Three-dimensional numerical modelling and inversion of magnetometric resistivity data

Abstract

Summary We develop an algorithm to model the magnetometric resistivity (MMR) response over an arbitrary 3‐D conductivity structure and a method for inverting surface MMR data to recover a 3‐D distribution of conductivity contrast. In the forward modelling algorithm, the second‐order partial differential equations for the scalar and vector potentials are discretized on a staggered‐grid using the finite‐volume technique. The resulting matrix equations are consequently solved using the bi‐conjugate gradient stabilizing (BiCGSTAB), combined with symmetric successive over relaxation (SSOR) pre‐conditioning. In the inversion method, we discretize the 3‐D model into a large number of rectangular cells of constant conductivity, and the final solution is obtained by minimizing a global objective function composed of the model objective function and data misfit. Since 1‐D conductivity variations are an annihilator for surface MMR data, the model objective function is formulated in terms of relative conductivity with respect to a reference model. A depth weighting that counteracts the natural decay of the kernels is shown to be essential in typical problems. All minimizations are carried out with the Gauss–Newton algorithm and model perturbations at each iteration are obtained by a conjugate gradient least‐squares method (CGLS), in which only the sensitivity matrix and its transpose multiplying a vector are required. For surface MMR data, there are two forms of fundamental ambiguities for recovery of the conductivity. First, magnetic field data can determine electrical conductivity only to within a multiplicative constant. Thus for a body buried in a uniform host medium, we can find only the relative conductivity contrast, not the absolute values. The choice of a constant reference model has no effect on the reconstruction of the relative conductivity. The second ambiguity arises from the fact that surface MMR cannot distinguish between a homogeneous half‐space and a 1‐D conductive medium. For a 3‐D body in a 1‐D layered medium, it is still difficult to obtain information concerning the general background 1‐D medium, if sources and receivers are at the surface. Overall, the surface MMR technique is useful so long as significant current flows through the body. This happens when the overburden is thin and moderately conductive (less than 10 times the conductivity of the underlying basement) and if the current sources are placed so there is good coupling with the body. Our inversion method is applied to synthetic examples and to a field data set. The low‐resolution image obtained from using traditional MMR data, involving one source and one magnetic component, illustrates the need for acquiring data from multiple sources if 3‐D structure of complex geometries are sought.

Two-Dimensional Magnetotelluric Modelling of Ore Deposits: Improvements in Model Constraints by Inclusion of Borehole Measurements

“…However, rather than measuring differences in electric potential between two electrodes, as in the ERT method, the components of the magnetic flux vector are measured leading to insensitivity to layered structures for MMR measurements made on the Earth's surface. Owing to the usage of galvanically coupled sources and magnetic field receivers, MMR measurements are sensitive to conductivity contrasts but not to absolute conductivity (Bishop et al 1997;Asten 2001;Chen et al 2002;Godber and Bishop 2007). In comparison, BHEM measurements are predominantly sensitive to conductive structures.…”

“…The cross-hole magnetometric resistivity (source and receivers in distinct boreholes; Nabighian et al 1984) and down-hole magnetometric resistivity (DHMMR; source on surface extended along strike and borehole receivers; Asten 1988) methods have been used with success in mineral exploration and led to discoveries of ore deposits that did not generate anomalous BHEM signals (e.g., Bishop et al 1997Bishop et al , 2000. Field evidence (Asten 1988;Bishop et al 1997) and numerical simulations (Chen et al 2002) suggest that the sensitivity of DHMMR and surface MMR data, respectively, is limited to lateral distances / 500 m off the borehole or receiver site, whereas BHEM methods may be sensitive to a comparable or smaller region around the borehole. Further, spatial resolution reported for DHMMR is poorer than that of BHEM (Asten 1988;Bishop et al 1997).…”

“…It turned out that fitting the Z 0 zx data of the deepest station immediately beneath the shallow ore body did not succeed (RMS = 2.76 for the Z 0 zx data of that station), which may be one reason for not improving the model at depth below the borehole. The limited sensitivity of the vertical electric transfer function data (Z 0 zx ) for structures at more than $ 400 m laterally off the borehole is reminiscent of the limited sensitivity of DHMMR and surface MMR data to structures at similar distance (e.g., Asten 1988;Bishop et al 1997;Chen et al 2002).…”

Marine Controlled Source Electromagnetics: Principles, Methodologies, Future Commercial Applications

“…The MOSES method has been used by my group in Cascadia (Nobes et al, 1986), the Beaufort Sea , by colleagues in Japan and at Woods Hole, USA (Evans et al, 1998). It has become a popular exploration method for detecting resistive and conductive zones in the sea floor and attracted the attention of 3D numerical modelers (Chen et al, 2002). The code developed is an example of the modification of pre-existing software for marine studies.…”

Time-dependent magnetometric resistivity anomalies of groundwater contamination: Synthetic results from computational hydro-geophysical modeling

“…We concentrate in particular on the magnetometric resistivity (MMR) method, as a follow-up study of our previous investigation on the D.C. resistivity method (Radulescu, et al, 2007), which involves the measurement of the low-level magnetic fi elds associated with non-inductive current flow in the ground and has greater sensitivity to conductive targets under a moderately conductive overburden compared with traditional geo-electrical techniques and other EM methods (Edwards et al, 1978;Chen et al, 2002). Since its invention by Edwards in early 1970s, the MMR method has been widely employed in various geological and geophysical applications (Edwards, 1974;Wolfgram et al, 1986;Nobes et al, 1992;Méndez-Delgado et al, 1999;Elders and Asten, 2004;Yang, 2005) as well as in imaging near-surface conductors associated with subsurface solute fl ow (Kulessa et al, 2002;LaBrecque et al, 2004).…”