Studying fractal geometry on submicron length scales by small-angle scattering

Recent studies have shown that internal surfaces of porous geological materials, such as rocks and lignite coals, can be described by fractals down to atomic length scales, In this paper, the basic properties of self-similar and self-affine fractals are reviewed and how fractal dimensions can be measured by small-angle scattering experiments are discussed.This paper was presented at Emerging Concepts, MGUS-87 Conference, Redwood City, California, 13–15 April 1987.     

Scaling of geological discontinuity normal load–deformation response using fractal geometry

The mechanical behaviour of discontinuities in rock, such as joints, is known to be size‐dependent. It is also suspected that the behaviour of larger size features, such as faults, is also size‐dependent. This size dependence has serious implications for performing numerical response simulations of geological media. In this paper, we develop a new mathematical theory for scaling of one particular discontinuity property, namely the interface normal stiffness. To accomplish this, we idealize an interface to have fractal geometry, and we develop analytical relations which show that the interface normal stiffness, which is commonly thought to be a size‐independent property, is in fact a size‐dependent property and has fractal characteristics that may be exploited to develop a fundamental theory for scaling. Copyright © 2001 John Wiley & Sons, Ltd.     

华北地区煤层气井压裂裂缝监测及其扩展规律

介绍了井温测试法、放射性同位素法、大地电位测试法和微地震测试法监测煤层水力压裂裂缝的基本原理。使用上述4种方法对华北地区施工的煤层气井压裂裂缝进行测量,得到了大量压裂井的裂缝方位和高度的监测数据。通过统计分析发现:压裂后的煤层裂缝一般都穿越其上下隔层,最大裂缝高度是压裂层厚度的6倍,裂缝长度大部分为50~90 m,裂缝形状基本以垂直裂缝为主,裂缝方向存在着随机性,扩展方向受地应力、局部地层构造和煤层割理共同作用。     

Correlation between geological units and mineralized zones using fractal modeling in Zarshuran gold deposit (NW Iran)

In this study, the relation between ore grade and geological characteristic has been studied as a principle and also important conceptual in Zarshuran gold deposit in NW Iran. The main subject in this study was identifying a correlation among the ore grade populations and rock types which could be used in other steps of local estimation in the deposit concentration–number (C–N) fractal model and logratio matrix. The C–N log–log plot reveals six geochemical zones defined by Au?<?0.02 ppm as non-mineralized zone and Au?>?0.02 ppm as mineralized zones. According to geological logging and field geology inspection, black gauge, jasperoid, fault gauge and breccia, and carbonaceous rocks are considered as main rock types which contain major Au mineralized zones. The correlation between geological and fractal modeling by logratio matrix shows that there is a good correlation between geological assumed host rocks and C–N fractal modeling. Black gauge rock type with 93.48 % of overall accuracy shows a significant correlation with supergene zone of fractal model, and jasperoid with 92.5 % and carbonaceous rock type with 52.90 % have a decent correlation with highly and lowly mineralized zone of fractal model relatively. Black gauge, jasperoid, and fault gauge and breccia have an approximately near cooperation in this zone for mineralization.     

The fractal geometry of tidal-channel systems in the Dutch Wadden Sea

Horton's hierarchical and fractal analysis of channel circumference reveals that tidal-channel systems in the Dutch Wadden Sea have similar branching patterns. Channel systems have the same characteristics as three- to four-times branching networks. The branch lengths of these channels decrease logarithmically. The channel systems can be regarded as statistical self-similar fractal networks, considering the natural variability in branch lengths and channel positions. Branching of channels does not continue below the 500 m scale. The channel-system circumference length is logarithmically related to the tidal prism and drainage area. The similarity of the channel systems, regardless of their size, relative amount of intertidal flats, and tidal amplitude, points to a self-organising nature. All processes depend on the feedback between morphology and hydrodynamics. At first sight, the channel systems can be regarded as an ebb-driven drainage network, governed by erosion. However, flood-dominated net sedimentation occurs in large parts of the drainage basins and modifies the ebb-driven network. The complex interaction of hydrodynamic and morphodynamic processes in tidal basins limits the applicability of process-based models. Behaviour-oriented modelling has a wide applicability and can be improved using the fractal geometry as the dynamical equilibrium morphology. The fractal-network geometry can also be used for stochastic reconstructions of fossil tidal-channel systems, when only limited observations are available.     

