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Seismic wavefield imaging of Earth’s interior across scales


Seismic full-waveform inversion (FWI) for imaging Earth’s interior was introduced in the late 1970s. Its ultimate goal is to use all of the information in a seismogram to understand the structure and dynamics of Earth, such as hydrocarbon reservoirs, the nature of hotspots and the forces behind plate motions and earthquakes. Thanks to developments in high-performance computing and advances in modern numerical methods in the past 10 years, 3D FWI has become feasible for a wide range of applications and is currently used across nine orders of magnitude in frequency and wavelength. A typical FWI workflow includes selecting seismic sources and a starting model, conducting forward simulations, calculating and evaluating the misfit, and optimizing the simulated model until the observed and modelled seismograms converge on a single model. This method has revealed Pleistocene ice scrapes beneath a gas cloud in the Valhall oil field, overthrusted Iberian crust in the western Pyrenees mountains, deep slabs in subduction zones throughout the world and the shape of the African superplume. The increased use of multi-parameter inversions, improved computational and algorithmic efficiency, and the inclusion of Bayesian statistics in the optimization process all stand to substantially improve FWI, overcoming current computational or data-quality constraints. In this Technical Review, FWI methods and applications in controlled-source and earthquake seismology are discussed, followed by a perspective on the future of FWI, which will ultimately result in increased insight into the physics and chemistry of Earth’s interior.

Key points

  • Modern numerical methods and high-performance computers have facilitated the characterization of Earth’s interior constrained by the physics of seismic-wave propagation.

  • Seismic full-waveform inversion (FWI) has enabled unprecedented imaging across nine orders of magnitude in frequency and wavelength, with applications ranging from medical imaging and nondestructive testing to global seismology.

  • FWI continues to be developed and improved, with opportunities for a more complete description of the physics of seismic-wave propagation (for example, anisotropy, attenuation and poroelasticity), as well as better and more effective optimization algorithms (such as source encoding, uncertainty quantification and Hamiltonian Monte Carlo methods).

  • Computers in the exascale era (~2020–2021) will enable global FWI at frequencies of up to ~1 Hz, potentially facilitating sub-10-km-scale imaging of Earth’s mantle.

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Fig. 1: Timeline of major developments in seismic FWI and notable applications.
Fig. 2: FWI workflow.
Fig. 3: Multi-parameter visco-acoustic FWI of the Valhall oil field.
Fig. 4: Teleseismic FWI experiment using the MAUPASACQ array in the western Pyrenees.
Fig. 5: Vertical cross sections of compressional wave-speed perturbations in various subduction zones.
Fig. 6: 3D morphology of the African superplume from two angles.


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The author is grateful to S. Operto and S. Beller for their feedback and input on controlled-source seismology applications of full-waveform inversion and for contributing figures. W. Lei and Y. Ruan also contributed figures to this article. Comments and suggestions by the reviewers helped improve an earlier version of the manuscript. This research used the resources of the Oak Ridge Leadership Computing Facility, which is a US Department of Energy Office of Science User Facility supported under contract DE-AC05-00OR22725. Additional computational resources were provided by the Princeton Institute for Computational Science and Engineering (PICSciE).

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Nature Reviews Earth & Environment thanks A. Fichtner, B. Romanowicz and the other, anonymous, reviewer for their contribution to the peer review of this work.

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Body waves

Seismic waves that travel through Earth’s interior as compressional or shear waves.

Surface waves

Seismic waves that rumble along Earth’s surface in the form of a Love wave with transverse linear particle motion or a Rayleigh wave with vertical and radial retrograde elliptical particle motion.

Misfit function

A multivariate function of a set of model parameters indicative of the fit between observed and simulated data.

Mantle waves

Very-long-period (>~120 s) surface waves.

Forward simulations

Numerical modelling of seismic-wave propagation given a set of source parameters and an Earth model.

Adjoint simulations

Numerical modelling based on an Earth model and a fictitious set of sources that inject measurements simultaneously from all receivers.

Fréchet derivatives

The derivatives of a misfit function with respect to model parameters, such as seismic wave speeds or source parameters.

Banana-doughnut kernels

A finite-frequency version of an infinite-frequency seismic ray, which, in a spherical Earth model, looks like a banana in the vertical plane between the source and receiver and like a doughnut in a cross section perpendicular to this plane.

Checkboard tests

Inversion experiments in which synthetic data are generated for a checkboard model parameter pattern. These data are then inverted to assess how well the checkboard pattern can be recovered.

Marmousi model

A fictitious model created by a consortium led by the Institut Français du Pétrole. The initial model was 2D acoustic but there is an elastic version called Marmousi2.

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Tromp, J. Seismic wavefield imaging of Earth’s interior across scales. Nat Rev Earth Environ 1, 40–53 (2020).

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