Full Waveform Inversion Research Articles

Optimising seismic imaging design parameters via bilevel learning

Abstract Full waveform inversion (FWI) is a standard algorithm in seismic imaging. It solves the inverse problem of computing a model of the physical properties of the earth’s subsurface by minimising the misfit between actual measurements of scattered seismic waves and numerical predictions of these, with the latter obtained by solving the (forward) wave equation. The implementation of FWI requires the a priori choice of a number of ‘design parameters’, such as the positions of sensors for the actual measurements and one (or more) regularisation weights. In this paper we describe a novel algorithm for determining these design parameters automatically from a set of training images, using a (supervised) bilevel learning approach. In our algorithm, the upper level objective function measures the quality of the reconstructions of the training images, where the reconstructions are obtained by solving the lower level optimisation problem—in this case FWI. Our algorithm employs (variants of) the BFGS quasi-Newton method to perform the optimisation at each level, and thus requires the repeated solution of the forward problem—here taken to be the Helmholtz equation. This paper focuses on the implementation of the algorithm. The novel contributions are: (i) an adjoint-state method for the efficient computation of the upper-level gradient; (ii) a complexity analysis for the bilevel algorithm, which counts the number of Helmholtz solves needed and shows this number is independent of the number of design parameters optimised; (iii) an effective preconditioning strategy for iteratively solving the linear systems required at each step of the bilevel algorithm; (iv) a smoothed extraction process for point values of the discretised wavefield, necessary for ensuring a smooth upper level objective function. The algorithm also uses an extension to the bilevel setting of classical frequency-continuation strategies, helping avoid convergence to spurious stationary points. The advantage of our algorithm is demonstrated on a problem derived from the standard Marmousi test problem.

Seismic evidence of an extremely thin crust along a 70 Ma slow-spreading crustal segment in the equatorial Atlantic Ocean

The oceanic crust at slow-spreading ridges is formed by a combination of magmatic and tectonic processes. Seismic tomographic studies, commonly used to determine crustal structures, indicate that mature slow-spreading crust has an average thickness of 6.1 ± 0.9 km, with a lower to upper crustal thickness ratio of 2.3. However, tomographic methods are based on high-frequency approximations and can only provide information about large-scale crustal structures. Using seismic full-waveform inversion applied to ocean bottom seismometer data, we report the presence of nearly uniform and extremely thin crust (4 ± 0.2 km) with a lower to upper crustal thickness ratio of 0.74 along an ∼100 km, 70 Ma crustal segment formed at the slow-spreading Mid-Atlantic Ridge in the equatorial Atlantic Ocean. This thin crust is underlain by a Moho transition zone that is 1 ± 0.5 km thick, resulting in a combined crustal and Moho transition zone thickness of 5 ± 0.6 km. The crustal thinning is primarily due to the thinning of the lower crust, suggesting that a significant part of the crust is formed by lava flows and dike intrusions. The presence of an extremely thin crust indicates a decrease in mantle temperature by at least 50 °C, suggesting a vast extent of the upper mantle thermal minimum in the equatorial Atlantic Ocean, and the absence of influence of the mantle from the Siera Leone mantle plume 70 m.y. ago.

Assessing the value of combined use of distributed acoustic sensing (DAS) and multicomponent vertical seismic profiling (VSP) data with network-based full waveform inversion and uncertainty quantification: A case study in Alberta, Canada

