A systematic and efficient method of computing normal modes for multilayered half-space

We present a systematic and efficient approach for computing the dispersion curves (i.e. phase velocities for a given frequency) as well as the eigenfunctions of normal modes in a multilayered half-space medium. Our approach is superior to previous approaches in the following aspects. First, it is a simple and self-contained algorithm for simultaneously determining both the phase velocities and the corresponding eigenfunctions. From the basic principle that the normal modes are non-trivial solutions of the free elastodynamic equation under appropriate boundary conditions, we naturally derive the phase velocities and eigenfunctions. Second, because we use the reflection/transmission coefficients of Luco & Apsel's version (Luco & Apsel 1983), which intrinsically exclude the growth terms, our algorithm not only exhibits the physical mechanism of the formation of normal modes, i.e. constructive interference, as Kennett's did (1979, 1983), but also is numerically more stable for high-frequency cases. Furthermore, we derive a high-frequency asymptotic solution of the fundamental Rayleigh mode. Therefore, our approach can provide efficient and accurate solutions in any frequency range, and it is expected to be a powerful and useful tool for simulating the Lg and Rg phases and complete seismograms at regional distances.