Model For Full Waveform Inversion Research Articles

Waveform inversion with structural regularizing constraint based on gradient decomposition

Abstract Full waveform inversion (FWI) can simultaneously update low-to-medium wavenumber velocity components and high-wavenumber velocity components. However, if seismic data lack large-offset data and effective low-frequency components, FWI updates will be dominated by high-wavenumber velocity perturbation. Meanwhile, providing that the initial model is inaccurate, inversion will have the problem of local minima. In this study, FWI is developed with structural regularizing constraint based on gradient decomposition (RGDFWI). By correlating the separated forward wavefield and backward wavefield with specific propagating direction, FWI gradient is decomposed into tomography-mode gradient and migration-mode gradient. We propose an optimized strategy taking full advantage of the two modes of FWI gradient. On the one hand, we use tomography-mode gradient to enhance low-to-medium wavenumber updates. On the other hand, we use migration-mode gradient to apply structural regularizing constraint by estimating structure dip and adding sparsity constraint in Seislet domain. During the inversion process, high-wavenumber structural information constrains and guides low-wavenumber model updates. The results of two numerical tests, Marmousi model test and Overthrust model test, validate the optimized strategy, which can produce a better initial velocity model for FWI. The inversion finally generates a high-precision and high-resolution velocity model.

REVEAL: A Global Full-Waveform Inversion Model

ABSTRACT We present REVEAL, a global-scale, transversely isotropic full-waveform inversion model. REVEAL builds upon the earlier construction of the long-wavelength Earth (LOWE) model by lowering the minimum period from 100 to 33 s and by more than doubling the number of included earthquakes to 2366. In the course of 305 quasi-Newton iterations, REVEAL assimilated a total of 6,005,727 unique three-component waveforms. The inversion method rests on the combination of a stochastic mini-batch optimization and wavefield-adapted spectral-element meshes. Although the former naturally exploits redundancies in the data set, the latter reduces the cost of wavefield simulations by reducing the effective dimension of the numerical mesh. As a consequence, the average cost of an iteration in this inversion is only around 0.62% of an iteration that uses the complete data set with a standard cubed-sphere-type mesh. We calculated 3D synthetic seismograms using a graphics processing unit-accelerated spectral-element wave propagation solver, accommodating the effects of anelasticity, topography, bathymetry, ocean loading, and ellipticity. For a diverse range of global wavepaths, REVEAL predicts complete three-component seismograms at 33 s period that have not been included in the inversion. This generalization to unseen data suggests applications of REVEAL in event location and characterization, as well as in ground-motion modeling.

Experimental full waveform inversion for elastic material characterization with accurate transducer modeling

For quality assurance and in-service safety, sufficient characterization of the materials is essential during the development, manufacture, and processing of a material in any industrial setting. Evaluation of elastic coefficients, material microstructures, morphological features, and related mechanical properties are all part of the process of characterizing a material. Ultrasonic signals are sensitive to material properties such as wave speeds, attenuation, diffusion backscattering, microstructural variation, and elastic characteristics (e.g., elastic modulus, hardness, etc.). Ultrasonic computed tomography (USCT) is an emerging imaging method that can be implemented to obtain a quantitative estimation of material properties. In this study, a source estimation technique was initially proposed to obtain the source time function for accurate forward modeling by constructing a linear inverse problem for the unknown transducer modeling. Finally, a material characterization approach was proposed with accurate source estimation to extract wave speed distribution from an elastic material by employing a wave-based method, known as full waveform inversion (FWI). Systematic performance analysis of the proposed FWI model with accurate source estimation was assessed using experimental and synthetic data obtained from a 6061 aluminum sample. Overall, the proposed FWI technique has successfully reconstructed the wave speed distribution, exhibiting the potential of the proposed method of material characterization in various engineering applications.

Faster determination of an initial velocity model for full-waveform inversion based on simulated annealing

Full-waveform inversion (FWI) is a prominent method commonly used to create detailed velocity models of the subsurface. However, because it relies on gradient methods, it suffers from the limitation of getting trapped in local minima. To avoid this problem, FWI needs to start from an initial velocity model that lies in the same region of convexity as the global minimum. Global optimization methods, such as simulated annealing, can be used to find such an initial velocity model. However, the iterative process of simulated annealing entails high computational cost, first because of the large number of iterations needed to explore the variables space, and second because of the large number of simulations needed to adjust the simulation parameters. Although the first issue is a common concern of previous work, the second issue is usually neglected, relying on trial and error. We introduce an approach to tackle the issues and then apply it within a simulated annealing framework we create. Our experiments using the Marmousi data yielded promising results when compared with previous work. We find that our approach almost eliminated the computational effort to fine-tune several simulation parameters. In addition, the number of iterations needed to explore the variables space is reduced by two orders of magnitude. FWI is able to find a detailed velocity model with high quality when using the initial velocity model generated by the method.

