CMP stacking simply means the summation of a collection of
seismic traces from different records into a single trace. It can
be considered as the simplest way for improving the SNR in prestack seismic data processing. It can help quickly obtain a meaningful poststack seismic image without wavefield continuation. The three steps in the CMP stacking process are NMO velocity analysis, NMO correction, and trace summation. Since its introduction by Mayne (1962), seismic CMP
stacking technique has been drawing great interest and
developed among the three mainstream seismic data
processing methods (deconvolution, CMP stacking and
migration). Though the CMP stacking technique has helped people explore
and exploit plenty of oil and gas reservoirs, the general
assumptions for conventional equal-weight or mean
stacking are strict: the amplitudes of all traces in the same event are equivalent, and all noises are random (Rashed, 2014). These
assumptions, however, are only perfectly valid in the
seismic data where the change of amplitudes in the same event is negligible, and
coherent noise have been removed. The concept of
weighted stacking first introduced by Robinson (1970)
continues to be a hot topic (Neelamani et al., 2006; Rashed, 2008; Tyapkin and Ursin, 2005; Anderson and McMechan, 1990; Liu et al., 2009; Schoenberger, 1996; Rashed et al., 2002). Anderson and McMechan (1990) introduced a weighted stack based on weighting traces using their signal amplitude decay and noise amplitudes. Schoenberger (1996) proposed a different weighted-stacking approach that can suppress the multiples effectively, by solving a set of optimization equations in order to determine the stacking weights. Rashed et al. (2002) came up with a weighted stack in which an optimum trace in each CMP gather is selected based on SNR and the other traces are weighted based on their distance from the optimum trace. Tyapkin and Ursin (2005) developed an optimum-weighted stacking by introducing a more realistic model that supposes a signal with an identical shape on each trace to be embedded in spatially uncorrelated irregular noise. Neelamani et al. (2006) took the signal structures into consideration and proposed a simultaneous stacking and denoising approach. Rashed (2008) improved weighted-stacking approach by excluding harmful
samples from the stack and applying more weight to the
central part of the samples, called smart stacking. All of these alternative weighted-stacking methods use weighting functions that are calculated by
SNR, offset, noise variance, or correlation with a reference trace. Alternatively, Liu et al. (2009) proposed a local-similarity-weighted stacking approach that designs the weights of each trace by calculating the local similarity between each trace and a reference trace, and this method was demonstrated to be superior than the other contemporary weighted-stacking approaches.

Weighted stacking of seismic AVO data
using hybrid AB semblance and local similarity