Bathymetric prediction from dense satellite altimetry and sparse shipboard bathymetry

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Abstract
The southern oceans (south of 30°S) are densely covered with satellite‐derived gravity data (track spacing 2–4 km) and sparsely covered with shipboard depth soundings (hundreds of kilometers between tracks in some areas). Flexural isostatic compensation theory suggests that bathymetry and downward continued gravity data may show linear correlation in a band of wave‐lengths 15–160 km, if sediment cover is thin and seafloor relief is moderate. At shorter wave‐lengths, the gravity field is insensitive to seafloor topography because of upward continuation from the seafloor to the sea surface; at longer wavelengths, isostatic compensation cancels out most of the gravity field due to the seafloor topography. We combine this theory with Wiener optimization theory and empirical evidence for gravity noise‐to‐signal ratios to design low‐pass and band‐pass filters to use in predicting bathymetry from gravity. The prediction combines long wavelengths (>160 km) from low‐pass‐filtered soundings with an intermediate‐wavelength solution obtained from multiplying downward continued, band‐pass‐filtered (15–160 km) gravity data by a scaling factor S. S is empirically determined from the correlation between gravity data and existing soundings in the 15–160 km band by robust regression and varies at long wave‐lengths. We find that areas with less than 200 m of sediment cover show correlation between gravity and bathymetry significant at the 99% level, and S may be related to the density of seafloor materials in these areas. The prediction has a horizontal resolution limit of 5–10 km in position and is within 100 m of actual soundings at 50% of grid points and within 240 m at 80% of these. In areas of very rugged topography the prediction underestimates the peak amplitudes of seafloor features. Images of the prediction reveal many tectonic features not seen on any existing bathymetrie charts. Because the prediction relies on the gravity field at wavelengths <160 km, it is insensitive to errors in the navigation of sounding lines but also cannot completely reproduce them. Therefore it may be used to locate tectonic features but should not be used to assess hazards to navigation. The prediction is available from the National Geophysical Data Center in both digital and printed form.