Three‐dimensional critical wedges: Tectonics and topography in oblique collisional orogens

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Abstract
In orogens deforming in oblique compression, both the long wavelength (mean) topography of averaged slopes and the higher frequency topography (first harmonic) of valleys and ridges are related to the mechanics of deformation in three dimensions and cannot be adequately modeled in two dimensions. A method of analysis of the principal stresses, failure planes, and topography is presented for three‐dimensional critical wedges. In a critical Coulomb orogen which is at failure throughout, the components of the stress tensor are interrelated through the failure condition defined in terms of the principal stresses. Variation of any of the Cartesian components must be accommodated by adjustment of one or more of the other components so that the orogen remains at failure. This coupling of Cartesian components to maintain the wedge at failure permits exploration of the behavior of a three‐dimensional, critical orogen in which shear stresses arise outside of the plane of convergence. Internal adjustment of shear stresses to externally imposed stress conditions results in the formation of characteristic orogen shapes. For an oblique collision zone such as the Southern Alps of New Zealand, the resultant mountain belt is one of an obliquely deforming outboard fold‐thrust belt with subdued relief rising abruptly into a steep backslope to the main divide which falls steeply to the indentor, forming the inboard slope. The outboard topographic slope is reduced in relation to that of the two‐dimensional orogen. The rigid indentor has a fixed strike and therefore imposes a failure orientation adjacent to the indentor that differs from that of the ideal three‐dimensional critical wedge solution. This produces several different slip orientations and minor partitioning of strain near the indentor. First harmonic topography of valleys and ridges arises due to nonlinear, heterogeneous behavior of both erosional and mechanical processes and is characterized by uplift‐controlled ridges in the outboard and incision‐controlled valleys in the inboard.