Waveform inversion in triclinic anisotropic media—a resolution study

<p>The seismic full waveform inversion (FWI), as one of important ways to obtain the seismic wave velocity, has made rapid development in the last decade. In response to problems of cycle-skipping artifacts, dependence on the initial model, and low-frequency information in FWI, researchers have made many improvements, such as multi-scale envelope inversion and low-frequency extension. Recently, deep learning has been also adopted seismic data processing and interpretation, because of its strong nonlinear mapping ability. However, these works depend on labels used for training heavily, especially for the velocity model in the inversion, which prevents them from real application. Referring to these studies, this work combines low-frequency extension commonly as well as multiscale inversion with deep learning, and proposes a multi-scale FWI gradient optimization method based on CNN. CNN we designed is trained to predict the inversion gradient corresponding to the low-frequency band data in FWI, so that multi-scale gradient optimization can be directly used in multi-scale inversion, expanding the low-frequency information in the actual data and reducing the calculation in FWI. With a specially designed dataset, CNN is trained to optimize the gradients computed from the high-frequency band data by predicting the gradients corresponding to the low-frequency band data and the gradients corresponding to the mid-frequency band data, respectively. The predicted gradients are used in different stages of the multi-scale inversion. The low-frequency gradients are used to invert the initial structural construction so as not to rely on a good initial model, and the high-frequency gradients are used to improve the accuracy of the inversion results. In this way, low-frequency expansion and multiscale inversion can be achieved simultaneously. Our method achieves good results on the initial model for a given uniform wave velocity, effectively alleviating the reliance on the initial model in FWI. This study provides a new idea of combining deep learning and full waveform inversion, which will be effectively used in seismic data processing.</p>

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.

In this paper we proposed an accurate and efficient numerical algorithm for solving the acoustic wave equation in three-dimensional heterogeneous media. Numerical solution of the wave equation has been used in various science and engineering applications, such as the seismic full waveform inversion (FWI) problem. FWI is a computationally intensive procedure, in which the acoustic wave equation is numerically solved (forward modelling) repeatedly during the iterative process. Therefore, efficiency and accuracy of the numerical method for solving the acoustic wave equation is critical in the success of seismic full waveform inversion. The new method is obtained by combining the Pade approximation and a novel algebraic manipulation with the Alternative Directional Implicit (ADI) method. Numerical experiments have shown that the new method is accurate, efficient and stable.

Seismic full waveform inversion (FWI) faces cycle-skipping problem when the seismic data lack low-frequency information and the initial velocity model is far from the true model. To address this challenge, we proposed a neural network-based weighted envelope correlation inversion with a learnable envelope power, which is referred to as FWI-NN-WECP. In this method, we constructed the loss function using an envelope-based misfit to enhance low-frequency components during the inversion. We also introduced a learnable envelope-power parameter to control the effective bandwidth of the data envelope. In addition, we applied a regularization term to further constrain the evolution of the power parameter, thereby guiding the inversion to progressively focus from shallow to deep parts of the velocity model. Synthetic data experiments demonstrated that the FWI-NN-WECP method significantly mitigates cycle skipping and successfully reconstructs complex geological structures, even when low-frequency data (below 5 Hz) are absent and the initial model is inaccurate. The field data experiment confirmed the accuracy of the inverted velocity models and demonstrated the potential of the proposed method to mitigate cycle-skipping through by using neural networks and a carefully designed loss function.

