Rapid Finite Fault Inversion for Megathrust Earthquakes

Abstract

The largest earthquakes take place at subduction zones, and their devastating impact in populated regions is often exacerbated by their ability to excite powerful tsunamis. Today, we understand that large subduction earthquakes, known as megathrust events, are caused by the sudden release of elastic strain energy stored at the plate boundaries where a localized, previously locked, section of the megathrust ruptures. The rupture process can propagate over hundreds of kilometres and slip on the fault can be tens of meters. Using ground motion data to image the spatio-temporal spread of slip over the fault surface is known as finite fault inversion (FFI). Over the past decade FFI has become almost routine, so that results produced by different groups are available within several days or even hours after a large event. However, these results typically require manual processing of the data, and are not accompanied by appraisals of uncertainty. My PhD research has focused on obtaining slip models for such events in near real time. I divided my analysis into three main projects that are discussed in this thesis.

First, I evaluated the performance of a long period seismic wave, the W-phase, which arrives between P and S waves, in a classic FFI scheme for the Maule (2010, Mw = 8.8) and Tohoku (2011, Mw = 9.1) events. I found that, despite its long period, the W-phase can resolve first order features of the rupture for both events. Since the W-phase is not very sensitive to 3D structure, the processing of data for the W-phase is generally simpler than it is for the body and surface waves that are commonly used for FFI. In addition, the W-phase is fast and can be obtained soon after the arrival of the P-wave.

Second, I improve the classic inversion scheme to increase robustness and rigour for rapid inversions. The most remarkable aspects of this inversion approach are that the faulting surface is constrained to follow the 3D subducting slab geometry and that the smoothness of the rupture is objectively determined. I used this approach for the recent Illapel event (2015, Mw = 8.3) and showed that a meaningful preliminary model can be obtained within 25 minutes from rupture onset. A refined solution can be obtained 1 hour from the origin time, which is still useful for the management of the disaster.

Finally, I have developed a novel linearized inversion method that allows slip uncertainties to be estimated during rapid finite fault inversion. This is an intrinsically complex problem as normally positivity constraints are imposed on finite fault models to ensure well behaved solutions. Uncertainties are typically unavailable for FFI results, but they can be crucial for meaningful interpretation of the slip models. To estimate them, I follow a probabilistic Bayesian framework but avoiding the computationally demanding Bayesian sampling. Instead, by using a coordinate transformation, the posterior distribution is approximated and obtained by linearized inversion. This inversion scheme was tested employing both simulated and real W-phase data, showing that meaningful uncertainty estimates can be inferred. Comparison with Bayesian sampling is also performed suggesting that the error of approximating the posterior is small. Including uncertainty estimates in early finite fault models will reduce the risk of working with misleading solutions.

The rigour, objectivity and robustness of the inversion techniques devised in this thesis can be a valuable contribution to the FFI community. Since I have utilized mostly open source software and a desktop computer to carry out this research, the tools I have developed can be easily used for early warning in most seismic observatories. I believe that, when facing such disastrous events, the methods developed here can be important to assist authorities with emergency response.