When Zero Doesnt Mean it and Other Geomathematical Mischief.
There is almost not a case in exploration geology, where the studied data doesnt includes below detection limits and/or zero values, and since most of the geological data responds to lognormal distributions, these zero data represent a mathematical challenge for the interpretation.We need to start by recognizing that there are zero values in geology. For example the amount of quartz in a syenite is zero, since quartz cannot co-exists with nepheline. Another common essential zero is a North azimuth, however we can always change that zero for the value of 360°. These are known as Essential zeros, but what can we do with Rounded zeros that are the result of below the detection limit of the equipment?Amalgamation, e.g. adding Na2O and K2O, as total alkalis is a solution, but sometimes we need to differentiate between a sodic and a potassic alteration. Pre-classification into groups requires a good knowledge of the distribution of the data and the geochemical characteristics of the groups which is not always available. Considering the zero values equal to the limit of detection of the used equipment will generate spurious distributions, especially in ternary diagrams. Same situation will occur if we replace die zero values by a small amount using non-parametric or parametric techniques (imputation).The method that we are proposing takes into consideration the well known relationships between some elements. For example, in copper porphide deposits, there is always a good direct correlation between the copper values and the molybdenum ones, but while copper will always be above the limit of detection, many of the molybdenum values will be rounded zeros. So, we will take the lower quartile of the real molybdenum values and establish a regression equation with copper, and then we will estimate the rounded zero values of molybdenum by their corresponding copper values.The method could be applied to any type of data, provided we establish first their correlation dependency.One of the main advantages of this method is that we do not obtain a fixed value for the rounded zeros, but one that depends on the value of the other variable.
R.A. Valls Alvarez
Valls Geoconsultant, 1008-299 Glenlake Ave, Toronto, Ontario, M6P4A6, Canada
国际会议
The 12th Conference of the International Association for Mathematical Geology(第12届国际数学地质大会)
北京
英文
689-692
2007-08-26（万方平台首次上网日期，不代表论文的发表时间）