Full-waveform inversion FWI is a challenging data-fitting procedure based on full-wavefield modeling to extract quantitative information from seismograms. High-resolution imaging at half the propagated wavelength is expected. Recent advances in high-performance computing and multifold/multicomponent wide-aperture and wide-azimuth acquisitions make 3D acoustic FWI feasible today. Key ingredients of FWI are an efficient forward-modeling engine and a local differential approach, in which the gradient and the Hessian operators are efficiently estimated. Local optimization does not, however, prevent convergence of the misfit function toward local minima because of the limited accuracy of the starting model, the lack of low frequencies, the presence of noise, and the approximate modeling of the wave-physics complexity. Different hierarchical multiscale strategiesaredesignedtomitigatethenonlinearityandill-posedness of FWI by incorporating progressively shorter wavelengths in the parameter space. Synthetic and real-data case studies address reconstructing various parameters, from VP and VS velocities to density, anisotropy, and attenuation. This review attempts to illuminate the state of the art of FWI. Crucial jumps, however, remain necessary to make it as popular as migration techniques. The challenges can be categorized as 1 building accurate starting models with automatic procedures and/or recording low frequencies, 2 defining new minimization criteria to mitigate the sensitivity of FWI to amplitude errors and increasing the robustness of FWI when multiple parameter classes are estimated, and 3 improving computational efficiency by data-compression techniquestomake3DelasticFWIfeasible.

/pdf/an-overview-of-full-waveform-inversion-in-exploration-59sei7fzvh.pdf

An overview of full-waveform inversion in exploration geophysics

Elastic full-waveform inversion is an ill-posed data-fitting procedure that is sensitive to noise, inaccuracies of the starting model,definitionofmultiparameterclasses,andinaccuratemodeling of wavefield amplitudes. We have investigated the performance of different minimization functionals as the least-squares norm 2, the least-absolute-values norm 1, and combinations of both the Huber and so-called hybrid criteria with reference to twonoisyoffshoreValhallmodelandonshoreoverthrustmodel synthetic data sets. The four minimization functionals were implemented in 2D elastic frequency-domain full-waveform inversion FWI, where efficient multiscale strategies were designed by successive inversions of a few increasing frequencies. For the offshore and onshore case studies, the 1-norm provided the most reliable models for P- and S-wave velocities VP and VS, even when strongly decimated data sets that correspond to fewfrequencieswereusedintheinversionandwhenoutlierspolluted the data. The 2-norm can provide reliable results in the presence of uniform white noise for VP and VS if the data redundancyisincreasedbyrefiningthefrequencysamplingintervalin the inversion at the expense of computational efficiency. The 1-norm and the Huber and hybrid criteria, unlike the 2-norm, allowforsuccessfulimagingoftheVSmodelfromnoisydataina soft-seabed environment, where the P-to-S-waves have a small footprint in the data. However, the Huber and hybrid criteria are sensitive to a threshold criterion that controls the transition between the criteria and that requires tedious trial-and-error investigations for reliable estimation. The 1-norm provides a robust alternativetothe2-normforinvertingdecimateddatasetsinthe frameworkofefficientfrequency-domainFWI.

/pdf/which-data-residual-norm-for-robust-elastic-frequency-domain-27z3mh7pxj.pdf

Which data residual norm for robust elastic frequency-domain full waveform inversion?

By interpreting the full wavefield, full waveform inversion has the potential to become a key tool to interpret seismic data acquired in complex geological settings. However, its application requires low frequencies and large offsets to avoid ending up in a local minimum. This approach has been illustrated with marine data sets and acoustic full waveform inversion. Acoustic full waveform inversion can also be applied with land data sets when the acquisition and the pre-processing are planned correctly. To demonstrate the relevance of this dedicated approach, we invert a land data set acquired with low frequencies down to 1.5 Hz and 20 km offset. We show that the velocity retrieved by full waveform inversion supersedes the one derived by handpicked nmo-gather velocity analysis even when we start with a crude 1D model. With the acquisition of low frequencies and long offsets and a dedicated preprocessing, a high-resolution seismic migrated image could be obtained over this land area.

