Statistics of the values of a normalized slip in the points of an earthquake fault

Abstract

In order to develop a statistical description for the values of a final slip (dislocation) in different points of an area of an earthquake source fault, we analyzed the recently compiled collection extendedfault descriptions, obtained by solution of the corresponding inverse problem. The probability distribution func� tion was studied for the normalized average slip in a subfault (an element of a large fault). Each large fault yielded by an individual inversion was normalized by division of the slip value in a subfault to the mean value averaged across the subfaults of a given fault. The processing included the following steps: informal rejection of less reliable inversions, normalization, and construction of empirical distribution functions for individual earthquakes and for the pooled sample. We estimated the parameters of the empirical functions and approx� imated them by simple standard distribution laws. The statistical structure of the values of the slip is found to be rather stable. The individual empirical samples have the coefficient of variation 0.98 ± 0.28 and, generally, resemble those with the exponential distribution law. The upper tail of the distribution rather sharply tapers off, following, on average, the power law with the exponent α being approximately from -3.5 to -4. The composite distribution has a noticeable atom at zero with a weight of about 10%. The presence of this atom impedes approximation of the observed distribution by a simple law. We proposed a reasonable approximation by a modified lognormal law; the modification includes shifting to the left and winsorization at zero. The appearance of the atom at zero is possibly due to the unbreakable barriers at propagation of a rupture; at the same time, we cannot rule out the possibility for it to be an artifact generated by the procedure of inversion. Our results provide good grounds for practical simulations of the scenario earthquakes; they also are of inter� est for the physics of the earthquake source.