Optimum stacking of seismic records with irregular noise: Fid-Bau Portal

Optimum stacking of seismic records with irregular noise

Yuriy Tyapkin / Bjorn Ursin

Conventional straight stacking has proved to be an effective tool to extract the signal from a multichannel seismic record. However, it maximizes the signal-to-noise ratio only when a rather simple and generally rare model of the record is true. For this reason, some authors try to optimize stacking using more complicated record models. They assume that either the signal amplitudes are allowed to vary from trace to trace in any manner with the noise variances being constant or vice versa. However, in practice, it is commonly the case that these model assumptions are seriously violated. Then, methods based on them become ineffective or even deleterious. We show that these methods produce signal estimates distorted to a considerable extent right up to being absolutely uncorrelated with the sought-for actual signal. This fact motivates our search for new methods for better estimating seismic signals. We therefore introduce a more realistic model that supposes a signal with an identical shape on each trace to be embedded in spatially uncorrelated irregular noise. The signal amplitudes and the noise autocorrelations are allowed to vary across the traces in an arbitrary manner. Given this model, a solution to the maximum likelihood estimation of the signal shape is derived. The effectiveness of the method is highly dependent on the accuracy of determining the signal amplitudes and the noise autocorrelations prior to stacking. We therefore supply the method with estimates of the required parameters. When the noise autocorrelations are trace independent to within a scale factor, the variance, the method becomes much easier to embody and yields the well-known optimum weighted stack (OWS). We compare the performance of the OWS theoretically with that of the straight stack and show that the optimum procedure has obvious advantages over the conventional one. This paper is mainly focused on further developing the OWS. With the complicated record model used, the shortcomings of the above imperfect stacking algorithms can be cancelled. The results of testing our approach to optimum stacking on a variety of field data, some of which are demonstrated, indicate that in many circumstances it can significantly outperform straight stacking and should therefore be prescribed as a better choice than the conventional process.