A theory for In Situ stresses in isotropic and transverseley isotropic rock

Abstract An elasto-static thermal stress model of the earth is presented for estimating crustal stresses considering the variation of elastic constants, density and thermal expansion coefficient through the crust and mantle. The stresses obtained from the model are shown to be an average fit to stress measurement data. The factor responsible for causing higher values of the horizontal-to-vertical stress ratio k nearer to the surface is shown to be the earth's curvature. The model and its one variation which considers transverse isotropy indicate that the horizontal stress depends on the elastic modulus measured in the horizontal direction. An equation is proposed for obtaining the horizontal stress in soft, jointed or generally weaker formations when stress measurement is carried out in competent rocks at the same location. It is shown that stress values measured in one rock cannot be extrapolated to other rocks in the same area if their elastic moduli are different. The dependence of horizontal stress on elastic modulus is corroborated by 46 published stress measurement data and average prediction equations for horizontal stress and k are proposed in terms of the elastic modulus.