Correction of electric and magnetic fields and gradients measured within and around an insulating sensor capsule in seawater

Abstract

The presence of a highly conductive medium around a measurement capsule influences electromagnetic measurements made in the ocean and fundamentally alters the structure of the magnetic gradient tensor. Additional effects arise if seawater is flowing past the sensor package. This paper presents a quantitative analysis of these effects and describes the corrections that need to be applied to obtain accurate absolute measurements of electromagnetic fields and gradients in the ocean. For example, for a small spherical cavity within a 1D horizontal quasistatic electric current distribution, the electric field within the cavity is parallel to the unperturbed applied field and larger by 50%, and the magnetic field at the centre of the cavity is equal to the unperturbed magnetic field that existed at the same point in the conductive medium, prior to insertion of the measurement capsule. The symmetric magnetic gradient tensor within the cavity is uniform. If the unperturbed electric current is parallel to the x axis, the only non-zero components of the magnetic gradient tensor within the cavity are B <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">yz</sub> = B <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">zy</sub> . These components are each equal to half the value of ∂B <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">y</sub> /∂z that is produced by the unperturbed current flow in the conductive medium. The external perturbation of the electric field around the cavity has the configuration of a dipole field and the external magnetic field due to the cavity is that of an elementary current dipole. An ellipsoidal cavity has an anisotropic response, except in the degenerate case where all axes are equal and the cavity is spherical. Unless the applied field lies along a principal axis of the ellipsoid, the internal field is not parallel to the applied field, but is deflected away from the major axis and towards the minor axis. An applied electric field is amplified within the cavity. For a disk-like cavity the amplification of the applied electric field normal to the disk can be very large within the cavity. The anomalous magnetic field within the ellipsoidal cavity due to electric current flow around the cavity is nonuniform, but has a uniform gradient. At the center of the ellipsoidal cavity the magnetic field is equal to the field that existed at that point before insertion of the cavity. The resultant internal magnetic gradient tensor is symmetric and traceless, as required. Seawater motion past a sensor package produces easily detectable effects that can represent an important source of electromagnetic noise. In the vicinity of a measurement capsule, water velocities of the order of 1 ms <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> produce perturbations of ~45 μVm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> in electric field, ~75 pT in magnetic field, and produce magnetic gradients of ~150 pT/m.