Marina Corradini, Ian W. McBrearty, Claudio Satriano , Daniel T. Trugman, Paul A. Johnson, Pascal Bernard

The retrieval of earthquake finite-fault kinematic parameters after the occurrence of an earthquake is a crucial task in observational seismology. Routinely-used source inversion techniques are challenged by limited data coverage and computational effort, and are subject to a variety of assumptions and constraints that restrict the range of possible solutions. Back-projection (BP) imaging techniques do not need prior knowledge of the rupture extent and propagation, and can track the high-frequency (HF) radiation emitted during the rupture process. While classic source inversion methods work at lower frequencies and return an image of the slip over the fault, the BP method underlines fault areas radiating HF seismic energy. HF radiation is attributed to the spatial and temporal complexity of the rupture process (e.g., slip heterogeneities, changes in rupture speed and in slip velocity). However, the quantitative link between the BP image of an earthquake and its rupture kinematics remains unclear. Our work aims at reducing the gap between the theoretical studies on the generation of HF radiation due to earthquake complexity and the observation of HF emissions in BP images. To do so, we proceed in two stages, in each case analyzing synthetic rupture scenarios where the rupture process is fully known. We first investigate the influence that spatial heterogeneities in slip and rupture velocity have on the rupture process and its radiated wave field using the BP technique. We simulate different rupture processes using a 1D line source model. For each rupture model, we calculate synthetic seismograms at three teleseismic arrays and apply the BP technique to identify the sources of HF radiation. This procedure allows us to compare the BP images with the causative rupture, and thus to interpret HF emissions in terms of along-fault variation of the three kinematic parameters controlling the synthetic model: rise time, final slip, rupture velocity. Our results show that the HF peaks retrieved from BP analysis are better associated with space-time heterogeneities of slip acceleration. We then build on these findings by testing whether one can retrieve the kinematic rupture parameters along the fault using information from the BP image alone. We apply a machine learning, convolutional neural network (CNN) approach to the BP images of a large set of simulated 1D rupture processes to assess the ability of the network to retrieve from the progression of HF emissions in space and time the kinematic parameters of the rupture. These rupture simulations include along-strike heterogeneities whose size is variable and within which the parameters of rise-time, final slip, and rupture velocity change from the surrounding rupture. We show that the CNN trained on 40,000 pairs of BP images and kinematic parameters returns excellent predictions of the rise time and the rupture velocity along the fault, as well as good predictions of the central location and length of the heterogeneous segment. Our results also show that the network is insensitive towards the final slip value, as expected from a theoretical standpoint.