The Selection of Fitting Curve in Time-Depth Transformation of Deep-Seated Strata and Crust

Polynomial and power functions have been used to fit the time-depth relation based on data from wells in the Baiyun sag, Pearl River Mouth basin, northern South China Sea.For the time-depth relation of the strata deeper than the termination depth of the wells, the 3rd-order polynomial function may be applicable only if the coefficient of its 3rd-oder term is negative and the coefficient of its 2nd-order term is positive.This function, however, is not applicable to the depth because it inevitably leads to the velocity inversion at depth.The fitting of 2nd-order polynomial function does not cause the velocity inversion, but the velocity increases linearly towards the depth, violating the natural law that the velocity increment decreases downwards in the Earth's strata and crust.The power function D=at^b+c with 1 < b < 2 may approximate the time-depth relation for both shallow and deeper strata and crust without the problems encountered by using 3rd-and 2nd-order polynomial functions.It is not guaranteed, however, that for each well the fitted power function is suitable for the entire region and all the depths.For a regional time-depth conversion, the best practice is to divide the region and fit the power function for multiple wells, and then select the best functions for each sub-regions.