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Grain size distribution expressed as tanh ‐functions
Author(s) -
P°SSE TORE
Publication year - 1997
Publication title -
sedimentology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.494
H-Index - 108
eISSN - 1365-3091
pISSN - 0037-0746
DOI - 10.1111/j.1365-3091.1997.tb02175.x
Subject(s) - log normal distribution , sediment , hyperbolic function , grain size , distribution (mathematics) , geology , hydrogeology , process (computing) , function (biology) , mathematics , geotechnical engineering , statistics , geometry , mathematical analysis , computer science , geomorphology , biology , operating system , evolutionary biology
The grain size distribution within a unimodal sediment can be described as a lognormal distribution when the distribution is formed by only one process. However, most sediments are formed by more than one process giving polymodal sediments. Polymodal sediments have to be described as the sum of several normal distributions, one for each process involved within the formation. Grain size distributions are usually interpreted with the help of graphical methods. Interpretations of polymodal sediments require mathematical methods. In mathematical terms a unimodal sediment can be described as a tangential hyperbolic function (tanh) and a polymodal sediment can generally be described by the sum of two or three tanh ‐functions. The tanh ‐method is a tool for identifying and estimating the number of modes within a grain size distribution and helps interpret the processes involved within the formation of a deposit. The mathematical method can also be used to computerize sediment data, allowing storage with just a few numbers. Different samples can easily be compared and classified. Also, this method could be a valuable tool for calculations of various sediment parameters both in geotechnology and hydrogeology.