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Characteristics of geological evolution based on the multifractal singularity theory: A case study of Heyu granite and Mesozoic tectonics

  • Wenchao Dong EMAIL logo , Zhongfeng Jiang , Peixin Zhang , Yuchan Zhang and Leyi Liu
Published/Copyright: August 7, 2025
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Open Geosciences
From the journal Open Geosciences Volume 17 Issue 1

Abstract

Tectonic movement and magmatic activity are complex geological processes resulting from the interaction of multiple factors. These processes are often characterized by local singularities with nonlinear characteristics. This study drew on the Multifractal Local Singularity theory and took the Heyu granite magmatism and the Mesozoic tectonic evolution of the Xiong’er Mountain as examples to explore singularity characteristics in the process of tectonic evolution and magmatism. The aim was to enhance the understanding of geological evolution and offer new perspectives for studying geological evolution processes. The research showed that during the four stages of the Heyu granite magmatism, the early phase exhibited a low singularity index, weak magmatic activity, and relatively rapid crystallization. In the middle phase, the singularity index and eruption intensity gradually increased, whereas the crystallization rate decreased. The third stage had the highest singularity index and peak eruption intensity, with the lowest crystallization rate. In the final stage, the singularity index decreased, eruption intensity weakened, and crystallization rate increased. In the case of the Mesozoic tectonic evolution of the Xiong’er Mountain, three distinct stages were identified: early-stage compression and warming, mid-stage structural transformation, and late-stage decompression and extension. The singularity characteristics show a progressive increase from the early to the late stages, indicating a gradual intensification of tectonic activity.

Keywords: tectonic movement; magmatic activity; singularity characteristic; Heyu granite; Xiong’er Mountain

1 Introduction

The North China Craton is the largest and oldest craton in China, undergoing a complete tectonic transition during the Mesozoic from an early compressional to a late extensional environment. This period was marked by large-scale tectonic movements, magmatic activity, and mineralization [1,2]. The tectonic movement and magmatic activities in this area have effectively recorded the evolutionary process of the destruction of the North China Craton, making them a focus area for research on tectonic movement and magmatism related to the failure of the North China Craton. Additionally, large-scale mineralization in the North China Craton led to the formation of significant gold-polymetallic metallogenic belts, such as the Xiaoqinling and Xiong’er-Wafang Mountain belts. These extensive metallogenic events have drawn considerable attention from both domestic and international researchers [3–5]. With the accumulation of extensive research data from regional studies, integrating, analyzing, and reusing these data to interpret macro-geological information and uncover internal relationships and patterns can become a key focus of future regional geological research.

Mathematical geology provides tools to enhance the quantification and precision of geochemical research [6]. Common methods include fuzzy mathematical, neural network, multifactor, and factor analyses, all of which are significantly advanced geochemical studies. These methods typically rely on specific mathematical distributions derived from geochemical data such as linear or normal distributions [7–10]. However, numerous studies have indicated that tectonic movement and magmatic activity often exhibit heterogeneous and nonlinear characteristics, which limit the applicability of traditional mathematical approaches. Singularity theory is a key component of fractal and multifractal modeling in geochemistry and can address these limitations by analyzing phenomena involving intense energy release or high material enrichment within small spatial or temporal domains [11]. The processes of geological tectonic evolution, magmatic activity, and metallogenic events involve significant energy release and material enrichment over short timescales and within limited spatial ranges, characterized as local singularity features [12]. According to Gao [13], these processes are complex, resulting from the interaction of multiple factors, and typically exhibit nonlinear local singularities. Analyzing the nonlinear and singular characteristics of tectonic movement, such as that in the central orogenic belt, enables an effective quantitative analysis of geological evolution, offering new insights into local singularity patterns. This study focused on the formation of the Heyu granite on the southern margin of the North China Craton and the tectonic evolution of the Xiong’er Mountain area. By employing nonlinear and local singularity analyses, we calculated the singularity characteristics at various stages of regional magmatic and tectonic evolution, providing a quantitative evaluation of tectonic movements and magmatic activities across different stages. The findings offer new methodologies and perspectives for studying regional tectonic and magmatic evolutions.

2 Geological profile of research area

The North China Craton, the largest and oldest craton in China, consists of the Eastern Block (EB), the Central Orogenic Belt (TNCO), and the Western Block (WB). Following a series of tectonic, magmatic, and metamorphic processes, the craton was fully formed by 1.85 Ga [14]. Xiong’er Mountain is situated on the southern margin of the North China Craton and north of the Qinling Orogenic Belt, extending from Waifang Mountain in the east to Xiaoshan Mountain in the west, embodying the typical characteristics of a craton margin (Figure 1).

