Predicting Method for Transformation of Infragravity Waves with Interferometric Green's Functions

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A stochastic forcing model has been developed to estimate the heights of infragravity waves excited by short gravity surface waves. The model includes a wave equation for infragravity waves with the external force term due to pressure disturbances by short gravity waves. The analytical solution of the wave equation was obtained, and the root-mean-square value of the surface elevation of infragravity waves was estimated.. The rms value is proportional to the square root of the spectral moment of -2 order, m_<-2>, of short gravity waves, which is also proportional to the product of the wave height and the peak wave period or the significant wave period of short gravity waves.The propagation of infragravity waves in intermediate water depths near and in a port is investigated with field observations. A Green function method which is used for seismic interferometry is applied to estimate wave profiles of infragravity waves. It is shown that when external forces are uncorrelated noise source, Green functions between two points can be retrieved by taking cross-correlation of records. The wave profiles of infragravity waves are estimated with the Green function and compared with the measured data. The agreement between them shows fairly good.