Seismic and geodynamic observational data will be employed to infer a unified dynamic earth model through solution of the joint nonlinear inverse problem governed by high-resolution mantle convection and seismic wave propagation models. This will lead to a merging of the diverse data used to constrain plate tectonics and mantle convection, providing a new 4-D picture of earth's surface and interior over the last 50 million years. The inverse problem entails severe mathematical, computational, and geophysical challenges, which conventional methods are incapable of addressing. There are several parts of this project that are planned to overcome these challenges. We will devise inverse methods that can extract full information from the large volumes of seismic and geodynamic data by creating algorithms to solve the coupled full waveform seismic and geodynamic inverse problem, and use those methods to invert for global and regional earth models from broadband seismic and geodynamic data. We will develop inversion algorithms that can scale to the large numbers of CPU cores and complex memory hierarchies characterizing emerging multi-petaflop systems. We will also extend adaptive mesh refinement (AMR) ideas from large-scale forward simulation to the setting of large-scale inverse problems. Beyond the scientific impact, the project has a program of outreach and education that is highlighted by dissemination of 4-D animations of dynamic earth models. This project fits within the "From Data to Knowledge" and "Understanding Complexity" themes of the CDI Program.
The earth is a four-dimensional dynamic system where mantle convection drives plate tectonics and continental drift and, in turn, controls much activity ranging from the occurrence of earthquakes and volcanoes to mountain building and long-term sea level change. Despite the central role mantle convection plays in our understanding of earth, we have enormous first-order gaps in our knowledge, with questions that are as basic as what are the principal driving and resisting forces on plate tectonics to what is the energy balance of the planet as a whole. However, rapidly-expanding volumes of geophysical data, the arrival of the petaflop computing era, and the emergence of high-resolution forward model simulation capabilities now provide an opportunity to merge the geophysical data into dynamic earth models to greatly enhance our understanding of earth structure. This project could catalyze a shift in the field of geodynamics, since it will lead to rigorous inference of earth models from data employing high-resolution forward models. Moreover, the project could be transformative for many other fields with similar needs, through the development of parallel mesh algorithms for large-scale inverse problems, scalable methods for large-scale nonlinear inverse problems, and inverse methods for joint inversion of data for large complex multi-physics forward models. All of these computational/mathematical advances will benefit a much wider community of scientists working on a much broader set of problems than the ones encountered in this project.
This project is concerned with the design and implementation of fastalgorithms for forward and inverse problems related to plate tectonicsand mantle convection. Our overarching goal is to employ seismic andgeodynamic observational data to infer a dynamic earth model throughsolution of nonlinear inverse problems governed by high-resolutionmantle convection and seismic wave propagation simulations. Theforward problems alone—simulation of wave propagation in the wholeearth, or convection in the mantle—are formidable and require the mostsophisticated numerical algorithms and most powerful high performancecomputing (HPC) systems available today. Solving the seismic or mantleconvection inverse problems separately, which require hundreds if notthousands of high-resolution forward simulations, has beenprohibitive, and thus represents a challenge of the highest order. Theseismic–geodynamic global-scale inverse problem is essential forsystematically assimilating the broad range of geophysical data into acoherent and unified picture of solid earth as a dynamical system. Upon completion of the project we would like to report the followingoutcomes. - We have designed, implemented and released a fast Stokes solvers forproblems with variable coefficients; such solvers can be used formantle convection simulation. - We have designed parallel algorithms for inverse scattering problemswith multiple sources. This technology allows the assimilation of datafrom a large number of seismic events. - Studied solvers for inverse transport problems, like those in mantle convection. - Trained two graduate students and two postdoctoral researchers. - Provided summer internships for undergraduate students. - Organized several minisymposia on SIAM conferences. - Further disseminated this work through presentations and invited talks. The codes described above are available at:http://padas.ices.utexas.edu/software
