4:00 PM - 4:15 PM
[SSS07-13] Simultaneous FDM calculation of seismic waves and tsunamis, distinguishing Eulerian and Lagrangian changes
Keywords:tsunami, simultaneous calculation of seismic waves and tsunamis
When an earthquake occurs beneath the seafloor, several types of waves are excited, including seismic waves, ocean acoustic waves and tsunamis. A unified modeling scheme of these waves is desired to better understand rupture processes at faults, to issue robust early warnings of tsunamis, and to accurately interpret distant tsunami data. Such modeling requires numerical calculations that correctly couple the elastic response of the solid Earth with the response of compressible seawater under gravity.
Maeda and Furumura (2013) and Lotto and Dunham (2015) presented the simultaneous calculation of seismic waves and tsunamis. We point out that they adopted approximated equations and boundary conditions, and their methods need to be verified. When calculating the deformation of elastic bodies and fluids under gravity, at the first order of displacement, one needs to distinguish Eulerian and Lagrangian changes, which are not fully distinguished in their formulation.
In this study, we first derive governing equations and boundary conditions that distinguish Eulerian and Lagrangian changes, and compare them with the equations used in the previous studies.
Next, based on the derived equations, numerical simulations are performed for the two-dimensional P-SV case. The finite difference method (FDM) is used for the calculations.
It is known that the phase velocity of tsunamis decreases by several percent at long periods (more than a few hundred seconds) due to the coupling between the solid Earth and the ocean (Watada et al. 2014). We would like to confirm whether this phenomenon can be reproduced computationally. Furthermore, to verify the numerical simulations, we derive the theoretical tsunami dispersion relation based on the propagator matrix method, and compare it with our results and those of previous studies.
Maeda and Furumura (2013) and Lotto and Dunham (2015) presented the simultaneous calculation of seismic waves and tsunamis. We point out that they adopted approximated equations and boundary conditions, and their methods need to be verified. When calculating the deformation of elastic bodies and fluids under gravity, at the first order of displacement, one needs to distinguish Eulerian and Lagrangian changes, which are not fully distinguished in their formulation.
In this study, we first derive governing equations and boundary conditions that distinguish Eulerian and Lagrangian changes, and compare them with the equations used in the previous studies.
Next, based on the derived equations, numerical simulations are performed for the two-dimensional P-SV case. The finite difference method (FDM) is used for the calculations.
It is known that the phase velocity of tsunamis decreases by several percent at long periods (more than a few hundred seconds) due to the coupling between the solid Earth and the ocean (Watada et al. 2014). We would like to confirm whether this phenomenon can be reproduced computationally. Furthermore, to verify the numerical simulations, we derive the theoretical tsunami dispersion relation based on the propagator matrix method, and compare it with our results and those of previous studies.