Conventional Full Waveform Inversion Research Articles

GPU accelerated sparse curvelet-constrained wavefield reconstruction inversion with source estimation: Application to Chevron Benchmark 2014 blind test data set

Full-waveform inversion (FWI) is a pivotal tool in seismic exploration and seismology but encounters a persistent challenge known as “cycle-skipping,” causing it to frequently converge to local minima. Wavefield reconstruction inversion (WRI) has emerged as a potential solution to mitigate the risk of cycle skipping. Researchers have provided numerical examples indicating that WRI is less prone to being ensnared in local minima caused by the absence of low-frequency component data and the absence of a well-defined initial model compared with conventional FWI. Despite its potential, the computational demands of WRI have hindered its widespread application, especially in scenarios involving ocean towed streamer seismic acquisition and unknown sources, where the augmented systems differ from source to source. In our study, we introduce a novel approach — sparse curvelet-constrained WRI with source estimation (WRI-SE-CC) — accelerated by graphics processing unit (GPU). Real-time source function estimation is achieved through the variable projection method, and noise-related artifacts are suppressed using sparse curvelet constraints. By optimizing the utilization of hundreds of computation processors within a GPU for parallel computing of matrix-vector multiplications, we present a GPU-based grouped conjugate gradient method to accelerate the computation of WRI-SE-CC. Numerical experiments demonstrate a significant 240-fold acceleration compared with the preconditioned conjugate gradient using one CPU core for computations involving multiple sources. Inversion experiments with the overthrust model demonstrate the capability of our method in mitigating local minima and suppressing noise-related artifacts. Furthermore, we validate the framework on the Chevron 2014 blind test data set, showcasing its effectiveness in addressing practical challenges in the field.

Cross-correlation adjustment full-waveform inversion with source encoding in ultrasound computed tomography

Full-waveform inversion (FWI) is one of the leading-edge techniques in ultrasound computed tomography (USCT). FWI reconstructs the images of sound speed by iteratively minimizing the difference between the predicted and measured signals. The challenges of FWI are to improve its stability and reduce its computational cost. In this paper, a new USCT algorithm based on cross-correlation adjustment FWI with source encoding (CCAFWI-SE) is proposed. In this algorithm, the gradient is adjusted using the intermediate signals as the inversion target rather than the measured signals during iteration. The intermediate signals are generated using the travel time difference calculated by cross-correlation. In the case of conventional FWI failure, using the proposed algorithm, the estimated sound speed can converge toward the ground truth. To reduce the computational cost, an intermittent update strategy is implemented. This strategy only requires one time for the calculation of the travel time difference per stage, so that the source encoding can be used. Simulation and laboratory experiments are implemented to validate this approach. The experiment results show it has successfully recovered the sound speed model, while conventional FWI failed when the initial model greatly differed from the ground truth. This verifies that our approach improves the stability of the reconstruction in USCT. In practice, additional computational costs can be reduced by combining our approach with existing methods. The proposed approach increases the robustness of the FWI and expands its application.

Truncated Gauss-Newton full-waveform inversion of pure quasi-P waves in vertical transverse isotropic media

Full-waveform inversion (FWI) uses the full information of seismic data to obtain a quantitative estimation of subsurface physical parameters. Anisotropic FWI has the potential to recover high-resolution velocity and anisotropy parameter models, which are critical for imaging the long-offset and wide-azimuth data. We develop an acoustic anisotropic FWI method based on a simplified pure quasi P-wave (qP-wave) equation, which can be solved efficiently and is beneficial for the subsequent inversion. Using the inverse Hessian operator to precondition the functional gradients helps to reduce the parameter tradeoff in the multi-parameter inversion. To balance the accuracy and efficiency, we extend the truncated Gauss-Newton (TGN) method into FWI of pure qP-waves in vertical transverse isotropic (VTI) media. The inversion is performed in a nested way: a linear inner loop and a nonlinear outer loop. We derive the formulation of Hessian-vector products for pure qP-waves in VTI media based on the Lagrange multiplier method and compute the model update by solving a Gauss-Newton linear system via a matrix-free conjugate gradient method. A suitable preconditioner and the Eisenstat and Walker stopping criterion for the inner iterations are used to accelerate the convergence and avoid prohibitive computational cost. We test the proposed FWI method on several synthetic data sets. Inversion results reveal that the pure acoustic VTI FWI exhibits greater accuracy than the conventional pseudoacoustic VTI FWI. Additionally, the TGN method proves effective in mitigating the parameter crosstalk and increasing the accuracy of anisotropy parameters.

