Premium
Least squares inversion of self‐potential (SP) data and application to the shallow flow of ground water in sinkholes
Author(s) -
Jardani A.,
Revil A.,
Akoa F.,
Schmutz M.,
Florsch N.,
Dupont J. P.
Publication year - 2006
Publication title -
geophysical research letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.007
H-Index - 273
eISSN - 1944-8007
pISSN - 0094-8276
DOI - 10.1029/2006gl027458
Subject(s) - sinkhole , water table , geology , vadose zone , aquifer , groundwater , piezometer , bedrock , plume , inversion (geology) , ground penetrating radar , permeability (electromagnetism) , soil science , mineralogy , geotechnical engineering , geomorphology , karst , radar , meteorology , paleontology , telecommunications , physics , structural basin , membrane , biology , computer science , genetics
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 m 2 . 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.