Multifractal Analysis of Earthquakes in the Southeastern Iran-Bam Region

Earthquakes in Iran and neighbouring regions are closely connected to their position within the geologically active Alpine-Himalayan belt. Modern tectonic activity is forced by the convergent movements between two plates: The Arabian plate, including Saudi Arabia, the Persian Gulf and the Zagros Ranges of Iran, and the Eurasian plate. The intensive seismic activity in this region is recorded with shallow focal depth and magnitude rising as high as M_w = 7.8. The study region can be attributed to a highly complex geodynamic process and therefore is well suited for multifractal seismicity analysis. Multifractal analysis of earthquakes (m_b ≥ 3) occurring during 1973 – 2006 led to the detection of a clustering pattern in the narrow time span prior to all the large earthquakes: M_w = 7.8 on 16.9.1978; M_w = 6.8 on 26.12.2003; M_w = 7.7 on 10.5.97. Based on the spatio-temporal clustering pattern of events, the potential for future large events can be assessed. Spatio-temporal clustering of events apparently indicates a highly stressed region, an asperity or weak zone from which the rupture propagation eventually nucleates, causing large earthquakes. This clustering pattern analysis done on a well-constrained catalogue for most of the fault systems of known seismicity may eventually aid in the preparedness and earthquake disaster mitigation.     

On estimating the earthquake-induced changes in hydrogeological properties of the Choshuishi Alluvial Fan, Taiwan

The hydrological response of the Choshuishi alluvial fan to the 1999 Chi-Chi earthquake shows that the earthquake did impact the aquifer. The possible earthquake-induced changes in hydrogeological properties were investigated in this study. First, contour maps of the hydrologic anomaly, seismic factors, and vertical ground-surface displacement were compared qualitatively. Bulls eye patterns were found on the contour maps of hydraulic conductivity, coseismic groundwater-level change and vertical ground-surface displacement but did not occur with other seismic factors. The more permeable zones of the aquifer were found to coincide with the locations of greater vertical ground-surface displacement and coseismic groundwater-level change in the 1999 Chi-Chi earthquake. This indicates that the change of the hydrogeologic properties of Choshuishi alluvial fan due to the 1999 Chi-Chi earthquake may have mainly occurred in the highly permeable zones. Fractal, cross semivariogram and cross correlogram analyses were performed to quantitatively measure the persistency, variability and similarity, respectively, of spatial hydrologic response, seismic factors and hydraulic conductivity. The groundwater-level change, earthquake intensity, and vertical ground-surface displacement were found to show antipersistent tendencies while other factors showed the opposite. Higher correlations were found between hydraulic conductivity and groundwater-level change in aquifers 2–1 and 2–2, and between hydraulic conductivity and vertical ground-surface displacement in aquifer 3. Changes in porosities and hydraulic conductivity were evaluated in the main aquifers of the Choshuishi alluvial fan based on the data of hydrologic anomaly and the vertical ground-surface displacement. While both approaches show that the 1999 Chi-Chi earthquake has impacted the Choshuishi alluvial fan by reducing its porosity and hydraulic conductivity, these changes were not significant relative to natural variation in hydraulic conductivity.This revised version was published in May 2005 with correction to the rubric.     

Scattering from a fractal surface: acoustical experiments and comparison with near-nadir models

A homogeneous resin print of the surface of a naturally-fractured granite block with an experimental Hurst exponent H?0.7 is placed in a water tank. An acoustical source insonifies the surface in a near-nadir direction and the backscattered waves are recorded near the source. Such measurements are made at different positions along a profile above the surface in order to obtain the energy spectrum of the mean backscattered wavefield. The wavelength range considered is 0.58?λ?8.72 mm in water. A synthetic energy spectrum is obtained from a model [Shepard and Campbell, Icarus 141 (1999) 156] which represents the rough surface as an ensemble of point scatterers and assumes a single-scattering regime. This model reasonably fits with the experimental spectrum with the largest discrepancies observed for λ<2.5 mm. The fit is improved in the whole wavelength interval by accounting for the long-range topography variations occurring along the averaging profile.     

Lakes on fractal surfaces: A null hypothesis for lake-rich landscapes

A class of stochastic processes known as fractional Brownian motion (fBm) provides strikingly realistic simulations of certain types of terrain, particularly those which appear to be unmodified by geomorphological and geological processes. In addition to their less serious applications in video games and science fiction movies, fractal terrain simulations have proven useful in a number of areas of spatial analysis. For example, they can provide sample data sets for testing the efficiency of data structures and algorithms designed for topographic applications. Previous work has shown that stream networks simulated on fBm surfaces show the same deviations from accepted theories of channel network topology as do real stream networks, implying that such deviations originate in the geometrical constraints of packing channels onto surfaces, rather than from geological or other environmental controls. In effect, this work demonstrates the usefulness of fBm as a null hypothesis for terrain. One difficulty, however, stems from the abundant pits which occur in the simulations, because peaks and pits are equally likely. Flooding of pits on fBm surfaces was simulated to obtain lakes. Lake-rich stream networks were extracted and represented with a suitable integer code. The relative frequencies of various network topologies and groups of topologies were compared to known characteristics of channel networks on real lake-rich landscapes. Lake-string topologies are significantly less abundant than in glaciated landscapes. Lake areas show good fits to hyperbolic distributions, but lake in-degrees do not fit the negative binomial model. fBm surfaces are appropriate null hypotheses of scale-free, lake-rich landscapes.This paper was presented at Emerging Concepts, MGUS-87 Conference, Redwood City, California, 13–15 April 1987.     