Acoustic 2-D Full-Waveform Inversion with Non-Balanced Finite differences and Adaptive Weight Decay Methods

Full waveform inversion (FWI) is a powerful seismic imaging technique that aims to achieve high-resolution subsurface models by iteratively comparing recorded seismic waveforms with modeled waveforms. The success of FWI relies on the precision of forward modeling algorithms and the effectiveness of optimization strategies. In this study, we propose a FWI methodology that leverages non-balanced staggered-grid finite differences schemes (NBFD) in the forward modeling process. By employing operators with spatial differencing of varying lengths, these schemes enhance the efficiency of forward modeling.For the optimization process, we employ adaptive gradient-based optimization with weight decay, a widely-used approach in machine learning and deep learning algorithms for model training. These methods demonstrate efficient optimization processing for large data volumes with high precision. The objective of adaptive gradient-based optimization is to dynamically adjust the update rate model parameters during the iterative process. This facilitates improved convergence speed, enhances stability, and overcomes challenges associated with traditional fixed-rate adjustment methods.To ensure accurate inversion results and avoid local minima in the cost function minimization, we implement a Multiscaling inversion strategy within the workflow. The obtained results are compared with those achieved through conventional FWI using standard staggered finite differences and various optimization methods. Our findings demonstrate that employing non-balanced staggered-grid finite differences scheme leads to significant improvements compared to the previously reported results in the literature.

Robust joint adaptive multiparameter waveform inversion with attenuation compensation in viscoacoustic media

Full-waveform inversion (FWI) has been proven as an effective method to estimate subsurface parameters by iteratively reducing the data residual between the predictions and the observations. Nevertheless, FWI is greatly dependent on the initial model, and a poor initial model will lead to an incorrect solution. Furthermore, owing to the anelasticity of the earth, seismic waves will attenuate during propagation, which results in an attenuated gradient and makes the convergence rate of FWI even worse in viscoacoustic medium. Commonly, multiparameter (e.g. velocity and Q) waveform inversion can be used to mitigate these problems. Benefiting from the theory of Q-compensated wavefield propagation, we develop a Q-compensated joint multiparameter waveform inversion method to weaken the nonlinearity of the FWI objective function, which enables it to cope with challenges related with attenuation-induced gradient energy loss and cycle skipping simultaneously. We refer to our Q-compensated joint multiparameter FWI scheme as QJMFWI. The main contributions of QJMFWI are as follows: (1) given the difficulty associated with the estimation of velocity and Q simultaneously in viscoacoustic media, QJMFWI provides a straightforward waveform inversion method for velocity and Q model construction, by which we can obtain velocity and Q information with improved accuracy and resolution; and (2) compared with conventional FWI methods, QJMFWI relaxes the requirement for a good initial velocity and Q model, which can avoid trapping into local minima. Numerical and field data examples demonstrate that QJMFWI is an effective method to invert for accurate subsurface parameters in viscoacoustic media.

Full waveform inversion based on hybrid gradient

The low-wavenumber components in the gradient of full waveform inversion (FWI) play a vital role in the stability of the inversion. However, when FWI is implemented in some high frequencies and current models are not far away from the real velocity model, an excessive number of low-wavenumber components in the gradient will also reduce the convergence rate and inversion accuracy. To solve this problem, this paper firstly derives a formula of scattering angle weighted gradient in FWI, then proposes a hybrid gradient. The hybrid gradient combines the conventional gradient of FWI with the scattering angle weighted gradient in each inversion frequency band based on an empirical formula derived herein. Using weighted hybrid mode, we can retain some low-wavenumber components in the initial low-frequency inversion to ensure the stability of the inversion, and use more high-wavenumber components in the high-frequency inversion to improve the convergence rate. The results of synthetic data experiment demonstrate that compared to the conventional FWI, the FWI based on the proposed hybrid gradient can effectively reduce the low-wavenumber components in the gradient under the premise of ensuring inversion stability. It also greatly enhances the convergence rate and inversion accuracy, especially in the deep part of the model. And the field marine seismic data experiment also illustrates that the FWI based on hybrid gradient (HGFWI) has good stability and adaptability.