Figure 1 Geological map of the Xiong’er Mountain region. EB – Eastern plate; TNCO – The central orogenic belt; WB – Western plate; K-Belt – Khondalite belt; JL – Belt -Jiaoliao Belt (modified after He et al. [15]).
Figure 1

Geological map of the Xiong’er Mountain region. EB – Eastern plate; TNCO – The central orogenic belt; WB – Western plate; K-Belt – Khondalite belt; JL – Belt -Jiaoliao Belt (modified after He et al. [15]).

The outcrops of strata observable in the field are comparatively few in the studied area, the regional crystalline basement is composed of gneiss from the Taihua Group, while the main overlying strata include the Xiong’er Group, the Guandaokou Group, and Quaternary deposits. The region has undergone a long-term, complex tectonic-magmatic evolution, characterized by well-developed fault structures, primarily the nearly EW-trending Machaoying Fault, detachment faults, and numerous NE-trending faults. NE-trending faults significantly influence the spatial distribution of strata, magmatic rocks, and ore deposits. Frequent magmatic activity has played a central role throughout the geological history of the region [16], including the formation of the Precambrian crystalline basement, Mesoproterozoic plate spreading and rifting, Paleozoic plate tectonic evolution, and Mesozoic intracontinental development [17,18]. During the Paleozoic, the tectonic regime transitioned from early plate compression to extension, accompanied by extensive magmatism, leading to the formation of granitic rock masses such as the Wuzhangshan, Huashan, and Heyu granite (Figure 2).

Figure 2 Distribution map of granite in the Xiong’er Mountain region. 1 – Quaternary sediments; 2 – Taihua Group; 3 – Guandaokou Group; 4 – Xiong’er Group; 5 – Magmatic of Yanshanian; 6 – Fault; 7 – Detachment faults; 8 – Unconformity geological boundary; 9 – Gold deposit; 10 – Mo deposit; 11 – Ag–Pb–Zn deposit.
Figure 2

Distribution map of granite in the Xiong’er Mountain region. 1 – Quaternary sediments; 2 – Taihua Group; 3 – Guandaokou Group; 4 – Xiong’er Group; 5 – Magmatic of Yanshanian; 6 – Fault; 7 – Detachment faults; 8 – Unconformity geological boundary; 9 – Gold deposit; 10 – Mo deposit; 11 – Ag–Pb–Zn deposit.

The Heyu granite body, located in the southern part of the study area, is dumbbell-shaped and annular, covering an area of 784 km2. It is the largest Yanshanian granite in the Xiong’er Mountain region [19]. According to Li et al. [20], the Heyu granite is a complex formed through four magmatic intrusions with distinct contact relationships between the stages. Despite similar mineral compositions across the intrusions, differences were observed in phenocryst size, mineral composition ratios, and grain size. The first intrusion, located at the center, consists primarily of porphyraceous biotite monzogranite with potassium feldspar phenocrysts comprising 1–5% and measuring between 6 mm × 12 mm and 10 mm × 15 mm. The second intrusion forms a ring around the first, featuring porphyritic biotite monzogranite with potassium feldspar phenocrysts of 6–18% and size 14 mm × 26 mm. The third intrusion is situated at the outermost part and is composed of macroporphyritic biotite monzogranite, with potassium feldspar phenocrysts constituting 23–45% and locally reaching 65%, along with the highest biotite content. The fourth and final magmatic intrusions form various granitic veins, primarily syenite and fine-grained rocks, that intruded into the early granite (Figure 3).

Figure 3 Distribution map of Heyu granite. 1 – Porphyraceous fine-grained biotite monzonitic granite; 2 – Porphyraceous medium grain porphyritic biotite monzogranite; 3 – Porphyritic medium grain porphyritic biotite monzogranite; 4 – Macroporphyritic biotite monzogranite; 5 – Gneissic granite; 6 – Fine-grained quartz diorite; 7 – Syenite granite; 8 – Proterozpic strate; 9 – Taihua Group; 10 – Fault (modified after Li et al. [20]).
Figure 3

Distribution map of Heyu granite. 1 – Porphyraceous fine-grained biotite monzonitic granite; 2 – Porphyraceous medium grain porphyritic biotite monzogranite; 3 – Porphyritic medium grain porphyritic biotite monzogranite; 4 – Macroporphyritic biotite monzogranite; 5 – Gneissic granite; 6 – Fine-grained quartz diorite; 7 – Syenite granite; 8 – Proterozpic strate; 9 – Taihua Group; 10 – Fault (modified after Li et al. [20]).

