Multi-parameter Full Waveform Inversion Research Articles

Elastic full waveform inversion with probabilistic petrophysical clustering

ABSTRACTFull waveform inversion aims to use all information provided by seismic data to deliver high‐resolution models of subsurface parameters. However, multiparameter full waveform inversion suffers from an inherent trade‐off between parameters and from ill‐posedness due to the highly non‐linear nature of full waveform inversion. Also, the models recovered using elastic full waveform inversion are subject to local minima if the initial models are far from the optimal solution. In addition, an objective function purely based on the misfit between recorded and modelled data may honour the seismic data, but disregard the geological context. Hence, the inverted models may be geologically inconsistent, and not represent feasible lithological units. We propose that all the aforementioned difficulties can be alleviated by explicitly incorporating petrophysical information into the inversion through a penalty function based on multiple probability density functions, where each probability density function represents a different lithology with distinct properties. We treat lithological units as clusters and use unsupervised K‐means clustering to separate the petrophysical information into different units of distinct lithologies that are not easily distinguishable. Through several synthetic examples, we demonstrate that the proposed framework leads full waveform inversion to elastic models that are superior to models obtained either without incorporating petrophysical information, or with a probabilistic penalty function based on a single probability density function.

A numerical study of multi-parameter full waveform inversion with iterative regularization using multi-frequency vibroseis data

We study the inverse boundary value problem for time-harmonic elastic waves, for the recovery of P- and S-wave speeds from vibroseis data or the Neumann-to-Dirichlet map. Our study is based on our recent result pertaining to the uniqueness and a conditional Lipschitz stability estimate for parametrizations on unstructured tetrahedral meshes of this inverse boundary value problem. With the conditional Lipschitz stability estimate, we design a procedure for full waveform inversion (FWI) with iterative regularization. The iterative regularization is implemented by projecting gradients, after scaling, onto subspaces associated with the mentioned parametrizations yielding Lipschitz stability. The procedure is illustrated in computational experiments using the continuous Galerkin finite element method of recovering the rough shapes and wave speeds of geological bodies from simple starting models, near and far from the boundary, that is, the free surface.

Land seismic multiparameter full waveform inversion in elastic VTI media by simultaneously interpreting body waves and surface waves with an optimal transport based objective function

SUMMARY Land seismic multiparameter full waveform inversion in anisotropic media is challenging because of high medium contrasts and surface waves. With a data-residual least-squares objective function, the surface wave energy usually masks the body waves and the gradient of the objective function exhibits high values in the very shallow depths preventing from recovering the deeper part of the earth model parameters. The optimal transport objective function, coupled with a Gaussian time-windowing strategy, allows to overcome this issue by more focusing on phase shifts and by balancing the contributions of the different events in the adjoint-source and the gradients. We first illustrate the advantages of the optimal transport function with respect to the least-squares one, with two realistic examples. We then discuss a vertical transverse isotropic (VTI) example starting from a quasi 1-D isotropic initial model. Despite some cycle-skipping issues in the initial model, the inversion based on the windowed optimal transport approach converges. Both the near-surface complexities and the variations at depth are recovered.

Multi-parameter reconstruction of velocity and density using ultrasonic tomography based on full waveform inversion

In this paper, an ultrasonic tomography method based on acoustic multi-parameter full waveform inversion (FWI) is developed for high-resolution reconstructions of velocity and density in metal components. The challenging issue in multi-parameter FWI is to deal with the trade-off effects between different parameters of different natures. Moreover, different parameters have different orders of amplitudes in the wave-field which make the inversion ill-conditioned. The inverse Hessian has been shown to mitigate the coupling effects and rescale the amplitudes of different parameters, and then the reliable updates of different parameters are available. The simultaneous reconstructions of velocity and density by using the truncated Gauss–Newton method, in which the inverse Hessian can be considered through a matrix-free conjugate gradient solution of the Gauss–Newton normal equation, are investigated by simulation as well as experiment on the centred inclusions. The results show that this method can effectively alleviate the trade-off effects between velocity and density, and thus the velocity of the inclusion is accurately reconstructed and the reconstruction of the density is well achieved.

