Abstract
Abstract. We investigated how the noise in satellite magnetic data affects magnetic lithospheric field models derived from these data in the special case where this noise is correlated along satellite orbit tracks. For this we describe the satellite data noise as a perturbation magnetic field scaled independently for each orbit, where the scaling factor is a random variable, normally distributed with zero mean. Under this assumption, we have been able to derive a model for errors in lithospheric models generated by the correlated satellite data noise. Unless the perturbation field is known, estimating the noise in the lithospheric field model is a non-linear inverse problem. We therefore proposed an iterative post-processing technique to estimate both the lithospheric field model and its associated noise model. The technique has been successfully applied to derive a lithospheric field model from CHAMP satellite data up to spherical harmonic degree 120. The model is in agreement with other existing models. The technique can, in principle, be extended to all sorts of potential field data with "along-track" correlated errors.
Highlights
All geophysical data are contaminated by signals that cannot be described by models
We have calculated the Gauss coefficients describing the noise leaking in lithospheric magnetic field models when derived from satellite data
We consider that the orbits are exactly polar, that they are at constant radius and that the sampling rate along an orbit is “ideal” – i.e. the relation Pl|m|, Pl|m| ∝ δll is verified
Summary
All geophysical data are contaminated by signals that cannot be described by models. From a practical point of view, scientists have been relatively successful in estimating a priori the noise in gravity or magnetic data sets, correlations between errors have been mostly ignored This is partly because, when known, the full covariance matrix for the data errors is generally so large that it cannot be handled even on modern computers (but see for example Langel et al (1989); Holme and Bloxham (1996); Rygaard-Hjalsted et al (1997); Holme (2000), where correlated errors are accounted for in geomagnetism). To the authors’ knowledge, such techniques have never been applied to magnetic models, we should note the attempt to estimate the model covariance matrix in Lowes and Olsen (2004) In this manuscript we present and apply such a post-processing scheme for a model of the magnetic lithospheric field derived from ten years of CHAMP satellite data (Reigber et al, 2005).
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