Robust and efficient waveform-based velocity model building by optimal transport in the pseudotime domain: An ocean-bottom cable case study in the North Sea

Full-waveform inversion (FWI) in the North Sea has demonstrated its imaging power starting from low-resolution models obtained by traveltime tomography, enriching them with geologically interpretable fine-scale details. However, building a traveltime-based kinematically accurate starting model for FWI is a time-consuming and rather subjective process requiring phase identification and selection. The two main problems faced by FWI starting from noninformative initial models are the susceptibility to cycle skipping and a lack of sensitivity to low wavenumbers in the deep subsurface not sampled by turning waves. On a North Sea ocean-bottom cable 3D data set, a novel [Formula: see text] building methodology is applied that addresses those issues by jointly inverting reflections and refractions (joint full-waveform inversion [JFWI]) using a robust misfit function in the vertical traveltime domain (pseudotime). Pseudotime addresses reflectivity-velocity coupling and attenuates phase ambiguities at short offsets, whereas a graph-space optimal transport (GSOT) objective function with dedicated data windowing averts cycle skipping at intermediate-to-long offsets. A fast and balanced reflectivity reconstrution is obtained prior to JFWI thanks to an asymptotic-preconditioned impedance waveform inversion ([Formula: see text]WI). Starting from a linearly increasing one-dimensional model, GSOT-pseudotime JFWI is effective at obtaining a meaningful P-wave velocity macromodel down to depths sampled by reflections only, without phase identification and picking. P-wave FWI, starting from the JFWI-based model, injects the high wavenumbers missing in the JFWI solution, attaining apparent improvements in shallow and deep model reconstruction and imaging compared with the previous studies in the literature, and a satisfactory prediction of the ground-truth logs.

Simultaneous waveform inversion of seismic-while-drilling data for P-wave velocity, density, and source parameters

Full-waveform inversion (FWI), as an optimization-based approach to estimating subsurface models, is limited by incomplete acquisition and illumination of the subsurface. The incorporation of additional data from new and independent raypaths should be expected to result in significant increase in the accuracy of FWI models. In principle, seismic-while-drilling (SWD) technology can supply these additional raypaths; however, it introduces a new suite of unknowns, namely precise source locations (i.e., drilling path), source signature, and radiation characteristics. A new FWI algorithm is formulated in which the source radiation patterns and positions join the velocity and density values of the grid cells as unknowns to be determined. Several numerical inversion experiments are then conducted with different source settings using a synthetic model. The SWD sources are supplemented by explosive sources and multicomponent receivers at the surface, simulating a conventional surface acquisition geometry. The subsurface model and SWD source properties are recovered and analyzed. The analysis is suggestive that SWD involvement can enhance the accuracy of FWI models, with varying degrees of enhancement depending on factors such as trajectory inclination, source density, and drill path extension. The impact of SWD-FWI over standard FWI is reduced when low-frequency data are missing, but improvements over the models constructed with no subsurface sources remain. This formulation permits general source information, such as position and moment tensor components, to be independently obtained. This inversion scheme may lead to a range of potential applications for which medium properties and source information are required.

Efficient 1.5D full waveform inversion in the Laplace-Fourier domain

Accurate near-surface characterization and velocity model building are important for a number of geotechnical and geophysical applications. 3D full waveform inversion (FWI) can be used to generate a detailed velocity model, but must be provided with a good initial velocity model. A method for producing such an initial velocity model is explored in this paper. Assuming that the near-subsurface can be locally approximated by an effective flat-layered medium, a specialized form of acoustic FWI is proposed. The inversion is based on regularized least-squares in the Laplace-Fourier domain as a measure to mitigate the cycle-skipping problem. Forward modeling is carried out by solving a number of independent finite-difference problems in parallel, for a set of horizontal wavenumbers. The set is determined adaptively, using a pair of algorithms discussed in detail. A numerical implementation of the inverse Hankel transform, used to synthesize data in the frequency-offset domain, is also described. The forward modeling scheme is validated against analytic solutions of the Helmholtz equation, showing good agreement between the two. FWI is tested by inverting a synthetic dataset consisting of flat layers with embedded velocity anomalies. Important features are recovered after inversion at a small number of complex frequencies, providing a detailed initial model for successive 3D FWI.

