Robust Wavelet Estimation and Quality Measures

We describe a stochastic method of wavelet estimation tying well logs to seismic data. It is insensitive to outliers in the reflection coefficients and in the seismic data. This is achieved by generating random perturbations to an initial wavelet and comparing the resulting synthetics to the seismic data by means of a robust norm. A set of best-matching wavelets is determined, providing uncertainty estimates for the wavelet and the synthetics. We use an iterative process to weight residuals by a function of the misfit determined in the previous iteration, thereby downweighting those parts of the data where the seismic and synthetic are in poor agreement.<br>Perhaps more important than the wavelets themselves are the resulting quality measures. Uncertainties in the wavelets’ amplitude and phase spectra are obtained. Wavelets from multiple wells within an area can then be compared quantitatively to ensure that the seismic phase is consistent. The weights also indicate where there is a mismatch between logs and seismic data. Such mismatches may be due to problems in the logs, such as poor log editing, or to seismic problems such as residual multiples. In either case the weights show where the data need further processing before reservoir characterisation work.<br>