Fractal characteristics of karst geology in large-scale thrust-nappe tectonic settings
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摘要: 大型逆冲推覆构造对区域地质环境具有显著影响，是控制喀斯特体系发育的重要因素。探究在此背景下的喀斯特地质分形特征，能够为分析复杂喀斯特系统非线性问题提供科学依据。以青峰大断裂喀斯特区为研究对象，采用地质分形理论盒维数法量化区内各典型要素，探讨区域要素及流域单元要素分形特征，确定各典型要素分维值及分形特征。研究结果表明：区域和流域单元地层线均具有明显分形特征，喀斯特化进程对地层线具有明显的增维作用，喀斯特越发育，分维值越大；同时逆冲推覆构造及构造运动对水系分形特征影响较大，会改变地表水系与地下水系的一般映射关系，地表水系分维值与地下喀斯特水系统分维值呈现近似正相关规律。青峰断裂带喀斯特区峰体表现为幼年期峰丛地貌，表明其现处于喀斯特旋回发育的早期。区内喀斯特具有分形特征，峰体演化遵循一般喀斯特区的三段式演化规律，地表水系与地下水系表现出正相关的分形规律，地层线分维值对喀斯特发育程度具有明显的指示意义。明确逆冲推覆构造区的喀斯特自相似性，可为研究断裂构造与喀斯特分布、发育程度及演化规律提供定量化分析的参考和理论依据，也为解决同类地区中喀斯特地质问题提供了新思路。Abstract:
Objective Large-scale thrust-nappe structures have a significant impact on the regional geological environment and are important factors controlling the development of karst systems. Quantitative analysis of karst geological fractal characteristics in such settings provides essential scientific insights into the nonlinear behavior of complex karst systems. Methods Focusing on the karst region along the Qingfeng fault zone, the box-counting dimension method of geological fractal theory was used to quantify key geological elements. We evaluated the fractal characteristics across both regional scales and watershed units to determine their fractal dimensions and scaling properties. Results The stratigraphic boundaries at both regional and watershed scales exhibit pronounced fractal characteristics. Karstification significantly enhances boundary complexity, leading to higher fractal dimensions in areas with more advanced karst development. Furthermore, thrust-nappe structures and tectonic movements strongly influence drainage network fractals, modifying the conventional spatial mapping between surface and groundwater systems. The fractal dimensions of surface drainage systems show a positive correlation with those of subsurface karst drainage systems. Peak landforms in the study area exhibit youth-stage peak-cluster characteristics, indicating an early stage in the regional karst geomorphic cycle. Conclusions Karst in the region exhibits fractal characteristics, and the peak evolution follows the three-stage patterns common in karst areas. Surface and groundwater systems have positively correlated fractal patterns, and stratigraphic boundary dimensions serve as a robust indicator of karst development intensity. Significance Clarifying the self-similarity of karst in thrust-nappe tectonic zones provides a quantitative reference and theoretical basis for assessing the relationships between faulting, karst distribution, and evolutionary dynamics, offering a valuable methodological approach for addressing similar karst geological issues. -
Key words:
- thrust-nappe structures /
- karst /
- fractal dimension /
- dimension enhancement /
- fractal characteristics
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图 3 水系（高祖河）线性回归曲线
