Interferometric, Target-Enclosing Waveform Inversion: a Comparison of Approaches

This study investigates the effectiveness and the applicability of full waveform inversion (FWI) method to estimate underwater sound velocity structures. We use a frequency domain full waveform inversion method in this study. We use an adjoint-state method for the calculation of the gradient in an iterative inversion based on a preconditioned conjugate gradient method. We first apply the FWI method to a synthetic dataset that is simulated for a sound velocity structure. The results of our inversion are then compared with those from a conventional ray-based traveltime inversion (TTI) method to evaluate the effectiveness of the method. The results show that the full waveform inversion method could provide more precise image with higher resolution than the ray-based method. The FWI method is also applied to a field dataset acquired by a vertical-cable-seismic (VCS) data acquisition experiment in Lake Biwa. In spite of very limited raypath condition using only direct arrival wave, the full waveform inversion method could reproduce a horizontally stratified velocity structure whose vertical profile showed the existence of a seasonal thermocline in the lake that was to be confirmed by temperature measurements after the VCS experiment. We conclude that the FWI method could be the key success factor for the higher resolution at estimation of underwater sound velocity structure.

Ultrasound computed tomography (UCT) is considered to have great potential for the early diagnosis of knee joint injuries. Combining prior knowledge and sound speeds of tissues, UCT can diagnose a variety of symptoms and the extent of tissue lesion. However, no existing studies can reconstruct the sound speed distributions of knee joints in UCT. Therefore, in this study, sound speed distributions of knee joints are reconstructed to provide an imaging basis for the formulation of a treatment plan. In addition, Full waveform inversion (FWI) methods are utilized to estimate highresolution images. However, for media with large variations in sound speeds, traditional FWI methods may lead to a cycle-skipping phenomenon and incorrect convergence direction. Hence, this study proposes a multi-centerfrequency source based FWI method to overcome the above limitations. A penalized least-squares optimization problem is constructed to obtain a numerical solution of the sound speed distribution. Computer simulations are conducted to prove the effectiveness and robustness of the proposed method. Furthermore, the reasons for selecting the center frequencies of sources are analyzed. Two numerical knee joint phantoms are used to evaluate the performance. The results suggest that the biases of the reconstructed images are less than 1% under a 5% noise condition.

Traditional full-waveform inversion (FWI) methods only render a “best-fit” model that cannot account for uncertainties of the ill-posed inverse problem. Additionally, local optimization-based FWI methods cannot always converge to a geologically meaningful solution unless the inversion starts with an accurate background model. We seek the solution for FWI in the Bayesian inference framework to address those two issues. In Bayesian inference, the model space is directly probed by sampling methods such that we obtain a reliable uncertainty appraisal, determine optimal models, and avoid entrapment in a small local region of the model space. The solution of such a statistical inverse method is completely described by the posterior distribution, which quantifies the distributions for parameters and inversion uncertainties. To efficiently sample the posterior distribution, we introduce a sampling algorithm in which the proposal distribution is constructed by the local gradient and the diagonal approximate Hessian of the local log posterior. Our algorithm is called the gradient-based Markov chain Monte Carlo (GMCMC) method. The GMCMC FWI method can quantify inversion uncertainties with estimated posterior distribution given sufficiently long Markov chains. By directly sampling the posterior distribution, we obtain a global view of the model space. Theoretically speaking, statistical assessments do not depend on starting models. Our method is applied to the 2D Marmousi model with the frequency-domain FWI setting. Numerical results suggest that our method can be readily applied to 2D cases with affordable computational efforts.

