On the azimuthally dependent contribution of crustal magnetization to the magnetic field

The way in which induced or remanent magnetization contributes to the crust al magnetic field at a point r on or above the Earth's surface is investiga ted. It is shown that only smoothly varying components of magnetization alo ng an azimuth phi about r contribute to the crustal magnetic field. Stated mathematically, if the distribution of magnetization is expanded in a discr ete Fourier basis in phi, only wavenumbers k=0, +/- 1, +/- 2 contribute to the crustal field. On the other hand, there is no such simplifying expansio n of the magnetization distribution in the radial direction. In the case wh ere the induced magnetic field is due to a local variation of susceptibilit y in a smooth inducing field such as the core field, this result can be ext ended to the distribution of susceptibility itself. Then, when induced and inducing magnetic field vectors are defined in the same local spherical sys tem of coordinates, the matrix relating these two fields presents a very we ll-defined and simple structure.