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

Quantitative imaging of the elastic properties of the subsurface at depth is essential for civil engineering applications and oil- and gas-reservoir characterization. A realistic synthetic example provides for an assessment of the potential and limits of 2D elastic full-waveform inversionFWIof wide-aperture seismic data for recovering high-resolution P- and S-wave velocity models of complex onshore structures. FWI of land data is challengingbecauseoftheincreasednonlinearityintroducedbyfreesurface effects such as the propagation of surface waves in the heterogeneous near-surface. Moreover, the short wavelengths of the shear wavefield require an accurate S-wave velocity starting modeliflowfrequenciesareunavailableinthedata.Weevaluated different multiscale strategies with the aim of mitigating the nonlinearities. Massively parallel full-waveform inversion was implemented in the frequency domain. The numerical optimization relies on a limited-memory quasi-Newton algorithm that outperforms the more classic preconditioned conjugate-gradient algorithm. The forward problem is based upon a discontinuous Galerkin DG method on triangular mesh, which allows accuratemodelingoffree-surfaceeffects.Sequentialinversionsofincreasingfrequenciesdefinethemostnaturallevelofhierarchyin multiscale imaging. In the case of land data involving surface waves, the regularization introduced by hierarchical frequency inversions is not enough for adequate convergence of the inversion. A second level of hierarchy implemented with complexvalued frequencies is necessary and provides convergence of the inversion toward acceptable P- and S-wave velocity models. Amongthepossiblestrategiesforsamplingfrequenciesintheinversion, successive inversions of slightly overlapping frequency groups is the most reliable when compared to the more standard sequential inversion of single frequencies. This suggests that simultaneous inversion of multiple frequencies is critical when consideringcomplexwavephenomena.

/pdf/seismic-imaging-of-complex-onshore-structures-by-2d-elastic-46hmegoe8a.pdf

Seismic imaging of complex onshore structures by 2D elastic frequency-domain full-waveform inversion

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?

Multiparameter full waveform inversion (FWI) is a challenging quantitative seismic imaging method for lithological characterization and reservoir monitoring. The difficulties in multiparameter FWI arise from the variable influence of the different parameter classes on the phase and amplitude of the data, and the trade-off between these. In this framework, choosing a suitable parametrization of the subsurface and designing the suitable FWI workflow are two key methodological issues in non-linear waveform inversion. We assess frequency-domain visco-acoustic FWI to reconstruct the compressive velocity (VP), the density (ρ) or the impedance (IP) and the quality factor (QP), from the hydrophone component, using a synthetic data set that is representative of the Valhall oil field in the North Sea. We first assess which of the (VP, ρ) and (VP, IP) parametrizations provides the most reliable FWI results when dealing with wide-aperture data. Contrary to widely accepted ideas, we show that the (VP, ρ) parametrization allows a better reconstruction of both the VP, ρ and IP parameters, first because it favours the broad-band reconstruction of the dominant VP parameter, and secondly because the trade-off effects between velocity and density at short-to-intermediate scattering angles can be removed by multiplication, to build an impedance model. This allows for the matching of the reflection amplitudes, while the broad-band velocity model accurately describes the kinematic attributes of both the diving waves and reflections. Then, we assess different inversion strategies to recover the quality factor QP, in addition to parameters VP and ρ. A difficulty related to attenuation estimation arises because, on the one hand the values of QP are on average one order of magnitude smaller than those of VP and ρ, and on the other hands model perturbations relative to the starting models can be much higher for QP than for VP and ρ during FWI. In this framework, we show that an empirical tuning of the FWI regularization, which is adapted to each parameter class, is a key issue to correctly account for the attenuation in the inversion. We promote a hierarchical approach where the dominant parameter VP is reconstructed first from the full data set (i.e. without any data preconditioning) to build a velocity model as kinematically accurate as possible before performing the joint update of the three parameter classes during a second step. This hierarchical imaging of compressive wave speed, density and attenuation is applied to a real wide-aperture ocean-bottom-cable data set from the Valhall oil field. Several geological features, such as accumulation of gas below barriers of claystone and soft quaternary sediment are interpreted in the FWI models of density and attenuation. The models of VP, ρ and QP that have been developed by visco-acoustic FWI of the hydrophone data can be used as initial models to perform visco-elastic FWI of the geophone data for the joint update of the compressive and shear wave speeds.

