Dictionary:Semblance

{{#category_index:S|semblance}} (sem’ bl∂nz) A measure of multichannel coherence. If $f_{ij}$ is the$j^{th}$ sample of the $i^{th}$ trace, then the semblance coefficient $S_{c}$ is

$S_{c}(k)={\frac {\sum _{j=k-N/2}^{k+N/2}(\sum _{i=1}^{M}f_{ij})^{2}}{\sum _{j=k-N/2}^{k+N/2}\sum _{i=1}^{M}f_{ij}^{2}}}$,

where $M$ channels are summed; the coefficient is evaluated for a window of width $N$ centered at $k$. It is basically the energy of the stack normalized by the mean energy of the components of the stack. This is equivalent to the zero-lag value of the unnormalized autocorrelation of the sum trace divided by the mean of the zero-lag values of the autocorrelations of the component traces. Perfect agreement yields a value of unity.

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