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In this paper, we propose a unified and high order accurate fully-discreteone-step ADER Discontinuous Galerkin method for the simulation of linearseismic waves in the sea bottom that are generated by the propagation of freesurface water waves. A hyperbolic reformulation of the Serre-Green-Naghdi modelfor nonlinear dispersive free surface flows is coupled with a first ordervelocity-stress formulation for linear elastic wave propagation in the seabottom. Cartesian non-conforming meshes are defined and the coupling isachieved by an appropriate time-dependent pressure boundary condition in thethree-dimensional domain for the elastic wave propagation, where the pressureis a combination of hydrostatic and non-hydrostatic pressure in the watercolumn above the sea bottom. The use of a first order hyperbolic reformulationof the nonlinear dispersive free surface flow model leads to a straightforwardcoupling with the linear seismic wave equations, which are also written infirst order hyperbolic form. It furthermore allows the use of explicit timeintegrators with a rather generous CFL-type time step restriction associatedwith the dispersive water waves, compared to numerical schemes applied toclassical dispersive models. Since the two systems employed are written in thesame form of a first order hyperbolic system they can also be efficientlysolved in a unique numerical framework. We choose the family of arbitrary highorder accurate discontinuous Galerkin finite element schemes. The developedmethodology is carefully assessed by first considering several benchmarks foreach system separately showing a good agreement with exact and numericalreference solutions. Finally, also coupled test cases are addressed. Throughoutthis paper we assume the elastic deformations in the solid to be sufficientlysmall so that their influence on the free surface water waves can be neglected.

High order ADER-DG schemes for the simulation of linear seismic waves induced by nonlinear dispersive free-surface water waves