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

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.

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

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.

We present a new target-enclosing full waveform inversion (FWI) method based on a interferometric objective function, where the inversion is driven by the misfit between the wavefields reconstructed in a subdomain of interest via the convolution and correlation representation formulas. The method is fully local in the sense that it does not depend on the reconstruction of the physical properties outside the local domain, and only requires a kinematic velocity model estimate for redatuming. We compare the proposed method to another fully local FWI method based on the convolution representation formula and to full-model surface-data FWI. We demonstrate the potential of the proposed interferometric full waveform inversion method to achieve higher resolution images at a comparable or lower cost than the other methods.

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.

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.

<p>Transcranial ultrasound has been used to image the brain since 1942. Currently, it is regaining interest and full-waveform inversion (FWI) methods are now employed to reconstruct speed-of-sound profiles of the brain. Many of these methods require a good starting model. Here, we test the applicability of contrast source inversion (CSI) as a FWI method to reconstruct two-dimensional speed-of-sound profiles of the soft brain tissue enclosed by the skull. The advantage of CSI is that it can handle large acoustic contrasts without the need for a good starting model. To test the performance of CSI, we first compute synthetic data. The resulting pressure field clearly shows a significant amount of multiple scattering caused by the skull that acts as a hard acoustic contrast. Next we invert the resulting synthetic data within the Born approximation as well as by applying CSI as a FWI method. The results clearly show that Born inversion can only image the soft brain tissue in the absence of the skull whereas it generates erroneous results when the skull is present. On the other hand, with CSI it is feasible to reconstruct both the skull and the soft brain tissue accurately. Importantly, as compared to other methods CSI does not require any a priori information about the contrast, a mask or a heterogeneous starting model to reconstruct the soft tissue enclosed by the skull.</p>

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.

Ultrasound computed tomography (USCT) is a noninvasive and non-ionizing imaging technique for soft tissue and limb bones. Full waveform inversion (FWI) has received increased interest due to its high resolution. The difficulties in FWI are twofold: high computational burden and poor convergence. To address these issues, an envelope inversion with source coding (EI-SE) algorithm is proposed in this paper. The envelope-based objective function measures the matching degree between the predicted and measured envelopes. It can provide the low-frequency components of the signal that are not available to FWI. Therefore, the EI can provide an accurate solution even when the initial model is far from the ground truth and low-frequency data are missing. The simulations are conducted to demonstrate the validity of the proposed algorithm. The root mean squared error (RMSE) of the proposed algorithm is much smaller than that of conventional FWI. The results show that EI-SE is effective in avoiding cycle skipping.

Strong-scattering medium can usually form a good sealing medium for oil and gas resources. However, conventional elastic full-waveform inversion (EFWI) methods are difficult to build reliable velocity models under the condition of lacking low-frequency information. The elastic direct envelope inversion (EDEI) method has been proven to be able to model large-scale Vp and Vs structures of strong-scattering media. The successive use of EDEI and EFWI can obtain fine structures of the strong scatterers and their shielding areas. However, the inversion effects of inner velocity and bottom boundaries of strong scatterers by the existing methods need to be improved. In this paper, we propose the elastic direct envelope inversion with anisotropic total variation constraint (EDEI-ATV). The anisotropic total variation (ATV) constraint has the advantage of making the velocity more uniform inside the layer and sharper on boundaries, which can be used to improve the inversion results of EDEI. During the iterations, the ATV constraint is directly applied to the update of Vp and Vs, and the alternately iterative algorithm can achieve good results. After obtaining reliable large-scale Vp and Vs structures, the EFWI with anisotropic total variation constraint (EFWI-ATV) is performed to obtain high-precision Vp and Vs structures. Numerical examples verify the effectiveness of the proposed method.

Traditional iteration-based full-waveform inversion (FWI) methods encounter serious challenges if the initial velocity model is far from the true model or if the observed data are lacking low-frequency content. As such, the optimization algorithm may be trapped in local minima and fail to go to a global optimal model. In addition, the traditional FWI method requires long-offset data to update the deep structure of a velocity model with diving waves. To overcome the disadvantages of traditional FWI under these circumstances, we have developed a reflection intensity waveform inversion method. This method aims to minimize the seismic intensity differences between the modeled reflection data and field data. Our method is less dependent on the starting model, and long-offset data are no longer required. The wave intensity, proportional to the square of the original data amplitude, can have a low-frequency band and a higher frequency band, even for waveforms without initial low-frequency content. Our multiscale intensity inversion starts from the low-frequency information in the intensity data, and it can largely avoid the cycle-skipping problem. Synthetic and field data examples demonstrate that our method is able to overcome cycle skipping in handling data with no low-frequency information.

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.