Deconvolution of squared velocity waveform as applied to the study of a noncoherent short-period radiator in the earthquake source

Abstract

We consider an inverse problem of determination of short-period (high-frequency) radiator in an extended earthquake source. This radiator is assumed to be noncoherent (i.e., random), it can be described by its power flux or brightness (which depends on time and location over the extended source). To decide about this radiator we try to use temporal intensity function (TIF) of a seismic waveform at a given receiver point. It is defined as (time-varying) mean elastic wave energy flux through unit area. We suggest estimating it empirically from the velocity seismogram by its squaring and smoothing. We refer to this function as “observed TIF”. We believe that one can represent TIF produced by an extended radiator and recorded at some receiver point in the earth as convolution of the two components: (1) “ideal” intensity function (ITIF) which would be recorded in the ideal nonscattering earth from the same radiator; and (2) intensity function which would be recorded in the real earth from unit point instant radiator (“intensity Green's function”, IGF). This representation enables us to attempt to estimate an ITIF of a large earthquake by inverse filtering or deconvolution of the observed TIF of this event, using the observed TIF of a small event (actually, fore-or aftershock) as the empirical IGF. Therefore, the effect of scattering is “stripped off”. Examples of the application of this procedure to real data are given. We also show that if one can determine far-field ITIF for enough rays, one can extract from them the information on space-time structure of the radiator (that is, of brightness function). We apply this theoretical approach to short-periodP-wave records of the 1978 Miyagi-oki earthquake (M=7.6). Spatial and temporal centroids of a short-period radiator are estimated.