A SIMPLE FRACTURE-MECHANICAL MODEL FOR THE EVOLUTION OF SEISMICITY

A simple model is presented in which a fault is represented by a one-dimensional array of elements to which a remote stress is applied. The fracture toughnesses of the fault elements are initially generated by a random walk function, but the fracture system quickly becomes organized into a fractal set characterised by a (box-counting) fractal dimension. The slope, b, of the frequency-magnitude distribution and the fractal dimension of die crack population are measured at each step, and found to vary in a similar manner to the seismic b-value and fractal dimension of earthquake epicentres. The model also predicts the observed variation of b-value of acoustic emissions in laboratory experiments.