Bathymetry is foundational data, providing basic infrastructure for scientific, economic, educational, military, and political work. High resolution, deep ocean bathymetry is critical for: (a) understanding the geologic processes responsible for creating ocean floor features unexplained by simple plate tectonics, such as abyssal hills, seamounts, microplates, propagating rifts, and intraplate deformation; (b) determining the effects of bathymetry and seafloor roughness on ocean circulation, ocean mixing, and climate; and (c) understanding how marine life is influenced by seafloor depth, roughness, and interactions of currents with the seafloor (Yesson et al., 2011). The Seabed 2030 project (https://seabed2030.org) "aims to bring together all available bathymetric data to produce the definitive map of the world ocean floor by 2030 and make it available to all." The Seabed 2030 global

Seamounts are isolated elevations in the seafloor with circular or elliptical plans, comparatively steep slopes, and relatively small summit areas (Menard, 1964). The vertical gravity gradient (VGG), which is the curvature of the ocean surface topography derived from satellite altimeter measurements, has been used to map the global distribution of seamounts (Kim and Wessel, 2011). We used the latest grid of VGG to update and refine the global seamount catalog; we identified 10,796 new seamounts, expanding the catalog by 1/3. 739 well-surveyed seamounts, having heights ranging from 421 m to 2500 m, were then used to estimate the typical radiallysymmetric seamount morphology. First, an Empirical Orthogonal Function (EOF) analysis was used to demonstrate that these small seamounts have a basal radius that is linearly related to ix their height -their shapes are scale invariant. Two methods were then used to compute this characteristic base to height ratio: an average Gaussian fit to the stack of all profiles and an individual Gaussian fit for each seamount in the sample. The first method combined the radial normalized height data from all 739 seamounts to form median and median-absolute deviation. These data were fitted by a 3-parameter Gaussian model that explained 99.82 percent of the variance. The second method used the Gaussian function to individually model each seamount in the sample and further establish the Gaussian model. Using this characteristic Gaussian shape, we show that VGG can be used to estimate the height of small seamounts to an accuracy of about 270 m.x

Bathymetry is foundational data, providing basic infrastructure for scientific, economic, educational, military, and political work. High resolution, deep ocean bathymetry is critical for: (a) understanding the geologic processes responsible for creating ocean floor features unexplained by simple plate tectonics, such as abyssal hills, seamounts, microplates, propagating rifts, and intraplate deformation; (b) determining the effects of bathymetry and seafloor roughness on ocean circulation, ocean mixing, and climate; and (c) understanding how marine life is influenced by seafloor depth, roughness, and interactions of currents with the seafloor (Yesson et al., 2011). The Seabed 2030 project (https://seabed2030.org) "aims to bring together all available bathymetric data to produce the definitive map of the world ocean floor by 2030 and make it available to all." The Seabed 2030 global

The ocean floor consists of primary tectonic features that form at spreading ridges including abyssal hills, transform faults, and propagating ridges as well as volcanic seamounts which form in a variety of off-ridge settings. Seamounts are active or extinct volcanoes with heights that reach at least 1,000 m (Menard, 1964) although this definition has been broadened to include much smaller isolated volcanoes (Staudigel et al., 2010). They are basaltic in composition, volcanic in origin, and formed in one of three tectonic settings: near mid-ocean ridges, intraplate hotspots, and island arcs (Wessel, 2007). (a) The majority of small seamounts form near mid-ocean ridges. The lithosphere at divergent plate boundaries is thin and fractured; this allows magma to migrate through the lithosphere and form small seamounts that are tens to thousands of meters high (Batiza, 1981;Smith & Cann, 1990;Wessel, 2007). (b) Intraplate seamounts that form away from the spreading ridges, usually on older seafloor, are generally attributed to hotspots, although hotspots alone cannot easily explain the wide geographic spread of seamounts on the ocean floor (Vogt, 1974;Wessel, 2007). The hotspot hypothesis states that as the plate passes over a relatively stationary mantle upwelling (i.e., plume), melt generated at the lithosphere/asthenosphere migrates to the surface forming an age-progressive seamount chain (Morgan, 1971;Wilson, 1963). (c) Island arc seamounts form in the overriding plate at subduction zones. When the oceanic crust of the subducting plate reaches a depth of about 150 km it undergoes dehydration reactions that release water that lowers the melting temperature in the mantle wedge; the partial melt migrates to the surface forming island arc volcanoes (Fryer, 1996).The means of formation also has an effect on seamount size and distribution. For one, flanks of spreading centers tend to have many small seamounts (<2.5 km tall) since the lithosphere is thin (Batiza, 1981). However, if a seamount is created by a mantle plume beneath thick lithosphere, it can reach a peak of 3-10 km above the seafloor (Wessel, 2007). The distribution of seamounts differs among ocean basins and this variation can be due to the distribution of mantle plumes as well as changes in intraplate stresses. Researchers have found that the global distribution of seamounts height follows an exponential or a power-law model (Smith & Jordan, 1988;