A data inversion technique for four-detector gamma-ray logging in cased holes

Scattered-gamma-ray logging in a cased hole not only offers cased-hole formation evaluation parameters, but also enables better cement bond evaluation when there is a microannulus outside the casing. Therefore, it is essential to study the response relations of measured values from cased-hole scattered-gamma-ray logging to casing thickness, cement sheath density, cement sheath thickness and formation density, as well as the data-processing methods used to solve for such parameters. In this paper, we outline the design of a four-detector scattered-gamma-ray logging tool for cased holes, apply Monte Carlo numerical simulation to study the response relations of the above four parameters to detector-measured values, thereby establishing the forward equations of values measured by the four detectors, and then use optimization inversion to solve for casing thickness, cement sheath density, cement sheath thickness and formation density, respectively. Inverted values of casing thickness had high accuracy and were less vulnerable to environmental impact. More accurate cement sheath density values were obtained at greater cement sheath thickness. Inverted values of cement sheath thickness had poor accuracy, being greatly affected by borehole and formation. Accurate formation density values were obtained, though they were influenced by the density and thickness of the cement sheath.