Imaging quasi‐layered conductive structures by simple processing of transient electromagnetic data

Geophysics ◽  
1987 ◽  
Vol 52 (4) ◽  
pp. 545-554 ◽  
Author(s):  
James Macnae ◽  
Yves Lamontagne

An “imaged” conductivity section of a layered earth can be obtained by simple transformation of step‐response electromagnetic data measured in the quasi‐static zone. This method of data transformation is presented as an alternative to conventional apparent conductivity transformations. At each delay time, the variation of the step response as a function of geometry (transmitter and receiver location) is transformed to an equivalent reference depth h, which can be related to the depth of electromagnetic field diffusion. The behavior of h as a function of delay time is nearly independent of the source‐receiver geometry. The slowness dt/dh divided by the magnetic permeability is almost exactly proportional to the cumulative conductance measured from the surface down to a depth h. Thus we can estimate an apparent conductivity, which we call the “imaged conductivity,” at depth to be [Formula: see text]. The cost of this transformation is a fraction of the cost of conventional data inversion, and it does not require an a priori constraint on the number of parameters used in the inversion. The empirically developed technique was used successfully to process UTEM field data measured over a quasi‐layered earth.

2006 ◽  
Vol 37 (4) ◽  
pp. 348-354 ◽  
Author(s):  
R. Schaa ◽  
J.E. Reid ◽  
P.K. Fullagar

Geophysics ◽  
2002 ◽  
Vol 67 (2) ◽  
pp. 438-447 ◽  
Author(s):  
Niels Bøie Christensen

This paper presents a fast approximate 1-D inversion algorithm for transient electromagnetic (EM) data that can be applied for all measuring configurationsand transmitter waveforms and for all field components. The inversion is based on an approximate forward mapping in the adaptive Born approximation. The generality is obtained through a separation of the forward problem into a configuration-independent part, mapping layer conductivities into apparent conductivity, and a configuration-dependent part, the half-space step response. The EM response from any waveform can then be found by a convolution with the time derivative of the waveform. The approach does not involve inherently unstable deconvolution computations or nonunique transformations, and it is about 100 times faster than ordinary nonlinear inversion. Nonlinear model responses of the models obtained through the approximate inversion fit the data typically within 5%.


Geophysics ◽  
2008 ◽  
Vol 73 (4) ◽  
pp. F165-F177 ◽  
Author(s):  
A. Abubakar ◽  
T. M. Habashy ◽  
V. L. Druskin ◽  
L. Knizhnerman ◽  
D. Alumbaugh

We present 2.5D fast and rigorous forward and inversion algorithms for deep electromagnetic (EM) applications that include crosswell and controlled-source EM measurements. The forward algorithm is based on a finite-difference approach in which a multifrontal LU decomposition algorithm simulates multisource experiments at nearly the cost of simulating one single-source experiment for each frequency of operation. When the size of the linear system of equations is large, the use of this noniterative solver is impractical. Hence, we use the optimal grid technique to limit the number of unknowns in the forward problem. The inversion algorithm employs a regularized Gauss-Newton minimization approach with a multiplicative cost function. By using this multiplicative cost function, we do not need a priori data to determine the so-called regularization parameter in the optimization process, making the algorithm fully automated. The algorithm is equipped with two regularization cost functions that allow us to reconstruct either a smooth or a sharp conductivity image. To increase the robustness of the algorithm, we also constrain the minimization and use a line-search approach to guarantee the reduction of the cost function after each iteration. To demonstrate the pros and cons of the algorithm, we present synthetic and field data inversion results for crosswell and controlled-source EM measurements.


Geophysics ◽  
2003 ◽  
Vol 68 (4) ◽  
pp. 1211-1223 ◽  
Author(s):  
Haoping Huang ◽  
Douglas C. Fraser

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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