The structural evolution of the Xiong’er Mountain area was selected as the research focus for several reasons: (1) located on the southern margin of the North China Craton, it exhibited typical craton margin characteristics, providing a detailed record of regional geological evolution, particularly the transition from an early compressive to a late extensional tectonic environment during the Mesozoic, and (2) the area contained extensive magmatic rocks with abundant isotopic age data, offering a robust dataset for analysis. The Heyu granite was used as the primary study object. As the largest Mesozoic granite mass in the region, it was formed within the context of tectonic-magmatic evolution, featuring multiple stages of intrusion. Each stage produced distinct magmatic rocks that captured complete Mesozoic magmatic evolution. Additionally, lithological variations and abundant isotopic age data across different intrusion stages provided a strong foundation for this study.

3 Theory and methods

Since Mandelbrot introduced the concept of fractals in 1967, fractal features based on self-similarity have been employed to describe nonlinear distributions of geological processes. Robb [21] suggested that geological evolution could be a complex physical and chemical process, characterized by generalized self-similarity and multifractal properties. These fractal and multifractal characteristics, along with the concept of self-similarity, have significantly influenced natural sciences, with widespread applications in geochemistry, mineral exploration, and coal gas prediction [22,23]. However, the effectiveness of these applications is often limited by the locality, randomness, and incompleteness of geochemical data. To address these challenges, Cheng et al. [22] proposed a theory of local singularity based on nonlinear and complex theories. This approach integrated the scale-invariant or generalized self-similarity inherent in geological evolution, suggesting that the resulting distribution laws exhibit fractal or multifractal characteristics. These features enhanced the extraction of target anomalies by mitigating the effects of abnormal data changes. The multifractal-based local singularity concept provides a more precise analysis of singularities in the local geological evolution, offering valuable insights into geological processes [24]. The principle is outlined as follows.

Suppose that B x (ε) represents any space position x in the range, ε represents the size of the box, and N(B x (ε)) represents the content (quantity) of the target value in the range of B x (ε). If the target eigenvalue exhibits multifractal local singularity characteristics, it adheres to the distribution of the power rate function (power law) expressed by the following equation:

(1) N ( B x ( ε ) ) = c ( x ) ε a ( x ) ,

where a(x) represents the local singularity index at the spatial position x, which is a scale-independent quantity and dimensionless, and its magnitude indicates the strength of the singularity of the target eigenvalue. c(x) represents the fractal density of dimension a(x) at space x, and its magnitude indicates the amplitude of variation in the degree of singularity.

If the density of the target eigenvalue in the box range is ρ(B x (ε)), then:

(2) ρ ( B x ( ε ) ) = N ( B x ( ε ) ) / ε E ,

where E represents the dimensions of European space, including 1, 2, and 3. By substituting equation (2) into equation (1), the following equation can be obtained:

(3) ρ ( B x ( ε ) ) = c ( x ) ε a ( x ) − E = c ( x ) ε − Δ a ( x ) .

In this study, the time parameter was applied as the target parameter, and the time parameter was substituted into equations (2) and (3) to obtain:

(4) ρ ( Δ t ) = N ( Δ t ) / Δ t = c ( x ) Δ t − Δ a ( x ) .

It was simplified as

(5) ρ ( Δ t ) = N ( Δ t ) / Δ t = c Δ t − k ,

where Δt represents the time interval of the testing age; k is the singularity index; c is the eigenvalue of the singularity, representing the variation range of the degree of singularity; N(Δt) represents the age of magmatic zircons in the t ± Δt age range, and ρ(Δt) represents the mean age density.

The results indicated that the core of the multifractal local singularity method was to determine the fractal density, singularity index, and variation degree at each stage by analyzing the number and density of the objective function over a specific time period. This method enabled a comparative analysis of variation characteristics across stages. Compared with traditional statistical methods, the multifractal local singularity approach emphasized data trends and significantly reduced the impact of outliers on the overall trend, thereby offering a novel perspective for applying mathematical methods to describe geological evolution processes.

4 Results of multifractal local singularity analysis

4.1 Multifractal local singularity analysis of Heyu Granite

The multifractal local singularity analysis of the Heyu granite was primarily based on age data of magmatic zircons. This study compiled extensive test data from previous research, considering the magmatic age of the Heyu granite as the weighted average age of its magmatic zircons. To investigate the multi-stage magmatic activity of the Heyu granite, the collected age data corresponded to the test points of the magmatic zircons. By summarizing prior research on the isotopic chronology of the Heyu granite, direct zircon ages were plotted (Figure 4; Table S1).

Figure 4 The Heyu granite magmatic zircon age distribution histogram.
Figure 4

The Heyu granite magmatic zircon age distribution histogram.