Mono-component multiparameter acoustic full waveform inversion in vertically transverse isotropic media using converted vector wavefields

In multiparameter full-waveform inversion (FWI) with acoustic-approximation for vertically transverse isotropic (VTI) media, it is important to choose an appropriate modeling technique for computational efficiency and numerical stability. In addition, because the gradient is determined by the modeling algorithm used in the FWI process, we need to examine if the modeling algorithm yields a gradient similar to that obtained from the elastic scattering theory. The decomposed equation with mono-component has been proposed because it is computationally efficient and does not generate shear-wave artifacts. However, the decomposed equation has the limitation that its numerical scattering potentials for the perturbations of anisotropic parameters do not properly simulate the theoretical elastic scattering potentials. To overcome the limitation, we propose using the vector virtual sources to compute the gradient in the FWI algorithm by converting the mono-component (pressure) source and receiver wavefields into the two-component particle displacements using the equation of motion on the staggered grids. Unlike the conventional method, our approach properly simulates PP radiation patterns for anisotropic parameters obtained under the elastic assumption, while retaining computational efficiency achieved by using the mono-component. Numerical examples show that anisotropic parameters are updated in the correct gradient direction by our method in the FWI process.

Full waveform inversion for velocity and density with rock physical relationship constraints

The trade-off between parameters in inversion increases the non-linearity of multiparameter full wave-form inversion (FWI). Density is difficult to reconstruct in multiparameter FWI, because it has the same radiation pattern in narrow apertures with that of P- velocity. Inversion with constraint is a good method to reduce the solution space of inversion problem. Since the same rock formations satisfy consistent lithological properties, systematic relationships between parameters, for example, P-wave and density, can be established for many different sedimentary rocks which can be used to provide a good constraint for multiparameter FWI. Utilizing the relationship between density and velocity in FWI, we propose a novel method to mitigate the trade-off between density and velocity and to improve the resolution of the inverted results. We introduce three terms in the definition of the FWI misfit function: the data misfit itself, the Tikhonov regularization term which can be used to smooth the models and rock physical relationship term to mitigate the trade-off between density and velocity. The rock physical relationship term can be calculated from a prior information, for example, logging data, which can provide a constraint within the whole model area in multiparameter FWI. Numerical tests on Gaussian-anomaly model and Marmousi-2 model in different circumstances show that the proposed method can improve the resolution of inversion results.

Frequency domain multiparameter acoustic inversion for transversely isotropic media with a vertical axis of symmetry

Multiparameter full-waveform inversion for transversely isotropic media with a vertical axis of symmetry (VTI) suffers from the trade-off between the parameters. The trade-off results in the leakage of one parameter’s update into the other. It affects the accuracy and convergence of the inversion. The sensitivity analyses suggested a parameterization using the horizontal velocity [Formula: see text], Thomsen’s parameter [Formula: see text], and the anelliptic parameter [Formula: see text] to reduce the trade-off for surface recorded seismic data. We aim to invert for this parameterization using the scattering integral (SI) method. The available Born sensitivity kernels, within this approach, can be used to calculate additional inversion information. We mainly compute the diagonal of the approximate Hessian, used as a conjugate-gradient preconditioner, and the gradients’ step lengths. We consider modeling in the frequency domain. The large computational cost of the SI method can be avoided with direct Helmholtz equation solvers. We applied our method to the VTI Marmousi II model for various inversion strategies. We found that we can invert the [Formula: see text] accurately. For the [Formula: see text] parameter, only the short wavelengths are well-recovered. On the other hand, the [Formula: see text] parameter impact is weak on the inversion results and can be fixed. However, a good background [Formula: see text], with accurate long wavelengths, is needed to correctly invert for [Formula: see text]. Furthermore, we invert a real data set acquired by CGG from offshore Australia. We simultaneously invert all three parameters using our inversion approach. The velocity model is improved, and additional layers are recovered. We confirm the accuracy of the results by comparing them with well-log information, as well as looking at the data and angle gathers.