Deep-Tomography: iterative velocity model building with deep learning

SUMMARY The accurate and fast estimation of velocity models is crucial in seismic imaging. Conventional methods, such as tomography, stereotomography, migration velocity analysis and full-waveform inversion (FWI), obtain appropriate velocity models; however, they require intense and specialized human supervision and consume much time and computational resources. In recent years, some works investigated deep learning (DL) algorithms to obtain the velocity model directly from shots or migrated angle panels, obtaining encouraging predictions of synthetic models. This paper proposes a new flow to recover structurally complex velocity models with DL. Inspired by the conventional geophysical velocity model building methods, instead of predicting the entire model in one step, we predict the velocity model iteratively. We implement the iterative nature of the process when, at each iteration, we train the DL algorithm to determine the velocity model with a certain level of precision/resolution for the next iteration; we name this process as ‘Deep-Tomography’. Starting from an initial model, that is an ultrasmooth version of the true model, Deep-Tomography is able to predict an appropriate final model, even in complete unseen during the training data, like the Marmousi model. When used as the initial model for FWI, the models estimated by Deep-Tomography can also improve substantially the final results obtained with FWI.

Hybrid domain frequency controllable envelope inversion with lowrank approximation for long-wavelength velocity model building

Full waveform inversion (FWI) needs an accurate initial model to guarantee convergence. Time domain frequency controllable envelope inversion (FCEI) is capable to build a long-wavelength velocity model that can be used as an initial model for conventional FWI. However, the implementation of time domain FCEI introduces tremendous burden in storage or computation, which hinders its efficient implementation especially on a memory-limited device. We propose a hybrid domain FCEI (HFCEI) method, in which the wave propagation is performed in the time domain while the computation of gradient is performed in the frequency domain. We demonstrate that the frequency control property of FCEI makes it suitable to be efficiently implemented in the hybrid domain. Only a few frequency domain wavefields need to be saved and no extra wave propagation is needed in calculating gradient. We also demonstrate that the frequency domain wavefields in HFCEI satisfy the lowrank assumption, which enables us to use the lowrank approximation to accurately represent the frequency domain wavefields to further reduce the storage requirement of the method. As a result, HFCEI has significant advantages than time domain FCEI in implementation especially for large-scale problems. Synthetic examples are given to verify the effectiveness of HFCEI and demonstrate its advantages over time domain FCEI.

Physics-guided deep autoencoder to overcome the need for a starting model in full-waveform inversion

Full-waveform inversion (FWI) is a popular technique to obtain high-resolution estimates of earth model parameters using all information present in seismic data. Thus, it can provide important information about the subsurface. The FWI algorithm is formulated as a data-fitting minimization problem that iteratively updates an initial velocity model using the gradient of the misfit until an acceptable match is obtained between the real and synthetic data under a tolerance level based on noise in the data. The inversion is computationally expensive and can converge to a local minimum if the starting model used is not close enough to an optimal model. Here, we propose an alternative approach using a combination of machine learning and the physics of the forward model. Unlike conventional supervised machine learning, known answers are not required to train our network. The shot gathers are input to a convolutional neural network-based autoencoder, the output of which is used as the velocity model that is used to compute synthetic seismograms. The synthetic data are compared against observed input data, and the misfit is estimated. The gradient of the misfit with respect to the velocity model parameters is calculated using the adjoint state method. The adjoint state gradient is then used to update the network weights using the automatic differentiation technique. Once the misfit term converges, the neural network can generate velocity models consistent with the observed data. We observe that the neural network can capture spatial correlations at different scales and thus can introduce regularization in our inverse problem. Experiments with the Marmousi model and SEG Advanced Modeling Corporation Phase 1 salt model suggest that the proposed method can overcome local minima, requires no starting model, and produces robust results in the presence of noise and complex salt body structures.