<p>Seismic full waveform inversion (FWI) produces high resolution images of the subsurface directly from seismic waveforms, and has been applied at global, regional and industrial spatial scales. FWI is traditionally solved using optimization methods, by iteratively updating a model of the subsurface so as to minimize the misfit between observed waveforms and those predicted by linearised (approximate) physics. Due to the nonlinearity of the physical relation between model parameters and seismic waveforms, a good starting model (derived from other methods) and hence strong prior information is required in order that the linearised physical relationships are reasonable in the vicinity of the true solution. Such linearised methods cannot provide accurate estimates of uncertainties, which are required if we are to understand and interpret the results appropriately.</p><p>To estimate uncertainties more accurately, nonlinear Bayesian methods have been deployed to solve the FWI problem. Monte Carlo sampling is one such algorithm but it is computationally expensive, and all Markov chain Monte Carlo-based methods are difficult to parallelise fully. Variational inference provides an efficient, fully parallelisable alternative methodology. This is a class of methods that optimize an approximation to a probability distribution describing post-inversion parameter uncertainties. Both Monte Carlo and variational full waveform inversion (VFWI) have been applied previously to solve FWI problems, but only with strong prior information about the velocity structure to limit the space of possible models. Unfortunately such strong information is almost never available in practice. In addition, VFWI has only been applied to wavefield transmission problems in which seismic data are recorded on a receiver array that lies above the structure to be imaged, given known, double-couple (earthquake-like) sources located underneath the same structure. In practice, knowledge of such sources is never definitive, and usually depends circularly on the unknown structure itself. In this study, we present the first application of VFWI to seismic reflection data acquired from known (deliberately fired) near-surface sources. We also apply variational inference (specifically, Stein variational gradient descent) to solve FWI problems with realistic prior information. We perform multiple inversions using data from different frequency ranges, and show that VFWI produces high resolution mean and uncertainty models using both low and high frequency data, and given only weak prior information. This is usually impossible using traditional linearised methods. We conclude that VFWI may be a useful method to produce high resolution images and reliable uncertainties, at least in smaller FWI problems.</p>

<p>Imaging of hyperextended zone and exhumed continental mantle rocks can improve our understanding of the tectonics of the final stages of rifting. In the Deep Galicia margin, the upper and lower crust are coupled allowing the normal faults to cut through the brittle crust and penetrate to the mantle leading to serpentinization of the mantle. Localized extensional forces caused extreme thinning and elongation of crystalline continental crust causing the continental blocks to slip over a lithospheric-scale detachment fault called the S-reflector.  </p><p>A high-resolution velocity model obtained using seismic full waveform inversion gives us deeper insights into the rifting process. In this study, we present results from three dimensional acoustic full waveform inversion performed using wide-angle seismic data acquired in the deep water environments of the Deep Galicia margin using ocean bottom seismometers. We performed full waveform inversion in the time domain, starting with a velocity model obtained using travel-time tomography, of dimensions 78.5 km x 22.1 km and depth 12 km. The high-resolution modelling shows short-wavelength variations in the velocity, adding details to the travel-time model. We superimposed our final model, converted to two-way time, on pre-stack time-migrated three-dimensional reflection data from the same survey. Compared to the starting model, our model shows improved alignment of the velocity variations along the steeply dipping normal faults and a sharp velocity contrast across the S-reflector. We validated our result using checkerboard tests, by tracking changes in phases of the first arrivals during the inversion and by comparing the observed and the synthetic waveforms. We observe a clear evidence for preferential serpentinization (45 %) of the mantle with lower velocities in the mantle correlating with the fault intersections with the S-reflector.</p>

Seismic full waveform inversion (FWI) is a powerful tool for monitoring subsurface changes during carbon capture and storage (CCS) operations, but its ill-posed nature makes uncertainty quantification (UQ) essential for reliable interpretation. Sampling-based Bayesian methods such as Markov chain Monte Carlo (McMC) provide rigorous UQ but are computationally demanding. In conventional FWI, elastic properties are assigned to densely discretized space-filling cells, resulting in a high-dimensional parameterization that makes large-scale elastic FWI computationally infeasible. To address this challenge, we propose a rock-physics-guided parameter-reduction strategy that compactly represents the CO2 plume geometry using cubic splines controlled by a limited number of nodes. This parsimonious parameterization not only significantly reduces the number of model parameters and the forward simulations required for an effective UQ using sampling methods but also has the potential to improve the practicality and efficiency of other types of UQ methods. Numerical experiments on a cross-well synthetic scenario and a field-scale case based on the Aquistore storage site in Saskatchewan, Canada, demonstrate that the method efficiently reconstructs the plume shape and its extent and that it converges to consistent posterior distributions across multiple Markov chains.

