It is common knowledge to applied geophysicists that, for determining spatially variable electromagnetic properties of the ground, the magnetic method is sensitive to magnetic permeability μ, the ground-penetrating radar method responds to dielectric permittivity e, and the dc resistivity method provides a good indication of ρ, the electrical resistivity. It is also commonly acknowledged that the electromagnetic induction (EMI) technique responds to electrical conductivity σ. The choice of which variable to report, ρ or its reciprocal σ, is largely a matter of convention decided upon by vocal adherents of the respective methods.
Electric and magnetic potentials in the Coulomb gauge provide a convenient formulation for finite-element modeling of electromagnetic (EM) induction in heterogeneous conductivity structure. The formulation uses standard linear finite elements defined on tetrahedra. The finite-element equations are solved by a sparse, ILU decomposition that ignores fill-in to achieve maximum storage efficiency. The formulation can handle models of interest to oil and gas exploration, mining, and environmental studies. It is applied here in spherical geometry to model EM induction in the upper mantle due to a magnetospheric ring current.
Visualisations of the flow of electromagnetic energy based on the time-averaged Poynting vector have yielded important and sometimes counter-intuitive physical insights in the case of electric circuits containing resistors and inductors. Less well-understood is the flow of electromagnetic energy in spatially contiguous media excited by grounded sources. In geophysics, for example, it is important for readers to recognise how geological structures help shape controlled-source electromagnetic responses. It is demonstrated herein using energy flow visualisations how a resistive layer impeding vertical electric current flow will produce a larger anomalous response to grounded-source excitation at the Earth's surface than an equivalent conductive layer.
A new 3D controlled-source electromagnetic finite element (FE) modeling algorithm is presented which is capable of handling local inhomogeneities in the magnetic permeability and electrical conductivity distribution of buried geologic and anthropogenic structures. An ungauged, coupled-potential formulation of the governing electromagnetic vector diffusion and scalar continuity equations is used. The formulation introduces magnetic reluctivity, the inverse of magnetic permeability, to facilitate a separation of secondary and primary potentials. The governing equations are solved using a tetrahedral edge-based FE method. The postprocessing steps to obtain electromagnetic fields are outlined. The code is validated for non-magnetic and permeable conductive structures by comparisons against analytic and previously published numerical solutions. Some limitations of the implementation are explored and directions are proposed for its further development.
Pointe du Hoc overlooking the English Channel in Normandy, France was host to one of the most important military engagements of World War II but is vulnerable to cliff collapses that threaten important German fortifications including the forward observation post (OP) and Rudder's command post. The objective of this study is to apply advanced 3-D resistivity tomography towards a detailed site stability assessment with special attention to the two at-risk buildings. 3-D resistivity tomography data sets at Pointe du Hoc in the presence of extreme topography and dense cultural clutter have been successfully acquired, inverted and interpreted. A cliff stability hazard assessment scheme has been designed in which regions of high resistivity are interpreted as zones of open, dry fractures with a moderate mass movement potential. Regions of low resistivity are zones of wet, clay-filled fractures with a high mass movement potential. The OP tomography results indicate that the highest mass movement hazard appears to be associated with the marine caverns at the base of the cliff that are positioned at the point of strongest wave attack. These caverns likely occupy the future site of development of a sea arch that will threaten the OP building. The mass movement potential at the Rudder's command post area is low to moderate. The greatest risk there is associated with soil wedge failures at the top of the cliffs.
