Estimating errors in autocorrelation functions for reliable investigations of reflection profiles.

Autocorrelation functions (ACFs) of vertically incident seismic waves are used to image subsurface reflectors. However, the reflection responses derived from ACFs usually contain many false signals. We present a method to quantify the errors in ACFs and extract true reflectors with high reliability. We estimated the errors for each earthquake at each station as follows. We calculated the amplitude of the observed waveform within the noise window and generated 1000 random noise traces that have this amplitude. By subtracting the random noise traces from the observed waveform, we created 1000 candidate earthquake waveforms. We computed the ACF for each of the 1000 waveforms and calculated the ensemble average and standard deviation of the 1000 different ACF amplitudes at each lag time. Then, we applied weighted stacking to the ACFs of many earthquakes to obtain the reflection response at the station. We calculated the standard deviation of the weighted stack to estimate errors in the reflection response. We evaluated the method by applying it to seismic data from the metropolitan area of Japan. The subsurface structure of the study area has been studied extensively and consists of a strong velocity discontinuity between sedimentary and basement layers. Following our method, the discontinuity was imaged as a clear reflector with an amplitude that was substantially greater than three times the standard deviation, which corresponds to statistical significance at the 99% confidence level. At other depths where reflectors are not expected to be present, the amplitudes of the peaks were less than or close to three times the standard deviation. The signal of the discontinuity was clearly visible at frequencies below 10 Hz and was less prominent at higher frequencies. [ABSTRACT FROM AUTHOR]