The semblance module computes the semblance panel for a given CDP gather. Velocity
analysis is usually a two-dimensional process for determining the optimal values of the
vertical two-way travel-time and stacking velocity. When the travel-time curve deviates
extensively from hyperbolic, the quartic term of the travel-time series must be part of
the computations. In its simplest form (with a_{2} = 0), the optimization of all parameters
becomes three dimensional. Repeating a conventional two-dimensional scan for each
change in of the quartic term produces the desired 3D time-velocity-anisotropy volume.
The traveltime function for a scan of this type is defined by Equation 1:

Equation 1:

The coefficients a_{1} and a_{2} are assumed to be small and, consequently, deviation from
hyperbolic arrival is also small. Triplications are beyond the scope of this program.

Semblance is defined by Equation 2:

Equation 2:

where n is the number of non-zero samples after muting, and d(t,j) is the jth trace in the input ensemble. Both the numerator and denominator are smoothed prior to the computation of this quotient.

When the pwr factor is greater than 1, it acts as both a compressor and expander, with the upper range of the semblance expanded and the lower range compressed. This tends to decrease the number of large values and makes picking an easier process.

Conversely, when the pwr factor is less than 1, this increases the number of large values and makes picking more difficult.