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| Titel |
Mixtures of multiplicative cascade models in geochemistry |
| VerfasserIn |
F. P. Agterberg |
| Medientyp |
Artikel
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| Sprache |
Englisch
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| ISSN |
1023-5809
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| Digitales Dokument |
URL |
| Erschienen |
In: Nonlinear Processes in Geophysics ; 14, no. 3 ; Nr. 14, no. 3 (2007-05-23), S.201-209 |
| Datensatznummer |
250012194
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| Publikation (Nr.) |
 copernicus.org/npg-14-201-2007.pdf |
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| Zusammenfassung |
| 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 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 log-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. |
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