r—网格边长；$ N\left(r\right) $—盒子数
Figure 3. Linear regression fit for the Gaozu River drainage system
r—grid size; $ N\left(r\right) $—number of boxes
图 5 峰体演化阶段示意图
a—喀斯特化阶段与峰体形态示意图；b—喀斯特化阶段峰体曲线示意图
Figure 5. Schematic diagram of peak evolution stages
(a) Karstification stages and peak morphology; (b) Peak profile curves across karstification stages
表 1 水系（高祖河）分形网格数
Table 1. Fractal grid counts of the Gaozu River drainage system
方形网边长r 网格数$ N\left(r\right) $ $ \lg r $ $ \lg N\left(r\right) $ 500 m 19 2.6990 1.2788 300 m 34 2.4771 1.5315 200 m 50 2.3010 1.6990 150 m 67 2.1761 1.8261 100 m 103 2.0000 2.0128 80 m 131 1.9031 2.1173 50 m 209 1.6990 2.3201 30 m 350 1.4771 2.5441 
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表 2 区域水系分形特征
Table 2. Fractal characteristics of regional drainage systems
方形网
边长（r）/m500 300 200 150 100 80 50 30 分维值 水系名称 网格数$ N\left(r\right) $ 高祖河 19 34 50 67 103 131 209 350 1.0311 泉河 38 72 106 143 221 287 446 739 1.0473 石甸河 8 14 22 28 42 50 85 134 0.9956 五石道河 3 4 5 6 9 11 19 30 0.8382
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表 3 区域地层线分形特征
Table 3. Fractal characteristics of regional stratigraphic boundaries
地层代号 喀斯特层组 方形网边长（r）/m 500 300 200 150 100 80 50 30 分维值 喀斯特发育程度 岩性 网格数N(r) Є2qn 夹层状碳酸盐岩 泥质白云岩 10 15 22 29 43 52 83 138 0.9399 弱 Є1t 夹层状碳酸盐岩 灰岩 11 15 20 28 43 55 89 149 0.9589 弱 Є1sl 纯层碳酸盐岩 灰岩 119 222 352 472 706 882 1410 2350 1.0475 强 Є1s 间互状碳酸盐岩 灰岩 90 151 231 316 476 597 953 1591 1.0137 中等 Z2dn 纯层碳酸盐岩 白云岩 43 60 93 123 184 231 366 609 1.0242 强
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表 4 流域单元地层线分形特征
Table 4. Fractal characteristics of stratigraphic boundaries in watershed units
单元编号 分维值 单元
编号分维值 单元
编号分维值 单元
编号分维值 单元
编号分维值 单元
编号分维值 单元
编号分维值 1 0.8523 16 / 31 / 46 1.0115 61 0.7553 76 0.8496 91 0.7503 2 0.8814 17 / 32 0.7664 47 0.8873 62 0.8506 77 92 0.7583 3 0.9111 18 0.8437 33 0.9520 48 0.8379 63 / 78 0.9170 93 / 4 / 19 / 34 0.8613 49 / 64 0.8916 79 0.8753 94 0.8836 5 / 20 / 35 0.9220 50 / 65 / 80 0.8889 95 / 6 0.8834 21 / 36 / 51 0.8726 66 0.9040 81 1.0267 96 / 7 / 22 0.9220 37 0.9329 52 0.8814 67 0.8287 82 0.8922 97 0.9018 8 0.9379 23 / 38 / 53 0.7356 68 0.9450 83 0.7805 98 / 9 / 24 / 39 / 54 0.8344 69 / 84 0.9225 99 0.8691 10 0.9144 25 0.9502 40 0.8646 55 0.9127 70 / 85 0.9992 100 / 11 / 26 / 41 0.9161 56 0.9401 71 / 86 / 101 0.8053 12 / 27 0.9174 42 / 57 0.7369 72 0.9085 87 / 102 0.7801 13 / 28 0.8994 43 0.9149 58 0.8287 73 0.9776 88 0.8860 103 / 14 0.9825 29 0.9613 44 0.8414 59 0.7533 74 0.8836 89 / 15 0.7342 30 / 45 / 60 0.7426 75 0.8048 90 1.0814 “/”表示该单元内无地层线
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表 5 区域−流域单元各地层线分形特征
Table 5. Fractal characteristics of stratigraphic boundaries in regional watershed units
级次 分形特征 地层代号 Є2qn Є1t Є1sl Є1s Z2dn 流域单元 分维值 0.8170 0.8589 0.9008 0.8607 0.8954 区域单元 0.9399 0.9589 1.0475 1.0137 1.0242
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