Shape reconstruction in seismic full waveform inversion using a level set approach and time reversal

With recent progress in resolution in global seismic mantle imaging provided by numerical wavefield computations using the Spectral Element Method and full waveform inversion, Jason Morgan’s suggestion from over 50 years ago that mantle plumes may be rooted at the core-mantle boundary (CMB) has been confirmed. Yet the imaged plumes present intriguing features that contrast with the classical thermal plume model and should inform our understanding of mantle dynamics. Among other features, they are broader than purely thermal plumes, and do not extend straight from the CMB to the corresponding hotspot volcanoes, but they are frequently deflected horizontally in the extended transition zone (400-1000 km depth), so that their lower mantle location can be significantly offset (as much as a 1000 km) from their surface expression. They appear to be thinner in the upper mantle. This, together with similar horizontal flattening observed in subduction zones suggests a change in the radial viscosity structure of the mantle that may occur deeper than usually assumed to be related to the 660 km phase change. The fattest plumes have been shown to be anchored within the perimeter of the large low shear velocity provinces (LLSVPs) and an increasing number of them appear to house mega-ultra low velocity zones within their roots.  Moreover, in the upper mantle, they appear to be associated with regularly spaced low velocity channels aligned with absolute plate motion.We discuss these features in the light of recent regional imaging updates in the south Atlantic and beneath Yellowstone, contrasting the corresponding mantle plumes, and in particular showing mounting evidence that the LLSVPs are not compact “piles” extending high above the CMB, but rather a bundle of thermo-chemical plumes feeding secondary scale convection in the top 1000 km of the mantle.

Seismic full-waveform inversion (FWI) is often based on forward modeling in the computationally attractive 2D domain. This implies the assumption of a line source extended in the out-of-plane medium invariant direction, with far-field amplitudes decaying inversely with the square root of distance. Realistic point sources, however, generate amplitudes that decay approximately with the inverse of distance. Conventionally, practitioners correct for this amplitude difference and the associated phase shift by transforming the recorded 3D field data to the approximate 2D equivalent by using simplistic asymptotic filter algorithms. Such filters assume straight raypaths, a constant velocity medium, and far-field recordings. We have assessed the validity of 3D-to-2D data transformation in the context of crosshole seismic full-waveform tomography by propagating 3D and 2D wavefields through 2D media and comparing 2D reference synthetics with their filtered 3D equivalent. The filter performs well in simple situations, which confirms the general applicability of the conventional asymptotic approach. However, we have observed substantial errors in more complex elastic models, associated with overlapping arrivals and strongly curved raypaths. To test if this error translates into deficient model reconstruction in FWI, we performed complementary inversion experiments using a frequency-domain algorithm. Purely acoustic waveform inversions of 3D-to-2D filtered data are only weakly affected, but in the case of elastic FWI, in which an S-wave influence is present, adverse effects increase substantially. Two-dimensional FWI in combination with filtering seems to be an acceptable strategy as long as the model is two-dimensional, the recording geometry is straight and perpendicular to strike, and only slight S-wave energy is contained in the data. The latter two conditions are generally met in exploration-type marine seismic surveys at short offsets and in some crosswell applications using explosive sources and nondirectional pressure receivers.

Summary Seismic full waveform inversion (FWI) has become a crucial tool in Earth model building. Over the past years, its application has evolved and now FWI regularly delivers high-resolution images. In complex geological settings, artefacts often contaminate acoustic FWI results, limiting its applicability for velocity model building and high-resolution imaging. The need for elastic modelling in FWI was recognized in the 1980’s. However, the high computational cost of elastic FWI has prevented its use for real-sized inversion. Recent advancements in high-performance computing have made it possible to derive high-resolution velocity and impedance images using a workflow based on elastic FWI in which the distinction between model building and imaging is vanishing

