Study of surface nuclear magnetic resonance inverse problems

Abstract

Motivated by the recent application of the Earth-field nuclear magnetic resonance (NMR) technique to the detection and mapping of subsurface groundwater (to depths of 100 m or so), and making use of a recently developed theory of the method, we consider in detail the resulting inverse problem, namely the inference of the subsurface water distribution from a given sequence of NMR voltage measurements. We consider the simplest case of horizontally stratified water distributions in a horizontally stratified conducting Earth. Inversion methods based both on the singular value decomposition (SVD) and Monte Carlo are used and compared. The effects of random measurement errors and of systematic errors in the assumed subsurface conductivity structure are studied. It is found that an incorrectly modeled highly conducting layer leads to a “screening effect” in which the water content of layers lying below it is severely underestimated. We investigate also the ability of different source-receiver loop geometries to provide complementary information that may improve a combined inversion. Finally, inversion of experimental data from Cherry Creek, CO, USA is performed. Since only the absolute magnitude of the NMR voltage is measured accurately, a nonlinear Monte Carlo inversion is performed.