Sea Bed Logging Applications: Predicting Hydrocarbon Depth Using Mathematical Equations

Abstract

The aim of this research is to develop 1-D mathematical equation that relates Normalized mean Square Error (NMSE) to depth of hydrocarbon (HC) for data processed using cubic spline interpolation in sea bed logging (SBL) application. Simulations were conducted using CST software that replicated real SBL environment to generate synthetic data. Frequency of 0.25Hz was used and sediment thicknesses were varied from 1000m to 3000m and incremented at every 250m. Data collected were interpolated using cubic spline and NMSE were calculated between original and interpolated data. Mathematical equation that relates NMSE (y) and depth of hydrocarbon (x) was constructed in terms of linear, exponential, logarithm and polynomial degree 2, 3, 4 and R2 were calculated for each equation. Mathematical equation using exponential function was adopted because it has reasonably high R2 and can be inversed easily. Average percentage error was calculated between calculated and measured data to achieve 5 % or lower values. If achievable, this model was accepted as forward mathematical model for SBL. Otherwise, the coefficients were adjusted and the processes repeated until minimum average error was achieved.