Numerical modeling of seismic waves by discontinuous spectral element methods

Abstract

We present a comprehensive review of Discontinuous Galerkin Spectral Element (DGSE) methods on hybrid hexahedral/tetrahedral grids for the numerical modeling of the ground motion induced by large earthquakes. DGSE methods combine the exibility of discontinuous Galerkin meth-ods to patch together, through a domain decomposition paradigm, Spectral Element blocks where high-order polynomials are used for the space discretization. This approach allows local adaptivity on discretization parameters, thus improving the quality of the solution without affecting the compu-tational costs. The theoretical properties of the semidiscrete formulation are also revised, including well-posedness, stability and error estimates. A discussion on the dissipation, dispersion and stability properties of the fully-discrete (in space and time) formulation is also presented. Here space dis-cretization is obtained based on employing the leap-frog time marching scheme. The capabilities of the present approach are demonstrated through a set of computations of realistic earthquake scenar-ios obtained using the code SPEED (http://speed.mox.polimi.it), an open-source code specifically designed for the numerical modeling of large-scale seismic events jointly developed at Politecnico di Milano by The Laboratory for Modeling and Scientific Computing MOX and by the Department of Civil and Environmental Engineering.

High-order Discontinuous Galerkin methods for the elastodynamics equation on polygonal and polyhedral meshes

“…Another numerical method that in recent years has been extensively used for elastic wave propagation is the Discontinuous Galerkin (DG) method, see e.g. [3,4,5,6,7,8,9,10,11,12,13] . We refer to [14,15,16] for a general overview on DG methods.…”

High–order Discontinuous Galerkin Methods on Polyhedral Grids for Geophysical Applications: Seismic Wave Propagation and Fractured Reservoir Simulations

“…and n F+ is the unit outward normal vector to F+ . In (17), the coefficients C i, j,k are defined as in ( 16), whereas X and Ỹ are defined as…”

“…To enhance the flexibility of spectral element methods, in recent years DG and DG spectral element (DGSE) methods has been extensively used for elastic waves propagation, see e.g. [132,131,83,110,91,29,121,6,92,125,25,11,10], and [17] for an overview on the numerical modeling of seismic waves by DGSE methods. Given their local nature, DG methods are particularly well suited to deal with highly heterogeneous media, or in soil-structure interaction problems, where local refinements are needed to resolve the different spatial scales [120].…”

On the Use of Interferometric Synthetic Aperture Radar Data for Monitoring and Forecasting Natural Hazards

“…Viscoelastic FE models have been used in Hu et al (2004) to analyze post-seismic deformation fields of the great 1960 Chile earthquake, providing promising results on the characterization of viscosity parameters and post-seismic seaward motion. More sophisticated mathematical models for seismic analysis combine the accuracy of spectral element techniques (Mazzieri et al 2011) with the flexibility of discontinuous Galerkin FE methods (Wollherr et al 2018 andAntonietti et al 2018). Such versatility, together with the ongoing progress of computational power, is likely to enable three-dimensional numerical simulations of different seismic excitation scenarios, such as the series of earthquakes analyzed by Paolucci et al (2014) that occurred in Haiti and Chile in 2010, New Zealand in 2010-2011, Japan in 2011, and Italy in 2012 Coupled multi-physics approaches modeling the Earth structure, the fault structure, stress states during large earthquakes, and the consequent tsunami generation have been proposed in Uphoff et al (2017) and in Ulrich et al (2019) for the 2004 Sumatra and 2018 Sulawesi earthquakes and tsunamis, respectively.…”