Earthquake Source Modeling: From a Hydraulically Controlled Fault Model to Near-Field Ground Motion Simulation
Most damage from large earthquakes occurs in close proximity to a fault, butour knowledge of the underlying physical processes of earthquake rupture is still limited. Studying earthquake source dynamics is therefore a critical task in order to improve rupture simulations for near-field ground motion prediction. Finite-fault rupture models have shown the spatio-temporal complexity of earthquake rupture, but what controls this source complexity? How can we efficiently generate physically self-consistent earthquake scenarios that capture the highly variable spatio-temporal slip evolution, as seen in dynamicrupture models? Moreover, near-source directivity effects are determined by the hypocenter position with respect to regions of high stress release on the fault. Which processes or geologic structures determine the location of these high-slip zones? What relates the point of rupture nucleation to the slip/stress distribution on the fault?
In this presentation, we will show initial results on a hydraulically controlled fault model (Hillers & Miller, 2002) that may be used to generate earthquake source models within a long-term evolutionary tectonic system. Such source models serve as a starting point to compose rupture scenarios using the pseudo-dynamic source characterization (Guatteri, Mai, Beroza, 2002). The pseudo-dynamic source model provides physically self-consistent rupture realizations that have been shown to result in realistic near-source ground motion simulations. Within the framework of this earthquake source modeling, we will also analyze the rupture initiation, and investigate how the hypocenter position is related to the final slip distribution
The Monte Carlo technique as a tool for solving seismological inverse problems
Almost all geophysical inference about the Earth's structure and physical processes going on inside the Earth, like, for example, core-mantle interaction, thermal convection, earthquake raptures to name a few are carried out on the base of the surface made measurements. This type of inference where the required information are not directly measured but rather extracted from other data called inverse problemscan be carried out in various ways. The oldest, simplest and most popular approach is a search for a model which the best fits (in a given sense) to observed data. This casts the inverse problem to an optimization task easily managed numerically. Classical least squares approach is an example of this approach. However, this technique has a serious disadvantage, namely it can hardly provide (especially in nonlinear cases) a reliable estimation of an accuracy of thesolution found. This limitation is overcome by the Bayesian approach to inverse problems.
The Bayesian method relies not on the search a single optimum model but rather constructs the posteriori probability density over the whole model space (space of all possible solutions) which expresses our knowledge that a given model is the true one. Simplifying matter one can say that the global maximum of the a posteriori probability corresponds to the optimum model found by optimization approach and additional information like width of the distribution, or generally its shape provides information on accuracy of the solution, correlation among parameters, existence of secondary solutions, etc. However, as the a posteriori distribution is usually a multi-parameter function its exploration requires very efficient numerical methods. Monte Carlo techniques are the most suitable methods that can be used nowadays for this purpose.
In the first part of this talk I shortly present and compare both optimization and Bayesian approaches to inverse problems followed by a short presentation of the Monte Carlo Sampling techniques (Markov Chain Monte Carlo). In the second part I would like to illustrate previous theoretical considerations by three seismological examples (if time permits) namely seismic velocity tomography, estimation of the earthquake source time function, and finally advanced acoustic location for ocean geodesy.