Investigating the influence of earthquake source complexity on back-projection images using convolutional neural networks

SUMMARY 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 highlights fault areas radiating HF seismic energy. Patterns in the HF radiation are attributable to the spatial and temporal complexity of the rupture process (e.g. slip heterogeneities, changes in rupture speed). 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 analysing 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 two different rupture processes using a 1-D line source model: a homogeneous process, where the kinematic parameters are constant along the line, and a heterogeneous process, where we introduce a central segment along the line that has a step change in kinematics. For each rupture model, we calculate synthetic seismograms at three teleseismic arrays and apply the BP technique to reveal how HF emissions are influenced by the three kinematic parameters controlling the synthetic model: the rise time, final slip and 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 1-D 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 theoretical results.