An initial value approach to the excitation of atmospheric Lamb and Pekeris waves

This paper aims to analytically elucidate the excitation mechanisms of atmospheric Lamb and Pekeris waves by formulating them as an initial value problem based on linear models. Previous studies on the excitation of atmospheric waves by eruptions or explosions have primarily relied on numerical simulations; no study has analytically derived the excitation amplitudes of these waves from a given initial disturbance. In this study, we first formulate the excitation process of Lamb waves analytically in both hydrostatic and non-hydrostatic models with an isothermal background atmosphere, utilizing Fourier transforms and residue integration in the complex frequency plane. Furthermore, we extend this method to present a novel residue-analytical method for determining the amplitudes of Lamb and Pekeris waves excited from an initial disturbance in an atmosphere with a realistic vertical temperature structure. The validity of the analytically derived amplitudes is verified by numerically calculating the time evolution of the initial value problem. In addition, we discuss the attenuation characteristics of these waves when the temperature structure up to the thermosphere is taken into account. The analytical approach presented in this study not only deepens the theoretical understanding of the excitation processes of atmospheric waves from initial disturbances, but also contributes to the validation of complex nonlinear numerical models.