Simulation of subsurface heterogeneity is important for modeling subsurface flow and transport processes. Previous studies have indicated that subsurface property variations can often be characterized by fractional Brownian motion (fBm) or (truncated) fractional Levy motion (fLm). Because Levy-stable distributions have many novel and often unfamiliar properties, studies on generating fLm distributions are rare in the literature. In this study, we generalize a relatively simple and computationally efficient successive random additions (SRA) algorithm, originally developed for generating Gaussian fractals, to simulate fLm distributions. We also propose an additional important step in response to continued observations that the traditional SRA algorithm often generates fractal distributions having poor scaling and correlation properties. Finally, the generalized and modified SRA algorithm is validated through numerical tests. 相似文献
This paper discusses the self-affinity dimensions of landscape surfaces at a short-range scale and the link to morphotectonic features of the young orogenic belts of Taiwan. The variogram method is adopted to estimate such parameters as the fractal dimension (D), the ordinate-intercept (γ) and the range (R) from data subsets of the digital elevation model (DEM) in a moving-window operation. The fractal morphology expressed by D and γ is found to be useful in defining geomorphic provinces that are related to tectonic features. The mountainous terrain is characterized by high gamma values and low fractal dimensions in contrast to the coastal plains where low gamma values and high fractal dimensions are found. A zone, defined by the fractal parameters (2.4<D<2.6 and 0<γ<2.4), is found to coincide with the most tectonically active zone of Taiwan. Active faults often occur at the boundary between landscapes with contrasting fractal patterns. In the flat lowlands along the western coast, the fractal morphology displays a west-facing amphitheatric pattern, which may be related to the indentation of the pre-Miocene Peikang Basement High. The fractal morphology may reflect some subtle changes in surface textures of a landscape sculpted by surface processes, which in turn are influenced by tectonic activities. The surface roughening and diffusive smoothing may concur to shape the landscape surface at the short ranges we discuss in this study. 相似文献
The time history of strong ground motion can be synthesized by empirical Green's function (EGF) method.Firstly a large seismic event is discretized into a series of subevents; secondly recordings of earthquakes with proper size and spatial distribution are chosen as time history (EGF) of those subevents; finally the EGFs are summated to get the time history of ground motion caused by the large event. 相似文献
Based on the analysis of newly collected data of plate tectonics, distribution of active faults and crustal deformation, the Taiwan area is divided into two seismic regions and six seismic belts. Then, correlation fractal dimensions of all the regions and belts are calculated, and the fractal characteristics of hypocenteral distribution can be quantitatively analyzed. Finally, multifractal dimensions Dq and f(α) are calculated by using the earthquake catalog of the past 11 years in the Taiwan area. This study indicates that (1) there exists a favorable corresponding relationship between spatial images of seismic activity described with correlation fractal dimension analysis and tectonic settings; (2) the temporal structure of earthquakes is not single but multifractal fractal, and the pattern of Dq variation with time is a good indicator for predicting strong earthquake events. 相似文献
Sand-rich submarine fans are radial or curved in plan view depending on the slope of the basin floor. They occur isolated or in coalescing systems. The fans' average lateral extent measures close to 25 km and their thickness usually less than 300 m. The thickness of outer fan sequences averages around 120 m and that of middle fan successions around 160 m. Rarely reported inner fan sequences have a maximum thickness of 80 m.
The formation of sand-rich fans is closely related to tectonic activity. Their sediment is coarse-grained and compositionally immature as indicated by significant feldspar content due to close provenance and rapid transport by short rivers with a steep gradient controlled by tectonism. Tectonic activity also provides for narrow shelves making the fans relatively insensitive to sealevel changes. Formation of sand-rich fans typically occurs in restricted continental basins. The tectonic settings are highly variable. Sand-rich fans typically receive their sediment through submarine canyons which intercept sand from longshore drift and/or are fed more or less directly by regional rivers.
The type of ancient fan system (radial, curved, isolated, coalescing) may be identified through paleocurrent map plots, facies map sketches, recognition of lateral thickness variations and sediment influx centers, as well as lateral bed correlations defining the minimum fan extent.
Important in distinguishing different environments of ancient fans are detailed measured sections, their comparison and correlation. Channelized inner fan and middle fan deposits may be distinguished from the unchannelized outer fan successions through bed correlation tests which reflect their different stratigraphic architectures and bedding patterns. Bedding in outer fan deposits (lobes) is relatively simple, parallel, and regular. The lateral bed continuity is relatively high. Channel fills, especially those of middle fan distributary channels, display a complicated bedding pattern with vertical and lateral random distribution of channel fills, axial erosion, and bed convergence towards the channel margins. Channel fills exhibit only linear bed continuity. Thus, the probability in carrying out local to regional scale lateral bed correlations is almost exclusively limited to outer fan deposits.
The measured sections will help further distinguish fan environments by revealing: (1) different facies associations in outer fan sequences (mainly B, C and D) and middle fan successions (mainly A, B, C, D, and channel margin facies); (2) greater average bed and layer thicknesses in middle fan as opposed to outer fan successions (“bed” and “layer” as used herein); (3) more frequent amalgamation surfaces in channel fills than in unchannelized outer fan deposits; (4) more frequent tabular amalgamation surfaces in outer fan sections; (5) more frequent nontabular amalgamation surfaces in channel fills; and (6) more frequent dish structures in middle fan than outer fan successions.
Rarely exposed fan valley fills may be identified by coarse conglomerates. Moreover, in proximity to fan valley fills, relatively mud-rich sediments may be observed that derive from the depositional system of the basin slope. 相似文献
Fractal modelling has been applied extensively as a means of characterizing the spatial distribution of geological phenomena
that display self-similarity at differing scales of measurement. A fractal distribution exists where the number of objects
exhibiting values larger than a specified magnitude displays a power-law dependence on that magnitude, and where this relationship
is scale-invariant. This paper shows that a number of distributions, including power-function, Pareto, log-normal and Zipf,
display fractal properties under certain conditions and that this may be used as the mathematical basis for developing fractal
models for data exhibiting such distributions. Population limits, derived from fractal modelling using a summation method,
are compared with those derived from more conventional probability plot modelling of stream sediment geochemical data from
north-eastern New South Wales. Despite some degree of subjectivity in determining the number of populations to use in the
models, both the fractal and probability plot modelling have assisted in isolating anomalous observations in the geochemical
data related to the occurrence of mineralisation or lithological differences between sub-catchments. Thresholds for the main
background populations determined by the fractal model are similar to those established using probability plot modelling,
however the summation method displays less capacity to separate out anomalous populations, especially where such populations
display extensive overlap. This suggests, in the geochemical data example provided, that subtle differences in the population
parameters may not significantly alter the fractal dimension. 相似文献
下载免费PDF全文