P- and S-wave energy flux density vectors

Abstract

The conventional energy flux density vector indicates the propagation direction of mixed P- and S-wave wavefields, which means when a wavefront of P-wave encounters a wavefront of S-wave with different propagation directions, the vectors cannot indicate both directions accurately. To avoid inaccuracies caused by superposition of P- and S-waves in a conventional energy flux density vector, P- and S-wave energy flux density vectors should be calculated separately. Because the conventional energy flux density vector is obtained by multiplying the stress tensor by the particle-velocity vector, the common way to calculate P- and S-wave energy flux density vectors is to decompose the stress tensor and particle-velocity vector into the P- and S-wave parts before multiplication. However, we have found that the P-wave still interfere with the S-wave energy flux density vector calculated by this method. Therefore, we have developed a new method to calculate P- and S-wave energy flux density vectors based on a set of new equations but not velocity-stress equations. First, we decompose elastic wavefield by the set of equations to obtain the P- and S-wave particle-velocity vectors, dilatation scalar, and rotation vector. Then, we calculate the P-wave energy flux density vector by multiplying the P-wave particle-velocity vector by dilatation scalar, and we calculate the S-wave energy flux density vector as a cross product of the S-wave particle-velocity vector and rotation vector. The vectors can indicate accurate propagation directions of P- and S-waves, respectively, without being interfered by the superposition of the two wave modes.