A downhole magnetometric resistivity technique for electrical sounding beneath a conductive surface layer

Abstract

The magnetometric resistivity (MMR) method has not been used systematically for vertical electrical sounding because surficial measurements of the magnetic field caused by static current flow from a point source of current at the surface are independent of the form of the variation of earth resistivity with depth. However, data obtained from an adaptation of the MMR method in which the ratio of the magnetic fields below and above a known conductive surface layer is measured as a function of the horizontal range from the current source can be inverted to obtain the unknown resistivity of deeper material. The practical limitation is that the integrated conductivity of the surface layer must not be much smaller than the integrated conductivity of the unknown zone in order to observe diagnostic ratios significantly different from unity. The expressions derived for the magnetic‐field ratio and for the sensitivity of the ratio to changes in the resistivity of a plane‐layered unknown zone are closed‐form inverse Hankel transforms. The transforms are evaluated analytically for a model of constant, uniform resistivity. One possible geotechnical application of the method is the detection of offshore, resistive permafrost beneath the shallow Beaufort Sea. A theoretical design study in which ratios of the magnetic fields at the bottom and top of the sea are synthesized and the sensitivity of those ratios to changes in sea‐floor resistivity is determined as a function of range and depth, respectively, reveals that the resistivity of a permafrost zone 50 m thick buried 20 m below the sea floor can be identified. The maximum range needed is of the order of 200 m, which appears to be smaller than the maximum spacing required for a Schlumberger sounding to yield similar information.