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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.

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A new graphical method is introduced that facilitates the representation and interpretation of the generally anisotropic in situ states-ofstress measured in rocks. The purpose of the method is to clearly and easily display these stress states, each measured in terms of three values, in two-dimensional space; this is done by projecting three-dimensional stress space onto a triangular-coordinate (ternary) diagram and plotting the measured stress states as points. Failure surfaces determined either by experiment or by invoking hypothetical failure criteria are plotted on the diagram to enclose the stability field. Thus, an anisotropic stress condition measured at a given depth in the Earth's crust is represented by a single point on the triangular diagram and its relative position in the enclosed stress space may yield useful information on the degree of mechanical stability of the rock mass at the point of measurement. The method also allows the representation of any number of measured stress states in a given locality, each plotted in its own position. This method is most useful as a reconnaissance tool, provided complete measurements of in situ stress as a function of depth are available, to correlate them with information obtained by different, more indirect methods. A variety of stress paths either associated with the measured stress-depth distribution, or modified by fluid injection or mined excavations, among others, can be traced or extrapolated to establish whether the imposed disturbance leads to failure of crustal rocks.