Reconstruction of the earthquake rupture process through coherent teleseismic imaging and statistical modeling

Many studies have attempted to illuminate rupture complexities of large earthquakes through the use of coherent imaging techniques such as back-projection (BP). Recently, Fukahata et al. (2013) suggested that, from a theoretical point of view, the BP image of the rupture is related to the slip motion on the fault. However, the quantitative relationship between the BP images and the physical properties of the earthquake rupture process still remains unclear. Our work aims at clarifying how BP images of the radiated wavefield can be used to infer spatial heterogeneities in slip and rupture velocity along the fault. We simulate different rupture processes using a line source model. For each rupture model, we calculate synthetic seismograms at three teleseismic arrays and we apply the BP technique to identify the sources of high-frequency (HF) radiation. This procedure allows for the comparison of the BP images with the originating rupture model, and thus the interpretation of HF emissions in terms of along-fault variation of the three kinematic parameters: rise time, final slip, rupture velocity. Our results show that the HF peaks retrieved from BP analysis are most closely associated with space-time heterogeneities of slip acceleration. We verify our findings on two major earthquakes that occurred 9 years apart on the strike-slip Swan Islands fault: the Mw 7.3 2009 and the Mw 7.5 2018 North of Honduras earthquakes. Both events followed a simple linear geometry, making them suitable for comparison with our synthetic approach. Despite the simple geometry, both slip-rate functions are complex, with several sub-events. Our preliminary results show that the BP image of HF emissions allows to estimate a rupture length and velocity which are compatible with other studies and that strong HF radiation corresponds to the areas of large variability of the moment-rate function. An outstanding question is whether one can use the BP image of the earthquake to retrieve the kinematic parameters along the fault. We build on the findings obtained in the synthetic examples by training a neural network model to directly predict the kinematic parameters along the fault, given an input BP image. We train the network on a large number of different synthetic rupture processes and their BP images, with the goal of identifying the statistical link between HF radiation and rupture kinematic parameters. Our results show that the neural network applied to the BP image of the earthquake is able to predict the values of rise time and rupture velocity along the fault, as well as the central position of the heterogeneity, but not the absolute slip values, to which the HF BP approach is relatively insensitive. Our work sheds some light on the gap currently existing between the theoretical description of the generation of HF radiation and the observations of HF emissions obtained by coherent imaging techniques, tackling possible courses of action and suggesting new perspectives.