Directional median filtering for regional‐residual separation of bathymetry

Abstract

[1] 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.

Study of Subsidence and Earthquake Swarms in the Western Pakistan

“…In order to assess the role of anthropogenic and tectonic processes in subsidence in the Quetta Valley, we adopted a novel technique that utilized a median filter commonly used in seismic data processing. A median filter operates by selecting the middle value of numbers within a window, which is then used as a geophysical tool for regional-residual separation [36,37].…”

Seamount detection and isolation with a modified wavelet transform

“…These significantly mitigate this problem, but still have some tendency to pass through, rather than beneath, seamounts where many seamounts co-exist [Hillier & Watts, 2004] or occur down trenches (Figure 12). A further improvement applicable to gridded data only uses directional filtering to improve the regional-residual separation for medians where the seafloor is sloping [Kim & Wessel, 2008]. Overall, these techniques perform well when the filter width (i.e.…”

“…This ORS technique provides a clear lower limit on the optimal filter width but less constraint on the upper limit [Wessel, 1998;Minshull & Charvis, 2001;Ali, 2003] and, for the Marquesas Islands at least, the optimal width is significantly changed by 'small changes due to choice of area included in the analysis' [Minshull & Charvis, 2001]. A fairly broad maximum still remains with the refinements of Kim & Wessel [2008]. Thus, despite proving an objective procedure, the area for analysis that must be specified a priori for each set of volcanoes and a substantial subjective factor remains.…”

“…Too small and the regional becomes shallow inside large seamounts, whilst too large and the regional cuts through seamounts standing in a depression. Progress has being made on automated width selection for a single feature [Wessel, 1998] and reducing artefacts for seamounts on slopes [Kim & Wessel, 2008], but have not yet been perfected and regional based techniques will always struggle where 'normal' unperturbed seafloor upon which to base the regional is rare [Hillier & Watts, 2004, 2005]. …”

3.11 Geovisualization

“…However if normal elevations are rare, perhaps where there are many volcanoes and little remaining original seafloor, bias can occur underestimating heights and volumes in the residual (Smith, 1990). 'Robust' statistics such as the median and mode can mitigate this substantially (Smith, 1990, Crosby, 2006Kim & Wessel, 2008), as can iterative statistical approaches (Marty & Cazenave, 1989;Wang et al, 2001). …”