Isostatic flexure of a finite slope due to sea-level rise and fall

Sea level has risen on order of 100 m since the last glacial maximum (LGM), increasing the load on continental shelves and inducing lithospheric flexure. An analytic solution for the deflection of a linear slope due to sea level fluctuations is derived, based on a one-dimensional elastic plate model. This analytic solution provides deflection estimates of global continental shelves, due only to increases in water loading, effective elastic thickness (which is a proxy for the strength of the lithosphere with 2°×2° resolution) and the local shape of LGM continental margins (one-arc minute resolution). Changes in eustatic sea level are thus disengaged from changes in relative sea level. Variations in water loading can alter the slopes of continental shelves on the order of 30%, but importantly the magnitude is regionally variable. Hydro-isostasy adds to the magnitude of a sea-level rise, long after the eustatic component of the sea-level rise has ended. A sea-level rise will produce a steepening of a continental shelf, while a sea-level drop causes a decrease in shelf gradient and an increase in the total shoreline regression. Quantifying this effect is essential to reconstructing stream gradients, estimating sediment delivered by rivers, for estimating accommodation space through a sea-level cycle, and to support the use of paleo-shoreline to estimate eustatic sea-level fluctuations.