Sea Floor Bathymetry Trackline Surface Fitting Without Visible Artifacts Using ODETLAP

摘要

High quality, artifact-free fitting a bathymetry (sea-floor) surface to very unevenly spaced depth data from ship track-lines is possible with ODETLAP (Overdetermined Laplacian Partial Differential Equation). The problem is that many data points, but with imprecise values, can be collected along and near the ships, e.g., with Multibeam Bathymetry, but there are no data between the tracklines, which may be a considerable distance apart. The numerous artifacts of previous surface fitting algorithms were so totally unacceptable that even Photoshop has been used to smooth them. In contrast, the implementation of this version of ODETLAP generates surfaces that do not exhibit artifacts even when displayed with techniques that highlight minor slope irregularities, which is, in the authors' opinion, the most appropriate evaluation metric. Since the data is imprecise, ODET-LAP's surface approximates, rather than interpolates, the data. ODETLAP can trade off smoothness and accuracy to capture the small features that are not artifacts. This extension to ODETLAP is a variable smoothness parameter so that points distant from a known depth are smoothed differently from points close to a known depth. The broader implication is that ODETLAP is a very powerful algorithm with many applications. The Matlab implementation is freely available for nonprofit research and education.