a b s t r a c tIn the present study, we applied a novel mesh-free method to solve acoustic wave equation. Although the conventional finite difference methods determine the coefficients of its operator based on the regular grid alignment, the mesh-free method is not restricted to regular arrangements of calculation points. We derive the mesh-free approach using the multivariable Taylor expansion. The methodology can use arbitrary-order accuracy scheme in space by expanding the influence domain which controls the number of neighboring calculation points. The unique point of the method is that the approach calculates the approximation of derivatives using the differences of spatial variables without parameters as e.g. the weighting functions, basis functions. Dispersion analysis using a plane wave reveals that the choice of the higher-order scheme improves the dispersion property of the method although the scheme for the irregular distribution of the calculation points is more dispersive than that of the regular alignment. In numerical experiments, a model of irregular distribution of the calculation points reproduces acoustic wave propagation in a homogeneous medium same as that of a regular lattice. In an inhomogeneous model which includes low velocity anomalies, partially fine arrangement improves the effectiveness of computational cost without suffering from accuracy reduction. Our result indicates that the method would provide accurate and efficient solutions for acoustic wave propagation using adaptive distribution of the calculation points.
SUMMARY We propose a forward wavefield simulation based on a particle continuum model to simulate seismic waves travelling through a complex subsurface structure with arbitrary topography. The inclusion of arbitrary topography in the numerical simulation is a key issue not only for scientific interests but also for disaster prediction and mitigation purposes. In this study, a Hamiltonian particle method (HPM) is employed. It is easy to introduce traction‐free boundary conditions in HPM and to refine the particle density in space. Any model with complex geometry and velocity structure can be simulated by HPM because the connectivity between particles is easily calculated based on their relative positions and the free surfaces are automatically introduced. In addition, the spatial resolution of the simulation could be refined in a simple manner even in a relatively complex velocity structure with arbitrary surface topography. For these reasons, the present method possesses great potential for the simulation of strong ground motions. In this paper, we first investigate the dispersion property of HPM through a plane wave analysis. Next, we simulate surface wave propagation in an elastic half space, and compare the numerical results with analytical solutions. HPM is more dispersive than FDM, however, our local refinement technique shows accuracy improvements in a simple and effective manner. Next, we introduce an earthquake double‐couple source in HPM and compare a simulated seismic waveform obtained with HPM with that computed with FDM to demonstrate the performance of the method. Furthermore, we simulate the surface wave propagation in a model with a surface of arbitrary topographical shape and compare with results computed with FEM. In each simulation, HPM shows good agreement with the reference solutions. Finally, we discuss the calculation costs of HPM including its accuracy.
Coda-Q is a stochastic parameter reflecting the heterogeneities of medium that seismic waves travel through. We confirmed that coda-Q would vary with the stress loaded to an elastic medium using numerical simulations of seismic wave propagation. When the stress is loaded, cracks in the crust could either close or newly open. The closure and opening of the cracks are not random but depending on the magnitude and the direction of the stress and the crack aspect ratio. The cracks in the medium after loading stress could be aligned in a specific orientation, and elastic wave velocity field would become anisotropic due to the alignment of specific crack orientations. Elastic wave velocity is in general faster along the direction corresponding with the crack orientation while slower along the perpendicular direction. In the numerical simulation, the effect of anisotropy in elastic wave velocity field due to the selective closure and opening of the cracks is calculated using a 2-D finite difference method assuming elastic wave velocity to be a function of the magnitude of loaded stress. The coda-Q calculated from seismic waves simulated for a model varies when the averaged normal stress changes. Our simulation indicated that the sensitivity of coda-Q −1 , that is the reciprocal of the coda-Q, would be 1.0 × 10 −2 (1.0 MPa -1 ) against the magnitude of the confining pressure and 1.0 × 10 −3 (1.0 deg -1 ) against the direction of principal stress. We would like to conclude that coda-Q, a stochastic parameter reflecting heterogeneities of subsurface medium, could become a quantitative state indicator of the stress field of the medium where seismic waves propagate through. Spatiotemporal variation of coda-Q reflects change in the stress field in the crust.
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