Dependences of the Omori and Gutenberg–Richter parameters

Abstract

Laboratory experiments on studying the aftershock regime are carried out with sandstone specimens under different axial loading and uniform compression and constant pore pressure. The aftershock sequences are modeled by the scenario of stepwise increasing axial loading of a specimen with strain control ensuring regular generation of aftershock sequences. The experiments are conducted on intact specimens and on the specimens with preliminarily formed shear macrofractures simulating natural faults. The experiments were conducted with multichannel recording of the acoustic emission (AE) signals which made it possible to locate the AE sources. Several types of the dependence of the acoustic activity relaxation parameters (parameters p and c of the modified Omori law and the Gutenberg–Richter b-value) on the level of acting stresses are revealed. The b-value decreases with the growth of axial stresses at all levels of uniform compression. In the case of fracture on the preexisting fault, the Omori relaxation parameter p increases with the growth of axial stresses whereas parameter c (the time delay before the onset of relaxation) decreases with the growth of axial stresses and increases with the rise of the level of uniform compression. In the case of a fracture of an undamaged specimen, parameter p remains unchanged as the axial stresses grow, whereas parameter c increases slightly. Parameter variations in the case of a complex stress state with both varying deviatoric (differential stresses) and spherical parts (effective pressure) of the stress tensor take on a unified form when expressed in terms of Coulomb stresses. It is hypothesized that the time delay of the aftershock activity relaxation is determined by the kinetics of fracture in accordance with the kinetic concept of strength in solids. This hypothesis is supported by exponential dependence of parameter c on stresses and on the effective strength of the medium revealed in the experiments. Under this hypothesis, the dependences of parameter c on the Coulomb stresses can be unified for different effective strength values with the use of Zhurkov’s formula for durability of materials. The obtained parameter estimates for the dependence of c on strength and stresses suggest that the c value is determined by the difference of the strength and the acting stresses, indicating how far the stress state of the medium is from the critical state corresponding to the ultimate strength.