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Sandwell, DT, Smith WHF.  2001.  Bathymetric Estimation. Satellite altimetry and earth sciences : a handbook of techniques and applications. ( Fu L, Cazenave A, Eds.).:441-457., San Diego, Calif. ; London: Academic Abstract
Smith, WHF, Sandwell DT.  1994.  Bathymetric Prediction from Dense Satellite Altimetry and Sparse Shipboard Bathymetry. Journal of Geophysical Research-Solid Earth. 99:21803-21824.   10.1029/94jb00988   AbstractWebsite

The southern oceans (south of 30 degrees 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 wavelengths 15-160 km, if sediment cover is thin and seafloor relief is moderate. At shorter wavelengths, 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 wavelengths. 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 bathymetric 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.

Sandwell, DT, Smith WHF, Gille S, Kappel E, Jayne S, Soofi K, Coakley B, Geli L.  2006.  Bathymetry from space: Rationale and requirements for a new, high-resolution altimetric mission. Comptes Rendus Geoscience. 338:1049-1062.   10.1016/j.crte.2006.05.014   AbstractWebsite

Bathymetry is foundational data, providing basic infrastructure for scientific, economic, educational, managerial, and political work. Applications as diverse as tsunami hazard assessment, communications cable and pipeline route planning, resource exploration, habitat management, and territorial claims under the Law of the Sea all require reliable bathymetric maps to be available on demand. Fundamental Earth science questions, such as what controls seafloor shape and how seafloor shape influences global climate, also cannot be answered without bathymetric maps having globally uniform detail. Current bathymetric, charts are inadequate for many of these applications because only a small fraction of the seafloor has been surveyed. Modern multibeam echosounders provide the best resolution, but it would take more than 200 ship-years and billions of dollars to complete the job. The seafloor topography can be charted globally, in five years, and at a cost under $100M. A radar altimeter mounted on an orbiting spacecraft can measure slight variations in ocean surface height, which reflect variations in the pull of gravity caused by seafloor topography. A new satellite altimeter mission, optimized to map the deep ocean bathymetry and gravity field, will provide a global map of the world's deep oceans at a resolution of 6-9 kin. This resolution threshold is critical for a large number of basic science and practical applications, including: determining the effects of bathymetry and seafloor roughness on ocean circulation, mixing, climate, and biological communities, habitats, and mobility; understanding the geologic processes responsible for ocean floor features unexplained by simple plate tectonics, such as abyssal hills, seamounts, microplates, and propagating rifts;. improving tsunami hazard forecast accuracy by mapping the deep-ocean topography that steers tsunami wave energy; mapping the marine gravity field to improve inertial navigation and provide homogeneous coverage of continental margins; providing bathymetric maps for numerous other practical applications, including reconnaissance for submarine cable and pipeline routes, improving tide models, and assessing potential territorial claims to the seabed under the United Nations Convention on the Law of the Sea. Because ocean bathymetry is a fundamental measurement of our planet, there is a broad spectrum of interest from government, the research community, industry, and the general public. Mission requirements. The resolution of the altimetry technique is limited by physical law, not instrument capability. Everything that can be mapped from space can be achieved now, and there is no gain in waiting for technological advances. Mission requirements for Bathymetry from Space are much less stringent and less costly than typical physical oceanography missions. Long-term sea-surface height accuracy is not needed; the fundamental measurement is the slope of the ocean surface to an accuracy of similar to 1 prad (1 mm km(-1)). The main mission requirements are: improved range precision (a factor of two or more improvement in altimeter range precision with respect to current altimeters is needed to reduce the noise due to ocean waves); - fine cross-track spacing and long mission duration (a ground track spacing of 6 km or less is required. A six-year mission would reduce the error by another factor of two); moderate inclination (existing satellite altimeters have relatively high orbital inclinations, thus their resolution of east-west components of ocean slope is poor at low latitudes. The new mission should have an orbital inclination close to 60 degrees or 120 degrees so as to resolve north-south and east-west components almost equally while still covering nearly all the world's ocean area); near-shore tracking (for applications near coastlines, the ability of the instrument to track the ocean surface close to shore, and acquire the surface soon after leaving land, is desirable).

Sandwell, DT.  1987.  Biharmonic Spline Interpolation of Geos-3 and Seasat Altimeter Data. Geophysical Research Letters. 14:139-142.   10.1029/GL014i002p00139   AbstractWebsite

Green functions of the biharmonic operator, in one and two dimensions, are used for minimum curvature interpolation of irregularly spaced data points. The interpolating curve (or surface) is a linear combination of Green functions centered at each data point. The amplitudes of the Green functions are found by solving a linear system of equations. In one (or two) dimensions this technique is equivalent to cubic spline (or bicubic spline) interpolation while in three dimension it corresponds to multiquadric interpolation. Although this new technique is relatively slow, it is more flexible than the spline method since both slopes and values can be used to find a surface. Moreover, noisy data can be fit in a least squares sense by reducing the number of model parameters. These properties are well suited for interpolating irregularly spaced satellite altimeter profiles. The long wavelength radial orbit error is suppressed by differentiating each profile. The shorter wavelength noise is reduced by the least squares fit to nearby profiles. Using this technique with 0.5 million GEOS-3 and SEASAT data points, it was found that the marine geoid of the Caribbean area is highly correlated with the sea floor topography. This suggests that similar applications, in more remote, areas may reveal new features of the sea floor.