Separation of Regional and Residual Components of Bathymetry Using Directonal Median Filtering

I propose a new filtering technique to separate bathymetric data into regional and residual components. Directional median (DiM) filtering divides a given filter circle into N "bow-tie" sectors, allocates the data points inside the filter circle to each bowtie sector based on their relative position with respect to the center of the filter circle, estimates a median value for each sector, and returns the lowest of these median values. This procedure is introduced to circumvent a shortcoming of conventional median filters, which return biased median estimates for data exhibiting short-Iengthscale features (e.g., seamounts) superimposed on sloping backgrounds (e.g., swells or slopes caused by thermal subsidence of lithosphere). By preserving the robust properties of spatial median filters and overcoming the limitation mentioned above, DiM filtering is able to efficiently isolate short-length-scale features from sloping regional components. Because DiM filtering results depend on the choice of filter width, I find effective filter widths, a range of filter widths enabling DiM filters to remove the given short-length-scale features completely, based on both the ratio of the volume to the area of estimated residual components and the width of the largest feature in the data domain. Furthermore, uncertainties in the predicted regional component are quantified by estimating median absolute deviation (MAD) values at each data point, which evaluate whether the DiM filters produce similar regional components within the chosen effective filter widths. The distribution of MAD values, therefore, can be used to identify the causes of large fluctuations in regional components and suggest ways to reduce these variations. The DiM filtering with associated MAD analysis is applied to both synthetic and actual bathymetric data of the seafloor around the EasterSalas y Gomez Seamount Chain and the Cape Verde Islands. These tests confirm that the DiM filtering allows researchers to prepare suitable input data (e.g., residual components used as applied loads in flexural studies) and quantify the uncertainties.