Fractal analysis of geochemical landscapes using scaling noise model

Chen, Guoxiong; Cheng, Qiuming

doi:10.1016/j.gexplo.2015.11.003

Cited by 13 publications

(3 citation statements)

References 32 publications

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“…A fractal entity is characterized by the inherent, ubiquitous occurrence of scaling laws that refer to systems for which all scales within some range are equally important, usually governing complex shapes with various degrees of singularity. Up to now, scaling/fractal nature has been evidenced as a widespread statistical property of crustal heterogeneity [e.g., Bean , ; Chen et al ., ; Leonardi and Kumpel , ; Lovejoy and Schertzer , ; Pilkington and Todoeschuck , , , ; Shiomi et al ., ; Wu et al ., ; Zhou and Thybo , ], shared by many upper crustal media characteristics regardless of property measured (e.g., density, velocity, resistivity, magnetic susceptibility, or geochemical concentration) or the lithology (e.g., crystalline or sedimentary). Such evidences for scaling behavior mainly come from well logs on oilfields, mineral deposits, and deep crustal sections.…”

Section: Introductionmentioning

confidence: 99%

Fractal density modeling of crustal heterogeneity from the KTB deep hole

Chen

Cheng

2017

JGR Solid Earth

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Fractal or multifractal concepts have significantly enlightened our understanding of crustal heterogeneity. Much attention has focused on 1/f scaling natures of physicochemical heterogeneity of Earth crust from fractal increment perspective. In this study, fractal density model from fractal clustering point of view is used to characterize the scaling behaviors of heterogeneous sources recorded at German Continental Deep Drilling Program (KTB) main hole, and of special contribution is the local and global multifractal analysis revisited by using Haar wavelet transform (HWT). Fractal density modeling of mass accumulation generalizes the unit of rock density from integer (e.g., g/cm3) to real numbers (e.g., g/cmα), so that crustal heterogeneities with respect to source accumulation are quantified by singularity strength of fractal density in α‐dimensional space. From that perspective, we found that the bulk densities of metamorphic rocks exhibit fractal properties but have a weak multifractality, decreasing with the depth. The multiscaling natures of chemical logs also have been evidenced, and the observed distinct fractal laws for mineral contents are related to their different geochemical behaviors within complex lithological context. Accordingly, scaling distributions of mineral contents have been recognized as a main contributor to the multifractal natures of heterogeneous density for low‐porosity crystalline rocks. This finally allows us to use de Wijs cascade process to explain the mechanism of fractal density. In practice, the proposed local singularity analysis based on HWT is suggested as an attractive high‐pass filtering to amplify weak signatures of well logs as well as to delineate microlithological changes.

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Section: Introductionmentioning

confidence: 99%

Fractal density modeling of crustal heterogeneity from the KTB deep hole

Chen

Cheng

2017

JGR Solid Earth

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“…Various calculated approaches for fractal dimensions-including the Hausdorff dimension [8], the box-counting dimension [9], the information dimension [10], and the correlation dimension [11], etc.-have been proposed and applied to describe the self-similarity [12] and self-affinity [13] of fractals for irregular shapes or complex objects in geology [14]. Multi-fractal theory, including spectrum-area (S-A) models and singularity analysis, is used to detect the true anomalies caused by mineralization [15,16] in geochemical [17][18][19][20], geophysical exploration [21,22] and signal detectors in seismology [23].…”

Section: Introductionmentioning

confidence: 99%

A Novel Approach to Edge Detection for a Gravity Anomaly Based on Fractal Surface Variance Statistics of Fractal Geometry

