Mixtures of multiplicative cascade models in geochemistry
By F. Agterberg. 2007
100 citations recorded by the source corpus.
Multifractal modeling of geochemical 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 distri- bution 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 sim- ple 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 modifi- cations include a single cascade model with ratio parame- ters 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 log-log paper does not pro- vide 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 singular- ity 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 ob- tained of the parameter of the Pareto distribution characteriz- ing 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.
Subfields: Artificial Intelligence, Environmental Engineering, Media Technology
View Paper: https://www.semanticscholar.org/paper/17fa6e20d75a9e44e8ff979848e8eec27b15f7f0
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Citations in the corpus
- Generalized binomial multiplicative cascade processes and asymmetrical multifractal distributions (2014, methodology): “Other modified models exist, e.g., a cascade model with functional redistribution rate (Agterberg, 2007b), a 2-”