Polynomial smoothing of quiet-time magnetic variations for an irregularly spaced array of sites

Abstract

Both magnetospheric and solid Earth geophysicists often employ two-dimensional arrays of recording variometers to reconstruct the spatial distribution of transient magnetic field variations at the Earth's surface. These discrete data are typically interpolated over a dense grid and the results, for example, are contoured. Few studies, however, have explored the efficacy of employing various polynomial forms for interpolating the same data set, nor have they examined how regional polynomial forms relate to magnetic variation sources on a global scale. The present study addresses some of these concerns. We quantify the characteristics of various smoothed models (i.e., low-order polynomial trend surfaces) for the same data set from a subglobal network of magnetic variometers. Using a relatively quiet interval of undisturbed diurnal variation, we characterize the spatial distribution of the three individual magnetic vector components at a single instant of time—or for what we call a ‘time slice’. We then explore how our model functions are affected by the presence or absence of various site data, i.e., what is the ‘information content’ of a particular site in our array and how important is it to constraining the final smooth model function that we derive? Finally, we explore how such local model functions are affected by including data from outside the array by studying the relation between our local polynomial forms and the global source fields from which they derive.