Full Waveform Inversion Algorithm Research Articles

Near-Borehole Formation Acoustic Logging Imaging: A Full Waveform Inversion Algorithm in Cylindrical Coordinates

Near-Borehole Formation Acoustic Logging Imaging: A Full Waveform Inversion Algorithm in Cylindrical Coordinates

An Auto-Calibration Algorithm for Hybrid Guided Wave Tomography Based on Full Waveform Inversion

Combining with the dispersion characteristics of ultrasonic guided waves, full waveform inversion method shows great application potential in the quantificational detections of defects in plate- and pipe- like structures. Owing to the inversion efficiency problem, the forward modeling is generally based on the acoustic equation approximation, and a reference signal unaffected by the defects needs to be artificially selected to correct the approximation forward simulation results. This study presents an auto-calibration (without artificial selection of the reference signal) and high-precision imaging method based on the combination of the full waveform inversion and ray tomography algorithm. The ray tomography results are not only used to automatically select the reference signal based on an auto-calibration process, but also used as the macro initial model for the full inversion method, which decreases the possibility of losing in local minimum values during the inversion process and enhances the robustness of the inversion method. Therefore, compared with the classical guided wave tomography method based on full waveform inversion, relatively high-frequency transducers can be used to acquire high-frequency signals, and thus, the imaging accuracy could be effectively improved. Simulation and experiment results have verified that the global relative error of the auto-calibration method is smaller than the classical method. The good imaging results of irregular complex defects confirmed the effectiveness and applicability of the new method.

Wasserstein Distance-Based Full-Waveform Inversion With a Regularizer Powered by Learned Gradient

Full-waveform inversion (FWI) is a powerful technique for building high-quality subsurface geological structures. It is known to suffer from local minima problems when a good starting model is lost. To obtain a desirable solution, regularization constraints are needed to impose suitable priors, in particular for salt models. Recent studies have allowed cooperating the denoising operator as a specific prior with optimization algorithms to effectively solve various image reconstruction tasks. Inspired by the promising performance of regularization by denoising (RED), we propose a flexible unsupervised learning FWI framework, in which the regularizer is an extensive variant of RED that powered by learned gradient for addressing salt models inversion. To further mitigate local minima issues, the Wasserstein distance induced by optimal transport theory with a new preprocessing transformation is applied as a measure in data domain. Integrating the physical constraints featured by the wave equation and the model priors featured by the deep convolutional neural network, our method is able to produce measurement consistent and high-resolution results. We experimentally compare the proposed method with traditional total variation regularized FWI and RED regularized FWI on the well-known geological models. The numerical results demonstrate the effectiveness of our method for handling the inversion task of high-contrast media in the presence of a free-surface case. Moreover, our framework is adaptive to restrict the solutions by leveraging the regularizer with learned gradient, whose training does not need any geological images, thus paving the way to develop FWI algorithms with state-of-the-art deep learning techniques in interdisciplinary research.

Feasibility of seismic time-lapse monitoring of CO2 with rock physics parametrized full waveform inversion

SUMMARY Carbon capture and storage is an important technology for greenhouse gas mitigation. Monitoring of CO2 storage should, in addition to locating the plume, provide quantitative information on CO2 saturation. We propose a full waveform inversion (FWI) algorithm for the prediction of the spatial distribution of CO2 saturation from time-lapse seismic data. The methodology is based on the application of a rock-physics parametrized FWI scheme that allows for direct updating of reservoir properties. We derive porosity and lithology parameters from baseline data and use them as input to predict CO2 saturation from monitor data. The method is tested on synthetic time-lapse data generated for the Johansen formation model. Practical issues associated with field data applications, such as acquisition limitations, construction of the initial model, noise and uncertainty in the rock physics model, are taken into account in the simulation. The results demonstrate the robustness of our approach for reconstructing baseline and monitor models. We also illustrate the potential of the approach as compared to conventional two-step inversion algorithms, in which an elastic FWI prediction of velocities and density is followed by rock physics inversion.

