沉积层序中的时空分形结构及其地质意义

doi:10.13745/j.esf.sf.2025.8.67

摘要/Abstract

摘要：

沉积层序的形成受控于构造活动、海(湖)平面变化及气候演化等多种地质过程,其时空结构复杂且具有多尺度性。传统方法难以揭示其内在规律,而分形理论为研究沉积层序提供了新的视角。本研究基于分形理论,以济阳坳陷沙河街组为例,系统分析了沉积层序的时空分形结构及其地质意义。首先,利用Hurst指数量化沉积层序的时间分形特征,并探讨其在沉积环境演化过程中的应用。其次,通过功率谱分析,揭示储层沉积系统的自组织临界性,并提出基于滤波方法的长程时-空关联结构提取技术。最后,研究了孔隙结构的分形特征,并量化评价其对储层渗透性的影响。研究结果表明,Hurst指数可用于定量刻画沉积环境的长期演化趋势,储层自组织临界性可用于优化储层参数分析,而分形理论在储层孔喉结构评价中具有重要应用价值。本研究不仅深化了对沉积层序复杂性的理解,也为油气资源的勘探和储层评价提供了新的理论支持和方法。

关键词: 分形理论, 时空分形结构, Hurst指数, 功率谱分析, 孔喉结构评价

Abstract:

The formation of sedimentary sequences is controlled by tectonic activity, sea (lake)-level change, and climate evolution, resulting in complex multiscale spatiotemporal structures. While traditional methods struggle to reveal their intrinsic patterns, fractal theory offers a novel approach. Using the Shahejie Formation in the Jiyang Depression as a case study, this research systematically analyzes the spatiotemporal fractal structures of sedimentary sequences and their geological implications. First, the Hurst index quantifies temporal fractal characteristics to interpret sedimentary environment evolution. Second, power spectral density analysis reveals self-organized criticality (SOC) of the sedimentary system, and a filter-based technique for extracting long-range spatiotemporal correlations is proposed. Finally, fractal dimensions of pore structures are characterized to quantitatively evaluate their impact on reservoir permeability. Results demonstrate that: (1) The Hurst index quantifies long-term sedimentary trends; (2) SOC optimizes reservoir parameter analysis; (3) Fractal theory critically supports pore-throat structure evaluation. This study advances understanding of sedimentary complexity and provides new theoretical/methodological foundations for hydrocarbon exploration and reservoir assessment.

Key words: fractal theory, spatio-temporal fractal structure, Hurst index, power spectrum analysis, pore throat structure evaluation

中图分类号:

阮壮, 王玥蕴, 常秋红, 于炳松. 沉积层序中的时空分形结构及其地质意义[J]. 地学前缘, 2025, 32(6): 350-366.

RUAN Zhuang, WANG Yueyun, CHANG Qiuhong, YU Bingsong. Spatio-temporal fractal structures in sedimentary sequences and their geological significance[J]. Earth Science Frontiers, 2025, 32(6): 350-366.

图/表 12

图1 Hurst指数的计算流程(据文献[61]修改)

Fig.1 Calculation process of Hurst index. Modified after [61].

图2 罗69、樊页1和牛页1井四级层序对比(据文献[72-75]修改)

Fig.2 Fourth cycle correlation between well L69, FY1 and NY1. Modified after [72-75].

图3 Hurst指数与随机振荡频率和演化方向性的拟合关系图 a—TOC序列的Hurst指数与随机振荡频率的拟合关系;b—TOC序列的Hurst指数与演化方向性的拟合关系;c—GR测井序列的Hurst指数与随机震荡频率的拟合关系;d—GR测井序列的Hurst指数与演化方向性的拟合关系。

Fig.3 Relationship diagram among Hurst index, FST and D

图4 来自GR测井序列的Hurst指数与沉积学特征的关系汇总图

Fig.4 Summary of HI, D, FST, lithological, and subfacies content for fourth cycles

图5 东营凹陷3口取心井储层参数的功率谱特征 a—FY1井TOC的功率谱;b—FY1井TOC的功率谱双对数图;c—FY1井孔隙度的功率谱;d—FY1井孔隙度的功率谱双对数图;e—NY1井TOC的功率谱;f—NY1井TOC的功率谱双对数图;g—NY1井孔隙度的功率谱;h—NY1井孔隙度的功率谱双对数图;i—LY1井TOC的功率谱;j—LY1井TOC的功率谱双对数图;k—LY1井孔隙度的功率谱;l—LY1井孔隙度的功率谱双对数图。

Fig.5 Power spectrum characteristics of reservoir parameters of 3 core wells in Dongying Depression

图6 曲率的定义

Fig.6 Definition of curvature

图7 东营凹陷3口取心井储层参数功率谱曲线函数拟合与曲率 a—FY1井TOC的功率谱;b—FY1井TOC拟合曲线曲率;c—FY1井孔隙度的功率谱;d—FY1井孔隙度拟合曲线曲率;e—NY1井TOC的功率谱;f—NY1井TOC的拟合曲线曲率;g—NY1井孔隙度的功率谱;h—NY1井孔隙度拟合曲线曲率;i—LY1井TOC的功率谱;j—LY1井TOC拟合曲线曲率;k—LY1井孔隙度的功率谱;l—LY1井孔隙度拟合曲线曲率。

Fig.7 Function fitting and curvature of reservoir parameter power spectrum curve of 3 core wells in Dongying Depression

图8 东营凹陷3口取心井储层参数滤波图 a—FY1井TOC滤波图;b—NY1井TOC滤波图;c—LY1井TOC滤波图;d—FY1井孔隙度滤波图;e—NY1井孔隙度滤波图;f—LY1井孔隙度滤波图。

Fig.8 Filter map of reservoir parameters of 3 core wells in Dongying Depression

图9 东营凹陷3口取心井储层参数与S1相关关系图 a—滤波前TOC vs S1;b—滤波前孔隙度 vs S1;c—滤波后TOC vs S1;d—滤波后孔隙度 vs S1。

Fig.9 Correlation diagram between reservoir parameters and S1 of 3 core wells in Dongying Depression

图10 东营凹陷基于高压压汞分类计算的孔喉大小及分布规律

Fig.10 The pore throat sizes and their distribution of sandstone samples in Dongying Sag

图11 东营凹陷样品E(x)与Df,τ和DT关系图 a—E (x)与Df关系; b—E(x)与τ关系; c—E(x)与DT关系。

Fig.11 Relationship between E(x) and Df, τ and DT in Dongying sag

图12 东营凹陷样品Df,τ和DT与logK关系图 a—K与Df对数关系; b—K与τ对数关系; c—K与DT对数关系。

Fig.12 Relationship between logK and Df, τ and DT in Dongying sag

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