Tectonic and gravitational stress in long symmetric ridges and valleys

Abstract

We present an exact elastic solution for the effects of topography on the near‐surface stresses caused by a uniform, uniaxial tectonic compression or tension acting normal to the axial planes of isolated symmetric ridges and valleys of realistic shape. The solution, obtained by the Kolosov‐Muskhelishvili method of complex potentials, gives stresses in the vicinity of these topographic features that, with the exception of the vertical component, are of the order of the regional tectonic stress. The effect of topography is to reduce a regional tectonic compression near the crest of a ridge and, if the ridge is sufficiently steep, to cause a stress reversal resulting in a small tension. Valleys, on the other hand, concentrate the far‐field tectonic stress. When a previously derived exact solution for the topographic effect on the gravity‐induced stress field is combined with the present solution for the topographic modification of a regional compressive tectonic stress, we find a slight increase in the lateral components of the gravity‐induced compressive stress at the ridge crest and, under the valley bottoms, a decrease in the gravity‐induced tensile stresses. The opposite effects occur when a far‐field tension is superposed on the gravity‐induced stress field.