活动断裂系统的分段性及其分形几何特征

文章应用分数维理论讨论了我国几条活动断裂系统的分段性。结果发现,活动断裂系在地质结构,运动特征,动力学特征,地球物理场异常和分形几何方面均存在分段行为。这个结论为活动构造区重大工程场址的选择与评价提供了更充分的依据。     

Modeling and mapping of solar radiation using geostatistical analysis methods in Iran

Because of economic and technical limitations, measuring solar energy received at ground level (R _s ) isn’t possible in all parts of the country, and in only 12% of synoptic stations is this parameter measured and recorded. Thus, it should be estimated and modeled spatially based on other climatic variables using mathematical methods. In this research, many attempts have been made to introduce an air temperature-based model for Rs estimation, and then, based on the output of the mentioned models, several geostatistical methods have been tested, and finally an elegant spatial model is proposed for (Rs) zoning in Iran. In this regard, the relationships between the measured amounts of monthly solar radiation and other climatic parameters, such as a monthly average, maximum and minimum temperature, precipitation, relative humidity, and the number of sunny hours during the period 1970–2010, are examined and modeled. It was revealed that based on the linear relationship between the monthly average air temperatures and solar radiation values recorded in each of the stations, that the best-fit linear model, with R ²  = 0.822, MAE = 1.81, RMSE = 2.51%, and MAPE = 10.08, can be introduced for Rs estimation. Then, using the outputs of the proposed model, the amounts of (R _s ) are estimated in another 171 meteorological stations (a total of 192 stations), and eight geostatistical methods (IDW, GPI, RBF, LPI, OK, SK, UK, and EBK) were investigated for zoning. Comparing the resulting variograms showed that in addition to proof of spatial correlation between solar radiation data, they can be applied for modeling changes in various directions. Analyzing the ratio of the nugget effect on the roof of the variograms showed that the Gaussian model with the lowest ratio (Co/Co + C = 0.883) and (R ²  = 0.972), could model the highest correlation between the data and, therefore, it was used for data interpolation. To select the best geostatistical model, R2, MAE, and RMSE were used. On this basis, it was found that the RBF method with R ²  = 0.904, MAE = 3.02, RMSE = 0.39% is the most effective. Also, the IDW method with R ²  = 0.90, MAE = 3.08, RMSE = 0.391%, compared to other methods is the most effective. In addition, for data validation, correlations between observed and estimated values of solar radiation were studied and found R ²  = 0.86.     

岩体结构多重分形方法的改进与应用

本文运用多重分形方法研究岩体结构,对关键参数作误差分析,进行算法改进。并选取鄂西恩施保扎滑坡与杨家山滑坡附近的4个代表性露头点进行岩体结构多重分形研究,得出多重分形维数值是对平均岩体质量的直接度量,多重分形谱宽反映了岩体质量的整体分布情况。岩体结构多重分形方法比传统的岩体质量指标更能反映岩体结构的整体性质,根据多重分形结果可建立初步的岩体质量评价方法。     

Strain-rate estimation using fractal analysis of quartz grains in naturally deformed rocks

The area-perimeter fractal dimension (D) of quartz grains has earlier been proposed as a strain-rate gauge based on experimental deformation of quartz aggregates. To test the application in naturally deformed rocks, D is calculated in (a) three quartzites belonging to the Lunavada Group of rocks (Aravalli Mountain Belt, NW India) that developed textures between 420–600°C and (b) one quartz reef sample from the Malanjkhand Granite (Central India), which underwent dynamic recrystallization between 250–400°C. Using the above T ranges and calculated D values, strain-rates are calculated for the two sets of samples. A 10^−12.7 s⁻¹ strain rate at 250°C is calculated for the quartz reef sample. However, at higher temperatures the calculated strain-rate is >10⁻¹⁰ s⁻¹ for the quartz reef and the quartzite samples. The quartzites show evidence of dynamic recrystallization by grain boundary migration (GBM) and subgrain rotation (SGR), while the quartz reef is replete with evidence of bulging (BLG) recrystallization. T and calculated strainrates are plotted on available recrystallization map of quartz. It is demonstrated that whilst the T/strain-rate of the quartzites does not fall in the region of GBM and SGR, the T/strain-rate of the quartz reef falls in the BLG region. The problems with strain-rate calculations using area perimeter fractal dimension are discussed. It is concluded that the method of strain-rate calculation can be used only for lower T.     

