Multichannel estimation of frequency‐department Q from VSP data1

Abstract

AbstractA Method of estimating attenauation from the first arrivals of VSP data is presented. The motivation is the desire to investigate the effects of scattering on wave propagation, and particularly the apparent attenuation and associated phase delay due to fine layering (the O'Doherty‐Anstey effect).In order to take account of the frequency dependence of the predicted scattering attenuation, and to provide robust statistics for the estimates, a beam‐forming method is used to measure the attenuation. This simularaneously estimates the slowness and polarization angle of the different wave modes, and results in attenuation measurements which are largely free of interference from reflected and mode‐converted energy. By working in the frequency domain and measuring amplitude decay with depth, the frequency dependence of the attenuation is also accounted for. The beam‐forming algorithm works in two passes, the first of which estimates slownesses and polarization angles over a small depth range, while the second uses the information from the first pass over a larger depth range to estimate attenuation.An approximate error analysis of the method shows that the standard variance of the estimated Q values is proportional to Q2 and the data quality (measured by its spectral coherence), and inversely proportional to the square of the analysis depth range and the square of the frequency. Hence the depth resolution is traded against the stability of the results.The method is applied to a zero‐offset three‐component VSP. The data are of good quality, with a bandwidth ranging from 180 Hz in the shallow part to 100 Hz in the deepest part. Stable results were obtained using a 450 m depth range. Above about 50 Hz, there is little evidence of frequency dependence in the attenuation. There is a clear division in depth into layers of higher and lower attenuation, with values of Q typically between 50 and 200. Below 50 Hz, however, attenuation increases rapidly with decreasing frequency throughout the depth range, with values of Q of less than 10 at 15 Hz. This behaviour appears anomalous since on physical grounds we expect very high values of Q at low frequency, and we have no explanation for these observations.