地球化学图纹理的多重分形模拟

MULTIFRACTAL SIMULATION OF GEOCHEMICAL MAP PATTERNS

利用一个简单的基于DeWijs模型的多重分形模型 ,可以模拟元素富集值的各种地球化学纹理 .每种纹理在平均值上是自相似的 ,因为将乘积阶次模型 (multiplicativecascademodel)应用到任何子区均能得出类似的纹理样式 .在其他的试验中 ,通过叠加一个二维趋势纹理 (2 dimensionaltrendpattern)以及把它与一个常值富集模型混合 ,原始的自相似纹理就产生畸变 .本文将要研究这些畸变是如何改变用三步矩 (3 stepmethodofmoments)所估测的多重分形谱 (multifractalspectrum) .推导出了满足DeWijs模型纹理的离散和连续频率分布模型 .这些模拟纹理满足离散频率分布模型 ,当乘积阶次模型 (multipicativecascademodel)无限细分时 ,假设离散频率分布模型的上界是一连续频率分布 ,这个离散分布就在形式上逼近该连续频率分布的上边界 .这一极限分布在中心是对数正态的 ,但有两个巴利多 (Pareto)分布的尾 .这种方法在矿产和油气评价中有重要的潜在意义 .

Using a simple multifractal model based on the model De Wijs, various geochemical map patterns for element concentration values are being simulated. Each pattern is self-similar on the average in that a similar pattern can be derived by application of the multiplicative cascade model used to any small subarea on the pattern. In other experiments, the original, self-similar pattern is distorted by superimposing a 2-dimensional trend pattern and by mixing it with a constant concentration value model. It is investigated how such distortions change the multifractal spectrum estimated by means of the 3-step method of moments. Discrete and continuous frequency distribution models are derived for patterns that satisfy the model of De Wijs. These simulated patterns satisfy a discrete frequency distribution model that as upper bound has a continuous frequency distribution to which it approaches in form when the subdivisions of the multiplicative cascade model are repeated indefinitely. This limiting distribution is lognormal in the center and has Pareto tails. Potentially, this approach has important implications in mineral and oil resource evaluation.