Methods of computation for estimating geochemical abundance

Abstract

Geochemical abundance of an element i•s regarded as the proportion of a total rock body, or group of rock 1 bodies, that is made up of the element and is equivalent to the population arithmetic mean of sample analyses, generally in units of percentage or parts per million. Computational problems encountered in estimation of abundances can arise from having limited ranges of analytical sensitivity, from having only small groups of data, and from reporting of data in broad geometric classes. 'l'hese problems can be partly .resolved by use of a combination of techniques described by Sichel (1952), Cohen (1959, 1961), and Krige (1960). The combination of techniques allows efficient estimation of geochemical a•bundances from a wide variety of frequency distributi'On types if the analytical discrimination is sufficient to allow effective use of data transformations. Examples of data •from the literature were used to demonstrate the techniques; up to 76 percent of the da•ta values were nrbitrarlly placed in the "not detected" class, and estimated arithmetic means agreed with those estimated from the complete data set to two significant figures. The types of frequency distributions displayed by the data •examples are generally representative of those commonly encountered in geochemical problems.

Distribution of selected elements in surficial marine sediments of the northern Gulf of Mexico continental shelf and slope

“…The arithmetic means of the analytical data were computed from the estimated geometric means and deviations by using the method described by Miesch (1967), which is based on the techniques presented by Cohen (1959) and Sichel (1952). The arithmetic means listed in table 3 are estimates of geochemical abundance (Miesch, 1967) and are directly comparable to the arithmetic means (geochemical averages) reported in the literature (Shacklette and others, 1971).…”

Airborne chemical elements in Spanish moss

“…7), whereas the limit of detection for arsenic is 1 ppm (table 2). Further discussions of the treatment of censored frequency distributions of geochemical data and of the use of geometric means and geometric deviations were given by Miesch (1967) and Shacklette, Sauer, and Miesch (1970).…”

Water quality of streams and springs, Green River Basin, Wyoming

“…Seven-tenths of the lower limit of detection was used by Miesch (1976). Methods given by Cohen (1959) and summarized by Miesch (1967) allow statistical analysis of censored-data distributions composed of greater than 20-percent qualified values. Jennings and Benson (1969) used a theorem of conditional probability to estimate probability of occurrence of annual floods from censored data.…”