Gravity anomalies and the flexure of the lithosphere in the Karakoram, Pakistan

The negative correlation between gravity anomalies in mountain regions and the topographic height implies a mass deficency beneath the range and adjacent regions. Classical compensation schemes in which roots of constant density form at a depth proportional to the topographic height (Airy scheme) or individual columns of laterally variable density develop to a constant depth (Pratt scheme) enable only part of the anomalies to be modeled and provide a “static” description of the structure of the crust and upper mantle, regardless of the vertical and horizontal motions associated with the origin and evolution of mountain belts. Early studies of isostatic anomalies across the Karakoram range, in northern Pakistan, have shown that the region is not in isostatic equilibrium in the Airy sense and have pointed to the need of a more refined model of the forces and stresses shaping the lithosphere than classical isostasy. The concept that the lithosphere should respond by flexure to applied loads as a thin, elastic, semi-infinite plate buoyant on a denser, inviscid fluid is used here as the basis to compute model Bouguer anomalies, estimate by least squares the deformation of the plate, and constrain some of the plate's elastic parameters. It is assumed that the forces responsible for the deformation are the topographic load, the hydrostatic response, and the elastic stresses within the plate. The plate itself is assumed to be separated into an Indian and an Asian portion, each with its own equivalent elastic thickness. At the border between the two portions an empirical infracrustal point load is assumed to act vertically. Gravity anomalies are then computed along five profiles crossing the range, as a function of the abscissa of the border point, the load acting at this point, the elastic thicknesses of the Indian and Asian portions of the plate, and the density contrast across the median section of the plate. The corresponding numerical values and associated formal uncertainties are determined by a least squares fit of the model anomalies to the observed Bouguer anomalies, along each of the five independent profiles. The postfit residuals are found to have essentially zero mean and an rms (root mean square) dispersion of the order of 20 mGal, which is consistent with the expected overall accuracy of the “observed” Bouguer anomalies interpolated to the profiles. The distribution of the post fit residuals still shows systematic components at the level of a few tens of mGal, that are likely to be caused by local, shallow geological structures. Overall the peak-to-peak excursion of the residual anomalies is considerably smaller than the classical isostatic anomalies for the same region. It is found that (1) the line connecting the estimated abscissas of the border points on each profile follows closely suture lines which have been independently identified from geological data and could be associated with the center of mass of the Kohistan-Ladakh island arc considered as a buried load; (2) for all profiles the elastic thickness of the Indian plate is systematically less than for the Asian plate, typically 80–100 km for India and 100–120 km for Asia; (3) there is a tendency of the elastic thickness of both portions to increase moving NW, towards the Pamirs. The gravity data are thus consistent with a relatively rigid Asian plate in the Tarim basin, unlike the Central Himalaya where Tibet, being indented by India, has zero strength.