Far-field surface wave and pressure in a compressible ocean induced by the ocean floor's sinusoidal vertical movement

Surface wave propagation mirroring tsunami waves induced by a sinusoidal-type spatial motion of a portion of the ocean floor, representing multi-fault submarine earthquakes and fundamental geometry to approximate generic motion using Fourier series expansion, is studied using a linearized water wave theory. Ocean water compressibility is included to facilitate the propagation of acoustic-gravity wave (AGW) modes and their influence on the surface gravity wave and ocean floor pressure profile. The sinusoidal movement is approximated with multiple opposite-moving, dual rectangular blocks of the ocean floor staggered consecutively. The far-field surface and bottom pressure profiles are obtained by solving the boundary value problem associated with the dual blocks using the Fourier transformation and the stationary phase approximation. The corresponding profiles for the sinusoidal-like motion are found using the superposition of the solution pertaining to individual dual-blocks. The model is validated with the existing literature and tested against cases of sinusoidal profiles with constant and decaying amplitudes. The far-field surface and pressure profiles show the dominance of the non-leading AGW modes over the leading mode when the number of sinusoidal ripples in the fault profile is high. The larger n-th AGW mode's dominance in the far-field response is entangled with higher ripple numbers. The temporal pulses of surface elevation and bottom pressure are narrower and shorter for higher ripple numbers. For seabed profiles with decaying sinusoidal motion, a higher decay rate sharpens the pulse structure and enhances late-time signals. The finding shows the importance of non-leading AGW modes, which are otherwise deemed insignificant.