Robust wavelet estimation and quality measures

In this paper we describe a stochastic method of wavelet estimation tying well logs to seismic data. It has the advantage over traditional methods that it is statistically robust, that is, 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 rather than a single solution, thus allowing us to attach uncertainty estimates to the wavelet and the synthetics. A further refinement is to use an iterative process similar to Huber regression in determining the bestmatching wavelets. This requires weighting the residuals by a function of the misfit determined in the previous iteration, thereby downweighting those parts of the data where the seismic data and synthetic are in poor agreement.