Full waveform inversion based on a spectral-element method and a scattering-integral algorithm

2017 ◽  
Author(s):  
Yuzhu Liu ◽  
Wenyi Zheng*
Keyword(s):  
Spectral Element Method ◽  
Waveform Inversion ◽  
Spectral Element ◽  
Full Waveform Inversion ◽  
Full Waveform ◽  
Element Method

Efficient time-domain 3D elastic and viscoelastic full-waveform inversion using a spectral-element method on flexible Cartesian-based mesh

Geophysics ◽  
2019 ◽  
Vol 84 (1) ◽  
pp. R61-R83 ◽  
Author(s):  
Phuong-Thu Trinh ◽  
Romain Brossier ◽  
Ludovic Métivier ◽  
Laure Tavard ◽  
Jean Virieux
Keyword(s):  
Time Domain ◽  
Spectral Element Method ◽  
Waveform Inversion ◽  
Spectral Element ◽  
Body Waves ◽  
P Wave ◽  
Full Waveform Inversion ◽  
Full Waveform ◽  
Anisotropic Elastic ◽  
Element Method

Viscoelastic full-waveform inversion is recognized as a challenging task for current acquisition deployment at the crustal scale. We have developed an efficient formulation based on a time-domain spectral-element method on a flexible Cartesian-based mesh. We consider anisotropic elastic coefficients and isotropic attenuation. Complete gradient expressions including the attenuation contribution spread into those of elastic components are given in a consistent way. The influence of attenuation on the P-wave velocity reconstruction is illustrated through a toy configuration. The numerical implementation of the forward problem includes efficient matrix-vector products for solving second-order elastodynamic equations for 3D geometries: An original high-order integration for topography effects is performed at nearly no extra cost. Combined adjoint and forward field recomputation from the final state and previously saved boundary values allows the estimation of misfit gradients for density, elastic parameters, and attenuation factors with no I/O efforts. Two-level parallelism is implemented over the sources and domain decomposition, which is necessary for a realistic 3D configuration. The misfit gradient preconditioning is performed by a so-called Bessel filter using an efficient differential implementation based on finite-element ingredients on the forward mesh instead of the often-used, costly convolution approach. A 3D synthetic illustration is provided on a subset ([Formula: see text]) of the SEG Advanced Modeling (SEAM) Phase II Foothills model with 4 lines of 20 sources. The structurally based Bessel filter and a simple data hierarchy strategy considering early body waves before all waves including surface waves allow a precise reconstruction of the P- and S-wavespeeds while keeping a smooth density description.

scholarly journals Accelerating numerical wave propagation by wavefield adapted meshes. Part II: full-waveform inversion

2020 ◽  
Vol 221 (3) ◽  
pp. 1591-1604 ◽  
Author(s):  
Solvi Thrastarson ◽  
Martin van Driel ◽  
Lion Krischer ◽  
Christian Boehm ◽  
Michael Afanasiev ◽  
...  
Keyword(s):  
Wave Propagation ◽  
Wave Equation ◽  
Waveform Inversion ◽  
Computational Cost ◽  
Spectral Element ◽  
Full Waveform Inversion ◽  
Full Waveform ◽  
Order Of Magnitude ◽  
Numerical Wave ◽  
Expected Complexity

SUMMARY We present a novel full-waveform inversion (FWI) approach which can reduce the computational cost by up to an order of magnitude compared to conventional approaches, provided that variations in medium properties are sufficiently smooth. Our method is based on the usage of wavefield adapted meshes which accelerate the forward and adjoint wavefield simulations. By adapting the mesh to the expected complexity and smoothness of the wavefield, the number of elements needed to discretize the wave equation can be greatly reduced. This leads to spectral-element meshes which are optimally tailored to source locations and medium complexity. We demonstrate a workflow which opens up the possibility to use these meshes in FWI and show the computational advantages of the approach. We provide examples in 2-D and 3-D to illustrate the concept, describe how the new workflow deviates from the standard FWI workflow, and explain the additional steps in detail.

scholarly journals Removing the CFL stability criterion of the explicit time-domain very high degree spectral-element method with eigenvalue perturbation

Geophysics ◽  
2021 ◽  
pp. 1-29
Author(s):  
Chao Lyu ◽  
Yann Capdeville ◽  
Gang Lv ◽  
Liang Zhao
Keyword(s):  
Time Domain ◽  
Stability Criterion ◽  
Spectral Element Method ◽  
Waveform Inversion ◽  
Spectral Element ◽  
Time Step ◽  
Transform Method ◽  
Time Dispersion ◽  
The Stability ◽  
Element Method