Seismic acoustic full waveform inversion based on the steepest descent method and simple linear regression analysis

Full waveform inversion (FWI) is a high-resolution imaging tool in seismic exploration. The steepest descent (SD) method is the simplest local optimization algorithm to update the P-wave velocity model in acoustic FWI, but it takes more iterations than other algorithms due to its inefficient search direction. In this study, we provide a SDSLR method, which can significantly shorten the convergence process of the SD method by using the simple linear regression (SLR) analysis. The SLR analysis has two important effects in this method: compute a SLR model to approximately estimate the recent variation trend of P-wave velocity model and directly predict the inversion result of the SD method of the next iteration. Based on the prediction of the SLR analysis, the SDSLR method can obtain the final inversion result of the traditional SD method with fewer iterations. Three numerical examples have tested the performance of the SDSLR method. Results show that the SDSLR method has great potential in constructing high-velocity anomalies. The computational efficiency of the SDSLR method is similar to that of the SD and L-BFGS methods, while the convergence rate and accuracy of the SDSLR method are clearly better than those of the SD and L-BFGS methods.

Using convolutional neural networks to develop starting models for near-surface 2-D full waveform inversion

SUMMARY Non-invasive subsurface imaging using full waveform inversion (FWI) has the potential to fundamentally change near-surface (<30 m) site characterization by enabling the recovery of high-resolution (metre-scale) 2-D/3-D maps of subsurface elastic material properties. Yet, FWI results are quite sensitive to their starting model due to their dependence on local-search optimization techniques and inversion non-uniqueness. Starting model dependence is particularly problematic for near-surface FWI due to the complexity of the recorded seismic wavefield (e.g. dominant surface waves intermixed with body waves) and the potential for significant spatial variability over short distances. In response, convolutional neural networks (CNNs) are investigated as a potential tool for developing starting models for near-surface 2-D elastic FWI. Specifically, 100 000 subsurface models were generated to be representative of a classic near-surface geophysics problem; namely, imaging a two-layer, undulating, soil-over-bedrock interface. A CNN has been developed from these synthetic models that is capable of transforming an experimental wavefield acquired using a seismic source located at the centre of a linear array of 24 closely spaced surface sensors directly into a robust starting model for FWI. The CNN approach was able to produce 2-D starting models with seismic image misfits that were significantly less than the misfits from other common starting model approaches, and in many cases even less than the misfits obtained by FWI with inferior starting models. The ability of the CNN to generalize outside its two-layered training set was assessed using a more complex, three-layered, soil-over-bedrock formation. While the predictive ability of the CNN was slightly reduced for this more complex case, it was still able to achieve seismic image and waveform misfits that were comparable to other commonly used starting models, despite not being trained on any three-layered models. As such, CNNs show great potential as tools for rapidly developing robust, site-specific starting models for near-surface elastic FWI.

Wave-equation migration velocity analysis via the optimal-transport-based objective function

Wave-equation migration velocity analysis builds a kinematically accurate macrovelocity model containing the large-scale structures of the model for seismic imaging or full-waveform inversion (FWI). Differential semblance optimization formulates the misfit function in the subsurface domain by applying a penalty to the unfocused subsurface-offset gathers or the nonflattened angle gathers. Such a penalty leads to gradients with strong artifacts and spurious oscillations, which then leads to slow convergence. We formulate the misfit function using the optimal transport (OT) among neighboring traces in angle-domain common-image gathers (CIGs). Specifically, we measure the unflatness of the gathers by comparing the Wasserstein distance of adjacent traces. Because CIGs are ideal to form a probability distribution, which is required by OT, it is natural to use OT to measure the time shifts between two distributions. Our objective function exhibits well-behaved convex and unimodal properties in a simple model with a single interface, and it is expected to be minimum for the correct velocity when the angle gathers are flat. A synthetic data set example on the Marmousi model indicates the ability of our method to provide an initial model for FWI that allows FWI to converge. We also apply the approach on a marine field data set to further demonstrate its effectiveness in estimating the macrovelocity model.

