Joint Full Waveform Inversion Research Articles

Crustal and uppermost mantle structures of the North American Midcontinent Rift revealed by joint full-waveform inversion of ambient-noise data and teleseismic P waves

The Midcontinent Rift (MCR), hosting several world-class ore deposits, is the fossil remnant of a massive Mesoproterozoic rifting event (1.1 Ga) that did not lead to the formation of an ocean basin. To better understand the lithospheric processes associated with the rifting stage and its subsequent failure, we developed a novel full-waveform joint inversion method using ambient noise data and teleseismic P waves for this seismically inactive region. We apply this approach to three years (2011-2013) of seismic recordings from the Superior Province Rifting EarthScope Experiment (SPREE) (~12 km average station spacing) and the USArray Transportable Array (~70 km average station spacing), and obtain a new 3D high-resolution Vs model down to 100 km depth, as well as Vp and density models down to 60 km depth. The model shows major velocity anomalies in agreement with previous seismic studies for the western arm of the MCR. In particular, we observe high density (2.8-3.0 g/cm3), Vp (6.3-6.5 km/s), and Vs (3.6-3.7 km/s) structures in the shallow upper crust within the rift, likely associated with volcanic rocks. Similar to a previously identified underplated layer, we also observe extensive normal-to-high Vs (3.8-4.2 km/s) along the whole rift axis and Vp (6.8-7.5 km/s) beneath the northern segment of the rift within the lower crust. However, the Vs and Vp values are lower than average for typical underplated materials. We suggest that this underplated layer may represent a combination of different intrusive rock types (e.g., gabbro, anorthosite) developed during magma differentiation processes, or contamination of the mafic magma by surrounding crustal material, or intrusions of sills.

Newton optimization and the Hessian matrix in scale-separation waveform inversion problems with reflected and transmitted waves

Summary Full waveform inversion (FWI) is often utilized for determining the medium parameters of the Earth by minimizing the misfit between observed and modelled waves. The conventional formulation of FWI is well suited to utilize transmitted waves to determine long-to-intermediate wavelength properties of the medium. Hovewer, the penetration depth of transmitted waves may be limited for a given acquisition. As a remedy, reflection waveform inversion (RWI) exploits the kinematic information in reflected waves to retrieve these long-wavelength properties, particularly below the maximum illumination depth of transmitted waves. Previous works have demonstrated the benefits of utilizing both transmitted and reflected waves, thereby considering a reconciliation of conventional FWI and RWI. One such formulation is known as joint full waveform inversion (JFWI), where reflected and transmitted waves are separately compared in the misfit functional. A disadvantage of gradient-based optimization schemes in RWI and JFWI is the presence of strong crosstalk due to mapping of reflected data residuals along the entire reflection wavepaths. Because RWI and JFWI require frequent least-squares migration, we are incentivized to determine well-focused search directions that allow large movements between the migration steps. Thus, we propose an improvement to RWI and JFWI by utilizing Newton methods to directly account for crosstalk between parameters. The crosstalk effects are described by the second-order sensitivities of the misfit functional, i.e. the Hessian matrix. We adopt the adjoint-state method to compute the first- and second order sensitivities of the misfit functional for any of these waveform inversion procedures in a unified framework and for arbitrary misfit functionals. Furthermore, we conceptually study the Hessian matrix in least-squares based full-, reflection- and joint full waveform inversion from a data-domain point of view. Synthetic examples and a three-dimensional field data example demonstrate that the truncated Gauss-Newton method is effective in attenuating artefacts due to crosstalk between spatially separated variables, thus substantially improving the spatial focusing of the search directions.

