We test the concept that seismicity prior to a large earthquake can be understood in terms of the statistical physics of a critical phase transition. In this model, the cumulative seismic strain release increases as a power law time to failure before the final event. Furthermore, the region of correlated seismicity predicted by this model is much greater than would be predicted from simple elastodynamic interactions. We present a systematic procedure to test for the accelerating seismicity predicted by the critical point model and to identify the region approaching criticality, based on a comparison between the observed cumulative energy (Benioff strain) release and the power law behavior predicted by theory. This method is used to find the critical region before all earthquakes along the San Andreas system since 1950 with M≥6.5. The statistical significance of our results is assessed by performing the same procedure on a large number of randomly generated synthetic catalogs. The null hypothesis, that the observed acceleration in all these earthquakes could result from spurious patterns generated by our procedure in purely random catalogs, is rejected with 99.5% confidence. An empirical relation between the logarithm of the critical region radius (R) and the magnitude of the final event (M) is found, such that log R∝0.5M, suggesting that the largest probable event in a given region scales with the size of the regional fault network.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/98JB00792

An observational test of the critical earthquake concept

Lithosphere-Atmosphere-Ionosphere Coupling (LAIC) Model - An Unified Concept for Earthquake Precursors Validation

[1] Earthquakes and the faults upon which they occur interact over a wide range of spatial and temporal scales. In addition, many aspects of regional seismicity appear to be stochastic both in space and time. However, within this complexity, there is considerable self-organization. We argue that the occurrence of earthquakes is a problem that can be attacked using the fundamentals of statistical physics. Concepts of statistical physics associated with phase changes and critical points have been successfully applied to a variety of cellular automata models. Examples include sandpile models, forest fire models, and, particularly, slider block models. These models exhibit avalanche behavior very similar to observed seismicity. A fundamental question is whether variations in seismicity can be used to successfully forecast the occurrence of earthquakes. Several attempts have been made to utilize precursory seismic activation and quiescence to make earthquake forecasts, some of which show promise.

https://www.eoas.ubc.ca/~mjelline/453website/eosc453/E_prints/2003RG000135.pdf

Statistical physics approach to understanding the multiscale dynamics of earthquake fault systems

http://projects.itn.pt/Methasource_2015/Etiope_Martinelli_2002.pdf

Migration of carrier and trace gases in the geosphere: an overview

Terrestrial gases in groundwater and soil air have been extensively studied in recent years in seismically active areas, especially in USSR, China, Japan, and United States, in search of premonitory changes that might be useful for earthquake prediction. Concentrations of radon, helium, hydrogen, mercury, carbon dioxide, and several other volatiles have been found generally to be anomalously high along active faults, suggesting that the faults may be paths of least resistance for the terrestrial gases generated or stored in the earth to escape to the atmosphere. Temporal gas concentration changes with durations of a few hours to many months have been observed before many large earthquakes at a relatively small number of favorably situated stations at epicentral distances of up to several hundreds of kilometers. These “sensitive” stations are generally located along active faults, especially at intersections or bends of faults, or some other structurally weak zones, possibly because of tectonic strain concentration at such places. However, gas concentrations, especially those measured at or near the ground surface, may also be significantly affected by meteorological, hydrological, and other nontectonic changes in the environment. The nontectonically induced variations must be carefully eliminated or recognized in the search of true earthquake-related anomalies.

Gas geochemistry applied to earthquake prediction: An overview

During the earthquake preparation a zone of cracked rocks is formed in the region of a future earthquake focal zone under the influence of tectonic stresses. In the study of the surrounding medium this region may be considered as a solid inclusion with altered moduli. The inclusion appearance causes a redistribution of the stresses accompanied by corresponding deformations. This paper deals with the study of deformations at the Earth's surface, resulting from the appearance of a soft inclusion. The Appendix contains an approximate solution of the problem for a soft elastic inclusion in an elastic half-space. It is assumed that the moduli of the inclusion differ slightly from those of the surrounding medium (by no more than 30%). The solution permits us to calculate the deformations at the Earth's surface for the inclusion with an arbitrary heterogeneity and anisotropy. The problem is solved by the small perturbation method. The calculation is made for a special case of a homogeneous isotropic inclusion where only the shear modulus decreases. The shear stresses act at infinity. The equations are deduced for the estimation of deformations and tilts at the Earth's surface as a function of the magnitude of the preparing earthquake and the distance from the epicentre. Comparison has shown a satisfactory agreement between the theoretical and field results. Let us assume that the zone of effective manifestation of the precursor deformations is a circle with the centre in the epicentre of the preparing earthquake. The radius of this circle called ‘strain radius’ may be calculated from the equation
 
$$\rho = 10^{0.43M} km,$$

 where M is the magnitude. It was shown that the precursors of other physical nature fall into this circle.

I. P. Dobrovolsky

Papers

Estimation of the size of earthquake preparation zones

Heterogeneity in the Elastic Half-Space (Deformations at Preparation of the Tectonic Earthquake)