Overview: Earthquakes, tsunamis, and volcanic eruptions are among the most devastating natural events that humans face. These events reshape Earth’s surface, transport mass and energy, and thereby influence the deformation and dynamics of the solid Earth. Our research provides a process-based understanding of natural hazards and related problems, primarily through theory and modeling. Our work has contributed to our understanding of ground shaking from earthquakes, fault-zone processes controlling how and why earthquakes occur, tsunami generation by offshore earthquakes, and wave propagation and oscillations in fluid-filled fracture systems. This work is grounded in solid and fluid mechanics, represented by differential equations that we solve to achieve predictive understanding of the natural system. For these unique problems, we develop numerical methods and codes.

Earthquakes and tsunamis: Our objective here is to develop process-based models of earthquakes and aseismic slip. We work at a variety of scales, ranging from naturally occurring events at the scale of Earth’s lithosphere to small earthquakes and aseismic slip in shallow reservoirs associated with energy-production operations. One fundamental component of earthquake modeling is a description of the evolution of frictional strength and the dissipation of energy during slip and rupture propagation. Our work therefore focuses on processes at the scale of fault zone, encompassing both highly localized shearing within the fault core and inelastic deformation within the surrounding damage zone. We account for friction on slip surfaces, changes in pore fluid pressure and temperature, and complex fault geometries. Fault damage zones provide pathways for fluid transport, so our models now include coupling between fluid flow, pressure diffusion, and fault slip. This coupling can lead to fluid-driven aseismic slip transients and earthquake swarms. Many open questions remain regarding the evolution of porosity and permeability over earthquake cycle time scales. It is also essential to consider the interplay between the fault zone and the surrounding rock. The latter transitions from elastic in the upper crust to viscoelastic in the lower crust and upper mantle. Deformation transitions from frictional shearing or sliding in seismogenic zone to viscous shearing in a ductile fault root. We are investigating this transition and viscous flow alters loading of the seismogenic zone and the occurrence of earthquakes. Our work also explores offshore earthquakes in subduction zones, where deformation of the seafloor generates tsunamis.

Volcanic eruptions: Our group is pursuing the development of models and workflows to calculate infrasound radiation (low frequency acoustic waves) in the atmosphere and seismic radiation (elastic waves) in the solid Earth from volcanic eruptions. We are also building conduit flow models that describe the ascent and eruption of magma. Our objective is to constrain otherwise unobservable processes like magma fragmentation, and the descent of the fragmentation front down the conduit, from infrasound and seismic data. We have also developed models for waves and oscillations around and within fluid-filled cracks. These models have application to magma-filled dikes and sills beneath volcanoes, water-filled crevasses and rifts in glaciers and ice sheets, and to hydraulic fractures created in energy production operations.

Numerical methods and scientific computing: Many of the problems we tackle involve wave propagation and solid mechanics, but often with complex coupling between additional processes. My group works on summation by parts (SPB) methods for solving partial differential equations. The SBP property, together with proper enforcement of boundary and interface treatment, allows proofs of stability using the energy method. Our work typically utilizes high order accurate finite difference SBP operators, although the SBP framework applies to a much broader class of methods including finite elements. We have developed methods for the variable coefficient acoustic and elastic wave equations in complex geometries as well as the variable coefficient plate equation, which we solve when modeling flexural-gravity waves in floating ice shelves. The SBP framework also allows us to implement nonlinear interface conditions, like fault friction laws, in a stable and accurate manner. We are also working on adjoint-based optimization/inversion methods for problems like full waveform inversion. With the SBP framework, we can develop dual-consistent methods; that is, methods for which the adjoint of the discrete problem is a stable and accurate discretization of the continuum adjoint problem.

Last updated: December 3, 2021