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SUMMARY In several analytical and numerical studies, the slip rate function and energy release rate for dynamic self-similar crack growth have been investigated, and the results obtained have contributed to a theoretical understanding and estimation of on-fault energetics. However, the relationships among physical parameters, including stress state, process zone size, rupture velocity, peak slip rate and energy release rate, are still unclear. Therefore, the aim of this study is to derive an analytical solution of the slip rate distribution of antiplane self-similar crack growth under distance-weakening friction that mimics slip-weakening friction. To satisfy the condition that the slip rate starts from zero at the rupture front, a trade-off relationship among rupture velocity, process zone size and breakdown stress-to-stress drop ratio is proposed. The peak slip rate, slip-weakening distance and fracture energy obtained using the proposed model provide a possible mechanism for the determination of the rupture velocity and the estimation of the fracture energy of the self-similar crack growth, based on the seismic observables.

Laboratory experiments with seismic measurements have the potential to be highly useful for understanding the physical process of water-induced landslides, and fundamental experiments are helpful for the appropriate interpretation of recorded seismograms. We developed a laboratory measurement system to investigate the relationships between wave propagation and water saturation in sand. We considered that the wavelength should be comparable to or sufficiently shorter than the sensing intervals. Furthermore, we embedded a wave source that can repeatedly emit an arbitrary and identical signal in an octave frequency band under both dry and nearly saturated conditions. We measured the transmitted waves by embedded accelerometers over 24 h under dry and nearly saturated conditions. The difference in the slowness between the two conditions was one-thousand-fold larger than the fluctuations in slowness over 24 h for each condition. Also, the difference in amplitude between the two conditions was about double the fluctuations in amplitude over 24 h for each condition. These results suggested that our system can monitor the water content change in sand via the change in spectral amplitude and phase slowness.

How does fault slip follow an earthquake rupture front propagating faster than the local shear-wave velocity (i.e., at supershear speed)? How does a supershear rupture front pass through a geometrically complex fault system? Resolving the evolution of such complex earthquake ruptures is fundamental to our understanding of earthquake-source physics, but these events have not been well captured by conventional waveform inversions of observational data. We applied a new framework of finite-fault inversion to globally observed teleseismic waveforms and resolved both the spatiotemporal evolution of slip and the fault geometry of the 2018 Palu earthquake (moment magnitude 7.6) in Sulawesi, Indonesia. We show that supershear rupture propagation for this event was sustained by transient slip stagnation and advancement as the rupture front passed through the geometrically complex fault system. This peculiar inchworm-like slip evolution was caused by the rupture front encountering fault bends with favorable and unfavorable orientations for rupture propagation. Our analysis also identified the possible existence of a fault junction beneath Palu Bay connecting an unmapped primary fault in northern Sulawesi with the Palu-Koro fault in the south.

We investigated the foreshock activity characteristics using the Japan Meteorological Agency Unified Earthquake Catalog for the last 20 years. Using the nearest-neighbor distance approach, we systematically and objectively classified the earthquakes into clustered and background seismicity. We further categorized the clustered events into foreshocks, mainshocks, and aftershocks and analyzed their statistical features such as the b-value of the frequency–magnitude distribution. We found that the b-values of the foreshocks are lower than those of the aftershocks. This b-value difference suggested that not only the stochastic cascade effect but also the stress changes/aseismic processes may contribute to the mainshock-triggering process. However, forecasting the mainshock based on b-value analysis may be difficult. In addition, the rate of foreshock occurrence in all clusters (with two or more events) was nearly constant (30–40%) over a wide magnitude range. The difference in the magnitude, time, and epicentral distance between the mainshock and largest foreshock followed a power law. We inferred that the distinctive characteristics of foreshocks can be better revealed using the improved catalog, which includes the micro-earthquake information.

We discuss the theoretical estimation of co-seismic energy release with respect to a random spatial distribution of stress drop, which is an extension of conventional stress drop modelling. For slip distributions characterized by the von Kármán-type power spectral density, we examine the dependence of the estimated energy release on the upper limit and decay rate of the power spectral density in the shorter wavelength band. Using this dependence, we quantify the potential underestimation of energy release when the wavelength band limitation is not considered or the k−2 model is incorrectly assumed. Moreover, we discuss the estimation of radiated energy with respect to high-frequency components and suggest a relationship between stress drop heterogeneity and high-frequency radiation.

Dynamic slip pulse propagation along a material interface is of great interest because many faults are known to lie along material interfaces and such interfaces may cause pulse‐like ruptures. This subject has been extensively studied numerically over the last two decades. It has not, however, been studied very thoroughly from an analytical standpoint, although analytical studies would complement numerical ones. In particular, an analytical solution for removing stress singularities has not yet been obtained, even after an asymptotic analysis. In this article, we employ three physically plausible conditions in our theoretical modeling: (1) arbitrary propagation speeds in the sub‐Rayleigh range, (2) a slip‐weakening friction law, and (3) boundedness of stress. We can construct an analytical solution under these conditions, and as a result of our parameter study, we determine the dependence of slip‐weakening distance and the ratio of process zone size to pulse length on rupture direction and velocity. These results enable us to discuss a mechanism for limiting rupture velocity and estimating the slip‐weakening distance in seismic inversion analyses.

In seismology, a faulting process as a source is linked with an elastic wavefield as an observable not only via a partial differential equation (PDE) but also via an integral equation. We conduct a review of these links and focus on the latter in terms of forward/inverse analyses of kinematic/dynamic modeling, which are investigated by many seismologists. Difficulties in the analyses are also mentioned: estimation and hyper-singularity of an integration kernel, determination of the number of parameters for modeling, and assumed dynamic friction on faults.