Application of Acoustic Full Waveform Inversion to a Low-frequency Large-offset Land Data Set

SUMMARY The validity of isotropic approximation to perform acoustic full waveform inversion (FWI) of real wide-aperture anisotropic data can be questioned due to the intrinsic kinematic inconsis- tency between short- and large-aperture components of the data. This inconsistency is mainly related to the differences between the vertical and horizontal velocities in vertical-transverse isotropic (VTI) media. The footprint of VTI anisotropy on 2-D acoustic isotropic FWI is illus- trated on a hydrophone data set of an ocean-bottom cable that was collected over the Valhall field in the North Sea. Multiscale FWI is implemented in the frequency domain by hierar- chical inversions of increasing frequencies and decreasing aperture angles. The FWI models are appraised by local comparison with well information, seismic modelling, reverse-time migration (RTM) and source-wavelet estimation. A smooth initial VTI model parameterized by the vertical velocity V0 and the Thomsen parameters δ andwere previously developed by anisotropic reflection traveltime tomography. The normal moveout (VNMO = V0 √ 1 + 2δ) and horizontal (Vh = V0 √ 1 + 2� ) velocity models were inferred from the anisotropic models to perform isotropic FWI. The VNMO models allows for an accurate match of short-spread reflection traveltimes, whereas the Vh model, after updating by first-arrival traveltime tomog- raphy (FATT), allows for an accurate match of first-arrival traveltimes. Ray tracing in the velocity models shows that the first 1.5 km of the medium are sampled by both diving waves and reflections, whereas the deeper structure at the reservoir level is mainly controlled by short-spread reflections. Starting from the initial anisotropic model and keeping fixed δ and � models, anisotropic FWI allows us to build a vertical velocity model that matches reasonably well the well-log velocities. Isotropic FWI is performed using either the NMO model or the FATT model as initial model. In both cases, horizontal velocities are mainly reconstructed in the first 1.5 km of the medium. This suggests that the wide-aperture components of the data have a dominant control on the velocity estimation at these depths. These high velocities in the upper structure lead to low values of velocity in the underlying gas layers (either equal or lower than vertical velocities of the well log), and/or a vertical stretching of the structure at the reservoir level below the gas. This bias in the gas velocities and the mispositioning in depth of the deep reflectors, also shown in the RTM images, are required to match the deep reflections in the isotropic approximation and highlight the footprint of anisotropy in the isotropic FWI of long-offset data. Despite the significant differences between the anisotropic and isotropic FWI models, each of these models produce a nearly-equivalent match of the data, which highlights the ill-posedness of acoustic anisotropic FWI. Hence, we conclude with the importance of considering anisotropy in FWI of wide-aperture data to avoid bias in the velocity reconstruc- tions and mispositioning in depth of reflectors. Designing a suitable parameterization of the VTI acoustic FWI is a central issue to manage the ill-posedness of the FWI.

/pdf/on-the-footprint-of-anisotropy-on-isotropic-full-waveform-gqd37eiqkb.pdf

On the footprint of anisotropy on isotropic full waveform inversion: the Valhall case study

The waveform inversion problem is inherently ill-posed. Traditionally, regularization schemes are used to address this issue. For waveform inversion, where the model is expected to have many details reflecting the physical properties of the Earth, regularization and data fitting can work in opposite directions: the former smoothing and the latter adding details to the model. We propose constraining estimated velocity fields by reparameterizing the model. This technique, also called model-space preconditioning, is based on directional Laplacian filters: It preserves most of the details of the velocity model while smoothing the solution along known geological dips. Preconditioning also yields faster convergence at early iterations. The Laplacian filters have the property to smooth or kill local planar events according to a local dip field. By construction, these filters can be inverted and used in a preconditioned waveform inversion strategy to yield geologically meaningful models. We illustrate with 2D syn...

Constrained full-waveform inversion by model reparameterization

Seismic velocities are conventionally obtained using ray-based reflection tomography and are often considered only for the purpose of depth imaging. We demonstrate using Valhall wide-azimuth field data that 3D frequency domain full waveform inversion prod

3D Waveform Inversion on Valhall Wide-azimuth OBC

Constraining Reservoir Uncertainty With Frequent 4D-Seismic Data at Valhall Field

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3D Waveform Inversion on Valhall Wide-azimuth OBC

Constraining Reservoir Uncertainty With Frequent 4D-Seismic Data at Valhall Field