Geodetic Imaging of Fault System Activity

Geodetic observations provide kinematic constraints on the behavior of tectonically active fault systems. Estimates of earthquake cycle activity derived from these constraints may depend on modeling assumptions and/or regularization of a geodetic inverse problem, which is often poorly conditioned. Common model assumptions may affect kinematic solutions and conclusions about physical properties of faults and fault zones. For example, within a geometrically complex fault system, parameterization of nearby faults may affect slip estimates on an individual fault. In addition, fault slip models are often regularized by assuming that slip varies smoothly in space, which may artificially smear slip estimates beyond physical boundaries. As an alternative to smooth regularization, the applied mathematics field of compressed sensing provides a suite of methods for recovering sparse solutions. Applied to GPS observations of the 2011 Tohoku earthquake, compressed sensing algorithms enable imaging of spatially localized slip during and following the earthquake, and identification of a sharp boundary between coseismic and postseismic slip. Similar algorithms recover quantized solutions and may be applied to models of plate boundary deformation. Beginning with a dense array of tectonic micro-plates bounded by mapped faults in North America, these methods can be used to detect coherent motions of groups of micro-plates behaving as larger active blocks, effectively quantifying the complexity of North America plate boundary deformation. By improving our ability to identify and compare kinematic constraints on earthquake cycle processes, we are able to characterize the spectrum of earthquake cycle behaviors and gain a deeper understanding of earthquake phenomenology and physics.