Distributed acoustic sensing (DAS) technology, deployed in a vertical seismic profiling (VSP) experimental configuration, has emerged as a candidate for non-disruptive and low-cost seismic monitoring of CO2 geostorage and plume evolution. Full waveform inversion (FWI) has likewise received significant attention because it uses relatively complete physical models of wave propagation and because of its sample-by-sample incorporation of data information. Recent artificial neural network-based FWI algorithms (built with, for instance, recursive neural networks, or RNNs) have added to FWI a range of flexible and efficient tools for gradient computation and options for uncertainty assessment and initial model proxies. An important current research area for the use of DAS data is to better understand how they change our confidence levels in models selected through FWI. In particular, we seek to understand whether either DAS data or conventional geophone data alone are optimal for FWI model selection in the CO2 problem, and if not, to what degree they complement each other. The Snowflake 4D VSP dataset, which includes multi-offset and multi-azimuth broadband sources illuminating both fiberoptic cable and densely sampled accelerometer phones in the borehole, was acquired by our group to directly address these questions. In this study, we quantify uncertainty (UQ) by sampling the posterior model covariance matrix from the inverse Hessian matrix at the end of RNN-FWI runs on the Snowflake baseline data, invoking a velocity-density parameterization, and involving mixtures of accelerometer and DAS data. In this UQ context, the complementary effect of combining accelerometer and DAS data is evident in the Vp and Vs models. Our confidence in the approach is bolstered by its independent prediction of a region of known high uncertainty. In the overall pursuit of reliable and low-cost monitoring tools, this supports continued consideration of a multicomponent sensors supported by DAS approach.

3D structural modelling of the Kopili fault zone in North-East India: Seismotectonic analysis utilising focal mechanism solutions of small-to-moderate earthquakes

This work presents new findings from recent seismic data which have never been exploited so far for the weak-to-moderately energetic (ML 2.3–6.4) earthquakes and to depict a 3D scheme for the Kopili Fault (KF) Zone. For the first time, we figure out different fault kinematics in the upper crust such as reverse and strike-slip mechanisms located along the KF zone. Moment Tensor (MT) solutions are successfully obtained through full-waveform inversions for 60 seismic events. The stress inversions are estimated based on the MT results as well as previous findings from 16 small to moderate earthquakes (MW 3.6–6.3). The MT solutions demonstrate that strike-slip kinematics is the most prevalent while a few thrust/normal earthquake events are observed in the area. The seismic cross-sections display that these earthquakes took place at a depth of 40 km and are mostly generated on the eastern side of the fault. According to the 3D spatial and temporal distribution of relocated events, the KF zone is not a completely vertical fault but rather one with a slight eastward dip. Our stress inversion results also indicate that this fault is equivalent to a fault plane with a dip angle of around 80˚, which is compatible with the previously estimated dip angle (75˚). We interpret that the research region is under a transpressional stress regime, which is likely to be the reason for the current activity of the KF zone. We postulate that our findings can be useful to enhance seismic hazard assessment in the densely populated region, which is also covered by vital infrastructure.

A global approach to detecting and characterizing water leakage in a concrete bridge deck: Parametric study to validate an adapted full-waveform inversion method

The objective of this study is to address issues related to defects in waterproofing membranes through the use of Ground Penetration Radar to detect water leakage into the concrete layer of bridge decks. Given that processing radar signals based solely on temporal data introduces significant estimation errors, an advanced method optimized from Full-Waveform Inversion (FWI) is employed. This method accounts for several unknown factors, including boundary conditions, antenna positioning inaccuracies, and approximations inherent in 2D modeling during the inversion process. The method is adaptable and capable of reconstructing both the dielectric and geometric parameters of a multilayered structure with any number of layers and unknown parameters using just a few A-scans (up to 10, depending on the number of parameters and layers). In contrast, other methods typically require several hundred A-scans. This efficiency is achieved due to the two-dimensional nature of the layer system. Additionally, the simplicity of the structure facilitates a much faster and more straightforward inversion algorithm, hence making these features especially advantageous for practical applications. The optimized Full-Waveform Inversion approach allows for an accurate determination of unknown parameters within a multilayered medium. The high accuracy of this method is validated through a direct comparison with experiments, wherein the exact parameters are known. Such an approach enables the attainment of a low relative error using the currently available measurement device.

