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

NMO velocity analysis using AB semblance

We propose to use AB semblance by Fomel (2009) for NMO velocity analysis to handle the AVO anomalies, especially in the data that show class II polarity reversal. Conventional semblance can be interpreted as a squared correlation coefficient of seismic data with a constant while AB semblance can be considered a squared correlation coefficient with a trend (Fomel, 2009). Equations 1 and 2 show the calculation of conventional semblance (Neidell and Taner, 1971) and weighted semblance (Chen et al., 2015), respectively. AB semblance is a special case of weighted semblance; that is, substituting the weighting function $w(i,j)$ in equation 2 with a trend function $A(i,j)+B(i,j)\varphi(i,j)$ , where $\varphi(i,j)$ is a known function related to the subsurface reflection angle or the surface offset. Here I choose surface offset for easy calculation.

$$s(k) = \frac{\displaystyle\sum_{i=k-M}^{k+M}\left(\displaystyle \sum_{j... ...2}{N\displaystyle\sum_{i=k-M}^{k+M}\displaystyle \sum_{j=0}^{N-1}d^2(i,j)} \;,$$ (1)

$$s_{w}(k) = \frac{\displaystyle\sum_{i=k-M}^{k+M}\left(\displaystyle \sum_{j... ...ystyle\sum_{j=0}^{N-1}w^2(i,j)\displaystyle\sum_{j=0}^{N-1}d^2(i,j)\right)} \;,$$ (2)

where $w(i,j)$ is the weighting function, $k$ is the center of the time window, $2M+1$ is the length of the time window, $N$ is the number of traces in one CMP gather, $d(i,j)$ is the $i$ th sample amplitude of the $j$ th trace in the NMO-corrected CMP gather. Appendix A gives a brief review of calculating $A(i,j)$ and $B(i,j)$ from the CMP gathers by least-squares fitting.

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