Impact of Ocean Compressibility, Earth Elasticity, and Background Density on Surface Gravity and Compressional Wave Dynamics

Traditionally, the ocean is treated as an incompressible fluid to simplify wave modeling. However, ocean compressibility—dictated by its density and bulk modulus—significantly impacts wave dynamics, particularly for long-period surface waves (>30 s) and compressional waves within the water column. Similarly, Earth's transition from rigid to elastic behavior under surface loads further influences wave propagation by altering phase speed and waveforms. These effects manifest as arrival time discrepancies and waveform modulation, as observed in tsunami and long-wave dynamics (Allgeyer & Cummins, 2014; Abdolali et al., 2017, 2019).This study explores the combined effects of ocean compressibility, Earth elasticity, and background density on wave characteristics across a wide frequency range, including infra-gravity (IG), storm surge, tidal waves, and compressional acoustic waves. Building on prior work, a dispersion relationship is derived, accounting for dynamic ocean compression under gravity interacting with a finite, multi-layered elastic Earth. By analyzing phase speed, group velocity, travel times, and pressure profiles, this research advances understanding of wave dynamics and offers a robust framework for improved modeling of tides and storm surges, coastal flooding, tsunamis, and acoustic wave propagation.Abdolali, A., & Kirby, J. T. (2017), Role of compressibility on tsunami propagation. Journal of Geophysical Research: Oceans, 122, 9780–9794.Abdolali, A., Kadri, U. & Kirby, J.T. (2019), Effect of Water Compressibility, Sea-floor Elasticity, and Field Gravitational Potential on Tsunami Phase Speed. Scientific Reports, 9, 16874Allgeyer, S., & Cummins, P. (2014). Numerical tsunami simulation including elastic loading and seawater density stratification. Geophysical Research Letters, 41(7), 2368-2375.