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<p>Gamma-ray (GR) well logs record multiscale lithological variability and provide important constraints on sedimentary heterogeneity. This study investigates the scale-dependent statistical behavior of GR increments from 23 IODP wells using a gradually truncated Lévy framework combined with mean square displacement (MSD), climacogram, and Hurst exponent analyses. A robust parameter-estimation workflow was developed based on core-mass matching, quantile-based scale estimation, CCDF-based cutoff detection, and profile-likelihood optimization to estimate the Lévy parameters across multiple depth lag scales. The results show persistent non-Gaussian behavior across all investigated scales, with Lévy stability indices generally ranging from ~ 0.6 to 1.2. The Lévy parameters, MSD scaling exponent, and Hurst exponent exhibit systematic scale-dependent evolution, indicating that the increment process is not scale invariant. Within the Lévy–Itô decomposition framework, GR increments can be interpreted as the combined effect of bounded small fluctuations within lithological units and intermittent large jumps associated with abrupt facies transitions or lithological interfaces. Consequently, Lévy parameters serve as effective statistical proxies for the intensity and organization of stratigraphic heterogeneity, while the Hurst exponent provides complementary evidence for long-range persistence and multiscale organization. Partial Gaussianization emerges in the central part of the increment distributions at larger scales through aggregation, yet heavy-tailed behavior commonly persists in the tails. These findings demonstrate that sedimentary heterogeneity is intrinsically hierarchical, governed by scale-dependent transitions between distinct geological fluctuation regimes rather than a single stationary scale-invariant process. The integration of truncated Lévy statistics and Hurst-based persistence analysis provides a physically interpretable framework for characterizing multiscale stratigraphic variability and offers a more realistic foundation for stochastic simulation of heterogeneous well-log systems. The Python implementation is open-source to ensure reproducibility.</p>

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Scale-dependent truncated Lévy modeling of Gamma-ray log increments for characterizing stratigraphic heterogeneity in IODP well logs

  • 期刊论文

  • 发表日期：

    2026年6月26日

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  • Zhicheng Lei

摘要

Gamma-ray (GR) well logs record multiscale lithological variability and provide important constraints on sedimentary heterogeneity. This study investigates the scale-dependent statistical behavior of GR increments from 23 IODP wells using a gradually truncated Lévy framework combined with mean square displacement (MSD), climacogram, and Hurst exponent analyses. A robust parameter-estimation workflow was developed based on core-mass matching, quantile-based scale estimation, CCDF-based cutoff detection, and profile-likelihood optimization to estimate the Lévy parameters across multiple depth lag scales. The results show persistent non-Gaussian behavior across all investigated scales, with Lévy stability indices generally ranging from ~ 0.6 to 1.2. The Lévy parameters, MSD scaling exponent, and Hurst exponent exhibit systematic scale-dependent evolution, indicating that the increment process is not scale invariant. Within the Lévy–Itô decomposition framework, GR increments can be interpreted as the combined effect of bounded small fluctuations within lithological units and intermittent large jumps associated with abrupt facies transitions or lithological interfaces. Consequently, Lévy parameters serve as effective statistical proxies for the intensity and organization of stratigraphic heterogeneity, while the Hurst exponent provides complementary evidence for long-range persistence and multiscale organization. Partial Gaussianization emerges in the central part of the increment distributions at larger scales through aggregation, yet heavy-tailed behavior commonly persists in the tails. These findings demonstrate that sedimentary heterogeneity is intrinsically hierarchical, governed by scale-dependent transitions between distinct geological fluctuation regimes rather than a single stationary scale-invariant process. The integration of truncated Lévy statistics and Hurst-based persistence analysis provides a physically interpretable framework for characterizing multiscale stratigraphic variability and offers a more realistic foundation for stochastic simulation of heterogeneous well-log systems. The Python implementation is open-source to ensure reproducibility.