Semblance

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Problem

Semblance is the ratio of the energy of a stack of traces to times the sum of the energies of the component traces, all summed over some time interval. Show that when the traces are identical.

Background

While crosscorrelation is a quantitative measure of the similarity of two traces, semblance is a measure of the similarity of a number of traces. Assuming traces, we sum (stack) the traces at time , square the sum to get the total energy, and sum the values over a time interval . The equation for is


(9.10a)

Solution

The sum of traces is and its energy is . If the traces are identical, the numerator of equation (9.10a) becomes . The denominator becomes . Since numerator and denominator are equal, .

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