Full-waveform inversion in acoustic orthorhombic media and application to a North Sea data set

Full-waveform inversion (FWI) in anisotropic media is challenging, mainly because of the large computational cost, especially in 3D, and the potential trade-offs between the model parameters needed to describe such media. By analyzing the trade-offs and understanding the resolution limits of the inversion, we can constrain FWI to focus on the main parameters the data are sensitive to and push the inversion toward more reliable models of the subsurface. Orthorhombic anisotropy is one of the most practical approximations of the earth subsurface that takes into account the natural horizontal layering and the vertical fracture network. We investigate the feasibility of a multiparameter FWI for an acoustic orthorhombic model described by six parameters. We rely on a suitable parameterization based on the horizontal velocity and five dimensionless anisotropy parameters. This particular parameterization allows a multistage model inversion strategy in which the isotropic, then, the vertical transverse isotropic, and finally the orthorhombic model can be successively updated. We applied our acoustic orthorhombic inversion on the SEG-EAGE overthrust synthetic model. The observed data used in the inversion are obtained from an elastic variable density version of the model. The quality of the inverted model suggests that we may recover only four parameters, with different resolution scales depending on the scattering potential of these parameters. Therefore, these results give useful insights on the expected resolution of the inverted parameters and the potential constraints that could be applied to an orthorhombic model inversion. We determine the efficiency of the inversion approach on real data from the North Sea. The inverted model is in agreement with the geologic structures and well-log information.

Optimal full-waveform inversion strategy for marine data in azimuthally rotated elastic orthorhombic media

The orthorhombic (ORT) anisotropic description of earth layers can allow the capture of much of the earth’s anisotropic complexity. The inversion for high-resolution azimuthal variation of anisotropy is important for reservoir characterization, among other applications. A high-resolution description of the azimuth of fractures can help us to predict flow preferences. To verify the feasibility of multiparameter full-waveform inversion (FWI) for marine data assuming azimuthally rotated elastic ORT media, we have analyzed the radiation patterns and gradient directions of ORT parameters to the reflection data. First, we express the gradient direction of the ORT parameters considering the azimuthal rotation of the symmetric planes. Then, to support our observations in the gradient direction, the radiation patterns of the partial derivative wavefields from each parameter perturbation are also derived under the rotated elastic ORT assumption. To find an optimal parameterization, we compare three different parameterizations: monoclinic, velocity-based, and hierarchical parameterizations. Then, we suggest an optimal multistage update strategy by analyzing the behavior of the rotation angle as a FWI target. To analyze the trade-off among parameters in different parameterizations, we calculate the gradient direction from a hockey-puck model, in which each parameter is perturbed at the different location on a horizontal layer. The trade-off analysis supports that the hierarchical parameterization provides us with more opportunities to build up subsurface models with less trade-off between parameters and less influence of the azimuthal rotation of ORT anisotropy. The feasibility of the proposed FWI strategy is examined using synthetic marine streamer data from a simple 3D reservoir model with a fractured layer.

3D elastic full-waveform inversion using P-wave excitation amplitude: Application to ocean bottom cable field data

We have developed an efficient elastic full-waveform inversion (FWI) based on the P-wave excitation amplitude (maximum energy arrival) approximation in the source wavefields. Because, based on the P-wave excitation approximation (ExA), the gradient direction is approximated by the crosscorrelation of source and receiver wavefields at only excitation time, it estimates the gradient direction faster than its conventional counterpart. In addition to this computational speedup, the P-wave ExA automatically ignores SP and SS correlations in the approximated gradient direction. In elastic FWI for ocean bottom cable (OBC) data, the descent direction for the S-wave velocity is often degraded by undesired long-wavelength features from the SS correlation. For this reason, the P-wave excitation approach increases the convergence rate of multiparameter FWI compared with the conventional approach. The modified 2D Marmousi model with OBC acquisition is used to verify the differences between the conventional method and ExA. Finally, the feasibility of the proposed method is demonstrated on a real OBC data from the North Sea.

Improvements to elastic full-waveform inversion using cross-gradient constraints

Seismic full-waveform inversion (FWI) is potentially a powerful method for obtaining high-resolution subsurface images, but the results are often distorted by nonlinear effects and parameter trade-offs. Such distortions can be particularly severe in the case of multiparameter FWI, such as elastic FWI, in which inversion is performed simultaneously for P- and S-wave velocities and density. The problem can be alleviated by adding constraints in the form of plausible a priori information. A usually well-justified constraint includes the structural similarity of different model parameters; i.e., an anomalous body likely exhibits variations in all elastic properties, although their magnitudes may be different. To consider such types of a priori information, we have developed a structurally constrained elastic FWI, which is based on minimization of the cross products of gradients of different model parameters. Our synthetic 2D experiments show that structurally constrained FWI can significantly improve model reconstruction. It is also demonstrated that our approach still leads to improved results, even when the structural similarity between the individual parameter types is not exactly met. Inversions of field data show that in comparison to conventional FWI, structurally constrained FWI is able to match the field data equally well while requiring less structural complexity of the subsurface.

