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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.

Source time functions are essential observable quantities in seismology; they have been investigated via kinematic inversion analyses and compiled into databases. Given the numerous available results, some empirical laws on source time functions have been established, even though they are complicated and fluctuated time series. Theoretically, stochastic differential equations, including a random variable and white noise, are suitable for modeling complicated phenomena. In this study, we model source time functions as the convolution of two stochastic processes (known as Bessel processes). We mathematically and numerically demonstrate that this convolution satisfies some of the empirical laws of source time functions, including non-negativity, finite duration, unimodality, a growth rate proportional to $$t^3$$ t 3 , $$\omega ^{-2}$$ ω - 2 -type spectra, and frequency distribution (i.e., the Gutenberg–Richter law). We interpret this convolution and speculate that the stress drop rate and fault impedance follow the same Bessel process.

We propose an objective threshold determination method for detecting outliers from the empirical distribution of cross-correlation coefficients among seismic waveforms. This method is aimed at dete...

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 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.

Seismological observational studies have revealed that earthquakes exhibit dynamic self-similar crack growth constituting 50–90% of the shear wave velocity. Remarkably, the peak slip velocity defined on the crack surface is scale-invariant, even from M1 to M9 earthquakes. However, a classical self-similar crack model with a singularity does not satisfy all the observed properties above. In this chapter, we review these discrepancies and introduce friction and damage models to solve them, which have been proposed in several numerical studies. We show that velocity-dependent friction can fulfill some requirements of the observations, while slip- or time-dependent friction cannot. We finally discuss the theoretical equivalence of friction and damage model for a self-similar crack in terms of energetics, which has previously only been implied by numerical studies.

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.

Waveform backprojection is a key technique of earthquake-source imaging, which has been widely used for extracting information of earthquake source evolution that cannot be obtained by kinematic source inversion. The technique enjoys considerable popularity, owing to the simplicity of its implementation and the robustness of its processing, but the physical meaning of backprojection images has remained elusive. In this study, we reviewed the mathematical representation of backprojection (BP) and hybrid backprojection (HBP) methods, following the pioneering work of Fukahata et al. (Geophys. J. Int. (2014) 196, 552–559), to clarify the physical implications of BP images. We found that signal intensity in BP and HBP images is scaled with the amplitude of the Greens function that corresponds to a unit-step slip, which results in the signal intensity being depth dependent. We propose variants of BP and HBP, which we call kinematic BP and HBP, respectively, to relate the BP signal intensity to slip motion of an earthquake by modifying the normalizing factors used in the original BP and HBP methods. The original BP and HBP images remain useful for assessing the spatiotemporal strength of the wave radiation, which scales with the amplitude of the Greens function, whereas the kinematic BP and HBP methods are suitable for imaging the slip motion that is responsible for the high-frequency radiation produced during the source-rupture process.

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.

The rupture process of the 2014 Iquique, Chile earthquake is inverted from teleseismic P wave data applying a novel formulation that takes into account the uncertainty of Green's function, which has been a major error source in waveform inversion. The estimated seismic moment is 1.5 × 1021 Nm (Mw = 8.1), associated with a 140 km long and 140 km wide fault rupture along the plate interface. The source process is characterized by unilateral rupture propagation. During the first 20 s, the dynamic rupture front propagated from the hypocenter to the large asperity located about 50 km southward, crossing a remarkably active foreshock area at high velocity (of about 3.0 km/s), but small and irregular seismic moment release rate. Our result may suggest that the 20 s long initial phase was influenced by the stress drop due to the foreshock activity near the main shock hypocenter. Moreover, the 2 week long swarm-like foreshock activity migrating roughly at 5 km/day toward the main shock hypocenter, and possibly associated slow slip, contributed to the stress accumulation prior to the Mw 8.1 megaquake. The main shock initial rupture phase might have triggered the rupture of the large asperity, which had large fracture energy.

During earthquakes , the rupture front propagates along faults at approximately 40–90 % of the shear or Rayleigh wave velocity, with slip rate often concentrated in a narrow region behind the front. Past studies have considered this phenomenon using a steady-state pulse-like rupture model and a slip-weakening friction law ; however, the results included a trade-off between rupture velocity and the scale of the pulse, which prevents the rupture velocity from being uniquely determined. In this study, we explore this issue and develop a model to determine rupture velocity by considering a friction law based on a numerical simulation of a past study for a slipping plane with its microscopic structure. We combine two models from past studies to construct a relationship between rupture velocity and some tectonophysical/geological parameters.

SUMMARY Major faults are known to lie along material interfaces, including plate interfaces and tectonic lines. Recent high-precision observations have revealed that there are also faults in the vicinity of material interfaces. This suggests that slip on a fault and stress changes near one can be affected significantly by the presence of a material interface. In this paper, we develop a new mathematical framework to derive an expression for a static slip response function by drawing on properties of complex functions. Our method is characterized by its unique ability to analyse both a fault lying along a material interface and a fault intersecting a material interface under a unified framework. A few previous studies have theoretically dealt with the problem of slip on a fault that intersects a material interface, but their mathematical techniques were so complicated that they had only limited utility for seismological applications. By contrast, our mathematical framework has a simple structure thanks to the characteristics of the complex functions. Using our formula, one can easily calculate the fault slip and the static stress changes nearby, if only the stress drop on the fault is given. The static stress is represented as a sum of stress changes due to the slip and a background stress that is generally discontinuous across a material interface. Understanding of the static stress state around a fault has important implications for evaluating the likelihood of secondary failures. We find that, when the fault is located along, or in the vicinity of, a material interface, the background stress plays a key role in the formation of the stress state around a fault, and accordingly also in the triggering of secondary failures.

