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

Production induced 4D seismic changes around individual perforations in a horizontal well can be transformed into the fractional contributions and presented in the same way as the inflow measured with Production Logging Tools (PLT). We refer to this way o

Seismic PLT – Linking Seismic Time-lapse Responses to Production and Injection Data

The frequent time-lapse observations from the Life of Field Seismic (LoFS) system across the Valhall field have provided a wealth of new information. Time-shift and amplitude changes are matched to the predicted responses from the reservoir simulation model and used to reduce uncertainties and validate reservoir properties. Streamlined workflows are implemented to convert the reservoir simulation properties to a synthetic seismic response for any time range. A match quality factor between the observed and predicted responses is calculated based on a correlation function that quantifies the visual comparisons. This match quality factor allows us to quantitatively compare multiple LoFS time ranges, well areas and alternative reservoir models and quickly choose the parameters that best match the seismic observations. Three different case studies are shown where this method has helped us narrow the uncertainty range associated with the reservoir model parameters, which in turn improves the predictive capabilities of the reservoir simulation model. The examples show positive results in a range of different problems.

Integrating Frequent Time-lapse Data into the Reservoir Simulation Modeling of the Valhall Field

In 2003 the Life of Field Seismic system was installed on the Valhall Field as the first full field ocean bottom permanent monitoring system. Monitoring of the waterflood was one of the main objectives of the installation of this seismic system. Dedicated water injection at Valhall started with two water injection wells in 2006 in the Central Crest and South Central Basins, followed in 2008 by water injection in the Northern Crest Basin. All these three wells show clear time-lapse observations of the injected water. In this paper we discuss the expected and the observed responses from these water injectors for the various seismic surveys. For all the wells we show how the time-lapse observations have improved the understanding of the waterflood and have had a clear impact on the reservoir management of the individual wells and the full field. Individual examples illustrate how this improved understanding was used to make better informed business decisions on new well placement and well work.

Business Impact of Frequent Time-lapse Observations Around Valhall Water Injection Well

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Papers

3D Waveform Inversion on Valhall Wide-azimuth OBC

Seismic PLT – Linking Seismic Time-lapse Responses to Production and Injection Data

Integrating Frequent Time-lapse Data into the Reservoir Simulation Modeling of the Valhall Field

Business Impact of Frequent Time-lapse Observations Around Valhall Water Injection Well