and engineering applications will act as test beds designed to ensure modularity, flexibility, and broad applicability of newly developed algorithms and associated software implementations. The approach over the three years of this proposal will be multi-pronged with several important objectives for the development of computational tools for Bayesian statistical inversions. These objectives include (1) developing new methods for exploring high-dimensional model parameter spaces, (2) developing new methods for adaptive and optimal refinement of model parameter spaces, (3) exploring the role of inducing sparseness in posterior distributions over parameter spaces, and (4) producing modular, portable software for the next generation of parallel platforms. Intellectual Merit: This proposal brings together geophysicists and engineers to construct the next wave of Bayesian analysis environments to treat high-dimensional ill-conditioned inverse problems based on large amounts of data. This effort will result in (1) a new generation of physically reasonable models of earthquake dynamics that integrate all relevant observations and (2) revolutionary approaches to inferring structural health of the built environment.
