Stochastic model of earthquake fault geometry

Summary An earthquake fault pattern is assumed to consist of a system of infinitesimal, elementary dislocation loops. After an initial dislocation, subsequent ruptures occur according to a critical branching process. The position of each secondary dislocation loop is randomly shifted, along the initial fault‐plane, from the location of the main shock. In addition, the orientations of the fault‐plane and slip vector of the secondary dislocations are rotated according to a three‐dimensional Cauchy distribution which has one intrinsic scaling parameter. In their turn, the secondary dislocations produce new dependent shocks according to the same law; the process cascades indefinitely. We simulate an earthquake fault system by the Monte Carlo method. This fault pattern is both visually and statistically similar to real earthquake faults. The model yields statistical spatial distributions that correspond to those of the analysis of the catalogue data of real earthquakes. We incorporate in our scheme the time‐magnitude model of earthquake occurrence developed earlier. By the Monte Carlo method we then simulate synthetic sequences that reproduce all known magnitude‐space‐time statistical properties of real earthquake catalogues. The results of these simulations make us question the suitability of some terms that are commonly used in the theory of an earthquake source. For example, as a consequence of the validity of the stochastic model, the concepts like ‘an individual earthquake’, ‘fault‐plane’ or ‘fault‐surface’, ‘crack‐tip’ or ‘fault‐tip’, and ‘friction’, do not have an unambiguous definition.