Low-Frequency Dispersion-Function Factorization and Classification of P-SV Modes by Wavenumber Limits

Abstract

The dispersion function for P‐SV wave propagation in a laterally homogeneous fluid‐solid medium is a characteristic function for a multi‐point boundary‐value problem, and it can be expressed as a product of compound‐matrix propagators. It is studied asymptotically when the frequency tends to zero, as a function of the horizontal wavenumber. An entire function is obtained, whose zeros determine the limits as the frequency tends to zero for the horizontal wavenumbers of the wave‐guide modes. The entire function can be factorized with scalar factors, which can be evaluated by solution of ordinary differential equation (ODE) systems. The order of its zero at the origin determines the number of modes with vanishing low‐frequency wavenumber limits. Interface waves and different types of bending waves are particular examples of such modes. In addition, there will be one factor from each fluid or solid region. Hence, the modes with nonzero wavenumber limits decouple into region‐dependent classes at low frequency, and they can be classified according to low‐frequency connection to the different regions. The decoupling is elucidated by an asymptotic analysis of the mode shapes.