Directional median filtering for regional-residual separation of bathymetry

Abstract

We present a new spatial filter designed to separate short-length-scale bathymetric features from regional bathymetry. The directional median (DiM) filter divides a given filter circle into N "bow tie" sectors, allocates data points inside the filter circle to each sector based on their relative position within the circle, estimates a median for each sector, and returns the lowest of these N medians. This approach prevents DiM filtering from choosing the biased medians near the features on a sloping regional trend, which is a serious artifact of standard median filtering. As the bathymetry comprises diverse length-scale features, the separated results vary with the choice of filter width. Such variations are spatially distributed. Using a finite range of filter widths, we evaluate the spatial distribution of variations in the DiM-based separation by estimating their median absolute deviation (MAD) at each data point. The distribution of MAD values is indicative of uncertainties inherent in the separation. We demonstrate the effectiveness of DiM filtering with both synthetic and actual bathymetric data. Copyright 2008 by the American Geophysical Union.