Our theoretical model of rupture arrest indicates that most of the injection-induced earthquakes have been self-arrested.

Among all the numerical methods in seismology, the finite-difference (FD) technique provides the best balance of accuracy and computational efficiency. This book offers a comprehensive introduction to FD and its applications to earthquake motion. Using a systematic tutorial approach, the book requires only undergraduate degree-level mathematics and provides a user-friendly explanation of the relevant theory. It explains FD schemes for solving wave equations and elastodynamic equations of motion in heterogeneous media, and provides an introduction to the rheology of viscoelastic and elastoplastic media. It also presents an advanced FD time-domain method for efficient numerical simulations of earthquake ground motion in realistic complex models of local surface sedimentary structures. Accompanied by a suite of online resources to help put the theory into practice, this is a vital resource for professionals and academic researchers using numerical seismological techniques, and graduate students in earthquake seismology, computational and numerical modelling, and applied mathematics.

Finite‐fault earthquake source inversions infer the (time‐dependent) displacement on the rupture surface from geophysical data. The resulting earthquake source models document the complexity of the rupture process. However, multiple source models for the same earthquake, obtained by different research teams, often exhibit remarkable dissimilarities. To address the uncertainties in earthquake‐source inversion methods and to understand strengths and weaknesses of the various approaches used, the Source Inversion Validation (SIV) project conducts a set of forward‐modeling exercises and inversion benchmarks. In this article, we describe the SIV strategy, the initial benchmarks, and current SIV results. Furthermore, we apply statistical tools for quantitative waveform comparison and for investigating source‐model (dis)similarities that enable us to rank the solutions, and to identify particularly promising source inversion approaches. All SIV exercises (with related data and descriptions) and statistical comparison tools are available via an online collaboration platform, and we encourage source modelers to use the SIV benchmarks for developing and testing new methods. We envision that the SIV efforts will lead to new developments for tackling the earthquake‐source imaging problem.

The finite-difference and finite-element modeling of seismic wave propagation and earthquake motion:

An earthquake's stress drop is related to the frictional breakdown during sliding and constitutes a fundamental quantity of the rupture process. High‐speed laboratory friction experiments that emulate the rupture process imply stress drop values that greatly exceed those commonly reported for natural earthquakes. We hypothesize that this stress drop discrepancy is due to fault‐surface roughness and strength heterogeneity: an earthquake's moment release and its recurrence probability depend not only on stress drop and rupture dimension but also on the geometric roughness of the ruptured fault and the location of failing strength asperities along it. Using large‐scale numerical simulations for earthquake ruptures under varying roughness and strength conditions, we verify our hypothesis, showing that smoother faults may generate larger earthquakes than rougher faults under identical tectonic loading conditions. We further discuss the potential impact of fault roughness on earthquake recurrence probability. This finding provides important information, also for seismic hazard analysis.

Summary. We analyse 13 3-D numerical time-domain explicit schemes for modelling seismic wave propagation and earthquake motion for their behaviour with a varyi