Abstract:
The effect of the stress in a rock medium on the seismic velocity in it can be predicted from a model of the elastic medium that assumes it to be physically nonlinear. Thus, to define the stress state of the given point from seismic data one must approximate the directional dependence of the group velocity of the waves arriving at that point by an ellipsoid. The directions of the axes of the ellipsoid overlap the directions of the principal axes of the strain tensor, and the lengths of its semiaxes allow one to find the tensor. Two possible solutions of this problem exist. The first case is when the velocities have been measured at a point on the Earth's surface. A second case is when the distribution of velocities in a specific space is know. In the first case, the additional conditions that produce the needed additional equations are the conditions for the absence of forces at the free surface. In the second case, the additional condition are the conditions governing the simultaneity of deformations. Presented method allows one to determine the orientation of the axes of principal stresses and to calculate the ratio of principal stresses.