Reducing the Backus Effect given some knowledge of the dip‐equator

Abstract

Abstract.Geomagnetic field models computed from intensity measurements on or near the Earth's surface are plagued with strong errors known as the "Backus effect". These errors are related to the mathematical non-uniqueness of the solution which can be theoretically removed by the knowledge of the dip-equator location. Here, we present. a new method for computing models using intensity data and additional information about the location of the dip-equator. We first give a numerical validation of this approach in an ideal case in which the dip-equator can be assumed to be perfectly located. We then show that in practice, updating a good past model of the field with a model of secular variation can constrain the location of the dip-equator sufficiently for our method to be useful. Implications for the planning of future satellite missions are briefly discussed.

Magnetic field modelling from scalar-only data: Resolving the Backus effect with the equatorial electrojet

“…Considerable effort has been devoted to finding a method by which satellite intensity data could be used to produce high-quality field models. It was found that including vector component data from magnetic observatories, especially close to the equator, would significantly reduce the effect of the non-uniqueness (Hurwitz and Knapp, 1974;Barraclough and Nevitt, 1976;Gubbins and Bloxham, 1985;Lowes and Martin, 1987;Ultré-Guérard and Achache, 1997). This observation was explained by Khokhlov et al (1997), who demonstrated that, in principal, the Backus effect could be eliminated with knowledge of the position of the geomagnetic dip equator, the points on the Earth's surface at which the vertical component of the field is zero.…”

“…This observation was explained by Khokhlov et al (1997), who demonstrated that, in principal, the Backus effect could be eliminated with knowledge of the position of the geomagnetic dip equator, the points on the Earth's surface at which the vertical component of the field is zero. Ultré-Guérard et al (1998) developed this result into a field modelling strategy. They suggested that beginning from an epoch when the field is constrained by vector data, a model of secular variation could be used to estimate the change in position of the dip equator through time.…”

What ancient scalar satellite data can tell us about the 1969 geomagnetic jerk?

“…Recall that in addition, the resulting solution is contaminated by the error caused by the Backus effect (Backus, 1970(Backus, , 1974. To reduce this effect, we have constrained the solution by imposing the geomagnetic equator position, estimated from different periods of modeling (Ultré- Guérard et al, 1998;Holme et al, 2005). Furthermore, considering that our aim is to describe the secular variation from these core field models, they are computed to a maximum degree and order 10.…”

The spinning Astrid-2 satellite used for modeling the Earth's main magnetic field

“…This means that the Backus effect has been heavily reduced by constraining the model only slightly, and the direction is resolved satisfactorily around the dip Equator. The discussion in [20], that "the error in the resulting model is simply constrained at the equator by our ability to update the location of this equator, and elsewhere by the quality of the scalar intensity data," applies equally well for the Astrid-2 scalar model.…”