correspondence
Isostasy can’t be ignored 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 layer 2. As Wager 3 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. ❐
Authors’ reply — We thank Peter Molnar for his interest in our work1, and for graciously (and quite correctly) pointing out the potential role of isostasy in the longterm volume balance of the Longmen Shan orogen. However, his point does not affect the primary message of our paper, which was to assess the instantaneous competition between erosional and tectonic processes associated with the earthquake. Instead, isostasy is yet another reason, in addition to those we previously presented, why this instantaneous imbalance we describe might not hold over long timescales — that is, over multiple earthquake cycles and viscoelastic
response times (>103 years). Indeed, we suggested in our paper that long-term rock uplift is unlikely to be a simple function of the 2008 coseismic displacements; it is produced by a combination of tectonic activity and flexural-isostatic deformation, but the relative importance of each component was not the focus of our study. Molnar calculates the isostatic response to an eroded mass ΔM, assuming that the lithosphere has no flexural rigidity, and asserts that a non-zero effective elastic thickness (Te) would not change the overall magnitude of the erosionally driven compensating mass. He also notes,
however, that non-zero values of Te will cause the flexural-isostatic response to be distributed more widely across the plateau margin and adjacent Sichuan Basin, thus decreasing the amount of erosionally driven rock uplift directly underneath the Longmen Shan. Estimates of Te in the Longmen Shan and western Sichuan Basin range from 20 to 45 km (refs 2–4), indicating that the response calculated by Molnar is most likely an overestimate. To evaluate this, we performed approximate deflection calculations using the simple linear model of Jordan5. Assuming a Te of 20 km (ref. 2) and spatially averaged
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References Parker, R. N. et al. Nature Geosci. 4, 449–452 (2011). Gunn, R. J. Frankl. Inst. 236, 373–390 (1943). Wager, L. R. Nature 132, 28 (1933). Holmes, A. Principles of Physical Geology 189–190 (Thomas Nelson and Sons, 1944). 5. Holmes, A. Principles of Physical Geology 2nd edn, 575–576 (Ronald Press, 1965). 6. Godard, V. et al. Tectonics 28, TC5009 (2009). 7. McConnell, R. K. Jr J. Geophys. Res. 73, 7089–7105 (1968). 1. 2. 3. 4.
Peter Molnar Department of Geological Sciences, Cooperative Institute for Research in Environmental Sciences (CIRES), University of Colorado at Boulder, Boulder, Colorado 80309-0399, USA. e-mail:
[email protected]
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correspondence erosion of 1 m over an across-strike distance of about 50 km (the approximate across-strike dimension of the area of highest landslide density6), erosionally driven rock uplift should replace only about 38% of the volume of rock removed from the orogen. If Te is 40 km (ref. 3), this amount decreases to 25%. Although this is a highly oversimplified model of a spatially heterogeneous orogen in which viscoelastic effects7 are likely to be important over the long term, this exercise demonstrates that the apparent volume imbalance is unlikely to be cancelled out within the orogen by the flexural-isostatic response. Finally, to Peter Molnar’s list of caveats, we would add another: the flexuralisostatic response to the Wenchuanearthquake-triggered landslides will be critically dependent on the details of how the landslide-derived clastic sediment is
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redistributed, which are almost totally unknown at present. Although we argued that long-term sediment storage in the Longmen Shan is unlikely, we simply do not know the rates and volumes of sediment movement within and out of the orogen. Moreover, the response will differ depending on whether that material is sequestered in the Sichuan Basin or exported from the region via the Yangtze River system, which makes more detailed flexuralisostatic calculations highly speculative. This highlights a pressing need to better understand fluxes of material into and out of orogens if the true volume balance, defined over a specific timescale, is to be known. ❐ References 1. Parker, R. N. et al. Nature Geosci. 4, 449–452 (2011). 2. Jiang, X. & Jin, Y. J. Geophys. Res. 110, B07407 (2005). 3. Jordan, T. A. & Watts, A. B. Earth Planet. Sci. Lett. 236, 732–750 (2005).
4. 5. 6. 7.
Li, Y., Allen, P. A., Densmore, A. L. & Qiang, X. Basin Res. 15, 117–138 (2003). Jordan, T. E. Am. Assoc. Petr. Geol. B 65, 2506–2520 (1981). Dai, F. C. et al. J. Asian Earth Sci. 40, 883–895 (2011). Godard, V, Cattin, R. & Lave, J. Geophys. J. Int. 179, 763–777 (2009).
Alexander L. Densmore1*, Robert N. Parker1, Nicholas J. Rosser1, Marcello de Michele2, Li Yong3, Huang Runqiu3, Siobhan Whadcoat1 and David N. Petley1 1 Institute of Hazard, Risk and Resilience and Department of Geography, Durham University, Durham DH1 3LE, UK, 2Bureau de Recherches Géologiques et Minières, Natural Risks Division, 45060 Orléans Cedex 2, France, 3 State Key Laboratory of Geohazard Prevention and Geoenvironment Protection, Chengdu University of Technology, Chengdu 610059, Sichuan Province, China. *e-mail
[email protected]
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