Seismic Evidence for Velocity Heterogeneity Along ∼40 Ma Old Oceanic Crustal Segment Formed at the Slow‐Spreading Equatorial Mid‐Atlantic Ridge From Full Waveform Inversion of Ocean Bottom Seismometer Data

AbstractIn slow spreading environments, oceanic crust is formed by a combination of magmatic and tectonic processes. Using full waveform inversion applied to active‐source ocean bottom seismometer data, we reveal the presence of a strong lateral variability in the 40–48 Ma old oceanic crust formed at the slow‐spreading Mid‐Atlantic Ridge in the equatorial Atlantic Ocean. Over a 120 km‐long section between the St Paul fracture zone (FZ) and the Romanche transform fault (TF), we observe four distinct 20–30 km long crustal segments. The segment affected by the St Paul FZ consists of three layers, an ∼2 km thick layer with a P‐wave velocity <6 km/s, a 1.5 km thick middle crust with a velocity of 6–6.5 km/s, and an underlying layer where velocity is ∼7 km/s, representing the lower crust. The segment associated with an abyssal hill morphology contains a high velocity of ∼7 km/s at 2–2.5 km below the basement, indicating the presence of primitive gabbro or serpenized peridotite. The segment associated with a low basement morphology seems to have 5.5–6.5 km/s velocity starting near the basement extending down to ∼4 km depth, indicating chemically distinct crust. The segment close to the Romanche TF, a velocity 4.5–5 km/s near the seafloor increasing to 7 km/s at 4 km depth indicates a magmatic origin. The four distinct crustal segments have a good correlation with the overlying seafloor morphology. These observed strong crustal heterogeneities could result from alternate tectonic and magmatic processes along the ridge axis, possibly modulated by thermal and/or chemical variations in the mantle during their formation along the ridge segment.

Modeling Rayleigh wave in viscoelastic media with constant Q model using fractional time derivatives

The propagation of seismic waves within the near-surface weathering layers, characterized by their low-quality factors (Q), is often accompanied by strong attenuation and dispersion phenomena. Among these, the Rayleigh wave, with its sensitivity to dispersion, has proven to be a powerful tool for near-surface exploration. We propose a novel approach for simulating Rayleigh wave propagation in such low-Q media. Our method uses the time-domain fractional wave equation with memory effect, based on Kjartansson's constant-Q (CQ) model, for accurate characterization of the propagation process. To solve numerically the wave equation with the fractional derivatives, we employ a finite-difference method combined with the auxiliary differential equation-perfectly matched layer (ADE-PML) and the acoustic-elastic boundary approach (AEA). The algorithm's high computational accuracy is verified through comparison with the conventional integer-order wave equation based on the nearly constant-Q (NCQ) models in strong attenuation media. The research in this paper deepens our understanding of the propagation characteristics of Rayleigh waves in strongly weathering layers. This new method strongly supports those seismic imaging and inversion methods depending on seismic modeling, including the reverse time migration and the full waveform inversion of the internal structure of low-Q media.

Enhancing Full Waveform Inversion of Field GPR Data: A Source-Independent Approach with Dynamic Reference Selection via SE-Wave-U-Net

Ground Penetrating Radar (GPR) is a widely-utilized non-destructive detection tool. Full Waveform Inversion (FWI) offers a reliable algorithm for accurately imaging GPR data. Despite its potential, FWI's effectiveness is often compromised by unknown excitation sources, which can lead to computational failures and/or diminished imaging accuracy. Addressing this challenge, this paper introduces a convolution-type objective function designed to mitigate the detrimental effects of these unknown excitation sources on FWI imaging. Critical to the success of this function is the precise selection of reference traces. Further refining the capability for signal separation, we have integrated Squeeze-and-Excitation (SE) modules into the traditional Wave-U-Net architecture, culminating in the development of the SE-Wave-U-Net framework. This framework is adept at dynamically extracting accurate reference traces from field GPR data, which are essential for the accurate FWI imaging. The efficacy, accuracy, and practical applicability of proposed methods are validated through extensive analysis of numerical, laboratory experiments, and field GPR data. The proposed algorithm not only establishes a high-precision computational framework for FWI but also enhances the reliability of GPR imaging in complex environments.

