The application of check shots to a synthetic is, in theory, relatively straightforward. In practice, it involves complicated datums and datum corrections. The following describes the basic check shot computation in GeoSyn:
A series of check shot time depth pairs are input to the program. The sonic log is integrated (i.e., converted to a time depth log), and a second set of time depth pairs that correspond in depth to the check shot time depth pairs are selected from it. A third set of time depth pairs are created by subtracting the sonic time depth pairs from the corresponding check shot time depth pairs. This third set represents the difference and therefore the correction between the sonic and the check shot at the depths defined by the check shots.
The next step is to calculate a best-fit cubic spline through the correction points. A cubic spline is a third-order polynomial log, with the added constraint that the second derivative of the log be continuous and smooth. Cubic splines tend to be more stable than polynomials, with less possibility of wild oscillation between the tabulated points. Future releases of GeoSyn will contain provision for polynomial fits of greater than 3 degrees.
The cubic spline function is used to calculate interpolated points corresponding to every depth sample from the integrated sonic log. These points are added to the integrated time at each integrated sonic depth point. A new sonic transit log is calculated by subtracting consecutive points from the corrected integrated log.
The final step involves adding new section at the top of the log to account for the difference between the top of the sonic log and the source datum elevation of the check shot survey. Check shots above the limits of the original log create block velocity zones in the newly expanded log.