Acoustic-gravity waves in a spherically layered atmosphere-solid Earth model generated by a point source on the ground

This study introduces a new method for calculating acoustic-gravity waves in a spherically layered atmosphere. The method introduces a model assumption and divides the atmosphere into finely stratified layers to solve the PDE with respect to the radial coordinate. The time-domain synthetic signal is obtained by summing over the orders of the associated Legendre functions and then applying the FFT. The method is applied to numerically simulate wave behaviour, including Earth curvature effects, and compares with the horizontally layered model (HLM). Results show that at near-field distances, our method aligns closely with HLM, but significant differences emerge in the far field, particularly beyond an epicentral distance of 50°, where Earth curvature becomes critical. Our method successfully simulates head waves of seismic phases, and Rayleigh waves, even for waves travelling multiple times around the Earth, which HLM cannot achieve. Simulations using a homogeneous Earth model reveal head wave characteristics consistent with previous studies, with the strongest energy observed in Rayleigh head waves. The application of the AK135 Earth model highlights the visibility of seismic phases through the Earth's core. We validate our method by comparing synthetic records with actual data from the 1999 Chi-Chi earthquake. The synthetic records show good agreement with observed seismic signals and ionospheric perturbations in terms of arrival time and wave envelope. These results demonstrate the accuracy of our method in simulating acoustic-gravity waves at large epicentral distances.