A consistent multiparameter Bayesian full waveform inversion scheme for imaging heterogeneous isotropic elastic media

SUMMARY The inversion of complete seismic waveforms offers new perspectives to better constrain the elastic properties of Earth’s interior. However, models of density and seismic velocities obtained from full waveform inversions are generally characterized by very different and uneven spatial resolutions. Because the 3-D structure of the Earth represents small deviations from average reference Earth models, the absolute values of density, VP and VS in the Earth are strongly correlated. Here, we exploit this strong correlation between model parameters as a priori information introduced into a new full waveform inversion algorithm, by considering a non-diagonal 3-D model covariance matrix in which the spatial correlations of elastic properties are described with an exponential covariance function. The inverse of such a model covariance matrix is easy to compute, and we thus have all the ingredients to construct a consistent Bayesian full waveform inversion scheme. We show that taking into account the correlations between density and seismic velocities can lead to dramatic improvements on the reconstructed models of density, seismic velocities and VP/VS ratio. This new imaging approach opens new perspectives for refining tomographic images of density and seismic velocities in the lithosphere and upper mantle on a regional scale by full waveform inversion of teleseismic body waves.

Full waveform inversion of common-offset ground-penetrating radar based on a special source wavelet and multiple integral wave-field transform

Ground-penetrating radar (GPR) can obtain the geological information by using the electrical difference between the abnormal body and the background field. Full waveform inversion (FWI) can process radar data and obtain a more accurate distribution of relative permittivity. However, when the electrical parameters between the anomalous body and the background field are quite different, the wavefield information is seriously disturbed. In that case, the FWI method can not obtain accurate physical parameters, which is worse for common-offset GPR because of the lack of illumination angles and of wavenumber coverage. To solve this problem, a novel GPR FWI method is proposed to improve the stability of inversion using a special source wavelet and multiple integral wave-field transform. The manuscript is composed as follows: first, a special wavelet is used to improve the gradient in FWI. Then the integral wave-field transform can provide low-frequency information of data. This process can make full use of the low-frequency components hidden in the original data, obtain the large-scale relative permittivity distribution structure, and reduce the instability of the full waveform inversion. Finally, three simulation examples and a practical example verify the effectiveness of the method. Especially when there is a large difference between the dielectric parameters of the abnormal body and the background field (more than ten times or even dozens of times), the proposed FWI algorithm can still obtain stable results.

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.

Love wave full-waveform inversion for archaeogeophysics: From synthesis tests to a field case

High precision detection of the shallow-surface structure is of great significance to geotechnical engineering and archaeological geophysical research. Surface wave Full waveform inversion (FWI) is attracting more and more attention in shallow seismic exploration. The FWI of Love waves is more straightforward and has a higher precision and resolution compared with Rayleigh waves. In the classic gradient-based FWI algorithm, the gradient amplitude does not scale with increasing depth due to the coupling effect and double scattering; thus, the inversion image cannot represent the significant small-scale characteristic structures in archaeogeophysics. To overcome the above limitations, a pre-conditioned FWI approach was presented, and a complete elastic Love waves FWI workflow was developed for archaeogeophysics. The superior performance of the developed method was verified through synthesis tests and a field experiment. The synthetic tests on a tomb model show that the pre-conditioned approach has a better parameter reconstruction capability, can characterize small-scale anomalies, improves the convergence rate, and has a strong anti-noise ability. In the field experiment, the pre-conditioned approach-based Love waves FWI workflow was adopted to invert the recorded Love waves datasets gathered in Xianyang City, China. The target of the survey was to determine the location and approximate size of a buried ancient tomb to provide reliable guidance for further excavation. The obtained FWI image revealed an underground profile with a depth of 9.5 m, and a low-velocity anomaly with a height of about 1.6 m and a length of about 4.7 m was delineated, which we identified as the tomb. The subsequent excavation confirmed this conclusion. The above results show that the complete Love wave FWI workflow developed has the ability to perform accurate imaging under the condition of few shots.

3D elastic multisource full waveform inversion on distributed GPU clusters

Full-waveform inversion (FWI) serves as a useful tool to quantitatively investigate the properties of the media. One of the greatest challenges is its enormous computational cost, especially for the three-dimensional (3D) case. The multisource encoding strategy is a crucial method to speed up FWI. However, current 3D elastic FWI algorithms with the simultaneous sources, such as random time series and random polarity methods, may be subjected to the crosstalk noise, which severely degrades inversion quality. We present a novel 3D elastic crosstalk-free multisource full-waveform inversion method (MFWI). The encoded sources with a series of single-frequency components are excited to perform the seismic wavefield simulation. Extracting the wavefield corresponding to each single-frequency harmonic source by phase-sensitive detection (PSD) algorithm, the multisource wavefield can be decomposed. Therefore, summing the gradients with respect to the model parameters of all decomposed single frequencies can effectively avoid the crosstalk in our MFWI algorithm. Furthermore, to increase the practicability and universality of the algorithm, we adopt the graphic processing unit (GPU) based on the domain decomposition to improve the MFWI algorithm. The multi-scale strategy with a flexible encoding number in each scale helps to enhance the robustness of our algorithm. The numerical examples demonstrate that our method can achieve domain decomposition simulation and obtain 3D crosstalk-free multisource elastic wave inversion results.

