Geological, geophysical and mathematical analysis of synthetic bulk density logs around the world- Part II- the use of non-linear regression on empirical parameters estimation

Abstract

The bulk density is a helpful petrophysics parameter, which is used in hydrocarbon oil exploration and other geophysics areas such as gravimetry and seismic. In this second part of the research, we applied a nonlinear regression to determine the coefficients of an empirical nonlinear model. The nonlinear model analyzed was the modified Gardner's traditional model as modified by Oloruntobi and Butt. Here, the inversion was performed based on the Levenberg-Marquardt method. The linear and nonlinear methods are then compared, observing the influence of geological age, geological, geophysical, and tectonic factors on the mathematical and physical aspects. The analysis of models proposed by the different authors under study was made to determine the most efficient mathematical regression for the construction of density logs. The density was estimated from the values of VSH and VP for the Oloruntobi and Butt formulation. The study results show that it is impossible to determine a stable value for the parameters (either in the linear or non-linear model) that can be applied to wells anywhere on the planet. The value of the parameters is affected by different factors that change according to the rock's content and the conditions that affect the study area. However, it is possible to determine values for a specific study zone with a margin of error of <1% (Mean Square Error-MSE). This error is lower than when compared with results from linear regression.