Ørsted total intensity data were analysed over the southern African region between 10° South and 45° South in latitude and between 10° East and 45° East in longitude, measured between May 1999 and October 1999. The satellite magnetic field measurements were selected corresponding to magnetic quiet conditions during local day and night times before carrying out an analysis of external fields by subdividing the data into Dst bins 5 nT wide, centred at multiples of 5 nT. The technique of Spherical Cap Harmonic Analysis (SCHA) was then applied to each of these Dst data bins to obtain external field coefficients, after removing the core field by means of the IGRF model. Combining all data sets after removing main - and external fields, enabled the compilation of a total intensity crustal anomaly map over southern Africa at an average satellite altitude of 800 km. The Walvis Ridge and Agulhas anomalies are understood to represent thickened remanently magnetised ocean crust. The Agulhas anomaly however, represents the remnant scar of the process that led to the Gondwana fragmentation.
 This paper discusses the modelling of near-earth Ørsted total intensity magnetometer data over southern Africa by means of Spherical Cap Harmonic Analysis (SCHA) to identify the external field and the subsequent identification of long-wavelength crustal anomalies. Previous analysis of Polar Orbiting Geomagnetic Survey (POGS) satellite measurements over the southern African region [Kotzé and Barraclough, 1997] revealed strong correlations between both continental and oceanic magnetic anomalies and major tectonic features as identified using Magsat data [Antoine and Moyes, 1992].
 The principal objective of the Ørsted mission [Neubert et al., 2001] is the accurate mapping of the Earth's magnetic field arising from internal sources as well as the characterisation of various current systems.
 This paper discusses the modelling of scalar Ørsted magnetic field data over southern Africa by means of Spherical Cap Harmonic Analysis (SCHA) in order to characterize external field perturbations as a function of Dst as well as local time. These external field corrections will be used to identify long wavelength crustal field anomalies at satellite altitude. Significant magnetospheric current systems exist that result in large magnetic fields described by various magnetic activity indices. Although Ørsted is affected by electrojets and field-aligned currents during its orbit, we assume for the purpose of this investigation that ring current effects dominate at the low latitudes considered and that these can be represented by the Dst index.
2. Spherical Cap Harmonic Analysis (SCHA)
 Spherical Cap Harmonic Analysis (SCHA) is a mathematical technique developed by Haines  to model a potential field and its spatial derivatives, or a general function and its surface derivatives, on a regional scale in order to overcome the non-orthogonality problem in the case of global spherical harmonic models when applied to restricted areas. SCHA was also used by Haines and Newitt  to derive a regional geomagnetic field model for Canada using Magsat data in addition to other field survey data sets. Similarly, De Santis et al.  and Torta et al.  employed spherical cap techniques to derive regional geomagnetic field models over Italy and Spain respectively, using both Magsat and ground vector data. Recently, Haines and Newitt  also used SCHA to model the secular variation and main field simultaneously over Canada, using various data sets that include both vector and scalar observations at ground and satellite altitudes. The SCHA modelling technique has also been used successfully to model the external field affecting POGS scalar data [Kotzé and Barraclough, 1997] in order to identify crustal magnetic anomaly features over southern Africa.
 The technique of SCHA has been used to model Ørsted external scalar field data as a general colatitude-longitude function on a cap-like region when all data are supposed to be distributed over a spherical shell without any altitude variations, i.e.:
where: θ and λ are, respectively, the colatitude and longitude corresponding to a spherical expansion developed on a cap-like region; = associated Legendre function with integral order m and real degree nk(m); k is an index that orders the nk(m); qkm, skm are the spherical cap coefficients.
 If the half-angle of the spherical cap is denoted by θ0, the nk(m) are determined as the roots of the equation, for given m:
and additionally, if differentiability with respect to θ is required:
If the expansion in Equation (1) is truncated at k = K, the number of model coefficients is (K + 1)2.
3. Data Selection and Pre-processing
 Ørsted total intensity data were selected over the southern African region between 10° South and 45° South in latitude and between 10° East and 45° East in longitude, measured between May 1999 and October 1999. The satellite magnetic field measurements were further restricted to intervals with a Kp index equal to or less than 2+, corresponding to magnetically quiet times. All measurements were further restricted to times when the absolute Dst index was less than or equal to 30 in order to ensure a reasonable geographical coverage with at least 1 measurement every 5°. The data were also selected within a narrow altitude band between 750 and 850 km. As the Ørsted total field data were supplied in a rectangular Earth-centred, Earth-fixed coordinate system, all measurements were converted to geodetic coordinates of latitude, longitude and altitude, using the International Astronomical Union ellipsoid to be compatible with our SCHA modelling routines. The IGRF 95 secular variation (SV) model [Barton, 1997] has been used to adjust all measurements to July 1999. The data were further separated into day and night intervals and the IGRF 2000 model, based on Ørsted magnetic field measurements [Olsen et al., 2000], subtracted from the Ørsted total field measurements to obtain residual values.
