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Traditional semblance

The traditional semblance is defined by Neidell and Taner (1971) as:

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

where $ i$ and $ j$ are time sample indices, $ s(i)$ denotes the semblance for time index $ i$ , $ 2M+1$ is the length of the smoothing window (in this formulation a boxcar filter is used), along time axis, $ a(j,k)$ is the trace amplitude at time index $ j$ and trace number $ k$ of the NMO-corrected common midpoint (CMP) gather, and $ N$ is the number of traces.