Chigarev A., Kireyeva I., Gudehus G.

Wave propagation in a hipoplastic medium describes some effects which are observed in during earthquakes. As the capacity of small parameter is taken the expression , where T, are stress tensor and initial stress tensor. The authors obtained the solutions of supplied problems at first approximation. We consider a finding of next approximation. If disturbance amplitudes of stresses are weak relative to initial stress state, so waves propa-gate as elastic waves in porous body with water. For homogeneous initial stress and constant den-sity these wave propagate with constant effective velocities. However already in this approximation we can consider plastic waves in case when grains of skeleton are under relative displacements with friction. The model of a hipoplastic medium with intergranular strain gives a possibility to calculate the speeds of plastic waves. Mathematical methods don’t allow considering the wave propagation in a hipoplastic medium for inhomogeneous initial stress state and variable density. In that article we consider the ray method which is the greatest in geometrical seismology. In bases of the ray method application for hypoplasticity we lie following repeated tested conditions: 1. A disturbance of field value propagates in medium of a wave surface. 2. The solutions of dynamical equations are the series, which describe field values change in a en-virons of wave surface along ray trajectory. 3. For the coefficients of these series are found the transfer equations, which are ordinary differen-tial equations and may be solved analytical. 4. Obtained solutions are right along ray trajectories. The trajectories of the rays are found from Fermat principle. 5. A power of a disturbance propagates inside of the ray pipe.