The quantitative reconstruction of subsurface earth properties from the propagation of waves follows an iterative minimization of a misfit functional. In marine seismic exploration, the observed data usually consist of measurements of the pressure field, but dual-sensor devices also provide the normal velocity. Consequently, a reciprocity-based misfit functional is specifically designed, and it defines the full reciprocity-gap waveform inversion (FRgWI) method. This misfit functional provides additional features compared to the more traditional least-squares approaches, in particular, in that the observational and computational acquisitions can be different. Therefore, the positions and wavelets of the sources from which the measurements are acquired are not needed in the reconstruction procedure and, in fact, the numerical acquisition (for the simulations) can be chosen arbitrarily. Based on 3D experiments, FRgWI is shown to behave better than full-waveform inversion in the same context. It allows for arbitrary numerical acquisitions in two ways: when few measurements are given, a dense numerical acquisition (compared to the observational one) can be used to compensate. However, with a dense observational acquisition, a sparse computational one is shown to be sufficient, for instance, with multiple-point sources, hence reducing the numerical cost. FRgWI displays accurate reconstructions in both situations and appears more robust with respect to crosstalk than least-squares shot stacking.

Since the Industrial Revolution in the 1700s, the high emission of gaseous wastes into the atmosphere from the usage of fossil fuels has caused a general increase in temperatures globally. To combat the environmental imbalance, there is an increase in the demand for renewable energy sources. Dams play a major role in the generation of “green" energy. However, these structures require frequent and strict monitoring to ensure safe and efficient operation. To tackle the challenges faced in the application of convention dam monitoring techniques, this work proposes the inverse analysis of numerical models to identify damaged regions in the dam. Using a dynamic coupled hydro-mechanical Extended Finite Element Method (XFEM) model and a global optimization strategy, damage (crack) in the dam is identified. By employing seismic waves to probe the dam structure, a more detailed information on the distribution of heterogeneous materials and damaged regions are obtained by the application of the Full Waveform Inversion (FWI) method. The FWI is based on a local optimization strategy and thus it is highly dependent on the starting model. A variety of data acquisition setups are investigated, and an optimal setup is proposed. The effect of different starting models and noise in the measured data on the damage identification is considered. Combining the non-dependence of a starting model of the global optimization strategy based dynamic coupled hydro-mechanical XFEM method and the detailed output of the local optimization strategy based FWI method, an enhanced Full Waveform Inversion is proposed for the structural analysis of dams.

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.

Full waveform inversion (FWI) is a technique used to estimate subsurface model parameters by minimizing the difference between observed and calculated seismic data. Sparsity-promoting regularization are useful tools for traditional FWI methods to tackle complex subsurface structures. Since the traditional regularization techniques can only impose some fixed priors, it is necessary to develop a regularization strategy to obtain more flexible priors. In this way, we develop a structural sparse representation method that exploits the non-local self-similarity prior of the model, which is achieved by grouping similar patches using graph matching operators and a dynamic group selection strategy. A group-based dictionary is trained with the aim of providing the best sparse representation of complex features and variations in the entire model perturbation. The dynamic selection strategy of the training method can balance computational efficiency and inversion accuracy by constantly updating and retaining groups during the processing. In addition, two loop algorithm framework is utilized to enhance the robustness and the efficiency of the proposed method. Numerical experiments are presented to demonstrate that the proposed method outperforms the total variation regularization method and the adaptive dictionary learning with non-local self-similarity in terms of robustness and resolution. This structural sparsity-promoting regularization is incorporated into the FWI problem through a two-loop algorithm framework, enhancing the robustness and efficiency of FWI results.

Summary We suggest a new method for the Laplace domain full waveform inversion (FWI) which use single damping constant. This method makes the Laplace domain FWI more efficient, because the proposed method uses only one damping constant during inversion process. To scale the gradient direction properly, we use simple depth window function to steepest descent direction. We demonstrate that the algorithm is working by numerical test using synthetic data set.

