On the Probability Distribution of Primary Reflection Coefficients From Logging Data Recorded by Scientific Ocean Drilling

Studying the statistical characteristics of primary reflection coefficients is crucial for gaining a deeper understanding of the structure of the Earth's rock layers. In this study, we collected 686 logging data from scientific ocean drilling sites worldwide, and after careful data cleaning, 328 logging data remained. Using a data-driven approach, we constructed an overall score index to measure the quality of the fit for various distribution models. This index comprised metrics, including the residual sum of squares (RSSs), Kolmogorov-Smirnov (KS) statistics, Wasserstein distance, and energy distance. From 80 distribution models, top 5 with the best overall fitting performance were the Johnson SU (Johnsonsu), $T$ , Tukey lambda, generalized normal, and double Weibull distributions. Further comparison of goodness-of-fit metrics that revealed the Johnsonsu distribution demonstrated the optimal fit for the primary probability distribution of reflection coefficients. In addition, logging data from three onshore wells in China's Dongying Shengli Oilfield provided validation support for the Johnsonsu distribution. Our results illustrated the advantages of the Johnsonsu distribution for simulating primary reflection coefficients and provided approximate parameter ranges for fitting the distribution.