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Alternative theory for signal contribution sections and depth of investigation characteristics in electrical prospecting
Author(s) -
GómezTreviño Enrique,
Flores Carlos
Publication year - 2015
Publication title -
geophysical prospecting
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.735
H-Index - 79
eISSN - 1365-2478
pISSN - 0016-8025
DOI - 10.1111/1365-2478.12214
Subject(s) - sensitivity (control systems) , signal (programming language) , prospecting , point (geometry) , inverse , field (mathematics) , boundary (topology) , mathematics , theoretical physics , mathematical analysis , calculus (dental) , physics , pure mathematics , computer science , geometry , geology , engineering , medicine , mining engineering , dentistry , electronic engineering , programming language
We present an alternative to Roy's theorem for direct current regimes with the aim of validating the theoretical basis of signal contribution sections in electrical prospecting. Roy's theorem establishes that the electrical potential at a point can be expressed as an integral over all space of the electric field weighted by the gradient of inverse distance. The integrand is interpreted to represent elementary contributions to the potential that can be analyzed to compare different electrode arrays. Signal contribution sections and depth of investigation characteristics can be beautifully illustrated with important practical applications. However, the electric potential, being the solution of a boundary value problem, cannot be uniquely decomposed into elementary contributions. There is no guarantee for the integrand of a given integral to be meaningful in all situations. In the case of Roy's theorem, the concept has been severely criticized by respected scholars who challenged the scientific legitimacy of his approach. If we are going to keep the concept of elementary contributions alive, we need to go beyond Roy's theorem. In this paper, we develop an alternative theorem and show that it merges with the concept of sensitivity, which is unique and mathematically sound, and is also open to physical validation. This prevents any possible contradictions in the future and, equally important, eliminates the dichotomy between sensitivity and elementary contributions.