Variance estimate in frequency-domain deconvolution for teleseismic receiver function computation

In this study, the problem of estimating the receiver function variance is discussed. The receiver function computation is performed through a frequency-domain deconvolution (Oldenburg 1981) of the vertical seismogram from the radial and tangential seismo-grams. This technique requires a knowledge of the noise contaminating the seismic signals, and provides an estimate of the receiver function variance. Oldenburg (1981) modelled this noise as additive; Ammon (1992) proposed to estimate the noise level from the power-spectral density in a pre-signal time window. In this paper, this approach is used jointly with an additional inversion, which yields a sequence of spikes as a model for the true receiver function. The resulting residual in a time window preceding the direct P pulse is used in order to evaluate the receiver function variance and the actual noise level involved in the frequency-domain deconvolution. This variance estimate is compared with the one provided by Oldenburg’s original method. The application of this method to teleseismic recordings of earthquakes (5.1 Imb 5 6.1) with similar backazimuths and distances shows that considering the additive noise only is not sufficient to explain the uncertainty measured from the pre-signal in the receiver function. Moreover, the estimated uncertainty seems to be independent of the seismic event magnitude, suggesting a signal-generated noise affecting the receiver function. The proposed approach provides a variance estimate for a single receiver function, allowing one to assess the statistical accuracy of its amplitudes in agreement with the uncertainty involved in a stacking procedure. This is particularly useful when poor-quality waveforms from relatively small earthquakes (mb = 5.1) are analysed and data from nearly co-located events are not available for stacking