Robust and efficient waveform-based velocity-model building by optimal transport in the pseudotime domain: Methodology

Full-waveform inversion (FWI) aims at a broadband reconstruction of the subsurface physical properties by fitting the entire recorded wavefield. In realistic exploration seismic surveys, however, conventional FWI often fails to retrieve the deep velocity model due to the limited penetration depth of diving waves. Joint FWI (JFWI) unifies reflection-waveform inversion and early arrival waveform inversion to reconstruct simultaneously the shallow and deep subsurface kinematics. However, several factors limit the appeal of JFWI velocity-model building: (1) conflict between fixed reflectivity and evolving kinematics, creating phase ambiguity at short offsets; (2) susceptibility to cycle skipping at mid-to-long offsets, thus reliance on the quality of the starting model; and (3) cost of building and updating the reflective model. We have developed a fully operational JFWI-based methodology that systematically addresses the aforementioned issues. JFWI is reformulated in the pseudotime domain, to enforce consistency between velocity and reflectivity in a cost-effective fashion, without repeated least-squares migrations. A JFWI graph-space optimal transport (GSOT) objective function is designed to avert cycle skipping, whereas nonuniqueness is mitigated at no extra cost by smoothing the velocity gradient along the structures extracted from the reflective model. A dedicated asymptotic-based preconditioner is developed for impedance waveform inversion, making it possible to obtain sharp and balanced reflective images in a fraction of the time. We determine that pseudotime GSOT-JFWI retrieves complex velocity macromodels from limited-offset data sets with minimal preprocessing, starting from noninformative initial solutions. Compared with depth-domain JFWI, the computing cost is reduced significantly, along with a simpler and less subjective design of data weighting and inversion strategy. Pseudotime GSOT-JFWI provides FWI with the necessary low wavenumbers to converge to the broadband model, reducing the need for accurate starting models, on the road to a fully waveform-based imaging workflow.

Application of Q-FWI-tomography and least-squares migration to improve seismic resolution in Tengiz oil field

Seismic image deterioration is a major problem for structures under complex overburdens. In areas under major faults and salt bodies, it is common to observe amplitude washout zones, poor structural definition, and relatively strong coherent and incoherent seismic noise. We developed a data-driven workflow of Q least-squares migration to mitigate these problems by enhancing the horizontal and vertical resolutions of seismic images. The workflow includes accurate velocity model building with joint full-waveform inversion and tomography to maximize the stacking power of P-wave primaries, Q tomography that balances weak-amplitude washout zones and minimizes swing noises, and least-squares migration with the aid of a constraint map that yields higher-resolution structural images. Its application on a wide-azimuth data set from the Tengiz oil field demonstrates the effective mitigation of fault shadow issues with an overall improvement of image quality. In addition, the uplift in focusing of diffracted energies shows promising improvements in enhancing seismic mega-amplitude events. Thus, the proposed method greatly increases the fidelity of seismic attribute analysis when compared with conventional vintage processing.

Joint FWI of Active Source Data and Passive Virtual Source Data Reconstructed Using an Improved Multidimensional Deconvolution

Traditional full waveform inversion (FWI) highly depends on sufficient low-frequency data or a good initial model. Passive seismic data contain rich low-frequency components, and passive seismic FWI using virtual source data by seismic interferometry (SI) is a promising method. However, the distribution of passive sources in the subsurface is always inhomogeneous, which will lead to artifacts in the reconstruction results by SI using cross-correlation (CC). SI by multidimensional deconvolution (MDD) can counteract the source inhomogeneity but requires the separation of the reference wavefields, which is difficult to achieve for noise source data. To mitigate this problem, we propose an improved SI method by linear Radon transform based multidimensional deconvolution (LRTMDD). The interferometric point-spread function can be extracted more accurately and efficiently in the linear Radon domain, thus improving the reconstruction results. The passive virtual source full waveform inversion (PVSFWI) based on LRTMDD is further proposed, which can effectively use the low-frequency information in the virtual source data to invert the macroscopic velocity structures even in the case of inhomogeneous source distributions, and without the need to estimate the virtual source wavelets. A joint multi-source FWI strategy is proposed to solve the problem of missing low-frequency data suffered by active source FWI. Numerical experiments on the Marmousi model and the SEG/EAGE overthrust model show that the proposed methods can fully combine the respective advantages of multisource seismic data to stably achieve high-accuracy velocity models in the case of inhomogeneous passive source distributions and the lack of low-frequency data in active seismic data.

