Uniformly asymptotic eigensolutions of the Earth's toroidal modes

Abstract

SUMMARY A novel approach to computing the Earth's normal modes is presented. With the Langer approximation incorporated into the framework of the theory of the generalized reflection/transmission coefficients, our method, when applied to calculate the toroidal modes, produces results that agree extremely well with the exact results from Mineos and successfully overcomes the limitations of the WKBJ analysis. Given any 1-D earth model, regardless of the number of discontinuities, our method can perform the calculations reliably with satisfactory accuracy at high frequencies. The success achieved with the toroidal modes encourages us to tackle in a future study the asymptotic computation of the spheroidal modes, especially those high-frequency trapped modes for which the accuracy of Mineos is demonstrably inadequate.