Greedy selection of optimal location of sensors for uncertainty reduction in seismic moment tensor inversion

We address an optimal sensor placement problem through Bayesian experimental design for seismic full waveform inversion for the recovery of the associated moment tensor. The objective is that of optimally choosing the location of the sensors (stations) from which to collect the observed data. The Shannon expected information gain is used as the objective function to search for the optimal network of sensors. A closed form for such objective is available due to the linear structure of the forward problem, as well as the Gaussian modeling of the observational errors and prior distribution. The resulting problem being inherently combinatorial, a greedy algorithm is deployed to sequentially select the sensor locations that form the best network for learning the moment tensor. Numerical results are presented to display the optimal network of sensors and how the uncertainty in the inferred seismic moment tensor contracts. The scenario of full three-dimensional velocity models or unknown earthquake source locations is treated as nuisance uncertainty, contributing to the overall uncertainty without being the focus of the inversion. This is addressed using a consensus approach over a set of realizations of the nuisance parameter. We analyzed the resulting network of stations for the moment tensor inversion under model misspecification, which reflects realistic data-generating processes.

Full waveform inversion with smoothing of dilated convolutions

Abstract Full waveform inversion (FWI) is a method for building subsurface models with high resolution by optimizing a data-fitting problem. However, it is still a challenge to apply the FWI method to complicated subsurface models, because FWI is a highly ill-fitting inversion problem. When the simulated data differ from the observed data by more than half a cycle, FWI tends to suffer from the cycle-skipping problems and get trapped in a local minimum. To help the inversion to converge to the accurate subsurface model, we typically build a reasonable initial model or use low-frequency data to start our inversion. Here, we developed a novel technique called smoothing of dilated convolutions inversion (SDCI) to generate low-frequency components from seismic data to recover low-wavenumber components of the subsurface. In the theory part, we first present the objective function of the SDCI method and then derive the gradient of the objective function relative to the velocity using the adjoint-state approach. We then apply the method to a set of simulated data from the Marmousi model. The SDCI method can reasonably estimate the subsurface model even if the simulated seismic record does not contain information below 5 Hz. The numerical examples prove the effectiveness and feasibility of the proposed method. From the SDCI results, the FWI method recovers the velocity with higher accuracy and resolution.

Adjoint-based inversion for stress and frictional parameters in earthquake modeling

We present an adjoint-based optimization method to invert for stress and frictional parameters used in earthquake modeling. The forward problem is linear elastodynamics with nonlinear rate-and-state frictional faults. The misfit functional quantifies the difference between simulated and measured particle displacements or velocities at receiver locations. The misfit may include windowing or filtering operators. We derive the corresponding adjoint problem, which is linear elasticity with linearized rate-and-state friction and, for forward problems involving fault normal stress changes, nonzero fault opening, with time-dependent coefficients derived from the forward solution. The gradient of the misfit is efficiently computed by convolving forward and adjoint variables on the fault. The method thus extends the framework of full-waveform inversion to include frictional faults with rate-and-state friction. In addition, we present a space-time dual-consistent discretization of a dynamic rupture problem with a rough fault in antiplane shear, using high-order accurate summation-by-parts finite differences in combination with explicit Runge–Kutta time integration. The dual consistency of the discretization ensures that the discrete adjoint-based gradient is the exact gradient of the discrete misfit functional as well as a consistent approximation of the continuous gradient. Our theoretical results are corroborated by inversions with synthetic data. We anticipate that adjoint-based inversion of seismic and/or geodetic data will be a powerful tool for studying earthquake source processes; it can also be used to interpret laboratory friction experiments.