Knowledge of planetary interior structure is essential for understanding the origin and evolution of the Solar System. Seismic full-waveform inversion (FWI) is currently the state-of-the-art method for imaging Earth's interior and has revealed mantle heterogeneities at increasingly finer scales. However, FWI solely images variations in seismic properties and, as a result, the thermal or/and chemical origin of such anomalies is poorly constrained. Mineral physics provides complementary constraints by linking seismic properties to temperature, pressure and composition through laboratory measurements. Over the past two decades, significant work has been done to integrate seismic observations with mineral physics predictions. Nevertheless, direct integration of FWI and thermodynamic calculations has not yet been achieved, limiting our ability to fully exploit the information contained in seismic waveforms to image changes in temperature and composition.In this contribution, we present a novel framework that integrates state-of-the-art FWI techniques with mineral physics to directly invert seismic waveforms for mantle temperature and chemical composition. The forward model is based on pre-calculated tables of mantle properties, which provide the seismic properties to carry out wave propagation. The inverse problem is formulated as an optimisation problem where gradients of the objective function with respect to temperature and composition are required. For the seismic component, we employ the adjoint method. For the thermodynamic component, we developed a formalism accounting for the pressure–density coupling which is combined with the seismic part by exploiting the chain rule. This approach is tested on 2-D synthetic models containing thermal and compositional anomalies where P–SV elastic wave propagation is simulated. The optimisation problem is solved using the L-BFGS algorithm. The proposed framework successfully recovers anomalies in temperature and composition, while revealing a strong trade-off. Such non-uniqueness reflects the importance of taking into account both thermal and compositional variations and a priori information about them. The proposed framework enables the integration of diverse geophysical datasets as well as the incorporation of additional information on the potential origin of certain mantle anomalies based on petrological constraints, which are crucial to tackle the non-uniqueness of the inverse problem.

Time lapse seismic imaging of injection of carbon dioxide (CO2) into the Utsira Sand at Sleipner, Norway, has proven to be a very succesful monitoring tool. However, complex propagation modes due to strong impedance contrast could impede deduction of quantitative information from migrated images. Here we use elastic 2D full waveform inversion (FWI) in the time lapse mode to quantify changes in P‐wave velocities (Vp) due to CO2 injection at the Sleipner site and compare these results with corresponding migrated seismic data. We find that the maximum amplitude change in migrated images does not always coincide with maximum CO2 saturation indicated by FWI. For example, there are places, where the inversion result suggests a relatively high CO2 saturation near the base of Utsira Sand and the migrated image indicates significant amplitude changes only in the upper half of the aquifer. Furthermore, CO2 saturation from FWI is laterally more heterogeneous than amplitude changes observed from migrated images suggest.

Full-waveform inversion (FWI) is a powerful technique to obtain high-resolution subsurface models, from seismic data. However, FWI is an ill-posed problem, which means that the solution is not unique, and therefore the expert use of the information is required to mitigate the FWI ill-posedness, especially when wide-aperture seismic acquisitions are considered. In this way, we investigate the multiscale frequency-domain FWI by using a weighting operator according to the distances between each source-receiver pair. In this work, we propose a weighting operator that acts on the data misfit as preconditioning of the objective function that depends on the source-receiver distance (offset) and the frequency used during the inversion. The proposed operator emphasizes information from long offsets, especially at low frequencies, and as a consequence improves the update of deep geological structures. To demonstrate the effectiveness of our proposal, we perform numerical simulations on 2D acoustic Marmousi2 case study, which is widely used in seismic imaging tests, considering three different scenarios. In the first two ones, we have used an acquisition geometry with a maximum offset of 4 and 8 km, respectively. In the last one, we have considered all-offsets. The results show that our proposal outperforms similar strategies, for all scenarios, providing more reliable quantitative subsurface models. In fact, our inversion result has the lowest error and the highest similarity to the true model than similar approaches.

ABSTRACTOptimized experimental design aims at reducing the cost of a seismic survey by identifying the optimal locations and amounts of sources and receivers. While the acquisition design in the context of seismic imaging applies criteria like fold, offset and spatial sampling, different attributes such as the sensitivity kernels are more relevant for seismic full waveform inversion. An ideal measure to quantify the goodness of an acquisition design relies on the eigenvalue spectrum of the approximate Hessian matrix, but this technique is computationally too expensive for practical use. A more affordable goodness measure has been proposed in the past, but we demonstrate that this measure is inappropriate for target‐oriented optimized experimental design. To address those issues, we derived a sequential receiver‐based procedure using a goodness measure based on the determinant of the approximate Hessian matrix. We show with numerical tests that it efficiently provides an optimized design for target‐oriented as well as for extensive full waveform inversion. This design allows a better reconstruction of the subsurface than an evenly spaced acquisition geometry. Furthermore, the optimization algorithm itself can easily be parallelized, therefore making it attractive for applications to large‐scale three‐dimensional surveys. In addition, our algorithm is able to incorporate variable costs, representing any kind of acquisition‐related costs, for every individual source location. The combined optimization with respect to the information content of sources and to the true cost will allow a more comprehensive and realistic survey planning and has a high potential for further applications.