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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.

Marks, KM, Sandwell DT, Vogt PR, Hall SA.  1991.  Mantle Downwelling beneath the Australian-Antarctic Discordance Zone - Evidence from Geoid Height Versus Topography. Earth and Planetary Science Letters. 103:325-338.   10.1016/0012-821x(91)90170-m   AbstractWebsite

The Australian-Antarctic discordance zone (AAD) is an anomalously deep and rough segment of the Southeast Indian Ridge between 120-degrees and 128-degrees-E. A large, negative (deeper than predicted) depth anomaly is centered on the discordance, and a geoid low is evident upon removal of a low-order geoid model and the geoid height-age relation. We investigate two models that may explain these anomalies: a deficiency in ridge-axis magma supply that produces thin oceanic crust (i.e. shallow Airy compensation), and a downwelling and/or cooler mantle beneath the AAD that results in deeper convective-type compensation. To distinguish between these models, we have calculated the ratio of geoid height to topography from the slope of a best line fit by functional analysis (i.e. non-biased linear regression), a method that minimizes both geoid height and topography residuals. Geoid/topography ratios of 2.1 +/- 0.9 m/km for the entire study area (38-degrees-60-degrees-S, 105-degrees-140-degrees-E), 2.3 +/- 1.8 m/km for a subset comprising crust less-than-or-equal-to 25 Ma, and 2.7 +/- 2.0 m/km for a smaller area centered on the AAD were obtained. These ratios are significantly larger than predicted for thin oceanic crust (0.4 m/km), and 2.7 m/km is consistent with downwelling convection beneath young lithosphere. Average compensation depths of 27, 29, and 34 km, respectively, estimated from these ratios suggest a mantle structure that deepens towards the AAD. The deepest compensation (34 km) of the AAD is below the average depth of the base of the young lithosphere (approximately 30 km), and a downwelling of asthenospheric material is implied. The observed geoid height-age slope over the discordance is unusually gradual at -0.133 m/m.y. We calculate that an upper mantle 170-degrees-C cooler and 0.02 g/cm3 denser than normal can explain the shallow slope. Unusually fast shear velocities in the upper 200 km of mantle beneath the discordance, and major-element geochemical trends consistent with small amounts of melting at shallow depths, provide strong evidence for cooler temperatures beneath the AAD.

Sandwell, DT.  1982.  Thermal isostasy; response of a moving lithosphere to a distributed heat source. Journal of Geophysical Research. 87:1001-1014., Washington, DC, United States (USA): American Geophysical Union, Washington, DC   10.1029/JB087iB02p01001   AbstractWebsite

Spreading ridges and hot spot swells are identified by their high surface heat flow, shallow seafloor, and high geopotential. To understand these and other thermotectonic features, the oceanic lithosphere is modeled as a thermomechanical boundary layer moving through a three-dimensional, time-independent heat source. The heat source mimics the heat advection associated with a spreading ridge or hot spot without introducing the nonlinearities of these flow processes. The Fourier transforms of three Green's functions (response functions), which relate the three observable fields to their common heat source, are determined analytically. Each of these reponse functions is highly anisotropic because the lithosphere is moving with respect to the source. However, the ratio of the gravity response function to the topography response function (i.e., gravity/topography transfer function) is nearly isotropic and has a maximum lying between the flexural wavelength and 2pi times the thickness of the thermal boundary layer. The response functions are most useful for determining the surface heat flow, seafloor topography, and geopotential for complex lithospheric thermal structures. In practice, these three observables are calculated by multiplying the Fourier transform of the heat source by the appropriate response function and inverse transforming the products. Almost any time-independent thermotectonic feature can be modeled using this technique. Included in this report are examples of spreading ridges and thermal swells, although more complex geometries such as ridges offset by transform faults and RRR-type triple junctions can also be modeled. Because forward modeling is both linear and computationally simple, the inverse of this technique could be used to infer some basic characteristics of the heat source directly from the observed fields.