Spectral-Element and Adjoint Methods in Seismology
By Jeroen Tromp, Dimitri Komatitsch, Qinya Liu. Communications in Computational Physics, 2008
445 citations recorded by the source corpus.
We provide an introduction to the use of the spectral-element method (SEM) in seismology. Following a brief review of the basic equations that govern seismic wave propagation, we discuss in some detail how these equations may be solved numerically based upon the SEM to address the forward problem in seismology. Examples of synthetic seismograms calculated based upon the SEM are compared to data recorded by the Global Seismographic Network. Finally, we discuss the challenge of using the remaining differences between the data and the synthetic seismograms to constrain better Earth models and source descriptions. This leads naturally to adjoint methods, which provide a practical approach to this formidable computational challenge and enables seismologists to tackle the inverse problem.
Subfields: Geophysics
View Paper: https://www.semanticscholar.org/paper/00eba0cc71169c02eec4a94dbb15e71c0255db5e
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In Geophysics
- Qinya Liu
- Jeroen Tromp
- Jeannot Trampert
- Barbara Romanowicz
- Ebru Bozdag
- Dimitri Komatitsch
- S. French
- Daniel Peter
Citations in the corpus
- High-order finite-element seismic wave propagation modeling with MPI on a large GPU cluster (2010, methodology): “However, an important limitation of the classical SEM is that one needs to design a mesh of hexahedra, which in the case of very complex geological models can be a difficult and time consuming process.”
- A Stable Finite Difference Method for the Elastic Wave Equation on Complex Geometries with Free Surfaces (2007, unknown): “Other methods include the well-established spectral element method [7, 13, 20], the pseudospectral method [8] and the discontinuous Galerkin method [12].”
- Misfit functions for full waveform inversion based on instantaneous phase and envelope measurements (2011, methodology): “A Lagrange-multiplier approach for the derivation of the adjoint wavefield may be found in Liu & Tromp (2006) and Tromp et al. (2008).”
- Whole-mantle radially anisotropic shear velocity structure from spectral-element waveform tomography (2014, background): “In a pure global SEM, such as SPECFEM3D_GLOBE (Tromp et al. 2008), the CFL condition is often dominated by high compressional velocities in the core.”
- Forward and adjoint simulations of seismic wave propagation on fully unstructured hexahedral meshes (2011, background): “For reviews of the SEM in seismology, see for example, Komatitsch et al. (2005), Chaljub et al. (2007), Tromp et al. (2008) and Fichtner (2010).”
- Global adjoint tomography: first-generation model (2016, methodology): “As described in Tromp et al. (2010), the Moho is honoured by the spectralelement mesh if the crust is less than 15 km thick (mainly oceanic crust) and thicker than 35 km (continental crust), and the Moho runs through mesh elements in ocean-continent transitions.”