The relative amplitude method: exploiting F-statistics from array seismograms

SUMMARY For earthquakes where teleseismic P and the depth phases pP and sP can be confidently identified, the relative amplitude method can be used to determine focal mechanisms that are compatible with the observed relative amplitudes of P, pP and sP. To allow for the uncertainty in phase amplitude caused by model and observational error, when applying the relative amplitude method, upper and lower amplitude bounds are placed on P, pP and sP by the analyst. The aim of these amplitude bounds is to specify nominal 100 per cent confidence limits on the amplitudes. Here we investigate using the output of the F-detector (a processing technique that under certain conditions optimally detects correlated signals crossing a seismometer array) as a tool for setting amplitude bounds for P, pP and sP. The output of the F-detector has a well-known statistical distribution. Using the inversion confidence interval principle, for a given confidence level, bounds that account for random noise interfering with coherent signals from the source region can be placed on its output. The relationship between F and the signal-to-noise ratio (SNR), means that uncertainty bounds on F can be converted into SNR bounds. Assuming the noise power is stationary in the vicinity of P, pP and sP, and hence cancels when pP/P and sP/P amplitude ratios are formed, these ratios can be used as the input to the relative amplitude method. Focal mechanisms compatible with SNR bounds at the 99 per cent confidence level for P, pP and sP are found for three previously studied earthquakes using the relative amplitude method and data recorded by medium-aperture (10‐ 20 km) seismometer arrays. For earthquakes deeper than about 15 km depth, the range of compatible focal mechanisms are similar to those found in previous studies using conventional nominal 100 per cent amplitude bounds. For shallow earthquakes (less than about 15 km), the phases P, pP and sP can overlap, making estimation of F for each individual phase difficult, and reliant on analyst judgement.