Regularization tunnelling for full waveform inversion

SUMMARY Prior knowledge can be a powerful source of information in seismic inversion, leading to substantially more accurate models than those derived from seismic data alone. Prior knowledge about clustering of rock physics properties, supplied by appropriate rock physics models, or nearby well-logs, may be especially informative. However, incorporating general forms of this type of information into local optimization methods, such as those used in full waveform inversion (FWI), is problematic, since it will often call for model updates involving a departure from the basin of a local minimum. Here, we propose an optimization strategy for FWI, in which global regularization information is partially accounted for, and in which a model can, under the right circumstances, ‘tunnel’ between basins, to honour prior information. The process is based on standard FWI updates and begins with an initial model in which every model grid cell is in one of a range of pre-defined clusters. At each iteration, a standard update is computed, but it is then followed by a second update, in which each grid cell tunnels to a new cluster if the move is warranted by the update history of the model (its ‘momentum’) and the model regularization penalty (its ‘potential’). To limit the ability of the tunnelling procedure from introducing spatial variations on scales smaller than those contained in the seismic data, these conditions are considered in combination with a small mode filter. We implement the procedure by building on an existing 2-D viscoelastic FWI algorithm, limited such that only the P-wave velocity and density are updated, and evaluate it by subjecting it to a variety of basic tests involving simulated data. We conclude that the basic approach, and this specific implementation, using a simple initial model, provides a combination of well-resolved structures and grid cells occupying appropriate clusters that cannot be produced by standard means.

Modeling the Effect of Anisotropy in Ultrasonic-Guided Wave Tomography.

Most of the existing ultrasonic-guided wave tomography approaches to map structural changes in plate-like waveguides are based on the assumption of an isotropic material model. However, there are many other engineering applications that are made of anisotropic materials and structures. Applying these techniques on such structures becomes complicated due to the anisotropic wave propagation behavior. The main challenge is to develop a suitable forward model that describes the wave propagation in such material, thereby enabling accurate reconstruction of the material properties. The present study proposes an anisotropic formulation of the acoustic forward model to map velocity variations induced by defects in anisotropic plates. The anisotropic behavior of the waves along the plate is simulated by implementing approximate anisotropic parameters. The velocity reconstruction is based on a full-waveform inversion algorithm, and its performance is investigated in the case of different degrees of anisotropy of the plate material and the defect. The results suggest that the method is highly suitable for imaging velocity changes due to defects. This is found to be the case when the defect has a similar anisotropic structure to the surrounding plate material. The validation experiment is performed on a multilayered composite plate with a circular defect of stiffness reduction using A0 mode, showing a very good performance of the reconstruction algorithm.

Nonlinear Waveform Inversion for Quantitative Ultrasound

Due to its non-invasive and non-radiating nature, along with its low cost, ultrasound (US) imaging is widely used in medical applications. Typical B-mode US images have limited resolution and contrast and weak physical interpretation. Inverse US methods were developed to reconstruct the media's speed-of-sound (SoS) based on a linear acoustic model. However, the wave propagation in medical US is governed by nonlinear acoustics, which introduces more complex behaviors neglected in the linear model. In this work we propose a nonlinear waveform inversion (NWI) approach for quantitative US, that considers a nonlinear acoustics model to simultaneously reconstruct multiple material properties, including the medium's SoS, density, attenuation, and nonlinearity parameter. We thus broaden current inverse US approaches, such as the full waveform inversion (FWI) algorithm, by considering nonlinear media, and additional physical parameters. We represent the nonlinear acoustic model by means of a recurrent neural network, which enables us to apply advanced optimization algorithms borrowed from the deep learning toolbox and achieve more efficient reconstructions compared to the FWI method. We evaluate the performance of our approach on in-silico data and show that neglecting nonlinear effects may result in substantial degradation in the reconstruction, paving the way of NWI into clinical applications.

Application of Full Waveform Inversion Algorithm in Laplace – Fourier Domain for High-Contrast Ultrasonic Bone Quantitative Imaging

Application of Full Waveform Inversion Algorithm in Laplace – Fourier Domain for High-Contrast Ultrasonic Bone Quantitative Imaging

Ultrasound Computed Tomography.