Ensemble-based uncertainty estimation in Full Waveform Inversion

SUMMARY Uncertainty estimation and quality control are critically missing in most geophysical tomographic applications. The few solutions to cope with that issue are often left out in practical applications when these ones grow in scale and involve complex modeling. We present a joint full waveform inversion and ensemble data assimilation scheme, allowing local Bayesian estimation of the solution that brings uncertainty estimation to the tomographic problem. This original methodology relies on a deterministic square root ensemble Kalman filter commonly used in the data assimilation community: the ensemble transform Kalman filter. Combined with a 2D visco-acoustic frequency domain full waveform inversion scheme, the resulting method allows to access a low-rank approximation of the posterior covariance matrix of the solution. It yields uncertainty information through an ensemble-representation, that can conveniently be mapped across the physical domain for visualization and interpretation. The combination of ensemble transform Kalman filter with full waveform inversion is discussed along with the scheme design and algorithmic details that lead to our mixed application. Both synthetic and field-data results are presented, along with the biases that are associated with the limited rank ensemble representation. Finally, we review the open questions and developments perspectives linked with data assimilation applications to the tomographic problem.

Crustal-scale depth imaging via joint full-waveform inversion of ocean-bottom seismometer data and pre-stack depth migration of multichannel seismic data: a case study from the eastern Nankai Trough

Abstract. Imaging via pre-stack depth migration (PSDM) of reflection towed-streamer multichannel seismic (MCS) data at the scale of the whole crust is inherently difficult. This is because the depth penetration of the seismic wavefield is controlled, firstly, by the acquisition design, such as streamer length and air-gun source configuration, and secondly by the complexity of the crustal structure. Indeed, the limited length of the streamer makes the estimation of velocities from deep targets challenging due to the velocity–depth ambiguity. This problem is even more pronounced when processing 2-D seismic data due to the lack of multi-azimuthal coverage. Therefore, in order to broaden our knowledge about the deep crust using seismic methods, we present the development of specific imaging workflows that integrate different seismic data. Here we propose the combination of velocity model building using (i) first-arrival tomography (FAT) and full-waveform inversion (FWI) of wide-angle, long-offset data collected by stationary ocean-bottom seismometers (OBSs) and (ii) PSDM of short-spread towed-streamer MCS data for reflectivity imaging, with the former velocity model as a background model. We present an application of such a workflow to seismic data collected by the Japan Agency for Marine-Earth Science and Technology (JAMSTEC) and the Institut Français de Recherche pour l'Exploitation de la Mer (IFREMER) in the eastern Nankai Trough (Tokai area) during the 2000–2001 Seize France Japan (SFJ) experiment. We show that the FWI model, although derived from OBS data, provides an acceptable background velocity field for the PSDM of the MCS data. From the initial PSDM, we refine the FWI background velocity model by minimizing the residual move-outs (RMOs) picked in the pre-stack-migrated volume through slope tomography (ST), from which we generate a better-focused migrated image. Such integration of different seismic datasets and leading-edge imaging techniques led to greatly improved imaging at different scales. That is, large to intermediate crustal units identified in the high-resolution FWI velocity model extensively complement the short-wavelength reflectivity inferred from the MCS data to better constrain the structural factors controlling the geodynamics of the Nankai Trough.

A study of full waveform inversion of seismic velocity structure under a rugged seafloor by using joint OBN and VSP synthetic seismic data

A numerical study of full waveform inversion (FWI) of seismic velocity structure was carried out by using synthetic ocean-bottom node (OBN) and vertical seismic profile (VSP) data. Based on an undulating seafloor modified from the commonly known Marmousi2 model, seismic forward modeling was performed to synthesize seismic P-wave data for the study. FWI experiments were performed using synthetic VSP, OBN and combined VSP + OBN data, separately, for the inversion of the velocity structure. The results show that the joint inversion of using the combined VSP + OBN synthetic data resulted in a very good velocity structure. Its accuracy is significantly higher than either using the VSP or OBN data alone. This suggests that the joint FWI using combined VSP + OBN data is a better image processing technique for the rugged seabed and complex structure below.

