To the Editor

In an elegant analysis of landslides following the 2008 Wenchuan earthquake in Sichuan, China, Parker et al.1 showed that estimates of the mass of material in landslides exceeds by two to six times the mass of material that moved upwards during the earthquake. With the sensible logic that the material within the landslides soon will be transported out of the Longmen Shan Mountains, they use this discrepancy to argue that erosion seems to remove mass faster than geodynamic processes supply it to the Longmen Shan. I applaud their analysis, but I think that they overlooked an aspect that renders this deduction only plausible at best, and quite likely false. That aspect is isostasy, Archimedes' principle applied to the Earth, which, when generalized to include an elastic surface layer, calls for equal pressure at any depth in the underlying mantle beneath the elastic layer2.

As Wager3 and Holmes4,5 recognized long ago, the isostatic compensation of mass removed from the surface of the Earth requires a net upward flux of mass, with respect to sea level, so that the creation of high peaks follows from the incision of deep valleys. If the mass removed is given by ΔM, the upward displacement of mass is ΔMρc/ρm, where ρc and ρm are the densities of crust and mantle, respectively. The factor of ρc/ρm arises because the mass removed, with crustal density, occupies a larger volume than the mass of mantle material that replaces it. With ρc = 2800 Mg m−3 and ρm = 3300 Mg m−3, a compensating mass of 0.85ΔM should rise in response to the removal of ΔM. Thus, removal of about 5–15 km3 of erodible material in landslides1 implies that when it is transported out of the Longmen Shan, about 4.2–12.8 km3 of rock should move upwards with respect to sea level, on the timescale over which isostasy responds to rapid unloading. If the net upward mass transport that Parker et al. associate with faulting during the earthquake (2.6±1.2 km3) is added to these estimates, only with a conspiracy of values would more material be removed than replaced by the combination of tectonic processes and isostatic compensation: about 6.4–15.2 (±1.2) km3 is obviously indistinguishable from about 5–15 km3.

A few caveats should be noted. First, Parker et al. pointed out that their estimate of around 5–15 km3 is a minimum estimate; hence their contention, and that of Godard et al.6, that the Longmen Shan is diminishing in size could still be right, even allowing for isostatic compensation of yet more mass removal. Second, both my analysis and that of Parker et al. ignore interseismic vertical movement, which could contribute additional upward mass flux. Third, although a finite flexural rigidity of the lithosphere will not alter the amount of isostatically compensated upward movement of mass, it will spread that upward displacement over an area wider than that of the landsliding. A sufficiently large value for the flexural rigidity might cause the compensating upward movement to occur so far from the Longmen Shan as to be irrelevant to the growth of that mountain belt. A sufficiently large flexural rigidity, however, seems unlikely, especially given the absence of a flexural basin southeast of the Longmen Shan. Finally, because of viscous flow in the underlying mantle, isostatic compensation is not instantaneous. The viscous response to an instantaneous redistribution of mass will exponentially approach an isostatically compensated state. Characteristic e-folding relaxation times of a few thousand years7 deduced from post-glacial rebound, however, suggest that isostatic compensation will occur on timescales comparable to recurrence intervals of Wenchuan-like earthquakes.

Although most Earth scientists appreciate the importance of isostasy in maintaining high terrain, many forget that present-day rock uplift owes its existence mostly (∼85%) to isostatic compensation of material that has been eroded and transported outside that terrain, and not to active tectonics.