Computation of modal solutions in layered, elastic media at high frequencies

Modal calculations of wave propagation in layered, elastic media exhibit numerical difficulties at high frequencies. This report shows that these difficulties are caused by the computation of squares of exponential terms which, although they cancel numerically, cause a loss of significant figures in the secular function and the components of certain matrix products. A matrix formulation is presented that avoids these difficulties and gives a natural decomposition of the modal solutions into source and receiver parts. The formulation is applied to layered systems containing both fluid and solid layers as well as to systems composed of solid layers alone.