A new mathematical technique for identifying potential sources of groundwater contamination

The observed hydrogeochemical condition of groundwater at a particular well is usually represented as a mixture of various sources of pollution and background conditions and is given in terms of measurements of multiple dissolved inorganic water contaminants such as total dissolved solids (TDS). Concentrations from a given set of wells can be compared against one another in a variety of ways, but the consideration as to which chemical concentrations are best related to one another is limited. In this analysis, an example is given to show that if there are a total of N concentration values, all N must be considered simultaneously in order to ascertain whether the observed conditions at the well can be explained as a mixture, and this can be done by solving a quadratic programming problem-convex hull.