Surface wave generation from a constant-slope-inducing asymmetric ocean floor motion: influence of compressible ocean

Ocean surface wave profile due to the movement of an asymmetric (sloping) block of the ocean floor is analytically derived under the assumption of linearized water wave theory and by using the Fourier transformation method. A slight compressibility of the ocean water allows for generating acoustic-gravity modes that travel much faster than tsunami waves, the detection of which can contribute towards a possible warning mechanism. The influence of different parameters of interest, namely ocean depth, length, and slope of the block, on the surface wave profile is shown in the frequency domain. Finally, the frequency-domain solution is utilized to provide the surface profile in the time domain. The stationary phase approximation is applied to extract the far-field behavior of the surface waves. The individual impact of the acoustic-gravity and pure gravity modes is shown. Due to the asymmetry of the bottom motion, two different types of far-fields in opposite directions of each other from the source of initial ocean floor motion are obtained. The classical solutions of horizontal and flat moving ocean floors studied by Yamamoto (DOI:https://doi.org/10.1016/0261-7277(82)90016-X) in the frequency domain and Stiassnie (DOI: https://doi.org/10.1007/s10665-009-9323-x) in the time-domain are recovered as special cases. The envelope amplitude of the far-field surface fluctuates less when slope exists. The contributions from the acoustic-gravity modes in the far-field surface amplitude in the opposite directions are in opposite phases. The pure-gravity mode contribution is higher towards the direction of increasing slope with more oscillation. These results show insight into the surface profile when a submarine earthquake moves the ocean floor asymmetrically, and they could lead to a possible estimation of the fault geometry. These results can also be utilized to approximate arbitrary bottom movement using superposition of piece-wise asymmetric moving ocean floor arranged in a line and may provide important information for early tsunami detection mechanisms in the future.