Vertical geodesy is undergoing a revolution because of two factors. First, new precise three-dimensional position measurement techniques used over very long distances and based on extraterrestrial reference systems provide a new class and precision of geometric data previously unavailable for geophysical investigations. Second, physical models in tectonic theory for large earthquakes predict crustal distortions that violate the conventional assumptions used to interpret gravity and leveling data. Leveling and geometric elevation measurements are not directly comparable because the interpretation of leveling data is density-model dependent. Estimates of pre-1071 San Fernando earthquake elevation changes based on leveling of about 10 cm may be as much as 3 cm, or 40%, too large. Pre-1964 Niigate earthquake leveling surveys, previously used as confirmation of the dilatancy model, do not require dilatancy as an explanation and easily allow an alternative model with a subsurface density increase. Gravity is also not a dependable estimator of elevation change. But a combination of gravity with either leveling, if the dimensions of the distorted body are known or small, or geometric elevation measurements is essential for the determination of crustal density and strain changes. The 1965--1967 Matsushiro earthquake swarm leveling and gravity data show a significant dilatant strain of 0.6--1.8 ¿10-4 if the proper model dimensions are used. This dilatant strain would be adequate to cause the observed drop in Vp/Vs, even if the crust were initially saturated prior to distortion. The combination of gravity, leveling, and the new geometric elevation measurements provides a useful parameter, gravitational potential, for the inversion of subsurface density distributions. Use of this parameter, defined as the free-air elevation anomaly, is illustrated for a nearly compensated mountain root structure and shows that this technique holds significant promise for the study of large, deep structures in the crust and upper mantle.