Elastic Oscillations of the Water Layer in a Tsunami Source

摘要

The theoretical analysis of water compression in the tsunami problem carried out in [1] allows us to state that the effects of compression are significant only at the stage of tsunami generation by an earthquake, while the propagation and onshore wave run-up can be described as incompressible fluid motion. In the case of a horizontal (absolutely rigid) bottom, the main difference in the behavior of a compressible ocean, as compared to an incompressible model medium, is in the formation of elastic oscillations of the water column that are characterized by a discrete set of normal frequencies v_k = c(1 + 2k)/4H, where k = 0, 1, 2, ..., H is the ocean depth, and c is sound velocity in water. Under the typical conditions in a tsunami source v_0 ～ 0.1 Hz. Actually, tsunami sources are located in a region with complex bathymetry. However, the slope of the ocean bottom is usually small (<0.1). Hence, at a certain point of the source, elastic oscillations with normal frequencies determined by the ocean depth at this point are formed first of all. Later, the spectrum of elastic oscillations may be enriched with high frequencies due to waves that have propagated from the neighboring shallow regions. Owing to the existence of the cut-off frequency, low-frequency oscillations formed in the neighboring deep regions do not propagate upward the slope.