Multi-parameter full waveform inversion using Poisson’s ratio for elastic media

In multi-parameter full waveform inversion (FWI), the success of recovering each parameter is dependent on characteristics of the partial derivative wavefields (or virtual sources), which differ according to parameterisation. Elastic FWIs based on the two conventional parameterisations (one uses Lamé constants and density; the other employs P- and S-wave velocities and density) have low resolution of gradients for P-wave velocities (or λ). Limitations occur because the virtual sources for P-wave velocity or λ (one of the Lamé constants) are related only to P–P diffracted waves, and generate isotropic explosions, which reduce the spatial resolution of the FWI for these parameters. To increase the spatial resolution, we propose a new parameterisation using P-wave velocity, Poisson’s ratio, and density for frequency-domain multi-parameter FWI for isotropic elastic media. By introducing Poisson’s ratio instead of S-wave velocity, the virtual source for the P-wave velocity generates P–S and S–S diffracted waves as well as P–P diffracted waves in the partial derivative wavefields for the P-wave velocity. Numerical examples of the cross–triangle–square (CTS) model indicate that the new parameterisation provides highly resolved descent directions for the P-wave velocity. Numerical examples of noise-free and noisy data synthesised for the elastic Marmousi-II model support the fact that the new parameterisation is more robust for noise than the two conventional parameterisations.

On the Scaling of the Update Direction for Multi-parameter Full Waveform Inversion: Applications to 2D Acoustic and Elastic Cases

Full waveform inversion (FWI) is traditionally designed as an iterative non-linear optimization problem. Thus, it is subject to scaling problems due to inappropriate choice of model parametrization. It is well known that the conventional gradient-based direction update of the parameters, although widely reported and used, does not have the correct physical units; thus, it needs to be properly weighted to provide an adequate model update. The purpose of this work is to examine this issue and to provide an alternative computation to the update directions for the multi-parameter FWI by taking into account the transformation properties of the Hessian and its approximations, since the Hessian contains information related to parameter scaling. To put in evidence the benefits of this approach, we present applications to mono-parameter acoustic and multi-parameter elastic FWI using the 2D Marmousi-2 synthetic model. The proposed direction of update properly scales the estimated models and provides a much faster convergence rate.

Simultaneous estimation of velocity and density in acoustic multiparameter full-waveform inversion using an improved scattering-integral approach

Density is known to be difficult to reconstruct in multiparameter full-waveform inversion (FWI). This difficulty results from the similarity of the diffraction patterns of velocity and density at small scattering angles. In addition, the sensitivities of seismic data with respect to velocity and density have different orders of magnitude which make the inversion ill-conditioned. The inverse Hessian has been shown to mitigate the coupling effects and rescale the magnitudes of different parameters, such that reliable updates for all parameters are available. We have investigated the possibility of simultaneous estimations of velocity and density in acoustic media using the truncated Gauss-Newton method. The model updates are calculated using a matrix-free conjugate gradient solution of the Gauss-Newton normal equation. The gradients of the misfit function with respect to the model parameters and the Hessian-vector products are computed using an improved scattering-integral approach. To give some insights into the trade-off effects between velocity and density, and the imaging resolution in FWI, the sensitivity kernels of both parameters are numerically calculated in homogeneous background models, and their spatial distributions and characteristics are analyzed. The synthetic experiments on a canonical inclusion model and the 2004 BP model confirm that, in cases in which the Gauss-Newton approximate Hessian, especially its off-diagonal blocks, is accurately taken into account, the truncated Gauss-Newton method can effectively mitigate the trade-off effects between velocity and density and provide accelerated convergence rate. Hence, well-resolved velocity and density models are expected.

