ASYMPTOTIC REPRESENTATION OF THE FILTRATION-WAVE FIELD IN THE LAYER OF AN INHOMOGENEOUS MEDIUM IN THE FORM OF A PLANE WAVE

The fi ltration-wave process in the central layer of a three-layer anisotropic medium is described as an equivalent plane wave with a modifi ed asymptotic method accurate in the mean. The initial problem is parametrized and broken down into simpler problems for the coeffi cients of expansion in an asymptotic parameter. The zero expansion coeffi cient describes the sought plane wave, whereas the fi rst coeffi cient ensures refi nement of the
wave-front geometry. The exact solution of the parametrized problem is obtained on the basis of the Fourier sine transformation. The correctness of the developed method is confi rmed by comparing the obtained asymptotic
solutions and the coeffi cients of Maclaurin-series expansion of the exact solution of the parametrized problem in a formal parameter.
The fi ltration-wave process in the central layer of a three-layer anisotropic medium is described as an equivalent plane wave with a modifi ed asymptotic method accurate in the mean. The initial problem is parametrized and broken down into simpler problems for the coeffi cients of expansion in an asymptotic parameter. The zero expansion coeffi cient describes the sought plane wave, whereas the fi rst coeffi cient ensures refi nement of the
wave-front geometry. The exact solution of the parametrized problem is obtained on the basis of the Fourier sine transformation. The correctness of the developed method is confi rmed by comparing the obtained asymptotic
solutions and the coeffi cients of Maclaurin-series expansion of the exact solution of the parametrized problem in a formal parameter.
Author:  A. I. Filippov, O. V. Akhmetova, and A. A. Koval′skii
Keywords:  wave equation, asymptotic method, wave pressure fi eld, exact solution, fi ltration, anisotropic medium
Page:  1410