An inversion method to analyze rupture processes of small earthquakes using stopping phases

Abstract

We propose a method to obtain source parameters, most importantly the rupture velocity, of small earthquakes on the basis of stopping phases. It is assumed that a rupture begins at one focus of an ellipse and spreads radially at a constant rupture velocity on the fault surface, eventually terminating on the elliptical boundary. This model allows us to investigate a wide variety of rupture configurations, ranging from a circular to a unilaterally propagating rupture. In this model we find that two high‐frequency stopping phases, Hilbert transformations of each other, are radiated and that the difference in arrival times between the two stopping phases is dependent on the average value of the rupture velocity, the radius of the major semiaxes of the ellipse, and its ellipticity. These parameters can be estimated by a nonlinear least squares inversion method. We perform simulation tests, which allow us to detect a Hilbert transform pair whose arrival times coincide with ones predicted by an assumed source model from noisy data. These simulation tests show that our inversion method is useful. Since our method does not require an a priori assumption of the average rupture velocity, the orientation of the fault plane, and the circular crack model, it provides us with a tool for estimating accurate source dimensions as well as rupture processes of small earthquakes.