Elastic orthorhombic anisotropic parameter inversion: An analysis of parameterization

The resolution of a multiparameter full-waveform inversion (FWI) is highly influenced by the parameterization used in the inversion algorithm, as well as the data quality and the sensitivity of the data to the elastic parameters because the scattering patterns of the partial derivative wavefields (PDWs) vary with parameterization. For this reason, it is important to identify an optimal parameterization for elastic orthorhombic FWI by analyzing the radiation patterns of the PDWs for many reasonable model parameterizations. We have promoted a parameterization that allows for the separation of the anisotropic properties in the radiation patterns. The central parameter of this parameterization is the horizontal P-wave velocity, with an isotropic scattering potential, influencing the data at all scales and directions. This parameterization decouples the influence of the scattering potential given by the P-wave velocity perturbation from the polar changes described by two dimensionless parameter perturbations and from the azimuthal variation given by three additional dimensionless parameters perturbations. In addition, the scattering potentials of the P-wave velocity perturbation are also decoupled from the elastic influences given by one S-wave velocity and two additional dimensionless parameter perturbations. The vertical S-wave velocity is chosen with the best resolution obtained from S-wave reflections and converted waves, and little influence on P-waves in conventional surface seismic acquisition. The influence of the density on observed data can be absorbed by one anisotropic parameter that has a similar radiation pattern. The additional seven dimensionless parameters describe the polar and azimuth variations in the P- and S-waves that we may acquire, with some of the parameters having distinct influences on the recorded data on the earth’s surface. These characteristics of the new parameterization offer the potential for a multistage inversion from high symmetry anisotropy to lower symmetry ones.

Multiparameter estimation with acoustic vertical transverse isotropic full-waveform inversion of surface seismic data

Obtaining accurate depth-migrated images demands an anisotropic representation of the earth. As a prominent tool for building high-resolution earth models, full-waveform inversion (FWI) therefore must not only account for anisotropy during wavefield simulation but also reconstruct the anisotropy fields. We have developed an inversion strategy to perform acoustic multiparameter FWI of surface seismic data in transversely isotropic media with a vertical axis of symmetry (VTI). During the early era of FWI practice, most studies only invert for the most dominant parameter, that is, the vertical velocity, and the rest of the model parameters are either ignored or kept constant. Recently, more and more emphases focus on inverting for more parameters, such as for the vertical velocity and the anisotropy fields; these are referred to as multiparameter inversion. Due to the dominant influence of the vertical velocity on the kinematics of surface seismic data, we have developed a hierarchical approach to invert for the vertical velocity first, but we kept the anisotropy fields unchanged and only switched to joint inversion of the vertical velocity and the anisotropy fields when the inversion for the vertical velocity approaches convergence. In addition, we have illustrated the necessity of incorporating the diving and reflection energy during inversion to mitigate the nonuniqueness of the solutions caused by the coupling between the vertical velocity and the anisotropy fields. We also demonstrate the success of our method for VTI FWI using synthetic and real data examples based on marine surface seismic acquisition. Our results show that incorporation of multiparameter anisotropy inversion produced better focused migration images.

Application of multiparameter full-waveform inversion in Central Luconia Basin, Sarawak

Reducing velocity inaccuracy in complex settings is of paramount importance for limiting structural uncertainties, therefore helping the geologic interpretation and reservoir characterization. Shallow velocity variations due, for instance, to gas accumulations or carbonate reefs, are a common issue offshore Malaysia. These velocity variations are difficult to image through standard reflection-based velocity model building. We have applied full-waveform inversion (FWI) to better characterize the upper part of the earth model for a shallow-water field, located in the Central Luconia Basin offshore Sarawak. We have inverted a narrow-azimuth data set with a maximum inline offset of 4.4 km. Thanks to dedicated broadband preprocessing of the data set, we could enhance the signal-to-noise ratio in the 2.5–10 Hz frequency band. We then applied a multiparameter FWI to estimate the background normal moveout velocity and the [Formula: see text]-parameter. Full-waveform inversion together with broadband data processing has helped to better define the faults and resolve the thin layers in the shallow clastic section. The improvements in the velocity model brought by FWI lead to an improved image of the structural closure and flanks. Moreover, the increased velocity resolution helps in distinguishing between two different geologic interpretations.