4. External Field Modelling
 After the initial data selection over southern Africa and residual values for total intensity (F) had been accomplished we proceeded to characterize Ørsted external field by SCHA. The residuals were assumed to be largely due to effects of external current systems, mainly, but not entirely, the ring current as at satellite altitudes external fields dominate crustal field effects. In order to carry out an analysis of Ørsted external fields, it was assumed that they could be characterized by the Dst index [Langel and Estes, 1985] and the day and night data sets were divided into Dst bins 5 nT wide, centred at multiples of 5 nT. Reasonable geographical coverage with at least 1 measurement every 5° could be obtained for Dst values between +25 nT and −20 nT.
 For the external field residual values to be modelled by SCHA we assumed F to be a general function of longitude and colatitude as in Equation (1). In the case of Ørsted the expansion in Equation (1) was truncated at K = 1, resulting in a total of four external field model coefficients, namely q00, q10, q11, and s11. Previous global field studies [Langel and Sweeney, 1971; Langel and Estes, 1985] have shown that most of the external field can be represented by first-degree terms of a global spherical harmonic expansion. The pole for each Dst distribution was determined by the barycentre of the coordinates of the measurements. This differed slightly for each Dst data distribution, centering around θ = 113° and λ = 23°, while a cap angle of θ0 = 30° could include all measurements. For each of the day and night Dst data intervals four expansion coefficients were derived, with q00 by far the most significant coefficient, representing the external field at an average satellite altitude of 800 km. Following the approach of [Langel and Estes, 1985] as well as [Kotzé and Barraclough, 1997], a regression analysis revealed a clearly linear relationship between the q00 coefficient and Dst for both day and night periods, as displayed in Figure 1:
 The model just described is not a potential field analysis, but is simply a fit to the residuals, as we did not solve simultaneously for both internal and external fields, with F approximated as a general function of co-latitude and longitude with no radial dependence.The variation with Dst as obtained in this investigation compares favourably with results obtained by Langel and Estes  using global spherical harmonic analysis for dawn/dusk Magsat data and Kotzé and Barraclough  using winter/summer POGS scalar measurements. It is however difficult to assign error bars to the data in Figure 1. A SCHA model coefficient is statistical significant if its absolute value is greater than times the standard deviation, using least-squares modelling procedures. Using F = 3.5, we estimate the q00 coefficient to be probably accurate to ±5 nT for Dst levels with adequate geographic coverage.
 Using Equations (4) and (5) we calculated the external field at each satellite measurement position as a function of latitude, longitude, altitude and Dst level. We subsequently followed the method of [Mayhew, 1979] by removing a linear/quadratic trend from each pass segment. This dramatically improved the internal consistency of the data by eliminating very long-wavelength trends due to external field effects and core-field bias over our study area. Residuals remaining were assigned to the lithospheric signal at Ørsted altitude, although induction fields due to time-varying external fields might contribute a negligibly small amount of contamination.
 Combining both day and night data sets enabled the compilation of a Ørsted crustal anomaly map at an average satellite altitude of 800 km as displayed in Figure 2a. Several prominent long-wavelength anomalies can be identified, which include the positive Agulhas Plateau and Walvis Ridge, while the negative Cape Vaal anomaly associated with the Karroo basin, can also be observed. These crustal magnetic anomalies as identified from Ørsted observations correlate spatially quite close with those observed using POGS data as shown in Figure 2b. An analysis of the magnetisation contrasts of the Walvis Ridge and Agulhas anomalies suggests that they may be ascribed to thickening of the oceanic crust, while it is generally accepted that the Walvis Ridge was created by a hot spot or plume [Morgan, 1971]. The Agulhas anomaly on the other hand, is the largest and most intense anomaly within the southern African region, and appears to have internal structure, delineated by several oceanic floor features: the eastern spur of the Agulhas anomaly is truncated by the Davie Ridge, while the northwestern boundary coincides with the Agulhas Fracture Zone which follows the continental shelf as far as the Maputo embayment. It was argued [Antoine and Moyes, 1992] that the Agulhas anomaly underlies a large portion of Gondwana, encompassing part of the Falklands Plateau and the microplates of West Antarctica. The Agulhas anomaly is therefore the remanant of an extensive region of the lithosphere which initiated the break-up of Gondwana in this region, underlying a fragmented region at the junction of the South America, Africa and Antarctica plates.
6. Summary and Conclusions
 The regional modelling technique of Spherical Cap Harmonic Analysis, based on the expansion of fractional Legendre functions in colatitude and Fourier functions in longitude, has been successfully employed to model Ørsted scalar data to characterize external fields as a function of the Dst index. Combining both day and night Ørsted data sets over southern Africa during May 1999 till October 1999, enabled the compilation of a crustal anomaly map at an average satellite altitude of 800 km. Prominent long-wavelength anomalies could be identified, including the Walvis Ridge and Agulhas Plateau, as well as the Cape Vaal anomaly associated with the Karroo basin, correlating closely with those identified from POGS observations. Both the Walvis Ridge and Agulhas oceanic anomalies are representative of thickened ocean crust. The Agulhas anomaly in particular, can be seen as the remnant scar of the process that started the fragmentation of Gondwana in this region.
 The Ørsted Project was made possible by extensive support from the Danish Ministry of Trade and Industry, the Ministry of Research and Information Technology as well as the Ministry of Transport. Additional international and crucial support was provided from NASA, ESA, CNES, and DARA.