Rayleigh-Taylor instability, lithospheric dynamics, surface topography at convergent mountain belts, and gravity anomalies

[1] Surface topography and associated gravity anomalies above a layer resembling continental lithosphere, whose mantle part is gravitationally unstable, depend strongly on the ratio of viscosities of the lower-density crustal part to that of the mantle part. For linear stability analysis, growth rates of Rayleigh-Taylor instabilities depend largely on the wave number, or wavelength, of the perturbation to the base of the lithosphere and weakly on this viscosity ratio, on plausible density differences among crust, mantle lithosphere, and asthenosphere, and on ratios of crustal to total lithospheric thicknesses. For all likely densities, viscosities, and thicknesses, the Moho is drawn down (pushed up) where the base of the lithosphere subsides (rises). For large viscosities of crust compared to mantle lithosphere (ratios> ~30), a sinking and thickening mantle lithosphere also pulls the surface down. For smaller viscosity ratios, crustal thickening overwhelms the descent of the Moho, and the surface rises (subsides) above regions where mantle lithosphere thickens and descends (thins and rises). Ignoring vertical variations of viscosity within the crust and mantle lithosphere, we find that the maximum surface height occurs for approximately equal viscosities of crust and mantle lithosphere. For large crust/mantle lithosphere viscosity ratios, gravity anomalies follow those of surface topography, with negative (positive) free-air anomalies over regions of descent (ascent). In this case, topography anomalies are smaller than those that would occur if the lithosphere were in isostatic equilibrium. Hence, flow-induced stresses—dynamic pressure and deviatoric stress—create smaller topography than that expected for an isostatic state. For small crust/mantle viscosity ratios (< ~10), however, calculated surface topography at long wavelengths is greater than it would be if the lithospheric column were in isostatic equilibrium, and at short wavelengths local isostasy predicts surface deflections of the wrong sign. For the range of wavelengths appropriate for convergent mountain belts (~150–600 km), calculated gravity anomalies are negative over regions of lithospheric thickening, especially when allowance for flexural rigidity of a surface layer is included. Correspondingly, calculated values of admittance, the ratio of Fourier transforms of surface topography and free-air gravity anomalies, are also negative for wave numbers relevant to mountain belts. For essentially all mountain belts, however, measured free-air anomalies and admittance are positive. Whether gravitational instability of the lithosphere affects the structure of convergent belts or not, its contribution to the topography of mountain belts seems to be small compared to that predicted for isostatic balance of crustal thickness variations.