Open AccessElectrical Potential Distributions in a Heterogeneous Subsurface in Response to Applied Current: Solution for Circular Inclusions
Author(s) -
Furman Alex,
Warrick A. W.,
Ferré Ty P. A.
Publication year - 2002
Publication title -
vadose zone journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.036
H-Index - 81
ISSN - 1539-1663
DOI - 10.2136/vzj2002.2730
Subject(s) - current (fluid) , laplace transform , laplace's equation , electrical resistivity tomography , electrical resistivity and conductivity , basis function , electrical resistance and conductance , boundary value problem , function (biology) , sensitivity (control systems) , electrical impedance tomography , mathematical analysis , mechanics , mathematics , materials science , physics , tomography , engineering , electronic engineering , thermodynamics , optics , electrical engineering , evolutionary biology , biology , composite material
An analytic solution to the Laplace equation for potential distribution in response to current flow in a heterogeneous, two‐dimensional semi‐infinite domain is studied. Circular heterogeneities of varying sizes and electrical conductivities are considered. We investigate the response of the stream function, the potential field, and, in particular, the potential at the top boundary relative to the background as a function of the size, location, and electrical conductivity of circular inclusions taken singly or multiply. The analytic solution sets the basis for the application of sensitivity analysis to the electrical resistance tomography (ERT) method, as an initial step toward improving the application of the method to tracking rapid hydrological processes.