A solution to the increasing greenhouse gas emissions is carbon capture and storage. At the Sleipner field, offshore Norway, carbon dioxide is separated from the produced gas and injected into the Utsira formation at approximately 1000m depth. The Utsira formation is a high porosity saline aquifer that is 200–300m thick in the injection area. In 1994, two years before the injection started, a seismic survey was acquired. The survey has been followed up by several seismic surveys acquired to monitor the migration of the injected gas. The full waveform inversion (FWI) method is a non-linear inverse method for estimating subsurface elastic parameters. Time-lapse FWI has recently been suggested as a monitoring tool for resolving time-lapse changes directly in the elastic parameter models. This paper presents an application of a three dimensional implementation of isotropic elastic time-lapse FWI applied on time-lapse field data from the Sleipner area. The baseline dataset is the 1994 dataset, whereas the monitor dataset is the survey acquired in 2006 after ten years of injection. Time-lapse FWI is used to estimate separate elastic parameter models for both the baseline and the monitor datasets. The results show that FWI is able to estimate detailed elastic parameter models that produce synthetic data that match the field data. The inverted models are used in a pre-stack depth migration method to yield detailed seismic images of the Sleipner before and after the injection of the gas. The gas cloud after ten years of injection is clearly visible on the monitor seismic images. The baseline and monitor seismic images show events and discontinuities that can explain the migration pathways of the injected gas through the Utsira formation.

This study considers the Full Waveform Inversion (FWI) method based on the asymptotic solution of the Helmholtz equation. We provide frequency-dependent ray tracing to get the wavefield used to compute the FWI gradient and calculate the modelled data. With a comparable quality of the inverse problem solution as applied to the standard finite-difference approach, the speed of calculations in the asymptotic method is an order of magnitude higher. A series of numerical experiments demonstrate the approach's effectiveness in reconstructing the macro velocity structure of complex media for low frequencies.

Full waveform inversion using a decomposed single frequency component from a spectrogram

Traditional full-waveform inversion (FWI) seeks to find the best model by minimizing an objective function defined as the difference between the model-predicted and observed data in amplitude and phase. In principle, FWI should fit all wave types including direct waves, diving waves, primaries, and multiples. However, when an initial model is far from the true model, FWI will encounter difficulties in matching multiples. Physically, multiples may contain more subsurface information compared to primary and diving waves. Multiples cover a wide range of reflection angles during wave propagation and offer the advantage of imaging the shadow zones that cannot be reached or are poorly illuminated by primary reflections. We have developed a new method of waveform inversion using multiples. We first separate the multiples into different orders. The objective function we seek to minimize consists of the data difference between the modeled data using a lower order multiple as the source and the higher order multiple as data. This method is called controlled-order multiple waveform inversion (CMWI). Our numerical examples determined that the CMWI is a promising method to improve velocity updates.

This study considers the full waveform inversion (FWI) method based on the asymptotic solution of the Helmholtz equation. We provide frequency-dependent ray tracing to obtain the wave field used to compute the FWI gradient and calculate the modeled data. With a comparable quality of the inverse problem solution as applied to the standard finite difference approach, the speed of the calculations in the asymptotic method is an order of magnitude higher. A series of numerical experiments demonstrate the approach’s effectiveness in reconstructing the macro velocity structure of complex media for low frequencies.

Long bones and green wood are two living materials with close structural characteristics. They evolve with age and they are in constant adaption to the environmental constraints. Their mechanical properties vary in successive stages from the juvenile state to the mature state. The study of the quality of these materials to improve the management of dysfunctions is the subject of advanced research. Quantitative ultrasound techniques have been previously used to evaluate bone quality, by giving information about the bone mechanical parameters. For trees, acoustic and ultrasound non-destructive imaging methods have been recently used to analyze their inner structures without altering their condition. This study aims to conduct a theoretical, numerical and experimental joint study of these two materials, in order to propose an efficient and optimized procedure for the characterization and cross-section imaging of growing living materials such as long bones or tree trunks. First, the interaction of acoustic waves with the growing material is modeled, to analyze the phenomena of wave interaction with these complex materials. Then, in order to solve the inverse problem, the Full Waveform Inversion (FWI) method is used. The imaging method is validated using measurements from reference materials.

Inner product preconditioned trust-region methods for frequency-domain full waveform inversion