An inversion method for calculating formation and borehole parameters in X-ray lithology density logging

The use of X-ray sources in place of the ¹³⁷Cs sources used in traditional lithology density logging methods has become a new trend in the development of nuclear logging techniques. How to eliminate the effects of drilling fluids or mudcake in the measurement process is a key question that determines the accuracy of measurement. In order to reduce the effects of mudcake and improve the accuracy of measurement of formation parameters, this paper presents an inversion method that can accurately calculate formation and borehole parameters and is suitable for X-ray lithology density logging. The general process of this inversion method is described below. First, a response model for broad-beam attenuation during X-ray lithology density logging is derived. Subsequently, the responses of four detectors under various formation and borehole conditions are studied by means of Monte Carlo simulation, and the energy spectra measured by each detector are divided into four energy windows (ranges) depending on the correlation with formation parameters. Finally, accurate values of formation and borehole parameters are obtained through iterative inversion using the Levenberg-Marquardt (LM) algorithm. The results of this study show that compared with previously established analysis methods, the inversion method based on forward modeling can effectively improve the accuracy of measurement of formation density and lithology index during X-ray lithology density logging, reduce the influence of the borehole environment, and overcome the deficiencies of data processing techniques based on the spine and ribs plot.