Individual and joint 2-D elastic full-waveform inversion of Rayleigh and Love waves

We investigate the performance of the individual 2-D elastic full-waveform inversion (FWI) of Rayleigh and Love waves as well as the feasibility of a simultaneous joint FWI of both wave types. The FWI of surface waves can provide a valuable contribution to near-surface investigations, since they are mainly sensitive to the S-wave velocity and hold a high signal-to-noise ratio. In synthetic reconstruction tests we compare the performance of the individual wave type inversions and explore the benefits of a simultaneous joint inversion. In these tests both individual wave type inversions perform similarly well, given that the initial P-wave velocity model is accurate enough. In this case the joint FWI further improves the result. For an inaccurate initial P-wave velocity model, we observe artifacts in the results of the Rayleigh wave FWI and the joint FWI. Subsequently, we recorded a near-surface field dataset to verify the results by a realistic example. In the field data application the Love wave FWI is superior to the Rayleigh wave FWI, possibly due to the initial P-wave velocity model. Also in this case the joint FWI further improves the inversion result.

Velocity model building by waveform inversion of early arrivals and reflections: A 2D case study with gas-cloud effects

Joint full-waveform inversion (JFWI) combines reflection waveform inversion (RWI) and early-arrival waveform inversion to build a large-scale velocity model of the subsurface from long-offset data. The misfit function of JFWI requires an explicit separation between the short-spread reflections and early arrivals, the feasibility of which is illustrated with a real data case study. JFWI is alternated with a waveform inversion/migration of short-spread reflections to provide a short-scale impedance model. This model is needed for building the sensitivity kernel of RWI along the two-way reflection paths. The large-scale velocity macromodel built by JFWI can be used as the initial model for classic FWI to enrich the high-wavenumber content of the subsurface model. We have developed an application of this workflow to a real 2D ocean bottom cable (OBC) profile across a gas cloud in the North Sea to review its main promises and pitfalls. Viscoacoustic VTI seismic modeling allows us to account for attenuation and anisotropy effects in a passive way during JFWI and FWI. Using a smoothed version of an existing traveltime tomographic model as the initial model, we first find that the JFWI velocity macromodel is more accurate than the RWI counterpart thanks to the key contribution of the diving waves. Second, we find that the large-scale velocity model updated by JFWI provides a more accurate initial model for classic FWI than does the original smoothed tomographic model. However, because a data difference-based misfit function is used, 2D JFWI still suffers from cycle skipping when a crude 1D velocity model is used as the initial model; therefore, more robust misfit function should be designed to mitigate cycle skipping.

Joint Inversion of Electromagnetic and Seismic Data Based on Structural Constraints Using Variational Born Iteration Method

An efficient 2-D joint full-waveform inversion method for electromagnetic and seismic data in a layered medium background is developed. The joint inversion method based on the integral equation (IE) method is first proposed in this paper. In forward computation, the IE method is employed, which usually has smaller discretized computation domain and less cumulative error compared with the finite-difference method. In addition, fast Fourier transform is used to accelerate the convolution between Green’s functions and induced sources due to the shift invariance property of the layered Green’s functions in the horizontal direction. In the inversion model, the cross-gradient function is incorporated into the cost function of the separate inversion to enforce the structure similarity between electric conductivity and seismic-wave velocity. We use the improved variational Born iteration method and two different iteration strategies to minimize the cost function and reconstruct the contrasts. Several typical models in geophysical applications are used to validate our joint inversion method, and the numerical simulation results show that joint inversion can improve the inversion results when compared with those from the separate inversion.

Joint acoustic full-waveform inversion of crosshole seismic and ground-penetrating radar data in the frequency domain

Integrating crosshole ground-penetrating radar (GPR) with seismic methods is an efficient way to reduce the uncertainty and ambiguity of data interpretation in shallow geophysical investigations. We have developed a new approach for joint full-waveform inversion (FWI) of crosshole seismic and GPR data in the frequency domain to improve the inversion results of both FWI methods. In a joint objective function, three geophysical parameters (P-wave velocity, permittivity, and conductivity) are effectively connected by three weighted cross-gradient terms that enforce the structural similarity between parameter models. Simulation of acoustic seismic and scalar electromagnetic problems is implemented using 2D finite-difference frequency-domain methods, and the inverse problems of seismic FWI and GPR FWI are solved using a matrix-free truncated Newton algorithm. The joint inversion procedure is performed in several hierarchical frequencies, and the three parameter models are sequentially inverted at each frequency. The joint FWI approach is illustrated using three numerical examples. The results indicate that the joint FWI approach can effectively enhance the structural similarity among the models, modify the structure of each model, and improve the accuracy of inversion results compared with those of individual FWI approaches. Moreover, joint inversion can reduce the trade-off between permittivity and conductivity in GPR FWI, leading to an improved conductivity model in which artifacts are significantly decreased.