Based on a summary of previous research and analysis of the magmatic zircon age histogram, the following conclusions were drawn: the first magmatic hydrothermal intrusion occurred before 144 Ma, the second between 144 and 134 Ma, the third between 134 and 127 Ma, and the fourth after 127 Ma.

A multifractal local singularity analysis was performed on the age data for each stage to investigate the variation and singularity characteristics of the four stages of Heyu granite. The average age density of each stage was calculated to facilitate power-law equation fitting and singularity index determination, followed by log–log fitting of the age density. The results are shown in Figure 5. In the Power-law model, the function was defined by the singularity index k and the correlation coefficient R 2. Notably, the Power-law fitting results for the second and fourth stages of the Heyu granite were relatively poor, likely because of the occurrence of several small-scale magmatic events during these stages, resulting in multiple episodes of magma upwelling.

Figure 5 Singularity analysis results of magmatic zircon ages from the Heyu granite. (a), (c), (e), and (g) represent Power-law equation fitting graphs of average age densities of the first, second, third, and fourth magma intrusions of Heyu Granite. (b), (d), (f), and (h) represent log–log graphs of average age densities of the first, second, third, and fourth intrusions of the Heyu granite.
Figure 5

Singularity analysis results of magmatic zircon ages from the Heyu granite. (a), (c), (e), and (g) represent Power-law equation fitting graphs of average age densities of the first, second, third, and fourth magma intrusions of Heyu Granite. (b), (d), (f), and (h) represent log–log graphs of average age densities of the first, second, third, and fourth intrusions of the Heyu granite.

4.2 Results of multifractal local singularity analysis of Mesozoic tectonic evolution in Xiong’er Mountain

Xiao et al. [25] suggested that the study of plate or crust formation and subsequent tectonic evolution was primarily achieved through analysis of granitic rocks formed by magmatism. Granitoids serve as key components of the continental crust and are closely linked to crust-mantle interactions and magmatic activity, serving as crucial windows for plate movement, accretion, and later transformation processes [26]. The multifractal local singularity analysis of the Mesozoic tectonic evolution in the Xiong’er Mountain region focuses on age data from magmatic zircons of granites, such as Huashan, Wuzhangshan, and Heyu. According to Guo [17], these granites formed during the transition of the plate tectonic system when the accreted lower crust extended, and acidic magma derived from the partial melting of the lower crust intruded due to significant depressurization and heating. These granites effectively recorded the Mesozoic tectonic evolution of the region. A magmatic zircon age histogram (Figure 6; Table S1) was developed based on previous isotopic studies. Chen et al. [3] concluded that the plate extrusion was observed in the Middle Jurassic with a tectonic system transition during the Jurassic-Cretaceous period, followed by lithospheric thinning at the end of the Cretaceous. Specifically, the tectonic regime shifted between 144 and 130 Ma, with late lithospheric extension and subsidence occurring between 130 and 120 Ma.

Figure 6 Age distribution histogram of Mesozoic magmatic zircon from the Xiong’er Mountain area.
Figure 6

Age distribution histogram of Mesozoic magmatic zircon from the Xiong’er Mountain area.

To analyze the Mesozoic tectonic evolution and singularity characteristics of the Xiong’er Mountain area, the multifractal local singularity of granite age data was calculated for three distinct stages: plate compression, tectonic regime transformation, and late plate extension. The average age density for each stage was determined, facilitating power-law equation fitting using the least squares method. The singularity index was then calculated, and log–log fitting of age density was performed. The results are shown in Figure 7.

Figure 7 Singularity analysis results of Mesozoic magmatic zircon ages from the Xiong’er Mountain area. (a), (c), and (e) represent the Power-law equation fitting maps of average age density of zircons from compressive/transformation and extension of Xiong’er Mountain area. (b), (d), and (f) represent the log–log graphs of average age densities of zircons from compressive, transformational, and extensional processes of the Xiong’er Mountain area.
Figure 7

Singularity analysis results of Mesozoic magmatic zircon ages from the Xiong’er Mountain area. (a), (c), and (e) represent the Power-law equation fitting maps of average age density of zircons from compressive/transformation and extension of Xiong’er Mountain area. (b), (d), and (f) represent the log–log graphs of average age densities of zircons from compressive, transformational, and extensional processes of the Xiong’er Mountain area.

