On intensity of high-frequency surface waves in anisotropic elastic media. The energy approach

Abstract

The present, paper deals with the solution of the transport equations for the principal order term <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">rarr</sup> A <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> of the asymptotics of surface waves near the surface of anisotropic elastic body. The space-time ray method is employed in contrast to the previous results of the author. For finding the intensity | <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">rarr</sup> A <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> | an alternative approach is suggested. Firstly, trivial transformations of the recurrent system for the coefficients of ray solution are applied. Secondly, the energy approach of averaging the flux carried along the rays is used. This yields transport equations for the amplitudes of two ray families near the surface S (for rays approaching S and for rays reflected by S). The transport equations are solved in standard ray form by choosing ray parameters in a special manner in the presence of space time caustics. The final formula for the intensity | <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">rarr</sup> A <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> | is obtained by bringing the point of tangency of the ray and the caustic to the surface S