J. Torquil Smith

Rapid inversion of two‐ and three‐dimensional magnetotelluric data

We have developed an efficient iterative inversion method applicable to both two-dimensional (2D) and three-dimensional magnetotelluric data. The method approximates horizontal derivative terms with their values calculated from the fields of the previous iteration. The equations at each horizontal coordinate then become uncoupled. At each iteration this allows separate inversions for the improved conductivity profile beneath each measurement site. Resultant profiles are interpolated to form a new multidimensional model for which the fields for the next iteration are calculated. The method is extremely fast, and tests with 2D data show very promising results.

Conservative modeling of 3-D electromagnetic fields, Part II: Biconjugate gradient solution and an accelerator

The preceding paper derives a staggered-grid, finite-difference approximation applicable to electromagnetic induction in the Earth. The staggered-grid, finite-difference approximation results in a linear system of equations Ax = b, where A is symmetric but not Hermitian. This is solved using the biconjugate gradient method, preconditioned with a modified, partial Cholesky decomposition of A. This method takes advantage of the sparsity of A, and converges much more quickly than methods used previously to solve the 3-D induction problem. When simulating a conductivity model at a number of frequencies, the rate of convergence slows as frequency approaches 0. The convergence rate at low frequencies can be improved by an order of magnitude, by alternating the incomplete Cholesky preconditioned biconjugate gradient method with a procedure designed to make the approximate solutions conserve current.

Magnetotelluric inversion for minimum structure

Structure can be measured in terms of a norm of the derivative of a model with respect to a function of depth f(z), where the model m(z) is either the conductivity σ or log σ. An iterative linearized algorithm can find models that minimize norms of this form for chosen levels of chi‐squared misfit. The models found may very well be global minima of these norms, since they are not observed to depend on the starting model. Overfitting data causes extraneous structure. Some choices of the depth function result in systematic overfitting of high frequencies, a “blue” fit, and extraneous shallow structure. Others result in systematic overfitting of low frequencies, a “red” fit, and extraneous deep structure. A robust statistic is used to test for whiteness; the fit can be made acceptably white by varying the depth function f(z) which defines the norm. An optimum norm produces an inversion which does not introduce false structure and which approaches the true structure in a reasonable way as data errors decrease...

Conservative modeling of 3-D electromagnetic fields, Part I: Properties and error analysis

Conservation of electric current and magnetic flux can be explicitly enforced by modeling Maxwell’s equations on a staggered grid, where the different field components are sampled at points offset relative to each other. A staggered finite‐difference (SFD) approximation gives divergence‐free magnetic fields and electric currents ensuring good behavior at all periods. Comparisons of SFD solutions with 2-D quasi‐analytic solutions are very good (∼1% rms error). When a modeled region can be subdivided into uniform subdomains, comparison of analytic solutions and SFD approximations show that the greatest differences occur near the Nyquist wavenumbers; the SFD solutions do not attenuate in space as rapidly as the analytic solutions. The accuracy of a computed SFD solution can be estimated from its wavenumber content. For test cases the accuracy estimates are surprisingly close to the actual accuracies. Grid requirements for modeling short horizontal wavelength components of a solution seem more demanding than ...

Approximating spheroid inductive responses using spheres

The response of high permeability ({mu}{sub r} {ge} 50) conductive spheroids of moderate aspect ratios (0.25 to 4) to excitation by uniform magnetic fields in the axial or transverse directions is approximated by the response of spheres of appropriate diameters, of the same conductivity and permeability, with magnitude rescaled based on the differing volumes, D.C. magnetizations, and high frequency limit responses of the spheres and modeled spheroids.

A Multisensor System for the Detection and Characterization of UXO

A prototype active electromagnetic system has been developed for detecting and characterizing UXO. The system employs two orthogonal vertical loop transmitters and a pair of horizontal loop transmitters spaced apart vertically by 0.7 m. Eight vertical field detectors are deployed in the plane of each of the horizontal loops and are arranged to measure offset vertical gradients of the fields. The location and orientation of the three principal polarizabilities of a target can be recovered from a single position of the transmitter-receiver system. Further characterization of the target is obtained from the broadband response. The system employs a bipolar half sine pulse train current waveform and the detectors are dB/dt induction coils designed to minimize the transient response of the primary field pulse. The target transient is recovered in a 40 mu sec to 1.0 msec window. The ground response imposes an early time limit on the time window and system/ambient noise limits the late time response. Nevertheless for practical transmitter moments and optimum receivers the size and the ratio of conductivity to permeability can be accurately recovered. The prototype system has successfully recovered the depths and polarizabilities of ellipsoidal test targets.