5 Discussion

5.1 Magma evolution of the Heyu granite and rock crystallization

Since the Mesozoic, the formation of the Heyu granite has undergone multiple stages of magmatic intrusion, effectively recording the magmatic evolution process. According to Gao [13], local singularity characteristics provide valuable insights into the magmatic hydrothermal evolution. A larger singularity index indicates stronger magmatic activity and faster magma eruption, whereas a smaller singularity index indicates weaker activity and slower eruption. Multifractal singularity analysis of the Heyu granite revealed that the singularity index for its first magmatic intrusion was 0.829, with a singularity characteristic value of 10.542. The singularity index for the second magma intrusion of the Heyu granite was 0.839, with a singularity characteristic value of 14.655. For the third intrusion, the singularity index was 0.967 with a characteristic value of 17.133, whereas the fourth intrusion had a singularity index of 0.951 and a characteristic value of 13.480. The singularity index initially increased, peaking during the third intrusion, and then declining. This trend indicated that the early magmatic intrusions were relatively weak, with slower magma eruption speeds. Magma activity and eruption intensity peaked in the third stage, followed by a gradual decline in the fourth stage. These findings align with those of Li et al. [20], who identified a third magmatic event as the most intense and extensive. Tang [4] suggested that during the late Cretaceous, the North China Plate underwent a tectonic system transformation influenced by the Paleo-Tethyan and Pacific tectonic domains, shifting from a compressive to a strike-slip and extensional regime. This tectonic shift led to crustal thinning and lithospheric dissolution, accompanied by upwelling of asthenospheric and lower crustal materials, contributing to the peak scale and intensity of the Heyu granite formation during the third stage.

The various stages of the Heyu granite differ not only in the intensity of magmatic activity but also in the gradual changes in the degree of rock crystallization. Swanson [27] proposed that granite phenocrysts typically crystallize under supercooled conditions, with phenocryst size proportional to the crystallization rate of the rock. Faster crystallization resulted in smaller phenocrysts, forming fine-grained or fine-spotted structures, whereas slower crystallization produced larger phenocrysts, often appearing as porphyritic or macroporphyritic structures. The lithologic characteristics of the Heyu granite revealed that from the first to the fourth stage (Table 1), the phenocryst grain size transitioned from small → large → small, corresponding to cooling rates of fast → slow → fast. Similarly, the singularity index followed the pattern of small → large → small. Overall, the variation in the phenocryst grain size and crystallization rate aligned with the trend of the singularity index, indicating that the singularity index effectively reflected the evolution of rock cooling and crystallization rates.

Table 1

The Heyu granite magmatic activity singularity analysis table

Magmatic epoch Age range (Ma) Lithology k c R 2
1 >144 Porphyraceous biotite monzogranite 0.829 10.542 0.812
2 144–134 Porphyritic biotite monzogranite 0.839 14.655 0.678
3 134–127 Macroporphyritic biotite monzogranite 0.967 17.133 0.895
4 <127 Fine crystalline dikes, rock strains 0.951 13.480 0.589

The intensity of magma eruption and the rate of magma crystallization are critical factors in studying magma evolution. This study analyzed the multifractal singularity characteristics of Heyu granite and discovered that the singularity index effectively reflected the trends in magma eruption intensity and crystallization rate (Figure 8). A low singularity index corresponded to a weak magma eruption intensity and fast crystallization, whereas a high singularity index demonstrated a strong eruption intensity and slower crystallization. The four magmatic intrusion events of the Heyu granite can be summarized as follows. In the early stage, the singularity index was low, with a weak eruption intensity and rapid crystallization. In the middle stage, the singularity index increased, accompanied by a rising eruption intensity and slow crystallization. In the third stage, the singularity index peaked, indicating the highest eruption intensity and the slowest crystallization rate. In the late stage, the singularity index declined, with gradually weakening eruption intensity and accelerated crystallization.

Figure 8 Schematic diagram of the relationship between singularity index, magma strength, and crystallization rate.
Figure 8

Schematic diagram of the relationship between singularity index, magma strength, and crystallization rate.

5.2 Singularity feature of the Mesozoic tectonic evolution of Xiong’er Mountain

Located on the southern margin of the North China Craton and northern margin of the Qinling orogenic belt, the Xiong’er Mountain region exhibits typical craton margin characteristics and is influenced by Qinling orogenic processes. Since the Mesozoic, the area has experienced complex tectonic movements and magmatic activities, which can be represented by the formation of multiple granites and large-scale mineralization. They are closely linked to Mesozoic plate movements [4]. Jamieson [28] categorized the orogenic belts into three stages: early extrusion and warming, mid-stage tectonic transformation, and late decompression and extension. Chen et al. [29] explored the collision orogenic belts in China, concluding that the late-stage decompression and warming were the key drivers of large-scale rock mass melting and mineralization, with granites from this period recording significant geological information. This study applied multifractal singularity analysis to granites in the Xiong’er Mountain area to examine the variation in singularity indices across different stages of tectonic evolution.

