Maps of the magnetic anomaly field at Earth's surface from scalar satellite data

Satellite measurements of the magnetic anomaly field intensity have been used to estimate components of the vector field at the Earth's surface, using a linear approximation to relate satellite scalar measurements to downward-continued vector components. The relation between data and model was inverted using a depleted harmonic spline basis to find an almost minimum norm solution, enabling the detail present in satellite data to be preserved over continental-sized areas. In their development of the depleted basis method, Parker and Shure (1982) advocated using a subset of the original data as points in the depleted basis. Here, it is shown that a depleted basis formed from vertical component data kernels is much more satisfactory than a subset of measured intensity data kernels; however, we do form the depleted basis at the physical locations of actual data. The downward-continued map over Africa agrees well with its counterpart produced from Magsat orthogonal component data.