Discrimination of sand dunes and loess deposits using grain-size analysis in northeastern Iran

Identification and characterization of aeolian deposits in arid environments provide information on mechanisms of loess and sand accumulation. The objectives of this study were to (i) identify the distribution of aeolian deposits, (ii) discriminate loess and sand deposits using granulometric data, and (iii) describe the aeolian deposition in Sarakhs area, northeastern Iran. Particle size distributions of 26 surface samples were determined using a laser grain-size analyzer. Fine sand, very fine sand, and very coarse silt were dominant fractions in studied sediments, and the sum of these fractions ranged from 46.9% in loess deposits to 93.8% in sand dunes. The mean grain size (M _z ) of sand dunes ranged from 3.31 to 3.54 ?, which gradually changed to 4.09 to 5.50 ? in loess deposits. Sorting, skewness, and kurtosis ranged from 0.84 to 1.94 ?, 0.18 to 0.49, and 0.76 to 2.38, respectively. Aeolian deposits in the area resulted in the incorporation of Hariroud River system and Kopeh Dagh Mountains for aeolian particle production and accumulation. Alluvial comminution in Hariroud River is suggested the main mechanism of sand and silt production and flood plain environment the main reservoir of these particles. The mountains of Kopeh Dagh act as a barrier and play a key role for sand and loess accumulation.     

Structural interpretation and hydrocarbon potential of Balkassar oil field,eastern Potwar,Pakistan, using seismic 2D data and petrophysical analysis

The Balkassar oil field is situated in the eastern Potwar sub-basin, lies on the southern flank of Soan syncline in Himalayan collisional regime. The area represents Indo-Pak and Eurasian blocks of Precambrian to recent time. Thrusting and folding of Himalayan, Indo-Pak plate movement and Salt Range uplift form the structural trap in Balkassar sub-surface (Balkassar anticline). On the basis of information from eleven seismic 2D lines and wells data six reflectors well data, four faults were identified and marked. The structural trend is northeast southwest. Interpretation of seismic 2D data reveals that the study area has undergone intense deformation as a consequence of development of thrusts and backthrusts.The Balkassar anticline is bounded by two thrust faults one from southeast and the other from northwest. Time and depth contour models shows that anticline limbs at north-western side are steep as compared to south-eastern limbs. Seismic interpretation indicates the presence of well-developed anticline bounded by three faults in the cover sequence and one fault in basement and thus the structure may act as a trap for hydrocarbons. The petrophysical analysis of Balkassar-OXY-1 well shows about 83.1% hydrocarbons saturation in the reservoir rocks, hence this study suggest that Balkassar Oilfield has potential to produce hydrocarbons.     

Determination of mineralization stages using correlation between geochemical fractal modeling and geological data in Arabshah sedimentary rock-hosted epithermal gold deposit,NW Iran

This research paper aims to delineate and recognize different gold mineralization stages based on surface lithogeochemical data using factor analysis and Spectrum-Area (S-A) modeling, as well as geological data in Arabshah sedimentary rock hosted epithermal gold deposit, NW Iran. Based on the factor analysis, Au and Mn were allocated to factor 2 (F2) and then classified by the S-A fractal modeling. In addition, Au and F2 values were transformed to spectrum data, which were categorized by the S-A log-log plots. Accordingly, the main mineralization phase contains Au and F2 (Au-Mn) values greater than 800 ppb and 0.3, respectively, and is associated with the occurrence of minerals such as pyrite, arsenian pyrite, realgar, orpiment and oxidized sulfides. The first phase of gold mineralization, where Au typically ranges between 80 and 350 ppb, is associated with base metal sulfides, arsenian pyrites and F2 values between 0.1 and 0.2. The second gold mineralization phase consists of Au values from 350 to 800 ppb and F2 values between 0.2 and 0.3. Combination of the S-A modeling, factor analysis and geological data outlined three gold mineralization stages in Arabshah gold deposit. The main mineralization stage showed a strong positive correlation with the NE-SW and NW-SE trending structures, the altered intrusive rocks such as microdiorite and granodiorite, and the altered subvolcanic dacitic domes.     

