Measuring Magnetic Field Gradients From Four Point Vector Measurements in Space

Abstract

The determination of all nine first order spatial gradients requires the knowledge of differences between the magnetic field measurements made simultaneously at (at least) four different points in space. As the first order differences between measurements are typically very small compared to the background field, even small errors resulting from an inadequate knowledge of the orientations, zero levels and scale factors of the magnetometer sensors affect the calculation of field gradients disproportionately and must be corrected with high accuracy. Other sources of error include the noise introduced in the data by propagating waves and pulsations and errors in the knowledge of inter-spacecraft spacing. We will discuss how each of these errors can be minimized by improved data processing techniques and in-flight calibration of the measurements. We first introduce an intra-spacecraft calibration technique suitable for spinning spacecraft which relies on the fact that errors in many of the calibration parameters generate monochromatic signals in the despun data at the first two harmonics of the spin frequency. We develop equations that relate the power in the two harmonics to the calibration parameters. In another procedure called inter-calibration use is made of the fact that ∇·B is zero everywhere and ∇×B is vanishingly small in certain regions of the magnetosphere. Calibration parameters are sought that minimize measured ∇·B and ∇×B in those regions.