Local functions can be used to represent adequately regional and local magnetic fields. A procedure is described in which separate local functions are used in each of many overlapping areas. Weighting functions remove any discontinuities at area boundaries. This procedure was applied to the 1-degree quadrangle means of the horizontal magnetic component for the United States using ten overlapping areas. Use of separate local functions could have distinct advantages over use of one function for the entire area, because more detail can be retained and the total area can be extended easily to include surrounding areas.Local anomaly maps must retain wavelengths as short as a few kilometers. A local function representation of part of the anomaly map of Nevada, developed by employing a double Fourier series, reduced the computer storage required to approximately one-fifth that required to store the original anomaly values, and displayed a partial interpretation of the map in terms of directional trends and depth to sources.