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

Abstract

The density of a rock is a physical property that is affected by compaction, pressure, temperature and rock's age in geological studies and it is used to define rock types. In hydrocarbon exploration, geology, and several other branches of geophysics, bulk density is a crucial petrophysical parameter. Compositional, lithological, and stratigraphic studies all benefit from this property. The examination of linear methods for calculating bulk density proposed by many authors in the literature is the focus of this article. The first part of this paper used least-squares regression to solve empirical models numerically. In this scenario, the density was calculated using VSH and VP logs in one model and only VP logs in the other. The mathematical, geophysical, tectonic, geological, and geochronological aspects of the regression coefficients have been investigated. The validity of these mathematical models was tested using data from oilfield wells in other parts of the world, which ranged from the area where the models were created. When we extrapolate the empirical equation from one field to another, the error between the estimated density and the actual density increases. In the same field, the mean squared error (MSE) is less than 2% and fits between real and synthetic logs for both models. This error can increase to 8% (for NPRA field-Alaska) when the age and composition of rock differ significantly from the geology of the well-log of reference (Araki field).