IMPROVED LOW‐FREQUENCY DECAY ESTIMATION USING THE MULTITAPER SPECTRAL ANALYSIS METHOD¹

Spectral analysis is one of the most ubiquitous signal processing tools used in exploration geophysics. Among many applications, it is used simply to look at the frequency content of seismic traces, to find notches, to estimate wavelets under the minimum‐phase assumption, and to match broadband synthetic seismograms to seismic data.

Seismic spectra exhibit very large dynamic ranges, particularly at low frequencies. Estimation of low‐frequency decay is very important for accurate modelling. However, when using traditional spectral estimates incorporating smoothing windows, too much sidelobe energy leaks from high power into low power areas, spoiling our ability to estimate low‐frequency spectral decay. The multitaper method of spectral analysis due to D. Thomson does not employ just a single window, but rather a set of orthogonal data tapers. It is possible to have much less sidelobe contamination, while maintaining a stable estimate.

The trace is tapered by each of a subset of the orthogonal tapers, and a raw spectral estimate produced in each case. These are combined to produce a final spectral estimate. The technique can be made adaptive by applying different weights to the different raw spectra at different frequencies.

A comparison of seismic spectral estimation using this multitaper technique with a traditional approach having the same analysis bandwidth and stability demonstrates the very different estimates of spectral decay in the areas of high dynamic range. The multitaper approach provides estimates with much reduced sidelobe leakage, and hence is a very appealing method for reflection seismology.