Least squares inversion of self-potential (SP) data and application to the shallow flow of ground water in sinkholes

Details Least squares inversion of self-potential (SP) data and application to the shallow flow of ground water in sinkholes Least squares inversion of self-potential (SP) data and application to the shallow flow of ground water in sinkholes

Oct 2006

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006georl..3319306j&link_type=abstract

Geophysical Research Letters, Volume 33, Issue 19, CiteID L19306

Statistics

Computation

9

Exploration Geophysics: Computational Methods: Potential Fields (1214), Exploration Geophysics: Data Processing, Exploration Geophysics: Magnetic And Electrical Methods (5109), Hydrology: Groundwater Transport, Physical Properties Of Rocks: Magnetic And Electrical Properties (0925)

Scientific paper

We propose a least squares inversion algorithm to determine the spatially variable depth of the water table in shallow unconfined aquifers using self-potential signals measured on the ground surface. Traditionally, the water table is determined only at few locations using piezometers. Our approach relates its shape with the distribution of the self-potential signals according to a Fredholm equation of the first kind. The latter is discretized to obtain a linear matrix formulation of the forward problem. This new formulation is very general and can account for the resistivity distribution of the vadose zone. It is used to setup the inverse problem using the approach of Tarantola (1987) for a test site located in Normandy (France) where 225 self-potential measurements were performed over an area of 15,400 m2. Ground water flows through the loess overlying a low permeability clay-with-flint weathered chalk, at a depth between 1 to 7 meters, into sinkholes in chalk bedrock. The method determines the water table with a precision of 0.4 m.

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