This chapter presents theoretical, numerical, and experimental frameworks for the use of Ultrasound Computed Tomography (USCT) for cortical bone tissue imaging. Most of the research conducted on this topic concerns adult bone, although some work presented in this chapter is specific to the study of child bone. USCT is recognized as a powerful method for soft tissue imaging. In bone imaging, the difficulties arise from the very high impedance contrast between tissues which alters the propagation of the ultrasonic waves and limits the linear inversion algorithms used. Solutions consist in optimally assessing non-linear effects in an iterative approach aiming at local linearization. When the problem can be reduced to the study of a fluid-like cavity buried in an elastic cylinder surrounded by water, the signal processing and/or compound algorithms can be added as an extension to the linear algorithms. The main limitation of these methods is the heavy experimental costs involved. We have then suggested the introduction of purely numerical non-linear full-waveform inversion algorithms. The performances and the limitations of these linear and non-linear methods applied to cortical bone tissue imaging problems are overviewed and discussed.

Full-waveform inversion for full-wavefield imaging: Decades in the making

Seismic imaging using full-wavefield data that includes primary reflections, transmitted waves, and their multiples has been the holy grail for generations of geophysicists. To be able to use the full-wavefield data effectively requires a forward-modeling process to generate full-wavefield data, an inversion scheme to minimize the difference between modeled and recorded data, and, more importantly, an accurate velocity model to correctly propagate and collapse energy of different wave modes. All of these elements have been embedded in the framework of full-waveform inversion (FWI) since it was proposed three decades ago. However, for a long time, the application of FWI did not find its way into the domain of full-wavefield imaging, mostly owing to the lack of data sets with good constraints to ensure the convergence of inversion, the required compute power to handle large data sets and extend the inversion frequency to the bandwidth needed for imaging, and, most significantly, stable FWI algorithms that could work with different data types in different geologic settings. Recently, with the advancement of high-performance computing and progress in FWI algorithms at tackling issues such as cycle skipping and amplitude mismatch, FWI has found success using different data types in a variety of geologic settings, providing some of the most accurate velocity models for generating significantly improved migration images. Here, we take a step further to modify the FWI workflow to output the subsurface image or reflectivity directly, potentially eliminating the need to go through the time-consuming conventional seismic imaging process that involves preprocessing, velocity model building, and migration. Compared with a conventional migration image, the reflectivity image directly output from FWI often provides additional structural information with better illumination and higher signal-to-noise ratio naturally as a result of many iterations of least-squares fitting of the full-wavefield data.

High-frequency localized elastic full-waveform inversion for time-lapse seismic surveys

Seismic full-waveform inversion (FWI) is a powerful method used to estimate the elastic properties of the subsurface. To mitigate the nonlinearity and cycle-skipping problems, in a hierarchical manner, one first inverts the low-frequency content to determine long- and medium-wavelength structures and then increases the frequency content to obtain detailed information. However, the inversion of higher frequencies can be computationally very expensive, especially when the target of interest, such as oil/gas reservoirs and axial melt lens, is at a great depth, far away from source and receiver arrays. To address this problem, we have developed a localized FWI algorithm in which iterative modeling is performed locally, allowing us to extend inversions for higher frequencies with little computation effort. Our method is particularly useful for time-lapse seismic, where the changes in elastic parameters are local due to fluid extraction and injection in the subsurface. In our method, the sources and receivers are extrapolated to a region close to the target area, allowing forward modeling and inversion to be performed locally after low-frequency full-model inversion for the background model, which by nature only represents long- to medium-wavelength features. Numerical tests show that the inversion of low-frequency data for the overburden is sufficient to provide an accurate high-frequency estimation of elastic parameters of the target region.

Application of an Improved Ultrasound Full-Waveform Inversion in Bone Quantitative Measurement

Inspired by the large number of applications for symmetric nonlinear equations, an improved full waveform inversion algorithm is proposed in this paper in order to quantitatively measure the bone density and realize the early diagnosis of osteoporosis. The isotropic elastic wave equation is used to simulate ultrasonic propagation between bone and soft tissue, and the Gauss–Newton algorithm based on symmetric nonlinear equations is applied to solve the optimal solution in the inversion. In addition, the authors use several strategies including the frequency-grid multiscale method, the envelope inversion and the new joint velocity–density inversion to improve the result of conventional full-waveform inversion method. The effects of various inversion settings are also tested to find a balanced way of keeping good accuracy and high computational efficiency. Numerical inversion experiments showed that the improved full waveform inversion (FWI) method proposed in this paper shows superior inversion results as it can detect small velocity–density changes in bones, and the relative error of the numerical model is within 10%. This method can also avoid interference from small amounts of noise and satisfy the high precision requirements for quantitative ultrasound measurements of bone.

