    Velocity analysis using semblance  Next: semblance: correlation with a Up: Theory Previous: Theory

## Semblance as correlation

The correlation coefficient between two sequences of numbers and is defined as (1)

The correlation coefficient is analogous to the cosine of the angle between two vectors and . It takes values in the range from to . Taking a correlation of a sequence with a constant sequence produces a measure , defined as (2)

Squaring the correlation with a constant yields the measure equivalent to semblance (3)

Semblance is maximized when the sequence has a uniform distribution. When seismic amplitude is uniformly distributed along a moveout curve, the semblance of a horizontal slice through the gather will be maximized when the event is flattened. This fact is the basis of the conventional velocity analysis originally developed by Taner and Koehler (1969). The approach fails, however, when the amplitude variation is distinctly non-uniform.    Velocity analysis using semblance  Next: semblance: correlation with a Up: Theory Previous: Theory

2013-07-26