Residual analysis of teleseismic P-wave energy magnitude estimates: inter- and intrastation variability

Computing the magnitude of an earthquake requires correcting for the propagation effects from the source to the receivers. This is often accomplished by performing numerical simulations using a suitable Earth model. In this work, the energy magnitude Me is considered and its determination is performed using theoretical spectral amplitude decay functions over teleseismic distances based on the global Earth model AK135Q. Since the high frequency part (above the corner frequency) of the source spectrum has to be considered in computing Me, the influence of propagation and site effects may not be negligible and they could bias the single station Me estimations. Therefore, in this study we assess the inter- and intrastation distributions of errors by considering the Me residuals computed for a large data set of earthquakes recorded at teleseismic distances by seismic stations deployed worldwide. To separate the inter- and intrastation contribution of errors, we apply a maximum likelihood approach to the Me residuals. We show that the interstation errors (describing a sort of site effect for a station) are within ±0.2 magnitude units for most stations and their spatial distribution reflects the expected lateral variation affecting the velocity and attenuation of the Earth's structure in the uppermost layers, not accounted for by the 1-D AK135Q model. The variance of the intrastation error distribution (describing the record-to-record component of variability) is larger than the interstation one (0.240 against 0.159), and the spatial distribution of the errors is not random but shows specific patterns depending on the source-to-station paths. The set of coefficients empirically determined may be used in the future to account for the heterogeneities of the real Earth not considered in the theoretical calculations of the spectral amplitude decay functions used to correct the recorded data for propagation effects.