We derive a generalized theory for gravitationally self-consistent, static sea level variations on earth models of arbitrary complexity that takes into account the redistribution of sediments. The theory is an extension of previous work that incorporated, into the governing equations, shoreline migration due to local sea level variations and changes in the geometry of grounded, marine-based ice. In addition, we use viscoelastic Love number theory to present a version of the new theory valid for spherically symmetric earth models. The Love number theory accounts for the gravitational, deformational and rotational effects of the sediment redistribution. As a first, illustrative application of the new theory, we compute the perturbation in sea level driven by an idealized pulse of sediment transport into the Gulf of Mexico. We demonstrate that incorporating a gravitationally self-consistent water load in this case significantly improves the accuracy of sea level predictions relative to previous simplified treatments of the sediment redistribution
