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

SUMMARY 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 seismograms. 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; Amnion (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 ≤ m b ≤ 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 ( m b ∼ 5.1) are analysed and data from nearly co‐located events are not available for stacking.