Local spherical harmonic power spectra from local magnetic or gravity data

We present a method to calculate local spherical harmonic power spectra directly from spacecraft magnetic and gravity data with varying spacecraft altitude. Previously published applications of local spherical harmonic power spectra have been formulated for data that are available at a single collection altitude, such as data evaluated from a global spherical harmonic model. Our approach consists of first solving for local models from local data and then obtaining local multitaper spectra from the local models. We demonstrate with numerical tests that this approach can produce reliable results. Our method is particularly useful in situations where data coverage does not allow for calculating global magnetic or gravity field models, or where data quality or quantity varies regionally and where local models could yield superior resolution or quality over global models.