WAVELET ESTIMATION USING THE MULTITAPER METHOD1

Abstract An accurate estimate of the seismic wavelet on a seismic section is extremely important for interpretation of fine details on the section and for estimation of acoustic impedance. In the absence of well‐control, the recognized best approach to wavelet estimation is to use the technique of multiple coherence analysis to estimate the coherent signal and its amplitude spectrum, and thence construct the seismic wavelet under the minimum‐phase assumption. The construction of the minimum‐phase wavelet is critically dependent on the decay of the spectrum at the low‐frequency end. Traditional methods of cross‐spectral estimation, such as frequency smoothing using a Papoulis window, suffer from substantial side‐lobe leakage in the areas of the spectrum where there is a large change of power over a relatively small frequency range. The low‐frequency end of the seismic spectrum (less than 4 Hz) decays rapidly to zero. Side‐lobe leakage causes poor estimates of the low‐frequency decay, resulting in degraded wavelet estimates. Thomson's multitaper method of cross‐spectral estimation which suffers little from side‐lobe leakage is applied here, and compared with the result of using frequency smoothing with the Papoulis window. The multitaper method seems much less prone to estimating spuriously high coherences at very low frequencies. The wavelet estimated by the multitaper approach from the data used here is equivalent to imposing a low‐frequency roll‐off of some 48 dB/oct (below 3.91 Hz) on the amplitude spectrum. Using Papoulis smoothing the equivalent roll‐off is only about 36 dB/oct. Thus the multitaper method gives a low‐frequency decay rate of the amplitude spectrum which is some 4 times greater than for Papoulis smoothing. It also gives more consistent results across the section. Furthermore, the wavelet obtained using the multi‐taper method and seismic data only (with no reference to well data) has more attractive physical characteristics when compared with a wavelet extracted using well data, than does an estimate using traditional smoothing.