An Empirical Method for Optimal Robust Regional-Residual Separation of Geophysical Data

Prior to interpretation and further analysis, many datasets must first be separated into regional and residual components. Traditional techniques are either subjective (e.g., graphical methods) or nonrobust (e.g., all least-squares based methods). Bathymetric data, with their broad spectrum, pose serious difficulties to these traditional methods, in particular those based on spectral decomposition. Spatial median filters offer a solution that is robust, objective, and often defines regional components similar to those produced graphically by hand. Characteristics of spatial median filters in general are discussed and a new empirical method is presented for determining the width of the robust median filter that accomplishes an optimal separation of a gridded dataset into its regional and residual components. The method involves tracing the zero-contour of the residual component and evaluating the ratio between the volume enclosed by the surface inside this contour and the contour's area. The filter width giving the highest ratio (or mean amplitude) is called the Optimal Robust Separator (ORS) and is selected as the optimal filter producing the best separation. The technique allows a unique and objective determination of the regional field and enables researchers to undertake reproducible separations of regional and residual components. The ORS method is applied to both synthetic data and bathymetry/topography of the Hawaiian Islands; ways to improve the technique using alternative diagnostic quantities are discussed.