Quantitative imaging for civil engineering by joint full waveform inversion of surface-based GPR and shallow seismic reflection data

Full waveform inversion (FWI) of ground penetrating radar (GPR) and seismic data is a promising imaging tool for the detailed characterization of latent cavities and tunnels. In this study, surface-based GPR FWI and seismic FWI are combined to quantitatively image the geometry and geophysical attributes of the subsurface. These two FWI methods are integrated into a joint procedure and linked by cross-gradient functions which can provide structural constraints between the parameters. The elastic and electromagnetic properties of the medium (P-wave velocity, permittivity, and conductivity) are linked and simultaneously inverted in the joint FWI approach. This joint FWI approach is tested using three numerical examples. In the first two examples, target objects with various shapes are contained in both homogeneous and inhomogeneous media. In the third example, two sediment-filled cavities and a fractured area are analyzed in the calcarenite layers. The results show that the joint FWI approach can integrate the common structure of models and correct the model structures that are inaccurately reconstructed in the individual FWI methods, providing a comprehensive structural interpretation of the study areas.

Time-lapse full-waveform inversion with ocean-bottom-cable data: Application on Valhall field

Knowledge of changes in reservoir properties resulting from extracting hydrocarbons or injecting fluid is critical to future production planning. Full-waveform inversion (FWI) of time-lapse seismic data provides a quantitative approach to characterize the changes by taking the difference of the inverted baseline and monitor models. The baseline and monitor data sets can be inverted either independently or jointly. Time-lapse seismic data collected by ocean-bottom cables (OBCs) in the Valhall field in the North Sea are suitable for such time-lapse FWI practice because the acquisitions are of a long offset, and the surveys are well-repeated. We have applied independent and joint FWI schemes to two time-lapse Valhall OBC data sets, which were acquired 28 months apart. The joint FWI scheme is double-difference waveform inversion (DDWI), which inverts differenced data (the monitor survey subtracted by the baseline survey) for model changes. We have found that DDWI gave a cleaner and more easily interpreted image of the reservoir changes compared with that obtained with the independent FWI schemes. A synthetic example is used to demonstrate the advantage of DDWI in mitigating spurious estimates of property changes and to provide cross validations for the Valhall data results.

Full waveform inversion of diving & reflected waves for velocity model building with impedance inversion based on scale separation

Full waveform inversion (FWI) aims to reconstruct high-resolution subsurface models from the full wavefield, which includes diving waves, post-critical reflections and short-spread reflections. Most successful applications of FWI are driven by the information carried by diving waves and post-critical reflections to build the long-to-intermediate wavelengths of the velocity structure. Alternative approaches, referred to as reflection waveform inversion (RWI), have been recently revisited to retrieve these long-to-intermediate wavelengths from short-spread reflections by using some prior knowledge of the reflectivity and a scale separation between the velocity macromodel and the reflectivity. This study presents a unified formalism of FWI, named as Joint FWI, whose aim is to efficiently combine the diving and reflected waves for velocity model building. The two key ingredients of Joint FWI are, on the data side, the explicit separation between the short-spread reflections and the wide-angle arrivals and, on the model side, the scale separation between the velocity macromodel and the short-scale impedance model. The velocity model and the impedance model are updated in an alternate way by Joint FWI and waveform inversion of the reflection data (least-squares migration), respectively. Starting from a crude velocity model, Joint FWI is applied to the streamer seismic data computed in the synthetic Valhall model. While the conventional FWI is stuck into a local minimum due to cycle skipping, Joint FWI succeeds in building a reliable velocity macromodel. Compared with RWI, the use of diving waves in Joint FWI improves the reconstruction of shallow velocities, which translates into an improved imaging at deeper depths. The smooth velocity model built by Joint FWI can be subsequently used as a reliable initial model for conventional FWI to increase the high-wavenumber content of the velocity model.