https://hal.archives-ouvertes.fr/hal-01052775/document

Multiparameter full waveform inversion of multicomponent ocean-bottom-cable data from the Valhall field. Part 1: imaging compressional wave speed, density and attenuation

SUMMARY

Elastic Full Waveform Tomography (FWT) aims to reduce the misfit between recorded and modelled data, to deduce a very detailed model of elastic material parameters in the underground. The choice of the elastic model parameters to be inverted affects the convergence and quality of the reconstructed subsurface model. Using the Cross-Triangle-Squares (CTS) model three elastic parametrizations, Lame parameters m1 = [λ, μ, ρ], seismic velocities m2 = [Vp, Vs, ρ] and seismic impedances m3 = [Ip, Is, ρ] for far-offset reflection seismic acquisition geometries with explosive point sources and free-surface condition are studied. In each CTS model the three elastic parameters are assigned to three different geometrical objects that are spatially separated. The results of the CTS model study reveal a strong requirement of a sequential frequency inversion from low to high frequencies to reconstruct the density model. Using only high-frequency data, cross-talk artefacts have an influence on the quantitative reconstruction of the material parameters, while for a sequential frequency inversion only structural artefacts, representing the boundaries of different model parameters, are present. During the inversion, the Lame parameters, seismic velocities and impedances could be reconstructed well. However, using the Lame parametrization -artefacts are present in the λ model, while similar artefacts are suppressed when using seismic velocities or impedances. The density inversion shows the largest ambiguity for all parametrizations. However, the artefacts are again more dominant, when using the Lame parameters and suppressed for seismic velocity and impedance parametrization. The afore mentioned results are confirmed for a geologically more realistic modified Marmousi-II model. Using a conventional streamer acquisition geometry the P-velocity, S-velocity and density models of the subsurface were reconstructed successfully and are compared with the results of the Lame parameter inversion.

On the influence of model parametrization in elastic full waveform tomography

Elastic full waveform inversion of seismic reflection data represents a data-driven form of analysis leading to quantification of sub-surface parameters in depth. In previous studies attention has been given to P-wave data recorded in the marine environment, using either acoustic or elastic inversion schemes. In this paper we exploit both P-waves and mode-converted S-waves in the marine environment in the inversion for both P- and S-wave velocities by using wide-angle, multi-component, ocean-bottom cable seismic data. An elastic waveform inversion scheme operating in the time domain was used, allowing accurate modelling of the full wavefield, including the elastic amplitude variation with offset response of reflected arrivals and mode-converted events. A series of one- and two-dimensional synthetic examples are presented, demonstrating the ability to invert for and thereby to quantify both P- and S-wave velocities for different velocity models. In particular, for more realistic low velocity models, including a typically soft seabed, an effective strategy for inversion is proposed to exploit both P- and mode-converted PS-waves. Whilst P-wave events are exploited for inversion for P-wave velocity, examples show the contribution of both P- and PS-waves to the successful recovery of S-wave velocity.

Elastic full waveform inversion of multi-component OBC seismic data

Elastic full waveform inversion of seismic reflection data represents an alternative to conventional stack based processing. Both travel-time and amplitude information within shot domain data are used to invert for the subsurface velocity, from a starting model containing the long wavelength features.

Elastic Full Waveform Inversion of Multi-Component OBC Seismic Data

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Elastic full waveform inversion of multi-component OBC seismic data

Elastic Full Waveform Inversion of Multi-Component OBC Seismic Data