Estimation of elastic constants for HTI media using Gauss-Newton and full-Newton multiparameter full-waveform inversion

In seismic full-waveform inversion (FWI), subsurface parameters are estimated by iteratively minimizing the difference between the modeled and the observed data. We have considered the problem of estimating the elastic constants of a fractured medium using multiparameter FWI and modeling naturally fractured reservoirs as equivalent anisotropic media. Multiparameter FWI, although promising, remains exposed to a range of challenges, one being the parameter crosstalk problem resulting from the overlap of Fréchet derivative wavefields. Parameter crosstalk is strongly influenced by the form of the scattering pattern for each parameter. We have derived 3D radiation patterns associated with scattering from a range of elastic constants in general anisotropic media. Then, we developed scattering patterns specific to a horizontal transverse isotropic (HTI) medium to draw conclusions about parameter crosstalk in FWI. Bare gradients exhibit crosstalk, as well as artifacts caused by doubly scattered energy in the data residuals. The role of the multiparameter Gauss-Newton (GN) Hessian in suppressing parameter crosstalk is revealed. We have found that the second-order term in the multiparameter Hessian, which is associated with multiparameter second-order scattering effects, can be constructed with the adjoint-state technique. We have examined the analytic scattering patterns for HTI media with a 2D numerical example. We have examined the roles played by the first- and second-order terms in multiparameter Hessian to suppress parameter crosstalk and second-order scattering artifacts numerically. We have also compared the multiparameter GN and full-Newton methods as methods for determining the elastic constants in HTI media with a two-block-layer model.

A recipe for practical full-waveform inversion in orthorhombic anisotropy

Multiparameter full-waveform inversion (FWI) usually suffers from the inherent tradeoff in the multiparameter nature of the model space. In orthorhombic anisotropy, such tradeoff is magnified by the large number of parameters involved in representing the elastic or even the acoustic approximation of such a medium. However, using a new parameterization with distinctive scattering features, we can condition FWI to invert for the parameters to which the data are sensitive at different stages, scales, and locations in the model. Specifically, with a combination made up of a velocity and particular ratios of the elastic coefficients, the scattering potential of the anisotropy parameters has stationary scattering radiation patterns as a function of the type of anisotropy. With our new parameterization, P-wave data are mainly sensitive to the scattering potential of four parameters: the horizontal velocity in the x1 direction, vh; ∊, which provides scattering mainly near zero offset in the x1-x3 vertical plane; ∊d, which is the ratio of the horizontal velocity squared in the x1 and x2 directions; and δ3 describing the anellipticity in the horizontal plane. Since, with this parameterization, the radiation pattern for the horizontal velocity and ∊ is azimuthally independent, we can perform an initial VTI inversion for these two parameters, and then use the other two parameters to fit the azimuthal variation in the data. This can be done at the reservoir level or any region of the model. Including the transmission from reflections, the migration velocity analysis (MVA) component, into the picture, multiazimuth surface seismic data are mainly sensitive to the long-wavelength components of vh, two dimensionless parameters through the diving waves, and three other dimensionless parameters in the transmission to or from reflectors (especially, in the presence of large offsets). They are also sensitive to the short-wavelength component of vh and ∊.

A review on the systematic formulation of 3-D multiparameter full waveform inversion in viscoelastic medium

In this paper, we study 3-D multiparameter full waveform inversion (FWI) in viscoelastic media based on the generalized Maxwell/Zener body including arbitrary number of attenuation mechanisms. We present a frequency-domain energy analysis to establish the stability condition of a full anisotropic viscoelastic system, according to zero-valued boundary condition and the elastic–viscoelastic correspondence principle: the real-valued stiffness matrix becomes a complex-valued one in Fourier domain when seismic attenuation is taken into account. We develop a least-squares optimization approach to linearly relate the quality factor with the anelastic coefficients by estimating a set of constants which are independent of the spatial coordinates, which supplies an explicit incorporation of the parameter Q in the general viscoelastic wave equation. By introducing the Lagrangian multipliers into the matrix expression of the wave equation with implicit time integration, we build a systematic formulation of multiparameter FWI for full anisotropic viscoelastic wave equation, while the equivalent form of the state and adjoint equation with explicit time integration is available to be resolved efficiently. In particular, this formulation lays the foundation for the inversion of the parameter Q in the time domain with full anisotropic viscoelastic properties. In the 3-D isotropic viscoelastic settings, the anelastic coefficients and the quality factors using bulk and shear moduli parametrization can be related to the counterparts using P and S velocity. Gradients with respect to any other parameter of interest can be found by chain rule. Pioneering numerical validations as well as the real applications of this most generic framework will be carried out to disclose the potential of viscoelastic FWI when adequate high-performance computing resources and the field data are available.