Zeng

Yan³

et al. 2022

Applied Sciences

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Fractal geometry has developed rapidly, and is widely used in various disciplines. However, only a few fractal dimension methods and techniques have been applied to the processing of gravity data, especially in the detection of geological edges and interfaces. In this paper, the definition, properties and characteristics of fractal dimensions are used to improve the edge detection of gravity anomalies, and a theoretical gravity model is established. At the same time, a new method of fractal surface variance statistics is applied and compared with traditional methods. The fractal gravity anomaly processing methods in different directions are analyzed, and the results show that the maximum value of the fractal surface variance statistical method on a fixed window can be used to delineate the geological edge of the ore body. When the method in this paper is applied to the Luobusha chromite deposit in Tibet, China, the fractal dimension corresponds well with the structural development zones of various faults, and it is also helpful to delineate the boundary of the chromite deposit and identify the interface with an obvious difference in gravity anomaly density.

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“…The fractal geometry of nature was introduced as a way of describing the complex erratic shape of nature and the self-similarity concept. The popular use of fractal dimension for landscape mapping has been noted across the world ( Chen et al., 2016 ; Feng and Liu, 2015 ; He et al., 2016 ; Juliani et al., 2016 ; Plexida et al., 2014 ). It has been used for image segmentation ( Sarkar and Chaudhuri, 1994 ; Xi and Zhao, 2011 ), image data compression ( Barnsley and Hurd, 1993 ; Fisher, 1994 , 2012 ; Saupe, 1995 ; Walach and Karnin, 1986 ), computer graphics ( Hughes et al., 2015 ; Kim et al., 2016 ; Peng et al., 2015 ; Shen et al., 2016 ), sedimentology ( Dufresne et al., 2016 ; García-Hidalgo et al., 2016 ; Laurita et al., 2016 ; Liu et al., 2016 ) and particle morphology ( Gonzalez-Jordan et al., 2016 ; Loh et al., 2012 ; Sarkar and Chaudhuri, 1994 ; Wu et al., 2016 ; Yang et al., 2016a , b ; Zimmerman et al., 2014 ).…”

Section: Introductionmentioning

confidence: 99%

Erosion potential mapping using analytical hierarchy process (AHP) and fractal dimension

Kabo-bah

Tang

Yang

et al. 2021

Heliyon

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Assessing landform vulnerability to soil erosion is crucial for improved sustainable land use planning and management. In the Loess Plateau of the Northern Shaanxi Province of China, soil erosion has been reported as a major threat to sustainable land management and impacts on driving the socio-economic benefits that can be accrued from the landforms. Several studies especially on Erosion Potential Mapping (EPM) in the region have been conducted but the role of the fractal dimension (FD) of the terrain features has been limited. In this study, the paper assessed the role of fractal terrain features on the overall EPM. The Analytical Hierarchical Process (AHP) was adopted using 6 criteria, FD of the terrain, Land Use Land Cover, Slope, Elevation, Geomorphology and Flow Accumulation. These were developed in a Geographic Information System (GIS) framework. Eight Scales (8) were evaluated in order to select the best Scale with the lowest Consistency Ratio (CR) and the Minimum Relative Error (MRE). The results from this study shows that fractal features of terrain when integrated with the rest of the criteria produced a reliable EPM for the study area. The absence of the FD also gives unrealistic results for the EPM. The EPM with FD distribution recorded 29.4% for low erosion potential whereas EPM without FD recorded 46.7%. A larger portion of the Shaanxi province (70%) is found to be at a higher risk of erosion. Therefore, it is hoped that the findings from this research would further boost the integration of fractals into EPM in China and similar regions across the World. The study further recommends that sustainable soil management measures are put in place to reduce the erosion risk in the province to protect the natural ecological habitat.

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Fractal analysis of geochemical landscapes using scaling noise model

Cited by 13 publications

References 32 publications

Fractal density modeling of crustal heterogeneity from the KTB deep hole

Fractal density modeling of crustal heterogeneity from the KTB deep hole

A Novel Approach to Edge Detection for a Gravity Anomaly Based on Fractal Surface Variance Statistics of Fractal Geometry

Erosion potential mapping using analytical hierarchy process (AHP) and fractal dimension

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