Pressure (P), temperature (T), and time (t) are crucial parameters for studying tectonic evolution. Chen et al. [30] proposed that these parameters followed a P-T-t trajectory during the tectonic evolution of orogenic belts. The Xiong’er Mountain region is located on the edge of the Qinling orogenic belt and exhibits orogenic evolutionary characteristics consistent with the P-T-t trajectory. The local singularity analysis effectively captured the tectonic evolution information, with a higher singularity index indicating stronger tectonic activity and vice versa. The magnitude of the pressure and temperature reflected the intensity of tectonic activity, establishing an internal correlation. Analysis of the P-T-t trajectory and singularity index for the tectonic evolution of Xiong’er Mountain (Figure 9) exhibited a gradual increase in the singularity index from the first to the third stage, aligned with the temperature curve in the P-T-t trajectory, indicating a positive correlation. Although the singularity index did not present a clear linear relationship with the pressure curve, the intensity of tectonic activity correlated with the amplitude of the pressure variation [31], suggesting a positive relationship between the singularity index and the curvature of the pressure curve.

Figure 9 Schematic diagram of relationship between P-T-t trajectory and singularity index during the tectonic evolution of the Xiong’er Mountain region (P-T-t trajectory adapted from Chen et al. [30]).
Figure 9

Schematic diagram of relationship between P-T-t trajectory and singularity index during the tectonic evolution of the Xiong’er Mountain region (P-T-t trajectory adapted from Chen et al. [30]).

Then, there are:

(6) lim Δ t → ∞ Δ p Δ t = c 1 k ( t ) ,

(7) c 2 Δ T ( t ) = k ( t ) ,

where Δt represents the time interval; Δp represents the amplitude of the pressure change; c 1 and c 2 are constants; ΔT(t) represents the temperature at a certain time interval; and k(t) represents the singularity index over a certain time interval.

In the early stages of plate compression and warming in the Xiong’er Mountain region, the singularity index was 0.759 with a characteristic value of 28.780. During the middle stage of the tectonic transition, the singularity index increased to 0.839, with a characteristic value of 14.655. In the late stage of decompression and extension, the singularity index reached 0.872 with a characteristic value of 32.427. This increasing trend in the singularity index indicated that the tectonic activity was more intense during the later decompression and extension stages compared to the earlier compression and warming and middle tectonic transition stages. The lithosphere in the region, initially thickened to 200 km owing to Mesozoic plate compression, underwent significant thinning as the compressive forces weakened, leading to enhanced decompression and extension. By the late Cretaceous, rapid lithospheric thinning occurred [32]. In summary, the multifractal singularity analysis effectively captured the key aspects of tectonic evolution and aligned well with the region’s tectonic history, offering a novel approach for studying the tectonic evolution of the Xiong’er Mountain region, the Xiaoqinling area, and the North China Craton.

6 Conclusion

  1. The magmatic activity of the Heyu granite and tectonic evolution of the Xiong’er Mountain region were the result of multistage, multifactor processes characterized by nonlinear local singularity. Analyzing multifractal singularity characteristics enhanced the understanding of the patterns and mechanisms of tectonic evolution and magmatic activity, offering a novel approach for studying geological evolutionary processes.

  2. The study of four magmatic intrusion events in the Heyu granite revealed singular distribution characteristics of magmatic evolution. In the early stage, the singularity index was low, indicating a weak magma eruption intensity and rapid crystallization. During the middle stage, the singularity index increased, reflecting a gradual increase in eruption intensity and a slow crystallization rate. During the third stage, the singularity index peaked, corresponding to the highest magmatic activity intensity and the slowest magmatic crystallization rate. In the late stage, the singularity index declined with the weakening magma eruption intensity and accelerating crystallization speed.

  3. Investigation of the Mesozoic tectonic evolution of Xiong’er Mountain revealed singularity characteristics across three stages: early compression and warming, middle tectonic transformation, and late decompression and extension. The singularity index presented an increasing trend from the early to late stages, indicating a gradual intensification of tectonic evolution.

  1. Funding information: This work was funded by the doctoral research project of the Henan University of Urban Construction, China (No. KQ2024009) and the Research on Key Technologies of Crop Identification and Yield Monitoring Based on Remote Sensing Data (242102320345).

  2. Author contributions: Wenchao Dong contributed significantly to the analysis, review, and editing of this manuscript. Zhongfeng Jiang, Peixin Zhang, Yuchan Zhang and Leyi Liu helped perform data curation. Each author has thoroughly reviewed and concurred with the finalized version of the manuscript prior to publication.