Subsoil density field reconstruction through 3-D FWI: a systematic comparison between vertical- and horizontal-force seismic sources

SUMMARY Bulk-density (ρ) of soil is an important indicator of soil compaction and type. A knowledge of the spatial variability of in situ soil density is important in geotechnical engineering, hydrology and agriculture. Surface geophysical methods have so far shown limited success in providing an accurate and high-resolution image of 3-D soil-density distribution. In this pursuit, 3-D seismic full-waveform inversion (FWI) is promising, provided the robustness and accuracy of density inversion via this approach can be established in the near-surface scale. However, simultaneous reconstruction of ρ and seismic wave velocities through multiparameter FWI remains a challenging task. Near-surface seismic data are commonly dominated by dispersive surface waves whose velocities are controlled by the value and distribution of shear-wave velocity (VS). One major difficulty in estimating reliably ρ from near-surface seismic data is due to the relatively low sensitivity of the seismic wavefield to ρ compared to seismic velocities. Additionally, the accuracy of the estimated ρ decreases due to error in VS—an issue known as parameter coupling. Parameter coupling makes it difficult to estimate accurately ρ within the framework of conventional gradient-based FWI. More sophisticated optimization approaches (e.g. truncated Newton) can reduce the effect of parameter coupling, but these approaches are commonly not affordable in near-surface applications due to heavy computational burden. In this research, we have investigated how choosing correctly the force direction of the seismic source can contribute to a higher accuracy of ρ estimates through 3-D FWI. Using scattered wavefields, the Hessian, and inversion tests, an in-depth and systematic investigation of data sets corresponding to different force directions has been carried out. A comparison of the scattered wavefields due to a point-localized ρ perturbation for different force directions shows the robustness of the horizontal-force data set to noise compared to the vertical-force data set. Furthermore, for a point-scatterer model, an analysis of the gradients of the misfit function using the Hessian shows that utilizing a horizontal-force source enables one to reconstruct the high-resolution gradient with relatively small parameter coupling. Finally, inversion tests for two different subsoil models demonstrate that 3-D FWI on a horizontal-force-source seismic data set is capable of providing a more accurate 3-D ρ distribution in soil compared to a vertical-force-source data set. Our results show that the use of a horizontal-force source might allow avoiding computationally demanding, costly optimization approaches in 3-D FWI.

Accelerating full-waveform inversion using source stacking: synthetic experiments at the global scale in a realistic 3-D earth model

SUMMARY The spectral element method is currently the method of choice for computing accurate synthetic seismic wavefields in realistic 3-D earth models at the global scale. However, it requires significantly more computational time, compared to normal mode-based approximate methods. Source stacking, whereby multiple earthquake sources are aligned on their origin time and simultaneously triggered, can reduce the computational costs by several orders of magnitude. We present the results of synthetic tests performed on a realistic radially anisotropic 3-D model, slightly modified from model SEMUCB-WM1 with three component synthetic waveform ‘data’ for a duration of 10 000 s, and filtered at periods longer than 60 s, for a set of 273 events and 515 stations. We consider two definitions of the misfit function, one based on the stacked records at individual stations and another based on station-pair cross-correlations of the stacked records. The inverse step is performed using a Gauss–Newton approach where the gradient and Hessian are computed using normal mode perturbation theory. We investigate the retrieval of radially anisotropic long wavelength structure in the upper mantle in the depth range 100–800 km, after fixing the crust and uppermost mantle structure constrained by fundamental mode Love and Rayleigh wave dispersion data. The results show good performance using both definitions of the misfit function, even in the presence of realistic noise, with degraded amplitudes of lateral variations in the anisotropic parameter ξ. Interestingly, we show that we can retrieve the long wavelength structure in the upper mantle, when considering one or the other of three portions of the cross-correlation time series, corresponding to where we expect the energy from surface wave overtone, fundamental mode or a mixture of the two to be dominant, respectively. We also considered the issue of missing data, by randomly removing a successively larger proportion of the available synthetic data. We replace the missing data by synthetics computed in the current 3-D model using normal mode perturbation theory. The inversion results degrade with the proportion of missing data, especially for ξ, and we find that a data availability of 45 per cent or more leads to acceptable results. We also present a strategy for grouping events and stations to minimize the number of missing data in each group. This leads to an increased number of computations but can be significantly more efficient than conventional single-event-at-a-time inversion. We apply the grouping strategy to a real picking scenario, and show promising resolution capability despite the use of fewer waveforms and uneven ray path distribution. Source stacking approach can be used to rapidly obtain a starting 3-D model for more conventional full-waveform inversion at higher resolution, and to investigate assumptions made in the inversion, such as trade-offs between isotropic, anisotropic or anelastic structure, different model parametrizations or how crustal structure is accounted for.

