A mode-matching method for models involving both horizontal and vertical interfaces is presented. In this method, the solution is represented in terms of modes inside and outside the borehole, and the modes are matched on the borehole wall to yield the solution. The method uses vertical modes (i.e. modes defined with respect to the vertical coordinate z). The receiver signal consists of a direct signal traveling within the borehole and a reflection signal bearing information about the rock formation outside the borehole. Compared to previous methods using modes defined with respect to the horizontal coordinate, the present method has advantages in terms of computational efficiency and data interpretation.
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