  3. Conflict of interest: The authors assert the absence of any conflicts of interest.

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Received: 2024-12-11
Revised: 2025-06-13
Accepted: 2025-06-29
Published Online: 2025-08-07

© 2025 the author(s), published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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https://doi.org/10.1515/geo-2025-0849
Keywords for this article
tectonic movement; magmatic activity; singularity characteristic; Heyu granite; Xiong’er Mountain
Creative Commons
BY 4.0

Articles in the same Issue

  1. Research Articles
  2. Seismic response and damage model analysis of rocky slopes with weak interlayers
  3. Multi-scenario simulation and eco-environmental effect analysis of “Production–Living–Ecological space” based on PLUS model: A case study of Anyang City
  4. Remote sensing estimation of chlorophyll content in rape leaves in Weibei dryland region of China
  5. GIS-based frequency ratio and Shannon entropy modeling for landslide susceptibility mapping: A case study in Kundah Taluk, Nilgiris District, India
  6. Natural gas origin and accumulation of the Changxing–Feixianguan Formation in the Puguang area, China
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  43. Debris flow hazard characteristic and mitigation in Yusitong Gully, Hengduan Mountainous Region
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  84. Sedimentology of the Phra That and Pha Daeng Formations: A preliminary evaluation of geological CO2 storage potential in the Lampang Basin, Thailand
  85. Improved classification algorithm for hyperspectral remote sensing images based on the hybrid spectral network model
  86. Map analysis of soil erodibility rates and gully erosion sites in Anambra State, South Eastern Nigeria
  87. Identification and driving mechanism of land use conflict in China’s South-North transition zone: A case study of Huaihe River Basin
  88. Evaluation of the impact of land-use change on earthquake risk distribution in different periods: An empirical analysis from Sichuan Province
  89. A test site case study on the long-term behavior of geotextile tubes
  90. An experimental investigation into carbon dioxide flooding and rock dissolution in low-permeability reservoirs of the South China Sea
  91. Detection and semi-quantitative analysis of naphthenic acids in coal and gangue from mining areas in China
  92. Comparative effects of olivine and sand on KOH-treated clayey soil
  93. YOLO-MC: An algorithm for early forest fire recognition based on drone image
  94. Earthquake building damage classification based on full suite of Sentinel-1 features
  95. Potential landslide detection and influencing factors analysis in the upper Yellow River based on SBAS-InSAR technology
  96. Assessing green area changes in Najran City, Saudi Arabia (2013–2022) using hybrid deep learning techniques
  97. An advanced approach integrating methods to estimate hydraulic conductivity of different soil types supported by a machine learning model
  98. Hybrid methods for land use and land cover classification using remote sensing and combined spectral feature extraction: A case study of Najran City, KSA
  99. Streamlining digital elevation model construction from historical aerial photographs: The impact of reference elevation data on spatial accuracy
  100. Analysis of urban expansion patterns in the Yangtze River Delta based on the fusion impervious surfaces dataset
  101. A metaverse-based visual analysis approach for 3D reservoir models
  102. Late Quaternary record of 100 ka depositional cycles on the Larache shelf (NW Morocco)
  103. Integrated well-seismic analysis of sedimentary facies distribution: A case study from the Mesoproterozoic, Ordos Basin, China
  104. Study on the spatial equilibrium of cultural and tourism resources in Macao, China
  105. Urban road surface condition detecting and integrating based on the mobile sensing framework with multi-modal sensors
  106. Application of improved sine cosine algorithm with chaotic mapping and novel updating methods for joint inversion of resistivity and surface wave data
  107. The synergistic use of AHP and GIS to assess factors driving forest fire potential in a peat swamp forest in Thailand
  108. Dynamic response analysis and comprehensive evaluation of cement-improved aeolian sand roadbed
  109. Rock control on evolution of Khorat Cuesta, Khorat UNESCO Geopark, Northeastern Thailand
  110. Gradient response mechanism of carbon storage: Spatiotemporal analysis of economic-ecological dimensions based on hybrid machine learning
  111. Comparison of several seismic active earth pressure calculation methods for retaining structures
  112. Mantle dynamics and petrogenesis of Gomer basalts in the Northwestern Ethiopia: A geochemical perspective
  113. Study on ground deformation monitoring in Xiong’an New Area from 2021 to 2023 based on DS-InSAR
  114. Paleoenvironmental characteristics of continental shale and its significance to organic matter enrichment: Taking the fifth member of Xujiahe Formation in Tianfu area of Sichuan Basin as an example
  115. Equipping the integral approach with generalized least squares to reconstruct relict channel profile and its usage in the Shanxi Rift, northern China
  116. InSAR-driven landslide hazard assessment along highways in hilly regions: A case-based validation approach