Seismic differential semblance-oriented migration velocity analysis — Status and the way forward

Differential semblance optimization (DSO) is a seismic waveform inversion approach. It has been developed to remove the limitation of conventional full-waveform inversion as a velocity model building tool when only reflected waves are available. It has connections with migration velocity analysis (MVA) techniques defined in the image domain to build macrovelocity models, with a split between the macromodel and the small-scale heterogeneities. Among the various DSO approaches, DSO-MVA has unique characteristics for velocity model building of complex structures, while ensuring the convergence to the global minimum in a local optimization approach: the wavefields are computed with the two-way wave equation operators, focusing panels are built in a survey-sinking mode, and the quality of the macrovelocity model is evaluated on common-image gathers in the subsurface-offset domain through a differential annihilator. We review the significant aspects that have been better understood over the past 15 years and discuss the way forward. The first identified issue has been the imprint of the small-scale heterogeneities on the macromodel update that is revealed with the use of wave equation-based Green’s functions and an ad hoc solution is subsequently developed by slightly modifying the definition of the objective function. A second important aspect has been the development of efficient approaches to compute the required quantitative migration based on approximate inverses to replace the previously used migrations. The issue of correctly interpreting the amplitudes has also moved into one of an improved model parameterization, i.e., from constant-density acoustics media to full acoustic media as a path toward fully viscoelastic media. Finally, we discuss the way forward with the challenges of extending DSO-MVA beyond the single scattering approximation, for processing diving waves and multiples, and also the challenge of numerical implementation, which remains critical even in two dimensions, for applicability to large-scale real data.

Field assessment of elastic full-waveform inversion of combined accelerometer and distributed acoustic sensing data in a vertical seismic profile configuration

Seismic data are a significant facilitator for monitoring in carbon capture and sequestration projects, providing high-resolution images of fluid migration, using, for example, full-waveform inversion (FWI). Distributed acoustic sensing (DAS), a relatively novel technology for wavefield sampling, is well suited for this type of monitoring. Using noninvasive optical fibers, DAS allows for dense spatial sampling along the entire length of the wellbore, without disrupting operations. Permanently installed in the wellbore, typically behind casing, DAS offers highly repeatable and dense sampling of the transmitted wave modes crucial to seismic monitoring of injected carbon dioxide ([Formula: see text]). However, the DAS data consist of measurements of strain along the tangent of the fiber and therefore do not transfer directly to conventional FWI algorithms. Incorporation of DAS data in their native strain (or strain-rate) form in standard FWI algorithms, requires changing the definition of the receiver sampling operator to use geometric information about the fiber to supply tangential strain measurements to the FWI residual. The theoretical developments are applied to invert field vertical seismic profile data acquired with DAS fiber and accelerometers at a [Formula: see text] sequestration site in Newell Country, Alberta. Our method incorporates DAS data and accelerometer data in one objective function and allows us to tune the relative importance we wish to place on each data set. This method also transfers to noncollocated sensors, for example, surface-deployed geophones and borehole fiber. The inverted models contain features expected from the geology of the field site, and data modeled in the inverted models compare favorably with the field data for these sensor types. The models are derived from data acquired prior to [Formula: see text] injection, representing baseline models for future time-lapse studies planned at the field research station.

