Shallow Earth Elasticity from Sweeping Atmospheric Pressure Waves in the Coupled Earth

The eruption of the Hunga Tonga-Hunga Ha’apai (hereafter referred to as Hunga-Tonga) on January 15, 2022, generated atmospheric pressure waves (Lamb waves) that traveled around the globe (Matoza et al., 2022). These waves were associated with ground deformation in the solid Earth and analyzed as a pressure-loading problem in a previous study by Anthony et al. (2022). Strictly speaking, the deformation of the solid Earth is an integral component of Lamb waves in the coupled Earth system. In this study, we develop an analysis method for Lamb waves within a coupled Earth model.

Our focus is on analyzing the ratio between vertical displacement and surface pressure, referred to as the compliance ratio, which provides critical insights into the elasticity of the upper crust. We demonstrate an inversion method to utilize this ratio for determining shallow crustal elasticity. This approach is analogous to the compliance method used for seismic noise to constrain the elasticity of sedimentary layers on the ocean floor (Crawford et al., 1991) and the elasticity of shallow structures at seismic stations equipped with co-located pressure sensors (e.g., Tanimoto and Wang, 2018, 2019).

Depth sensitivity kernels for the compliance ratio can be obtained through numerical differentiation. These compliance data primarily exhibit sensitivity to the near-surface shear modulus, with additional sensitivity to the shallow bulk modulus at hard rock sites. Given the Lamb wave phase speed of approximately 310 m/s and the high-coherence range limit of around 0.01 Hz, the depth range of reliable resolution is confined to the upper crust (approximately 5-15 km deep).

This method, initially developed for stations with co-located pressure and seismic sensors, can also be extended to stations equipped only with seismic sensors. This extension is feasible because Lamb wave waveforms exhibit minimal variation. By analyzing the coherence between seismic and pressure data from nearby locations, we can select suitable pairs of seismic and pressure data and apply our compliance method.

We demonstrate that this method can not only derive new information about shallow structures but also serve as a valuable tool for testing shallow structures in existing seismic velocity models. Improvements in our understanding of shallow elasticity structures are crucial for accurate ground motion predictions in seismically active regions worldwide.