Interactive inversion of dipole loop-loop electromagnetic data for layered earth models using numerical integration and complex image theory

Electromagnetic (EM) soundings in an intermediate range between quasi‐static and radar frequencies (e.g., 30 kHz – 300 MHz) were studied with an approximate inversion method for shallow‐layered earth models using complex image theory. The half‐space image theory formulas for calculating forward soundings for any dipole source are easily extended to accommodate a multilayered earth, and only involve elementary complex functions. Approximate inversion using the modified image formulas is compared with more exact numerical integration inversion for horizontal‐layered models to yield the conductivity, thickness, and dielectric permittivity of each layer. A nonlinear least‐squares algorithm was used to obtain parameter and linear parameter error estimates. The results, using known exact forward models and one field data case, indicate that approximate image inversion is more than an order‐of‐magnitude faster than numerical integration inversion. However, approximate inversion could not always resolve deeper layer parameters as well as with exact inversion. Accuracy of both methods, however, depends on the frequency range used. Nevertheless, approximate inversion can be a useful quick reconnaissance tool, and could easily be written for on‐site personal computers.

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Inversion of helicopter electromagnetic data to a magnetic conductive layered earth

Geophysics ◽

10.1190/1.1598113 ◽

2003 ◽

Vol 68 (4) ◽

pp. 1211-1223 ◽

Cited By ~ 50

Author(s):

Haoping Huang ◽

Douglas C. Fraser

Keyword(s):

Magnetic Permeability ◽

Field Data ◽

Model Parameters ◽

Relative Importance ◽

Magnetic Polarization ◽

Inversion Algorithm ◽

Layered Earth ◽

Electromagnetic Data ◽

Airborne Electromagnetic ◽

True Values

Inversion of airborne electromagnetic (EM) data for a layered earth has been commonly performed under the assumption that the magnetic permeability of the layers is the same as that of free space. The resistivity inverted from helicopter EM data in this way is not reliable in highly magnetic areas because magnetic polarization currents occur in addition to conduction currents, causing the inverted resistivity to be erroneously high. A new algorithm for inverting for the resistivity, magnetic permeability, and thickness of a layered model has been developed for a magnetic conductive layered earth. It is based on traditional inversion methodologies for solving nonlinear inverse problems and minimizes an objective function subject to fitting the data in a least‐squares sense. Studies using synthetic helicopter EM data indicate that the inversion technique is reasonably dependable and provides fast convergence. When six synthetic in‐phase and quadrature data from three frequencies are used, the model parameters for two‐ and three‐layer models are estimated to within a few percent of their true values after several iterations. The analysis of partial derivatives with respect to the model parameters contributes to a better understanding of the relative importance of the model parameters and the reliability of their determination. The inversion algorithm is tested on field data obtained with a Dighem helicopter EM system at Mt. Milligan, British Columbia, Canada. The output magnetic susceptibility‐depth section compares favorably with that of Zhang and Oldenburg who inverted for the susceptibility on the assumption that the resistivity distribution was known.

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