Abstract
Understanding the physics of earthquakes is a crucial step towards improving the prediction accuracy of earthquakes. Scale invariance or fractal features are often reported in earthquakes, such as the size distribution of earthquakes, the spatial distribution of hypocenters, and the frequency of aftershocks. Here we assess whether other key parameters and quantities involved in earthquakes also conform to the power law. By analyzing a large amount of data collected from the laboratory experiments and field monitoring of earthquakes, we find that the crack density on the two sides of small scale fracture or large scale fault decreases with increasing distance following the power law, and the crack number-crack length distribution is also scale invariant like natural faults. Besides, the earthquake b-value is found to decrease with increasing stress in a power law in the brittle regime of the Earth’s crust. The friction coefficient for dry fault and gouges or for partially saturated gouges decreases with the increasing effective normal stress in a power law. The stress dependency of b-value and friction coefficient is dictated by different mechanisms. Our findings will advance the understanding of earthquake physics, and will enable us to better model, predict and conduct hazard assessment of earthquakes.
Highlights
Earthquake is one of the most catastrophic natural disasters in the world
Both the trans-granular crack density and total crack density at 92.7% peak strength and after failure decrease non-linearly with the distance away from the medial plane of the shear fracture, the decrease of which can be well fit by the power law (in this study, the fitting relationship between the parameter (y) and the variable (x) is expressed by y = (a ± c1)x(−b±c2), a and b are constants, and c1 and c2 indicate the range of 95% confidence interval)
In the asymmetric uniaxial compression test performed on Aue granite cores, the microcrack density and the acoustic emission (AE) events on the two sides perpendicular to the shear fault were investigated[27] (Fig. 1b, re-plotted based on the data in Fig. 7 of ref.27)
Summary
Earthquake is one of the most catastrophic natural disasters in the world. the accurate prediction of the occurrence time and location of earthquakes still remains elusive[1], despite great efforts already devoted to improving techniques to monitor and analyze earthquakes in the last few decades. The most well-known power law is the Gutenberg-Richter (G-R) law, which describes the earthquake frequency-magnitude distribution[12]: log10N = a − bM, where N is the number of earthquakes larger than magnitude M, parameter a describes the total number of earthquakes, and b refers to as b-value The latter gives insights on the relative scaling of large versus small earthquakes[13], and it was often used to infer tectonic stress[14,15], predict impending large earthquakes[16,17,18,19] and aid seismic hazard assessments[20,21]. We comprehensively analyze large amounts of data compiled from the laboratory experiments and field monitoring of earthquakes, and examine whether these data conform to the power law distribution. When data values of some published plots are not available, we use the GetData Graph Digitizer software to digitize the plots and obtain the data values
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