On a new class of kinematic models: symmetrical and asymmetrical circular and elliptical cracks

Abstract

We propose a general asymmetrical elliptical crack model, and we investigate the far-field body wave radiation. Particular models such as symmetric circular/elliptical crack model or “unidirectional” asymmetric circular/elliptical crack models may be derived as particular cases of the results derived in the present investigation. The model is a “quasi-dynamic” one, as the slip is specified by employing Eshelby’s static solution at every instant in time, which, in turn, is consistent within a multiplicative factor with the solution derived by Burridge and Willis for self-similar elliptical cracks. We derive compact closed form expressions for the far-field pulse radiated by the source model. As expected, the radiation of the model exhibits azimuthal variation which depends on the asymmetry and ellipticity of the crack model. We investigate the “stopping phases” of the model that are emitted when the rupture front stumbles on the circular/elliptical barrier at the edge of the fault and we examine their radiation pattern. We study the seismic energy and seismic efficiency of the model, and compare them with those of the symmetrical circular crack model. We find that the seismic efficiency of the asymmetrical fault models is smaller by a factor of ∼2–4 (depending on the asymmetry and ellipticity of the crack), as compared to the seismic efficiency of the symmetrical circular crack model. This is explained by the fact that the average rupture velocity of the asymmetrical models is smaller as compared to that of the symmetrical model. Finally, we employ various “objective” definitions of the corner frequency and we investigate how their predictions compare with graphically picked corner frequencies.