Electromagnetic sounding in the resistive limit and the Backus-Gilbert method for estimating averages

doi:10.1016/0016-7142(87)90013-5

Geoexploration

Volume 24, Issue 6, December 1987, Pages 441-454

https://doi.org/10.1016/0016-7142(87)90013-5 Get rights and content

Abstract

The interpretation of electromagnetic soundings in the resistive limit can be formulated in terms of a linear integral equation. This equation is derived as a particular limit case from a nonlinear integral formulation for electromagnetic inverse problems. The source of the fields is a vertical magnetic dipole, and it is assumed that measurements of the vertical magnetic field are available on the surface of the earth.

An exact inverse operator for the integral equation is obtained as the inverse Laplace transform of the Hankel transform of the response. When the response is exactly known over the infinite range of transmitter-receiver separations, it is possible to make a perfect recovery of the vertical conductivity profile. This can not be done, however, if only a sampled version of the response is available. In this case only spatial averages of the conductivity profile can be recovered from the data. Estimating these averages when the data are random variables can only be done in a statistical sense. This classical three-stage process of increasing ambiguity can be clearly illustrated using the integral equation approach. The use of global spatial averages is briefly considered as an alternative for estimating conductance down to different depths.

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Electromagnetic sounding in the resistive limit and the Backus-Gilbert method for estimating averages

Abstract

Numerical applications of a formalism for geophysical inverse problems

Geophys. J.R. Astron. Soc.

The resolving power of gross earth data

Geophys. J.R. Astron. Soc.

Uniqueness in the inversion of inaccurate gross earth data

Phil. Trans. R. Soc. Lond., Ser. A

Inversion of the geomagnetic induction problem

Introduction to induction logging and application to logging of wells drilled with oil base mud

J. Pet. Technol.

The gravitational edge effect

J. Geophys. Res.

A uniqueness theorem for horizontal loop electromagnetic frequency soundings

Geophys. J.R. Astron. Soc.

Inversion of horizontal loop electromagnetic frequency soundings

Geophysics

Nonlinear integral equations for electromagnetic inverse problems

Geophysics