Geochemical anomaly definition using multifractal modeling,validated by geological field observations: Siah Jangal area,SE Iran

Recognition of geochemical anomalies is a pivotal assignment in exploration projects. This study aims to delineate different AuCu geochemical anomalies using number-size (N-S) and concentration-area (C-A) multifractal models in the Siah Jangal area, SE Iran. In this research, lithogeochemical datasets were applied for the exploration of Au and Cu. A comparison between geochemical anomaly maps based on the N-S and C-A fractal models shows the N-S fractal modeling is a powerful tool for separation of weak elemental geochemical anomalies in all of sampling zones. Based on a comparison between the results of these two methods and field studies, the geochemical anomaly zones, defined by the N-S fractal model, are more accurate than those recognized by the C-A fractal model. The obtained results of the N-S and C-A fractal models have been interpreted with the extensive set of information including structural interpretation, geological and alteration data. Au and Cu mineralization in the Siah Jangal area are hosted mainly by Oligocene-Miocene sub-volcanic rocks, especially strongly altered porphyric quartz diorite, hornblende diorite and diorite. Moreover, the positive dependence between various alteration zones and high concentrations of Au and Cu proves that strongly anomalous areas are correlated with these alteration zones. High grade Au (> 1000 ppb) and Cu (>150 ppm) are associated with the altered sub-volcanic rocks in the northern, eastern, and SW parts of the study area. Therewith, the strong anomaly populations are mostly occurred within the fault and fracture systems in the study area. This is a promising signal because quartz-sulfide veins and veinlets are associated with such structures.     

Geochemical analysis of evaporite sedimentation in the Gachsaran Formation,Zeloi oil field,southwest Iran

In this study, the paleo-sedimentary depositional environment of the Gachsaran Formation and the Asmari reservoir cap rock (i.e., the stratigraphically lowest member of the Gachsaran Formation) was investigated from elemental geochemical data and mineralogical data obtained XRF and SEM analyses, respectively, of anhydrite samples collected from two oil wells in the Zeloi oil field in southwestern Iran. The present data reveal that arid conditions and cycles of transgression–regression of the sea contributed to the formation of evaporite sequences of the Gachsaran Formation in a coastal sabkha-lagoon basin that was partly closed to the sea. This interpretation was based on synthesis of statistical correlation analysis the geochemical data, chemostratigraphic correlation of geochemical ratios, and textural analysis of salts observed in SEM images.     

Assessment of fractal dimension and geometrical characteristics of the landslides identified in North of Tehran,Iran

The aim of the presented study is to assess the fractal dimension (D) and the geometrical characteristics (length and width) of the landslides identified in North of Tehran, Iran. At first, the landslide locations (528 landslides) were identified by interpretation of aerial photographs, satellite images and field surveys, and then to calculate the fractal dimension (D), we used the computer programming named as FRACEK. In the next step, geometrical characteristics of each landslide such as length (L) and width (W) were calculated by ArcGIS software. The landslide polygons were digitized from the mentioned landslide inventory map and rotated based on movement direction. The fractal dimension for all landslides varied between 1.665 and 1.968. Subsequently, the relationship between the length/width ratios and theirs fractal D values for 528 landslides was calculated. The results showed that correlation coefficients (R), which are different regression models such as exponential, linear, logarithmic, polynomial, and power, between D and L/W ratio are relatively high, respectively (0.75, 0.75, 0.76, 0.78, and 0.75). It can be concluded that the fractal dimension values and geometry characteristics of landslides would be useful indices for the management of hazardous areas, susceptible slopes, land use planning, and landslide hazard mitigation.     

2D inversion of the magnetotelluric data from Mahallat geothermal field in Iran using finite element approach

The natural-field magnetotelluric (MT) method has proven very useful for mapping the geothermal fields as resistivity sections. The depth of investigation of the MT method is sufficiently large to penetrate deep into the upper crust. MT soundings along two transects across Mahallat geothermal field in Iran were carried out to determine the crustal structure in the region. The selected MT profiles in the region cross over the hydrothermally altered zones and different geological structures. Data were acquired along two profiles crossing the Mahallat hot springs with a total of 28 MT stations in a frequency range of 8,000 to 0.008 Hz. Spacing between stations was kept 500 m for a good resolution. We have used the code MT2DInvMATLAB for inversion using the method of finite elements for forward modeling. Apparent resistivity and phase data of transverse electric (TE), transverse magnetic (TM), and TE + TM modes along each profile were modeled. The geothermal fluid reservoir is resolved at 1,000 to 3,000 m depth and the geothermal resource is estimated to be located at 7,000 m or deeper.     

Aftershock probabilistic seismic hazard analysis for Bushehr province in Iran using ETAS model

Natural Hazards - Aftershock probabilistic seismic hazard analysis (APSHA) has a key role in risk management after a major earthquake. The main goal of the current study is to assess aftershock...