APPLICATION OF LINEAR PROGRAMMING TECHNIQUES TO THE INVERSION OF PROTON MAGNETIC RESONANCE MEASUREMENTS FOR WATER PROSPECTING FROM THE SURFACE

Abstract

In addition to direct detection of groundwater from the surface, the Proton Magnetic Resonance (PMR) method can provide important information concerning aquifers, such as their number, depth, thickness and water content. This requires the solution of an inverse problem that like many other geophysical inverse problems is ill posed and often leads to nonuniqueness of the solution.In this paper, we present the results of applying various techniques originally developed for gravity and magnetic inversion, such as linear programming, ‘ideal body’ and ‘compact body’, in order to select just one solution out of the solution space. These methods assume minimization of specific functionals that was obtained by using a linear programming technique and comparing with those obtained by the Tikhonov regularization method. Although mathematically equivalent in terms of fit between measured and synthetic data, the selected solutions may differ in their physical significance. Analysis of the obtained solutions provides additional information for the interpretation of field measurements.A few examples of both synthetic and field data inversion are presented to demonstrate that these techniques enable the groundwater distribution to be characterized through the following parameters: top and bottom depths of the acquifer formation, minimum and maximum concentration of water, water quantity, total water thickness, etc.