Slip Inversion

Abstract

Slip inversion is a widely used analysis method using seismic and/or geodetic data, which determines the spatial and temporal distribution of fault slip, namely, a slip model. This chapter reviews the history, formulation, application, and extension of slip inversion. Constituent elements of slip inversion problem are data preparation, model parameterization, and calculation of synthetic data. For each of these elements, we introduce typical treatments and provide total mathematical formulations. Frequently used data are far-field broadband seismograms, near-field strong motions, and various geodetic data. Both linear and nonlinear parameterizations are possible to represent slip models. While Green's functions for layered structure have been used for synthetic wave calculation, 3-D Green's function and empirical Green's functions are adequate for more complex structures. Different combinations of these constituents can lead to significant differences between slip models of the same event. We then discuss issues associated with the inversion method. Various optimization schemes are applicable to find the best estimates of parameters and their uncertainties. Sometimes, an inversion problem requires additional smoothing constraints for regularization because it tends to be partly underdetermined. The weight of these constraints can be determined objectively using Bayesian modeling. Another topic related to the method is the frequency characteristics of a slip distribution and slip inversion in the frequency domain. As an example of well-studied earthquake, we compare various slip models of the 1999 Chi-Chi, Taiwan, earthquake published by different research groups and find that there are common characteristics among the models. As another method to reveal the spatiotemporal complexity of earthquake rupture, I introduce the back-projection method and compare it with slip inversion, using some results for the 2011 Tohoku-Oki, Japan, earthquake. We also review derivative studies based on slip models. There are some common characteristics in many slip models, such as slip pulse, complementary distributions of aftershocks and large slips, and rupture directivity. Slip models can provide clues to find governing laws and properties of earthquake dynamic rupture directly or indirectly. Attempts to scale the complexity of earthquake ruptures have just started and will be important both for understanding the physics of earthquakes and for reliable strong-motion predictions.