# Dictionary:Semblance

(sem’ bl∂nz) A measure of multichannel coherence. If ${\displaystyle f_{ij}}$ is the${\displaystyle j^{th}}$ sample of the ${\displaystyle i^{th}}$ trace, then the semblance coefficient ${\displaystyle S_{c}}$ is
${\displaystyle S_{c}(k)={\frac {\sum _{j=k-N/2}^{k+N/2}(\sum _{i=1}^{M}f_{ij})^{2}}{\sum _{j=k-N/2}^{k+N/2}\sum _{i=1}^{M}f_{ij}^{2}}}}$,
where ${\displaystyle M}$ channels are summed; the coefficient is evaluated for a window of width ${\displaystyle N}$ centered at ${\displaystyle k}$. 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.