3D frequency-domain acoustic full-waveform inversion using diffraction-angle filtering

The success of seismic imaging techniques such as full-waveform inversion (FWI) depends on using a good starting velocity model or a background velocity model, which can be effectively built by long-wavelength components in the early stages of FWI. This study proposes an optimal strategy for performing 3D frequency-domain FWI with diffraction-angle filtering (DAF). This approach can perform optimized single-frequency FWI with lower computational costs and build a long-wavelength velocity structure by separating low-wavenumber components with DAF. Prior to applying this strategy, we confirm the performance of 3D frequency-domain FWI with DAF in the radiation pattern analysis. DAF effectively separates the diffraction energy of partial derivative wavefields according to the diffraction angle with a negligible increase in computational costs. We then apply our 3D FWI strategy with DAF on synthetic data generated from the 3D SEG/EAGE overthrust model. The wavenumber components are effectively separated, and a long-wavelength velocity model is estimated with DAF compared to conventional FWI. Finally, we apply our strategy to 3D ocean-bottom seismic data from the North Sea. As a result, we observe that 3D FWI with the DAF method successfully reconstructs a long-wavelength velocity structure on the real data using only a single-frequency component.

Wide‐spectrum reconstruction of a velocity model based on the wave equation reflection inversion method and its application

AbstractMost seismic data used for conventional exploration lack far‐offset signals and effective low‐frequency components. This makes it difficult for conventional full waveform inversion methods to recover the low‐wavenumber components of mid‐ and deep‐layer models. To resolve the bottleneck of ray‐theoretical reflection traveltime tomography, wave equations, such as reflection inversion methods, are receiving increasing attention. We reconstructed a wide‐spectrum velocity model based on the multiscale wave‐equation reflection inversion method for model decomposition. First, using the dynamic image warping method to obtain reflection traveltime residuals, the wave‐equation reflection traveltime inversion was used to recover the low‐wavenumber components of the background model, which also solved the cycle‐skipping problem. Second, the medium‐wavenumber component of the model is then supplemented by the reflection waveform inversion, while the reflectivity model is obtained relying on the least‐squares reverse time migration method. Based on this method, the background and perturbation models are updated alternately and iteratively. At the same time, the stratum structural tensor information was extracted using the perturbed model image to construct a preconditioned operator for the stratum structural constraint, suppress unreasonably high‐wavenumber components in the generalized gradient and improve the geological consistency of the inversion results. Testing of the model using the Sigsbee2b model and seismic field data from the East China Sea showed that, compared with the conventional reflection traveltime tomography method based on prestack depth migration, the wave‐equation reflection inversion strategy with well‐matched information from traveltimes to waveforms significantly improved the accuracy of the middle and deep velocity modelling and enhanced the imaging quality of the whole body.

A progressive data assimilation strategy in full-waveform adjoint tomography

Elastic full-waveform inversion (FWI) is powerful in resolving fine-scale structures in complex models, but suffering from strong nonlinearity and slow convergence rate, especially in the presence of cycle-skipping issues when the initial model is not well constrained. We present a progressive data assimilation (PDA) strategy to mitigate the cycle-skipping issue and boost the convergence rate. Specifically, we split each seismogram into several time windows with a constant length after the first arrival. At each iteration, the PDA strategy automatically screens the windows that are not cycle skipped for inversion according to the criteria of similarity measured between the observed and predicted waveform within a given window. Through the iterations, the model improves and more data will automatically be assimilated into the inversion, forming a positive feedback of model update, and speed up the convergence rate. To provide additional constraints and also stabilise the inversion at the beginning, we include low-frequency surface waves and examine their contribution to the inversion. We validate the effectiveness of the PDA strategy in FWI through numerical experiments using the 1D linear gradient velocity model and the Foothill model. Compared with the conventional FWI strategy, the proposed PDA strategy in an elastic FWI can effectively mitigate the cycle-skipping problem and significantly accelerate the convergence rate. We further apply this method to the field data, and it improves the shallow part of the model with only a fraction of the entire dataset, demonstrating the great potential for practical usage.

