A procedure for estimation of source and propagation amplitude corrections for regional seismic discriminants

We outline a procedure for the estimation of frequency‐dependent source and propagation amplitude corrections for regional seismic discriminants (source path amplitude correction (SPAC)). For a given station and phase a number of well‐recorded earthquakes are inverted for source and path corrections. The method assumes a simple Brune [1970] earthquake‐source model and a simple propagation model consisting of a frequency‐independent geometrical spreading and frequency‐dependent power law Q. The inverted low‐frequency levels are then regressed against mb to derive a set of corrections that are a function of mb and distance. Once a set of corrections is derived, effects of source scaling and distance as a function of frequency are applied to amplitudes from new events prior to forming discrimination ratios. The resulting discriminants are normally distributed and amenable to multivariate feature selection, classification, and outlier techniques. To date, most discrimination studies have removed distance corrections once a particular amplitude ratio is formed (distance corrected ratio (DCR)). DCR generally works well for phase ratios taken in a particular frequency band. However, when different frequency bands are combined (for phase spectral ratios or cross spectral ratios), significant source‐scaling effects (e.g., corner‐frequency scaling) can remain, causing the discriminants to vary as a function of event size and to be nonnormally distributed. It is then often necessary to construct nonphysical transformations in an attempt to make the discriminants multivariate normal. The SPAC technique can be used to construct discriminants that are multivariate normal by using simple physical seismic source and propagation models. Moreover, phase amplitude residuals as a function of frequency can be spatially averaged and used as additional path‐specific corrections to correct for additional propagation effects such as phase blockages.