Least squares restoration of Tertiary thrust sheets in map view, Tajik depression, central Asia

Abstract

The Tajik depression, located west of the Pamirs and south of the Tien Shan, is a compressional intermontane basin, bounded by basement overthrusts and filled with Mesozoic and Cenozoic sediments. The internal structure is typical of a thin‐skinned fold and thrust belt. Kinematic data available in the literature suggest that indentation of the Pamirs into Asia during the Cenozoic collision of India and Asia has been accommodated in various ways within the depression, including westward extrusion, thickening combined with wrenching along N‐S folds and thrusts, and counterclockwise rotations. These various deformation processes can be analyzed and quantified by reconstruction of the predeformed state of the depression. However, the combination of thrusting, wrenching and block rotations implies a nonplane deformation, which cannot be restored properly using balanced cross sections alone. We have therefore developed a numerical method for restoration of stratigraphic surfaces, designed for regions of nonplane compressional tectonics. The deformed region is represented in map view as a mosaic of fault‐bounded blocks, overlapping each other along the faults. Blocks are separately unfolded and then numerically packed together by least squares minimization of overlaps, yielding fields of finite horizontal translations and rotations about vertical axes. To analyze the deformation postdating the collision of India and Asia, we have restored a stratigraphic surface at the base of the Cenozoic. First, in order to test the numerical method, we restored a map that had previously been restored by a purely manual method. Restoration of a second map, drawn from newly available subsurface data, leads to geometrical inconsistencies: overlaps and gaps, which cannot be reduced, remain in the restored state. After correction of these inconsistencies, restoration yields a complex mode of deformation for the depression. Individual thrust slices have undergone counterclockwise rotations about vertical axes, the magnitudes increasing from west to east, up to a maximum of 40° near the Pamirs. Horizontal shortening is 150 km (35%) in the center of the depression and 240 km (85%) in the northeastern part, between the Pamirs and the Tien Shan. Strike slip motions, commonly not revealed by balancing cross sections, are associated with thrusting on faults striking N‐S. Independent paleomagnetic data and slip directions on small‐scale faults provide positive checks on the results of our restoration.