Seismic velocity inversion transformer

Velocity model inversion is one of the most challenging tasks in seismic exploration, and an accurate velocity model is essential for high-resolution seismic imaging. Recently, velocity inversion methods based on deep learning (DL), particularly convolutional neural networks (CNNs), have attracted considerable attention from the seismic exploration community. These researchers aim to directly estimate the velocity model from raw seismograms using a well-trained model. Although CNN-based velocity inversion methods have demonstrated remarkable performance in terms of intelligence and automation, their inversion performance is often constrained by a limited long-range dependence. Specifically, when conducting a convolutional operation on raw seismic data using small kernels (i.e., 1 × 1, 3 × 3, 5 × 5, and 7 × 7), CNN-based methods extract only the local features and neglect the weak spatial correlation between different local features that reflect the information of the same interface. This correlation could assist CNN in providing an overview of the seismic data and promote inversion performance when using DL. Furthermore, the time-varying properties of seismic data pose a challenge to the weight sharing of CNNs. Here, we have developed a new DL framework based on a transformer, called the seismic velocity inversion transformer (SVIT), to address the problem of velocity inversion. SVIT uses a self-attention mechanism to capture the long-range dependence of seismic data, rather than stacking multiple convolutional layers as in CNNs. Thus, SVIT can provide more informative remote features for building velocity models. The validity and reliability of the proposed method are demonstrated through numerical experiments using synthetic models. Compared with the conventional full-waveform inversion method and an existing CNN-based velocity inversion method, our SVIT indicates greater consistency with the target in terms of the velocity value, subsurface structures, and geologic interfaces and is expected to provide a new DL-based solution to resolve inversion problems.

Multi-objective particle swarm optimization for Rayleigh wave full waveform inversion

Conventional full waveform inversion (FWI) of Rayleigh wave updates the earth model iteratively by minimizing the difference between measured and synthetic data using single-objective function. However, FWI of Rayleigh wave is challenging due to its high nonlinearity and multimodality. Thus, single-objective inversion may lead to incorrect results, and multi-objective inversion is attractive to obtain global optimal solution. In this paper, we propose a multi-objective particle swarm optimization (MOPSO) scheme for FWI of Rayleigh wave. During the MOPSO inversion, the model is optimized iteratively by using multiple criteria simultaneously. We adopt four objective functions in our proposed MOPSO strategy to characterize the observed data: waveform, peak time, waveform envelope and phase velocity spectrum. The concept of Pareto optimal solution set is introduced in the MOPSO strategy to avoid the contradiction of multi-objective functions. Each non-dominated solution is recorded on the Pareto optimal set for model iteration. Both synthetic data and real field data demonstrate the effectiveness and practicability of the MOPSO strategy.

Finite-frequency sensitivity kernels and hierarchical traveltime and waveform inversion of direct and reflected waves from vertical seismic profile data

Wave-equation-based traveltime or waveform inversion updates the velocity model along finite-frequency sensitivity kernels and exhibits higher accuracy than ray-based tomography. Owing to special geometry, the kernels for vertical seismic profile (VSP) data are different from those for surface seismic data. We have used the Born approximation to compute the traveltime and waveform kernels for direct and reflected waves from VSP data. Based on the property of sensitivity kernels for different information and arrivals, we develop a hierarchical inversion scheme: joint wave-equation traveltime inversion (JWETI) of direct and reflected waves, joint waveform inversion (JWI) of direct and reflected waves, and full-waveform inversion (FWI) of the reflected wave. The traveltime kernels, the waveform kernels, and the migration isochrones are used to retrieve the long-, intermediate-, and short-wavelength components of the velocity model, respectively. Numerical tests on synthetic and real walkway VSP data reveal that the JWETI stage obtains a plausible velocity macromodel, which can be treated as a starting model for subsequent JWI and FWI stages. The JWI stage is a transition between JWETI and FWI and helps to improve the structures of the deep layers of the model. The FWI stage offers some high-wavenumber contents to the inverted model. For the VSP survey, the transmitted direct waves can be used to reduce the dependence of FWI on the initial model. However, the conventional reflection-based wave-equation traveltime inversion and FWI still suffer from cycle skipping when the initial model is far away from the real model. In contrast, the hierarchical inversion scheme can yield reasonable inversion results around the borehole, even when large velocity errors are present in the starting model.

