Estimation of the size of earthquake preparation zones

TLDR: In this article, an approximate solution of the problem for a soft elastic inclusion in an elastic half-space is presented. But the authors assume that the moduli of the inclusion differ slightly from those of the surrounding medium (by no more than 30%).

Abstract: 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.