  117. Attribution analysis of multi-temporal scale surface streamflow changes in the Ganjiang River based on a multi-temporal Budyko framework
  118. Maps analysis of Najran City, Saudi Arabia to enhance agricultural development using hybrid system of ANN and multi-CNN models
  119. Hybrid deep learning with a random forest system for sustainable agricultural land cover classification using DEM in Najran, Saudi Arabia
  120. Long-term evolution patterns of groundwater depth and lagged response to precipitation in a complex aquifer system: Insights from Huaibei Region, China
  121. Remote sensing and machine learning for lithology and mineral detection in NW, Pakistan
  122. Spatial–temporal variations of NO2 pollution in Shandong Province based on Sentinel-5P satellite data and influencing factors
  123. Numerical modeling of geothermal energy piles with sensitivity and parameter variation analysis of a case study
  124. Stability analysis of valley-type upstream tailings dams using a 3D model
  125. Variation characteristics and attribution analysis of actual evaporation at monthly time scale from 1982 to 2019 in Jialing River Basin, China
  126. Investigating machine learning and statistical approaches for landslide susceptibility mapping in Minfeng County, Xinjiang
  127. Investigating spatiotemporal patterns for comprehensive accessibility of service facilities by location-based service data in Nanjing (2016–2022)
  128. A pre-treatment method for particle size analysis of fine-grained sedimentary rocks, Bohai Bay Basin, China
  129. Study on the formation mechanism of the hard-shell layer of liquefied silty soil
  130. Comprehensive analysis of agricultural CEE: Efficiency assessment, mechanism identification, and policy response – A case study of Anhui Province
  131. Simulation study on the damage and failure mechanism of the surrounding rock in sanded dolomite tunnels
  132. Towards carbon neutrality: Spatiotemporal evolution and key influences on agricultural ecological efficiency in Northwest China
  133. Review Articles
  134. Humic substances influence on the distribution of dissolved iron in seawater: A review of electrochemical methods and other techniques
  135. Applications of physics-informed neural networks in geosciences: From basic seismology to comprehensive environmental studies
  136. Ore-controlling structures of granite-related uranium deposits in South China: A review
  137. Shallow geological structure features in Balikpapan Bay East Kalimantan Province – Indonesia
  138. A review on the tectonic affinity of microcontinents and evolution of the Proto-Tethys Ocean in Northeastern Tibet
  139. Advancements in machine learning applications for mineral prospecting and geophysical inversion: A review
  140. Special Issue: Natural Resources and Environmental Risks: Towards a Sustainable Future - Part II
  141. Depopulation in the Visok micro-region: Toward demographic and economic revitalization
  142. Special Issue: Geospatial and Environmental Dynamics - Part II
  143. Advancing urban sustainability: Applying GIS technologies to assess SDG indicators – a case study of Podgorica (Montenegro)
  144. Spatiotemporal and trend analysis of common cancers in men in Central Serbia (1999–2021)
  145. Minerals for the green agenda, implications, stalemates, and alternatives
  146. Spatiotemporal water quality analysis of Vrana Lake, Croatia
  147. Functional transformation of settlements in coal exploitation zones: A case study of the municipality of Stanari in Republic of Srpska (Bosnia and Herzegovina)
  148. Hypertension in AP Vojvodina (Northern Serbia): A spatio-temporal analysis of patients at the Institute for Cardiovascular Diseases of Vojvodina
  149. Regional patterns in cause-specific mortality in Montenegro, 1991–2019
  150. Spatio-temporal analysis of flood events using GIS and remote sensing-based approach in the Ukrina River Basin, Bosnia and Herzegovina
  151. Flash flood susceptibility mapping using LiDAR-Derived DEM and machine learning algorithms: Ljuboviđa case study, Serbia
  152. Geocultural heritage as a basis for geotourism development: Banjska Monastery, Zvečan (Serbia)
  153. Assessment of groundwater potential zones using GIS and AHP techniques – A case study of the zone of influence of Kolubara Mining Basin
  154. Impact of the agri-geographical transformation of rural settlements on the geospatial dynamics of soil erosion intensity in municipalities of Central Serbia
  155. Where faith meets geomorphology: The cultural and religious significance of geodiversity explored through geospatial technologies
  156. Applications of local climate zone classification in European cities: A review of in situ and mobile monitoring methods in urban climate studies
  157. Complex multivariate water quality impact assessment on Krivaja River
  158. Ionization hotspots near waterfalls in Eastern Serbia’s Stara Planina Mountain
  159. Shift in landscape use strategies during the transition from the Bronze age to Iron age in Northwest Serbia
  160. Assessing the geotourism potential of glacial lakes in Plav, Montenegro: A multi-criteria assessment by using the M-GAM model
  161. Flash flood potential index at national scale: Susceptibility assessment within catchments
  162. SWAT modelling and MCDM for spatial valuation in small hydropower planning
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