Accelerating Numerical Wave Propagation by Wavefield Adapted Meshes, Part II: Full-Waveform Inversion

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.

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Controlled-order multiple waveform inversion

Geophysics ◽

10.1190/geo2019-0658.1 ◽

2020 ◽

Vol 85 (3) ◽

pp. R243-R250 ◽

Cited By ~ 2

Author(s):

Yike Liu ◽

Bin He ◽

Yingcai Zheng

Keyword(s):

Wave Propagation ◽

Objective Function ◽

Waveform Inversion ◽

Full Waveform Inversion ◽

Initial Model ◽

Numerical Examples ◽

Full Waveform ◽

Wide Range ◽

True Model ◽

The Difference

Traditional full-waveform inversion (FWI) seeks to find the best model by minimizing an objective function defined as the difference between the model-predicted and observed data in amplitude and phase. In principle, FWI should fit all wave types including direct waves, diving waves, primaries, and multiples. However, when an initial model is far from the true model, FWI will encounter difficulties in matching multiples. Physically, multiples may contain more subsurface information compared to primary and diving waves. Multiples cover a wide range of reflection angles during wave propagation and offer the advantage of imaging the shadow zones that cannot be reached or are poorly illuminated by primary reflections. We have developed a new method of waveform inversion using multiples. We first separate the multiples into different orders. The objective function we seek to minimize consists of the data difference between the modeled data using a lower order multiple as the source and the higher order multiple as data. This method is called controlled-order multiple waveform inversion (CMWI). Our numerical examples determined that the CMWI is a promising method to improve velocity updates.

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spyro: a Firedrake-based wave propagation and full waveform inversion finite element solver

10.5194/gmd-2021-363 ◽

2021 ◽

Author(s):

Keith J. Roberts ◽

Alexandre Olender ◽

Lucas Franceschini ◽

Robert C. Kirby ◽

Rafael S. Gioria ◽

...

Keyword(s):

Finite Element ◽

Wave Propagation ◽

Model Building ◽

Seismic Velocity ◽

Waveform Inversion ◽

Higher Order ◽

Full Waveform Inversion ◽

State Equations ◽

Full Waveform ◽

Triangular Elements

Abstract. In this article, we introduce spyro, a software stack to solve acoustic wave propagation in heterogeneous domains and perform full waveform inversion (FWI) employing the finite element framework from Firedrake, a high-level Python package for the automated solution of partial differential equations using the finite element method. The capability of the software is demonstrated by using a continuous Galerkin approach to perform FWI for seismic velocity model building, considering realistic geophysics examples. A time-domain FWI approach is detailed that uses meshes composed of variably sized triangular elements to discretize the domain. To resolve both the forward and adjoint-state equations, and to calculate a mesh-independent gradient associated with the FWI process, a fully-explicit, variable higher-order (up to degree k = 5 in 2D and k = 3 in 3D) mass lumping method is used. We show that, by adapting the triangular elements to the expected peak source frequency and properties of the wavefield (e.g., local P-wavespeed) and by leveraging higher-order basis functions, the number of degrees-of-freedom necessary to discretize the domain can be reduced. Results from wave simulations and FWIs in both 2D and 3D highlight our developments and demonstrate the benefits and challenges with using triangular meshes adapted to the material properties.

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3D finite-difference frequency-domain modeling of visco-acoustic wave propagation using a massively parallel direct solver: A feasibility study

Geophysics ◽

10.1190/1.2759835 ◽

2007 ◽

Vol 72 (5) ◽

pp. SM195-SM211 ◽

Cited By ~ 183

Author(s):

Stéphane Operto ◽

Jean Virieux ◽

Patrick Amestoy ◽

Jean-Yves L’Excellent ◽

Luc Giraud ◽

...

Keyword(s):

Wave Propagation ◽

Finite Difference ◽

Frequency Domain ◽

Waveform Inversion ◽

Staggered Grid ◽

Full Waveform Inversion ◽

Domain Modeling ◽

Acoustic Wave Propagation ◽

Full Waveform ◽

Grid Points

We present a finite-difference frequency-domain method for 3D visco-acoustic wave propagation modeling. In the frequency domain, the underlying numerical problem is the resolution of a large sparse system of linear equations whose right-hand side term is the source. This system is solved with a massively parallel direct solver. We first present an optimal 3D finite-difference stencil for frequency-domain modeling. The method is based on a parsimonious staggered-grid method. Differential operators are discretized with second-order accurate staggered-grid stencils on different rotated coordinate systems to mitigate numerical anisotropy. An antilumped mass strategy is implemented to minimize numerical dispersion. The stencil incorporates 27 grid points and spans two grid intervals. Dispersion analysis showsthat four grid points per wavelength provide accurate simulations in the 3D domain. To assess the feasibility of the method for frequency-domain full-waveform inversion, we computed simulations in the 3D SEG/EAGE overthrust model for frequencies 5, 7, and [Formula: see text]. Results confirm the huge memory requirement of the factorization (several hundred Figabytes) but also the CPU efficiency of the resolution phase (few seconds per shot). Heuristic scalability analysis suggests that the memory complexity of the factorization is [Formula: see text] for a [Formula: see text] grid. Our method may provide a suitable tool to perform frequency-domain full-waveform inversion using a large distributed-memory platform. Further investigation is still necessary to assess more quantitatively the respective merits and drawbacks of time- and frequency-domain modeling of wave propagation to perform 3D full-waveform inversion.

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