The explicit time-domain spectral-element method (SEM) for synthesizing seismograms hasgained tremendous credibility within the seismological community at all scales. Althoughthe recent introduction of non-periodic homogenization has addressed the spatial meshing difficulty of the mechanical discontinuities, the Courant-Friedrichs-Lewy (CFL) stability criterionstrictly constrains the maximum time step, which still puts a great burden on the numericalsimulation. In the explicit time-domain SEM, the source of instability of using a time stepbeyond the stability criterion is that some unstable eigenvalues of the updated matrix are largerthan what can be accurately simulated. We succeed in removing the CFL stability condition inthe explicit time-domain SEM by combining the forward time dispersion-transform method,the eigenvalue perturbation, and the inverse time dispersion-transform method. Our theoretical analyses and numerical experiments both in the homogeneous, moderate and strong heterogeneous models, show that this combination can precisely simulate waveforms with timesteps dozens of the CFL limit even towards the Nyquist limit especially for the efficient veryhigh degree SEM, which abundantly saves the iteration times without suffering from the time-dispersion error. It demonstrates a potential application prospect in some situations such as thefull waveform inversion which requires multiple numerical simulations for the same model.

3-D seismic full-waveform inversion of the Taurus-Zagros region in Iran and Turkey

2020 ◽  
Author(s):  
Neda Masouminia ◽  
Dirk-Philip van Herwaarden ◽  
Sölvi Thrastarson ◽  
Habib Rahimi ◽  
Lion Krischer ◽  
...  
Keyword(s):  
Upper Mantle ◽  
Waveform Inversion ◽  
Spectral Element ◽  
Earth Model ◽  
Model Parameters ◽  
Full Waveform Inversion ◽  
Geophysical Research ◽  
Seismic Stations ◽  
Full Waveform ◽  
Seismic Waveform

<p><span>We present an interpretation of a 3-D velocity model resulting from a regional analysis of earthquake waveforms. This model contains 3-D structure of the crust and upper mantle beneath the Arabian-Eurasian collision zone in eastern Turkey and Iran. We use full-waveform inversion (FWI) of three-component recordings from permanent networks. FWI can exploit all parts of a seismogram, including body and multi-mode surface waves in a broad range of frequencies. This allows us to constrain seismic structure of both the crust and the upper mantle.</span></p><p><span>In our method we simulate 3-D visco-elastic wavefields using a spectral-element method (Fichtner <em>et al,</em>2018). Our numerical mesh honors topography of the surface. We compare observed and synthetic waveforms using time-frequency phase misfits. Using adjoint techniques, we then compute sensitivity kernels with respect to the model parameters, which are V<sub>SV</sub>, V<sub>SH</sub>, V<sub>PV</sub>, and V<sub>PH</sub>. Finally, the kernels enable the iterative solution of the nonlinear inverse problem with the help of the L-BFGS algorithm and without a need for crustal corrections.</span></p><p><span>For this study we obtained seismic waveform data of 59 earthquakes within the magnitude range of Mw 4.5 to 6.3 that occurred in the region between 2012 and 2016. These events were recorded by 398 broadband seismic stations belonging to the two national Iranian networks and freely available seismic stations of the Turkish Network, made available by IRIS.</span></p><p> <span>Starting from the first generation of the Collaborative Seismic Earth Model (Afanasiev <em>et al</em>.2019), we first constrained longer-wavelength structure. To this end, we considered 3-component recordings from a subset of 37 events in the period range from 50 to 80 s. This band was successively broadened by reducing the shorter period from 50 s to 40 s, and finally to 20 s. For each period band, the number and the length of measurement windows are increased; the number of events is also increased to 59 to use the complete dataset. After 46 iterations our model can explain recordings of events, which were not used in the inversion. The results provide to discuss about high-velocity anomaly beneath the Zagros and the shallow low velocities beneath Central Iran using cross-sections to investigate lateral variation of seismic velocity in the lithosphere.</span></p><p><span>REFERENCES</span></p><p><span>Afanasiev, M., Boehm, C., van Driel, M., Krischer, L., Rietmann, M., May, D. A., Knepley, M. G., Fichtner, A., 2019. Modular and flexible spectral-element waveform modelling in two and three dimensions. Geophysical Journal International 216, 1675-1692, doi: 10.1093/gji/ggy469.</span></p><p><span>Fichtner, A., van Herwaarden, D.-P., Afanasiev, M., Simute, S., Krischer, L., Cubuk-Sabuncu, Y., Taymaz, T., Colli, L., Saygin, E., Villasenor, A., Trampert, J., Cupillard, P., Bunge, H.-P., Igel, H., 2018. The Collaborative Seismic Earth Model: Generation I. Geophysical Research Letters 45, doi: 10.1029/2018GL077338.</span></p>

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