Fractal And Multifractal Properties Of Geochemical Fields

It's of great significance to study geochemical element distribution patterns by using fractal and multifractal methods. This dissertation will apply two fractal and multifractal methods called the method of moments and ACAF model to investigate whether it is a universal feature that a geochemical field is fractal or multifractal and whether lognormal or normal distribution data will yield a multifractal or single fractal with the additional use of QQ plot and histogram. Three important and interesting parts will be contained in this dissertation, including De Wijs modeling, Case studies and Monte Carlo Simulations.Based on simulations of two-dimensional De Wijs models with different parameters, high- and low-value suppression and local superimposition of other De Wijs models, this dissertation first simulated different geochemical element distribution patterns and then investigated their multifractal spectrum function shapes, ACAF distribution patterns and probability testing results. It can be drawn out that: ①Basic two-dimensional De Wijs modeling can produce a perfect continuous multifractal and such De Wijs construction is scale-invariant in space. If the spatial structure keeps the same, the multifractal spectrum shape will not change as neither relatively less or more iteration times nor the global division do have any effect on the multifractal shape.②Conventional De Wijs models exhibit symmetric multifractal spectra and parameters ???and ???increase monotonously with "enrichment factor" d. Any suppression of high values or low values in a simulating geochemical field will break this symmetry and make the spectrum curves f(?) deviate to right or to left, resulting in right-deviated multifractal(RM) and left-deviated multifractal(LM), respectively. The parameterΔ??can then be split intoΔ?L and Δ?R and their ratio R is called asymmetry index by the author and proves to be a pivotal parameter characterizing the underlying enrichment or pauperization mechanism. Local superimposition of De Wijs model of d1 by another De Wijs model of d2 will make the multifractal spectrum curves deviate left. With the increase of enrichment factor d2 of superimposed component, f(?) curves deviate more violently, and hence the parametersΔ?,Δ?L and asymmetric index R increases systematically with the enrichment factor of superimposed component, leaving its right side almost unchanged.③When the concentration bins and the corresponding frequency are drawn on log-log diagrams, the continuous multifractals of simulated geochemical fields following De Wijs construction can be categorized by two patterns: bi-segment pattern (BS pattern) and multi-segment pattern(MS pattern). Any basic De Wijs model follows BS pattern, whereas the De Wijs model with local superimposition obeys MS pattern, which is in agreement with the results of the method of moments.④The principle part of such kind of basic De Wijs modeling data is authentically of lognormal distribution. Whether the tails of it follow Pareto distribution is still in issue as there are so many repeated concentrations in such construction data that it's nearly impossible to detect the distribution patterns of any small part, such as the tails. For case studies, two distinct data sets will be employed, including elements in metallicgeochemical fields, as well as petroleum data from oil/gas regions. The former data set contains concentrations of 25 elements in 1448 whole rock samples from a region of 4290km2 in the north Guangdong Province, South China; 14 elements of 5489 and 4524 stream sediments in South and North Anhui Province, respectively, South China; and the latter with more than 15 hydrocarbons and other indices in 6418 soil samples from 4 oil/gas fields with total survey area 7000 km2 in Tarim Basin, North China. The results indicated that: ①Fractal and multifractal properties are quite universal in geochemical fields. However, metallic geochemical fields and oil/gas geochemical fields are intrinsically different from each other in spatial structu...