Self-Supervised Deep Learning for Nonlinear Seismic Full Waveform Inversion

Seismic full waveform inversion (FWI) is able to build high-resolution velocity model based on the full information carried by seismic wave. However, FWI requires an accurate enough initial model to ensure convergence. In this paper, we propose a new nonlinear FWI method to mitigate the initial model dependence problem. Specifically, we firstly propose a nonlinear operator within the hybrid model- and data-driven framework based on the frequency controllable envelope operator (FCEO) and a deep learning architecture U-Net. FCEO is used to obtain the envelope of a band-limited data and U-Net realizes the mapping from this envelope to that corresponding to a lower frequency band. The U-Net is trained in a self-supervised manner that avoids the reliance on labeled data and benefits the generalization ability. Based on the nonlinear operator, a nonlinear FWI method is proposed by defining a new misfit function. In addition, the calculation of gradient is derived using the adjoint-state method. Using numerical examples, we investigate the performance of the proposed nonlinear operator and the new nonlinear FWI method. The results clearly demonstrate that the proposed nonlinear operator is effective in obtaining low-frequency envelope data, and the new nonlinear FWI method has advantages over common method in mitigating cycle-skipping and building an initial model for conventional FWI.

Deep Learning for Low-Frequency Extrapolation of Multicomponent Data in Elastic FWI

Full waveform inversion (FWI) strongly depends on an accurate starting model to succeed. This is particularly true in the elastic regime: The cycle-skipping phenomenon is more severe in elastic FWI compared to acoustic FWI, due to the short S-wave wavelength. In this paper, we extend our work on extrapolated FWI (EFWI) by proposing to synthesize the low frequencies of multi-component elastic seismic records, and use those "artificial" low frequencies to seed the frequency sweep of elastic FWI. Our solution involves deep learning: we separately train the same convolutional neural network (CNN) on two training datasets, one with vertical components and one with horizontal components of particle velocities, to extrapolate the low frequencies of elastic data. The architecture of this CNN is designed with a large receptive field, by either large convolutional kernels or dilated convolution. Numerical examples on the Marmousi2 model show that the 2-4Hz low frequency data extrapolated from band-limited data above 4Hz provide good starting models for elastic FWI of P-wave and S-wave velocities. Additionally, we study the generalization ability of the proposed neural network over different physical models. For elastic test data, collecting the training dataset by elastic simulation shows better extrapolation accuracy than acoustic simulation, i.e., a smaller generalization gap.

Joint Traditional and Reflection Envelope Inversion

The envelope inversion (EI) is an effective method to recover low-wavenumber components, which helps to produce a good initial model for full-waveform inversion (FWI). However, when the initial model is not capable of generating reflections, it brings enormous challenges for EI to invert deep low-wavenumber components, especially for short offset data. In contrast, reflection waveform inversion (RWI) uses demigration data to fit the observed reflection, which focuses on the transmission information with short offset seismic data. However, the cycle skipping and high nonlinearity of the RWI misfit still exist when the low-frequency information is absent. In this letter, we develop a joint traditional and reflection envelope inversion (JREI) that utilizes both reflection and transmission waves with envelope low-frequencies to recover low-wavenumber components in the shallow and deep regions simultaneously. We then use the FWI with high-frequency seismic data to obtain the high-wavenumber components. Applications to the modified Marmousi and Overthrust models demonstrate that the JREI can invert a better starting velocity model for the FWI to achieve a high-resolution inversion result.

Constraining the 410-km discontinuity and slab structure in the Kuril subduction zone with triplication waveforms

SUMMARYThe detailed structure near the 410-km discontinuity provides key constraints of the dynamic interactions between the upper mantle and the lower mantle through the mantle transition zone (MTZ) via mass and heat exchange. Meanwhile, the temperature of the subducting slab, which can be derived from its fast wave speed perturbation, is critical for understanding the mantle dynamics in subduction zones where the slab enters the MTZ. Multipathing, i.e. triplicated, body waves that bottom near the MTZ carry rich information of the 410-km discontinuity structure and can be used to constrain the discontinuity depth and radial variations of wave speeds across it. In this study, we systematically analysed the trade-off between model parameters in triplication studies using synthetic examples. Specifically, we illustrated the necessity of using array-normalized amplitude. Two 1-D depth profiles of the wave speed below the Tatar Strait of Russia in the Kuril subduction zone are obtained. We have observed triplications due to both the 410-km discontinuity and the slab upper surface. And, seismic structures for these two interfaces are simultaneously inverted. Our derived 410-km discontinuity depths for the northern and southern regions are at 420$\pm $15 and 425$\pm $15 km, respectively, with no observable uplift. The slab upper surface is inverted to be located about 50–70 km below the 410-km discontinuity. This location is between the depths of the 1 and 2 per cent P-wave speed perturbation contours of a regional 3-D full-waveform inversion (FWI) model, but we found twice the wave speed perturbation amplitude. A wave speed increase of 3.9–4.6 per cent within the slab, compared to 2.0–2.4 per cent from the 3-D FWI model, is necessary to fit the waveforms with the shortest period of 2 s, indicating that high-frequency waves are required to accurately resolve the detailed structures near the MTZ.