Nondestructive Evaluation of Drilled Shaft Construction Anomalies Using Full Waveform Tomography of Simulated Crosshole Measurements

Construction of drilled shafts for transportation infrastructure presents quality assurance challenges related to structural anomalies, including voids and degraded concrete. Efforts to evaluate anomalies often use stress-wave non-destructive testing (NDT) techniques such as the crosshole sonic logging (CSL) method. CSL relies on the propagation of stress waves between access tubes inserted alongside the reinforcement cage. Differences in travel time and amplitudes can be used to estimate concrete quality within the source-receiver ray paths. Crosshole tomography (CT) advances this approach further and models ray paths to solve an inverse problem based on first arrival times. However, both stress-wave methods cannot typically evaluate anomalies smaller than 10% to 15% of the shaft cross sectional area. Recent advances in wave propagation modeling have led to the development of full waveform inversion (FWI) approaches. FWI attempts to generate a more detailed tomographic model that matches the entire waveform recordings. This paper presents findings from a numerical study where full waveform tomography was performed on a portion of a drilled shaft with a structural anomaly. Crosshole stress-wave propagation was simulated using a spectral element method (SEM) forward modeler. The resulting waveforms were then used as inputs into a CT travel-time inversion algorithm using ray-path modeling and into a FWI algorithm using the entire recorded signals. The results highlighted that FWI estimated concrete velocities and the geometry of the anomaly more accurately than CT in the idealized numerical model. This was the case even though information from more sources and receiver pairs was used for the CT inversion.

High-resolution bone microstructure imaging based on ultrasonic frequency-domain full-waveform inversion* *Project supported by the National Natural Science Foundation of China (Grant Nos. 11827808, 11874289, and 11804056), the National Science Fund for Distinguished Young Scholars of China (Grant No. 11525416), Shanghai Municipal Science and Technology Major Project, China (Grant No. 2017SHZDZX01), Shanghai Talent Development Fund (Grant No. 2018112), State Key Laboratory

The main challenge in bone ultrasound imaging is the large acoustic impedance contrast and sound velocity differences between the bone and surrounding soft tissue. It is difficult for conventional pulse-echo modalities to give accurate ultrasound images for irregular bone boundaries and microstructures using uniform sound velocity assumption rather than getting a prior knowledge of sound speed. To overcome these limitations, this paper proposed a frequency-domain full-waveform inversion (FDFWI) algorithm for bone quantitative imaging utilizing ultrasonic computed tomography (USCT). The forward model was calculated in the frequency domain by solving the full-wave equation. The inverse problem was solved iteratively from low to high discrete frequency components via minimizing a cost function between the modeled and measured data. A quasi-Newton method called the limited-memory Broyden–Fletcher–Goldfarb–Shanno algorithm (L-BFGS) was utilized in the optimization process. Then, bone images were obtained based on the estimation of the velocity and density. The performance of the proposed method was verified by numerical examples, from tubular bone phantom to single distal fibula model, and finally with a distal tibia-fibula pair model. Compared with the high-resolution peripheral quantitative computed tomography (HR-pQCT), the proposed FDFWI can also clearly and accurately presented the wavelength scaled pores and trabeculae in bone images. The results proved that the FDFWI is capable of reconstructing high-resolution ultrasound bone images with sub-millimeter resolution. The parametric bone images may have the potential for the diagnosis of bone disease.

Full-waveform inversion with borehole constraints for elastic VTI media

The nonlinearity of full-waveform inversion (FWI) and parameter trade-offs can prevent convergence toward the actual model, especially for elastic anisotropic media. The problems with parameter updating become particularly severe if ultra-low-frequency seismic data are unavailable, and the initial model is not sufficiently accurate. We introduce a robust way to constrain the inversion workflow using borehole information obtained from well logs. These constraints are included in the form of rock-physics relationships for different geologic facies (e.g., shale, sand, salt, and limestone). We develop a multiscale FWI algorithm for transversely isotropic media with a vertical symmetry axis (VTI media) that incorporates facies information through a regularization term in the objective function. That term is updated during the inversion by using the models obtained at the previous inversion stage. To account for lateral heterogeneity between sparse borehole locations, we use an image-guided smoothing algorithm. Numerical testing for structurally complex anisotropic media demonstrates that the facies-based constraints may ensure the convergence of the objective function towards the global minimum in the absence of ultra-low-frequency data and for simple (even 1D) initial models. We test the algorithm on clean data and on surface records contaminated by Gaussian noise. The algorithm also produces a high-resolution facies model, which should be instrumental in reservoir characterization.