Mixtures of multiplicative cascade models in geochemistry

被引:87
作者
Agterberg, F. P. [1 ]
机构
[1] Geol Survey Canada, Ottawa, ON K1A 0E8, Canada
关键词
D O I
10.5194/npg-14-201-2007
中图分类号
P [天文学、地球科学];
学科分类号
07 ;
摘要
Multifractal modeling of ocochemical map data can help to explain the nature of frequency distributions of element concentration values for small rock samples and their spatial covariance structure. Useful frequency distribution models are the lognormal and Pareto distributions which plot as straight lines on logarithmic probability and log-log paper, respectively. The model of de Wijs is a simple multiplicative cascade resulting in discrete logbinomial distribution that closely approximates the lognormal. In this model, smaller blocks resulting from dividing larger blocks into parts have concentration values with constant ratios that are scale-independent. The approach can be modified by adopting random variables for these ratios. Other modifications include a single cascade model with ratio parameters that depend on magnitude of concentration value. The Turcotte model, which is another variant of the model of de Wijs, results in a Pareto distribution. Often a single straight line on logarithmic probability or loo-log paper does not provide a good fit to observed data and two or more distributions should be fitted. For example. geochemical background and anomalies (extremely high values) have separate frequency distributions for concentration values and for local singularity coefficients. Mixtures of distributions can be simulated by adding the results of separate cascade models. Regardless , of properties of background, an unbiased estimate can be obtained of the parameter of the Pareto distribution characterizing anomalies in the upper tail of the element concentration frequency distribution or lower tail of the local singularity distribution. Computer simulation experiments and practical examples are used to illustrate the approach.
引用
收藏
页码:201 / 209
页数:9
相关论文
共 35 条
[1]  
AGTERBERG F., 1995, International Geology Review, V37, P1, DOI DOI 10.1080/00206819509465388
[2]  
Agterberg F.P., 2001, P IAMG ANN M CANC SE
[3]  
Agterberg FP, 2001, COMP AP EAR, P327
[4]  
AGTERBERG FP, 2007, MATH GEOL
[5]  
AHRENS LH, 1953, FUNDAMENTALS LAW GEO, V712, P1148
[6]  
AITCHISON J, 1957, IOGNORMAL DISTRIBUTI
[7]   SCALING LAWS AND GEOCHEMICAL DISTRIBUTIONS [J].
ALLEGRE, CJ ;
LEWIN, E .
EARTH AND PLANETARY SCIENCE LETTERS, 1995, 132 (1-4) :1-13
[8]  
[Anonymous], 1983, New York
[9]  
[Anonymous], 2003, FRACTAL GEOMETRY, DOI DOI 10.1002/0470013850
[10]  
BRINCK JW, 1974, P S FORM UR OR DEP A, P21