Cellular activation and functional cell surface markers were evaluated during experimentally-induced endotoxemia in healthy horses. Eight healthy adult horses were infused a low dose of endotoxin (lipopolysaccharide from Escherichia coli O26: B6, 30 ng/kg of body weight, IV) and five control horses were given an equivalent volume of sterile saline solution. Venous blood samples were collected for flow cytometric analysis of peripheral blood mononuclear cells (PBMCs) and to measure plasma endotoxin concentrations. Clinical signs of endotoxemia were recorded at 10, 20, 30, 40, 50 min, 1, 2, 3, 4, 8, 16, 24 and 48 hr after endotoxin or saline solution administration. Clinical findings characteristic of endotoxemia (tachycardia, tachypnea, increased rectal temperature, and leukopenia) occurred transiently in all horses administered endotoxin; however, plasma endotoxin concentrations were detectable in only 50% (4/8) of the endotoxin-infused horses. The percentage of CD4(+), CD5(+), and CD8(+) cells decreased while the percentage of CD14(+), IgM(+), and MHC class II(+) cells increased significantly after endotoxin infusion. Alterations in the immunophenotype of PBMCs from horses with experimentally-induced endotoxemia were associated with changes in vital signs, indicating that endotoxin altered the immuno balance.

The state of coffin bone displacement in a racehorse suffering from severe case of laminitis in right rear limb was monitored by conducting X-ray examination based on new indicators, and was treated with a method of shoeing combining 3 different therapeutic shoes together with sole protection materials, as well as rigorous correction of hoof shape and surgical treatment. As a result, the horse was cured after about 7 months of treatment.

A rare case of pulmonary edema due to cardiac valve obstruction has been encountered in a racehorse. It is suspected that the pulmonary edema was caused by high blood pressure in the lungs due to mitral insufficiency resulting from bacterial endocarditis. If pansystolic heart murmur and rough bronchial sounds are detected during auscultation of a horse exhibiting flu-like symptoms, pulmonary edema and mitral insufficiency should be suspected.

High-frequency seismic waves are generated by abrupt changes of rupture velocity and slip-rate during an earthquake. Therefore, analysis of high-frequency waves is crucial to understanding the dynamic rupture process. Here, we developed a hybrid back-projection method that considers variations in focal mechanisms by introducing a non-planar fault model that reflects the subducting slab geometry. We applied it to teleseismic P-waveforms of the Mw 8.8 2010 Chile earthquake to estimate the spatiotemporal distribution of high-frequency (0.5–2.0 Hz) radiation. By comparing the result with the coseismic slip distribution obtained by waveform inversion, we found that strong high-frequency radiation can precede and may trigger a large asperity rupture. Moreover, in between the large slip events, high-frequency radiation of intermediate strength was concentrated along the rupture front. This distribution suggests that by bridging the two large slips, this intermediate-strength high-frequency radiation might play a key role in the interaction of the large slip events.

Reasons for performing study: Overstrain injuries to the superficial digital flexor tendon (SDFT) and suspensory ligament (SL) are among the most common musculoskeletal injuries which contribute to the considerable wastage of racing Thoroughbreds. Many epidemiological studies have demonstrated the prevalence of and risk factors for tendon injury when racing but have not included those injuries sustained during training. However, since tendon injury during training is seen commonly in clinical practice, it is appropriate to determine the overall prevalence of tendon injury sustained during both training and racing. Objective: To determine the prevalence of overstrain injury to the SDFT and SL during training and racing among Thoroughbred flat racehorses in Japan in 1999. Methods: A retrospective study was performed using a sample population of 10,262 Thoroughbred racehorses. The medical information database of Thoroughbred racehorses registered by the Japan Racing Association (JRA) in 1999 was analysed for SDFT and SL overstrain injury diagnosed by a veterinarian employed by JRA during training and racing. Jump racehorses were excluded from this study. Results: The prevalence of forelimb SDFT tendonitis and SL desmitis was 11.1% (1130 cases) and 3.61% (370 cases) of the population, respectively. In the hindlimb, there were 0.06% (6 cases) and 0.14% (14 cases), respectively. Risks of SDF tendonitis in the forelimb in 3-year-olds or older horses were significantly higher than in 2-year-olds. In contrast, the risk of SL desmitis in the forelimb at age 3 and 4 years was 2.23 and 2.11 times higher, respectively, than in 2-year-olds, but this increased to 5.07 times in those age ≥5 years. Entire males were at greater risk in comparison to females and geldings. Conclusions: The results suggest that the prevalence of SDF tendonitis and SL desmitis in the forelimb was associated with the horse's age and sex. The prevalence of SL desmitis increased further with age compared with SDF tendonitis, possibly reflecting a more rapid accumulation of degeneration in this structure. Potential relevance: The age-related risk demonstrated in this study provides further support that overstrain injuries are associated with accumulated degeneration. These data provide a valuable resource for further research into the aetiology of tendon injury in the racehorse.