Full waveform inversion guided wave tomography with a recurrent neural network

Corrosion quantitative detection of plate or plate-like structure materials is crucial in industrial Non-Destructive Testing (NDT) for determining their remaining life. For doing that, a novel ultrasonic guided wave tomography method, incorporating recurrent neural network (RNN) into full waveform inversion (FWI) called as RNN-FWI, is proposed in this paper. When the wave equation of an acoustic model is solved by a forward model with the cyclic calculation units of an RNN, it is shown that the inversion of the forward model can be obtained iteratively by minimizing a waveform misfit function of quadratic Wasserstein distance between the modeled and measured data. It is also demonstrated that the gradient of the objective function can be obtained by automatic differentiation while the parameters of the waveform velocity model are updated by the adaptive momentum estimation algorithm (Adam). The U-Net deep image prior (DIP) is used as the velocity model regularization in each iteration. The final thickness maps of the plate or plate-like structure materials shown can be archived by the dispersion characteristics of guided waves. Both the numerical simulation and experimental results show that the proposed RNN-FWI tomography method performs better than the conventional time-domain FWI in terms of convergence rate, initial model requirement, and robustness.

Ultrasound computed tomography based on full waveform inversion with source directivity calibration

Ultrasound computed tomography based on full waveform inversion has the potential to provide high-resolution images of human tissues in a quantitative manner. A successful ultrasound computed tomography system requires the decent knowledge of acquisition array, including the spatial position and the directivity of each transducer, to meet the high-level demand of clinical applications. The conventional full waveform inversion algorithm assumes a point source with the omni-directional emission. Such assumption does not hold when the directivity of emitting transducer is not negligible. For a practical implementation, an efficient and accurate self-checking evaluation of directivity is crucial prior to the reconstruction of images. We propose to measure the directivity of each emitting transducer using the full-matrix captured data obtained with a water-immersed and target-free experiment. We introduce the weighted virtual point-source array to act as the proxy of emitting transducer during the numerical simulation. The weights of different points in the virtual array can be calculated from the observed data using the gradient-based local optimization method. Although the full waveform imaging method relies on the finite-difference solver of wave equation, such directivity estimation benefits from the introduction of analytical solver. The trick significantly reduces the numerical cost, enabling an automatic directivity self-check at boot. We verify the feasibility, efficiency, and accuracy of the virtual array method through simulated and experimental tests. For the experimental test, we also illustrate that full waveform inversion with directivity calibration can reduce the artifacts introduced by the conventional point source assumption, improving the quality of reconstructed images..

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.

Physics-driven self-supervised learning system for seismic velocity inversion

Seismic velocity inversion plays a vital role in various applied seismology processes. A series of deep learning methods have been developed that rely purely on manually provided labels for supervision; however, their performances depend heavily on using large training data sets with corresponding velocity models. Because no physical laws are used in the training phase, it is usually challenging to generalize trained neural networks to a new data domain. To mitigate these issues, we have embedded a seismic forward modeling step at the end of a network to remap the inversion result back to seismic data and thus train the neural network through self-supervised loss, i.e., the misfit between the network input and output. As a result, we eliminate the need for many labeled velocity models, and physical laws are introduced when back-propagating gradients through the seismic forward modeling step. We verify the effectiveness of our approach through comprehensive experiments on synthetic data sets, where self-supervised learning outperforms the fully supervised approach, which accesses much more labeled data. The superior performance is even more significant when compared with a new data domain that has velocity models with faults and more geologic layers. Finally, in case of unknown and more complex data types, we develop a network-constrained full-waveform inversion (FWI) method. This method refines the initial prediction of the network by iteratively optimizing network parameters other than the velocity model, as found with the conventional FWI method, and demonstrates clear advantages in terms of interface and velocity accuracy. With these measures (self-supervised learning and network-constrained FWI), our physics-driven self-supervised learning system successfully mitigates issues such as the dependence on large labeled data sets, the absence of physical laws, and the difficulty in adapting to new data domains.