Fractal Approach,Analysis of Images and Diagenesis in Pore Space Evaluation

Simple net model constructed by authors, facies analysis and compaction models, were applied to evaluate reservoir properties of sandstone facies of the Carpathian Flysch (the Istebna sandstones). The applied net model was built on the base of fractal approach proposed by Don Turcotte in 1977 and computer analysis of images. Laboratory measurements include porosity, density, permeability to nitrogen, mercury injection capillary pressure tests, and microscopic analysis of thin sections. D.W. Houseknecht's theory, proposed in 1987, was applied for compaction and cementation modeling. The residual saturation data were used to validate obtained results. Net model allows an evaluation of filtration properties of analyzed sandstones and to distinguish the classes of similarity of pore space. The extracted parameters of classes of similarity were correlated with facies scheme of the investigated geological structure. Influence of compaction and cementation on pore space parameters was discussed.     

非线性方法油气平面成像预测的研究

系统论和非线性方法为石油地球物理勘探注入了新的动力。本文试通过分形理论结合人工神经网络方法对测井资料进行解释,对油气分布进行平面成像预测。     

沉积过程分形表达及其冲淤幅度分析应用

根据１９８２－１９９５年在浙江沿岸椒江口、杭州湾、象山县大目涂取得的沉积柱样层序数据系列和重复沉积界面测量序列,利用分形理论进行沉积过程及冲淤幅度的分析。沉积过程和沉积地层层序存在自相似结构,两者之间在无特征尺度区存在着初始值以及分数维的传递。椒江河口和杭州湾南侧潮汐通道边坡沉积柱样泥层工的分数维在１．２－１．５之间。按潮汐沉积基本单元形成的时间为大小潮周期计算,沉积过程１年重现期的高程均方变幅为     

河系几何相似性的层次度量方法

已有的线群目标几何相似性度量方法主要基于数理统计的思想,通过统计整体变化信息计算几何相似性,缺少对局域特征的表达,并不适用于具有高度分形特征的河系。为此,本文将河系几何特征划分为3层次的信息特征：单条河流的形状特征、局部区域的结构特征、全局范围的分布特征。首先,结合角链码法与Hausdorff距离计算单条河流的形状相似度;然后,根据 “二八定律”确定局部特征区域,通过坐标系转换计算M： N的河系局域结构相似度;最后综合整体描述子得到全局分布相似度,并在该基础上,构建差异指标进行河系多尺度相似性计算与综合质量评价。实验表明,该方法的计算结果优于均值指标法,能有效应用于制图综合的质量评价。     

Geomorphometric pattern recognition of SRTM data applied to the tectonic interpretation of the Amazonian landscape

The Amazon landscape spatial variability and anisotropic trends in the Uatumã and Urubu River regions are evaluated using geomorphometric techniques such as fractal dimension, drainage network density and semivariogram. These procedures were applied to the digital elevation model (DEM) of the Shuttle Radar Topography Mission (SRTM). This evaluation facilitated the definition of geomorphometric domains with different degrees of roughness (fractal dimension) and elevation (semivariogram). These areas are consistent with known qualitative relief types. Furthermore, known geological structures in the subsurface and surface apparently influence the spatial variability of these geomorphometric variables. This is the Silves area case, where the hilly topography exhibits several annular and radial rivers, denoting subsurface control due to faults and folds that were mapped by seismic surveys. Another possible influence example is the spatial coincidence between structures mapped by magnetic data with low dissection zones delineated as a result of drainage network density analysis. In addition to the spatial distribution, the anisotropic trends of these geomorphometric variables were analyzed and compared with geological and geophysical information. Results indicate that the predominant directions for topographic semivariance anisotropy are NNE–SSW and NE–SW for the interfluvial regions, as well as NW–SE for the alluvial plains. The highest agglomeration direction in the drainage network, as shown by its anisotropy, coincides with the studied region’s current maximum horizontal stress direction, except in the floodplains. The direction with the most pronounced roughness, NNE–SSW, coincides with the direction of waterfalls and rapids. This study demonstrates that spatial variability knowledge and anisotropic trends of geomorphometric parameters is useful to understand the geology and geomorphology of the Central Amazon region.     

Monitoring stress levels on rice with heavy metal pollution from hyperspectral reflectance data using wavelet-fractal analysis

Remote sensing allows monitoring heavy metal pollution in crops for agricultural production and food security. This paper presents an approach to wavelet-fractal analysis for exploring a set of sensitive spectral parameters to monitor the heavy metal pollution levels in rice crops from hyperspectral reflectance data. Hyperspectral and biochemical data were collected from three study farms in Changchun, Jilin Province, China. Our study explored the fractal dimension of reflectance with wavelet transform (FDWT) that demonstrated a better performance than other existing methods. Our results obtained in this study show that the red edge position (REP) was the most sensitive indicator for monitoring the heavy metal pollution levels in rice crops among common indices. As compared with REP, the FDWT is more sensitive to biochemical composition, namely with respect to chlorophyll concentrations, N, Cu and Cd. The established linear models showed a correlation coefficient (R²) above 0.70, model efficiency (ME) above 0.65 and a root mean square error (RMSE) below 3.5. Minimum FDWT values occurred in rice with Level II pollution followed by Level I pollution, and finally the safe level. This study suggests that wavelet transform is well suited as a spectral analysis method to eliminate noise and amplify the stress information from heavy metals. The wavelet transform in conjunction with fractal analysis is promising for detecting heavy metal-induced stress in rice crops.