The Gravity Effect of Core Modes for a Rotating Earth

Previous work has shown that the surface gravity effect associated with core modes (undertones) for a non-rotating Earth model is at or below the nanogal level of detectability for a large earthquake excitation. The assumption in the non-rotating case is that each undertone consists of a single spherical harmonic. In this study we add the Coriolis force to the equations governing the oscillations in a rigid shell with the Boussinesq approximation. By including up to 20 additional harmonics, we find that there are many solutions that are still dominated by low-degree spherical harmonics when judged by the distribution of kinetic energy among the harmonics. For these modes the contribution of higher degrees to the eigenfunctions is not substantial, which suggests that the addition of rotation will probably not significantly change the gravity effects computed without rotation. This conclusion remains tentative until verified in a fuller treatment that explicitly evaluates the excitation for a rotating Earth model.