An accuracy analysis of a Hamiltonian particle method with the staggered particles for seismic-wave modeling including surface topography

Abstract

A Hamiltonian particle method (HPM), which is one of the mesh-free methods, can simulate seismic wavefields for models including surface topography in a simple manner. Numerical error caused by a curved free surface or by particles not aligned with the surface is not obvious in HPM. In general, the accommodation of irregular free surfaces requires more grids or particles in a minimum wavelength for achieving sufficient accuracy in the simulation. We tested the accuracy of HPM with staggered particles for simulating seismic-wave propagation including the surface topography, and we established the relationship between desired accuracy and spatial resolution. We conducted numerical simulations for models with a planar free surface aligned with the regular particle alignment and a dipping free surface. Our accuracy tests revealed that the numerical error strongly depends on the dipping angle of the slope. We concluded that about 25 particles in a minimum wavelength are required to calculate Rayleigh waves propagating along the irregular topography with good accuracy. Finally, we simulated Rayleigh wave propagation along irregular topography using a layered model with a hill. HPM can reproduce not only surface-wave propagation but also the reflected and refracted waves. Our numerical results were in good agreement with those from a finite-element method. Our investigations indicated that HPM could be a solution to simulate Rayleigh waves in the presence of complex surface topography.