Analysis of Multifractal Characteristics and Detrended Cross-Correlation of Conventional Logging Data Regarding Igneous Rocks

In the current context of the global energy landscape, China is facing a growing challenge in oil and gas exploration and development. It is difficult to evaluate the log data because of the lithological composition of igneous rocks, which displays an unparalleled degree of complexity and unpredictability. Against this backdrop, this study deploys advanced multifractal detrended fluctuation analysis (MF-DFA) to comprehensively analyze key parameters within igneous rock logging data, including natural gamma-ray logging, resistivity logging, compensated neutron logging, and acoustic logging. The results unequivocally demonstrate that these logging data possess distinct multifractal characteristics. This multifractality serves as a powerful tool to elucidate the inherent complexity, heterogeneity, and structural and property variations in igneous rocks caused by diverse geological processes and environmental changes during their formation and evolution, which is crucial for understanding the subsurface reservoir behavior. Subsequently, through a series of rearrangement sequences and the replacement sequence on the original logging data, we identify that the probability density function and long-range correlation are the fundamental sources of the observed multifractality. These findings contribute to a deeper theoretical understanding of the data-generating mechanisms within igneous rock formations. Finally, multifractal detrended cross-correlation analysis (MF-DCCA) is employed to explore the cross-correlations among different types of igneous rock logging data. We uncover correlations among different igneous rocks’ logging data. These parameters exhibit different properties. There are negative long-range correlations between natural gamma-ray logging and resistivity logging, natural gamma-ray logging and compensated neutron logging in basalt, and resistivity logging and compensated neutron logging in diabase. The logging data on other igneous rocks have long-range correlations. These correlation results are of great significance as they provide solid data support for the formulation of oil and gas exploration and development plans.