Frequency-domain reflection waveform inversion with generalized internal multiple imaging

Full-waveform inversion (FWI) has the potential to provide a high-resolution detailed model of the earth’s subsurface, but it often fails to do so if the starting model differs significantly from the true one. Reflection waveform inversion (RWI) is a popular method for building a sufficiently accurate initial model for FWI. In traditional RWI, the low-wavenumber updates are always computed and captured by smearing the data misfit along the reflection path with the help of migration/demigration. However, the success of RWI relies heavily on accurately reproducing the data in demigration. Thus, we have introduced a new generalized internal multiple imaging-based RWI (GIMI-RWI) implementation, in which we avoid the Born modeling and update the primary reflection kernel directly. In GIMI-RWI, we store one reflection kernel for each source-receiver pair, preserving the unique wavepath for every single source-receiver trace. Subsequently, the convolution between the data residuals and the corresponding reflection kernel can build the tomographic velocity updates. In this situation, the long-wavelength tomographic updates are free of migration footprints and will contribute a smoother background velocity to reduce the cycle-skipping risk and stabilize the followed FWI process. In addition, the GIMI-RWI method is source independent because it entirely relies on the data. Using a synthetic example extracted from the Sigsbee2A model, we find the reliable performance of the GIMI-RWI technique.

Efficient snapshot-free reverse time migration and computation of multiparameter gradients in full-waveform inversion

Computing images in reverse time migration and model parameter gradients from adjoint wavefields in full-waveform inversion (FWI) requires the correlation of a forward-propagated wavefield with another reverse-propagated wavefield. Although in theory only two wavefield propagations are required, one forward propagation and one reverse propagation, it requires storing the forward-propagated wavefield as a function of time to carry out the correlations, which is associated with significant input/output (I/O) cost. Alternatively, three wavefield propagations can be carried out to reverse propagate the forward-propagated wavefield in tandem with the reverse-propagated wavefield. We have determined how highly accurate reverse time migrated images and FWI model parameter gradients for anisotropic elastic FWI can be efficiently computed without significant disk I/O using two wavefield propagations by means of the principle of superposition.

SPiRaL: a multiresolution global tomography model of seismic wave speeds and radial anisotropy variations in the crust and mantle

SUMMARY SPiRaL is a joint global-scale model of wave speeds (P and S) and anisotropy (vertical transverse isotropy, VTI) variations in the crust and mantle. The model is comprised of >2.1 million nodes with five parameters at each node that capture velocity variations for P- and S-waves travelling at arbitrary directions in transversely isotropic media with a vertical symmetry axis (VTI). The crust (including ice, water, sediments and crystalline layers) is directly incorporated into the model. The default node spacing is approximately 2° in the lower mantle and 1° in the crust and upper mantle. The grid is refined with ∼0.25° minimum node spacing in highly sampled regions of the crust and upper mantle throughout North America and Eurasia. The data considered in the construction of SPiRaL includes millions of body wave traveltimes (crustal, regional and teleseismic phases with multiples) and surface wave (Rayleigh and Love) dispersion. A multiresolution inversion approach is employed to capture long-wavelength heterogeneities commonly depicted in global-scale tomography images as well as more localized details that are typically resolved in more focused regional-scale studies. Our previous work has demonstrated that such global-scale models with regional-scale detail can accurately predict both teleseismic and regional body wave traveltimes, which is necessary for more accurate location of small seismic events that may have limited signal at teleseismic distances. SPiRaL was constructed to predict traveltimes for event location and long-period waveform dispersion for seismic source inversion applications in regions without sufficiently tuned models. SPiRaL may also serve as a starting model for full-waveform inversion (FWI) with the goal of fitting waves with periods 10–50 s over multiple broad regions (thousands of kilometres) and potentially the globe. To gain insight to this possibility, we simulated waveforms for a small set of events using SPiRaL and independent waveform-based models for comparison. For the events tested, the performance of the traveltime-based SPiRaL model is shown to be generally on par with regional 3-D waveform-based models in three regions (western United States, Middle East, Korean Peninsula) suggesting SPiRaL may serve as a starting model for FWI over broad regions.