Deep neural helmholtz operators for 3D elastic wave propagation and inversion

Summary Numerical simulations of seismic wave propagation in heterogeneous 3D media are central to investigating subsurface structures and understanding earthquake processes, yet are computationally expensive for large problems. This is particularly problematic for full waveform inversion, which typically involves numerous runs of the forward process. In machine learning there has been considerable recent work in the area of operator learning, with a new class of models called neural operators allowing for data-driven solutions to partial differential equations. Recent works in seismology have shown that when neural operators are adequately trained, they can significantly shorten the compute time for wave propagation. However, the memory required for the 3D time domain equations may be prohibitive. In this study, we show that these limitations can be overcome by solving the wave equations in the frequency domain, also known as the Helmholtz equations, since the solutions for a set of frequencies can be determined in parallel. The 3D Helmholtz neural operator is 40 times more memory-efficient than an equivalent time-domain version. We employ a Helmholtz neural operator for 2D and 3D elastic wave modeling, achieving two orders of magnitude acceleration compared to a baseline spectral element method. The neural operator accurately generalizes to variable velocity structures and can be evaluated on denser input meshes than used in the training simulations. We also show that when solving for wavefields strictly on the surface, the accuracy can be significantly improved via a graph neural operator layer. In leveraging automatic differentiation, the proposed method can serve as an alternative to the adjoint-state approach for 3D full-waveform inversion, reducing the computation time by a factor of 350.

Soil water content estimation by using ground penetrating radar data full waveform inversion with grey wolf optimizer algorithm

AbstractSoil water content (SWC) estimation is important for many areas including hydrology, agriculture, soil science, and environmental science. Ground penetrating radar (GPR) is a promising geophysical method for SWC estimation. However, at present, most of the studies are based on partial information of GPR, like travel time or amplitude information, to invert the SWC. Full waveform inversion (FWI) can use the information of the entire waveform, which can improve the accuracy of parameter estimation. This study proposes a novel SWC estimation scheme by using the FWI of GPR, optimized by the grey wolf optimizer (GWO) algorithm. The proposed scheme includes a petrophysical relationship to link the SWC with the relative dielectric permittivity, 1D GPR forward modeling, and a GWO optimization algorithm. First, numerical modeling was carried out, and the proposed scheme was applied to both noise‐free and noisy data to verify its applicability. Then, the proposed method was applied to data collected from a field experimental site. These results, derived from both synthetic and real datasets, show that the proposed inversion scheme resulted in a good match between the observed and calculated GPR data. In the numerical modeling, it was observed that the SWC could be inverted accurately, even when noise was present in the data. These demonstrate that the GWO method can be applied for the quantitative interpretation of GPR data. The proposed scheme shows potential for SWC estimation by using GPR full waveform data.

Investigating the Use of Traveltime and Reflection Tomography for Deep Learning-Based Sound-Speed Estimation in Ultrasound Computed Tomography.

Ultrasound computed tomography (USCT) quantifies acoustic tissue properties such as the speed-of-sound (SOS). Although full-waveform inversion (FWI) is an effective method for accurate SOS reconstruction, it can be computationally challenging for large-scale problems. Deep learning-based image-to-image learned reconstruction (IILR) methods can offer computationally efficient alternatives. This study investigates the impact of the chosen input modalities on IILR methods for high-resolution SOS reconstruction in USCT. The selected modalities are traveltime tomography (TT) and reflection tomography (RT), which produce a low-resolution SOS map and a reflectivity map, respectively. These modalities have been chosen for their lower computational cost relative to FWI and their capacity to provide complementary information: TT offers a direct SOS measure, while RT reveals tissue boundary information. Systematic analyses were facilitated by employing a virtual USCT imaging system with anatomically realistic numerical breast phantoms. Within this testbed, a supervised convolutional neural network (CNN) was trained to map dual-channel (TT and RT images) to a high-resolution SOS map. Single-input CNNs were trained separately using inputs from each modality alone (TT or RT) for comparison. The accuracy of the methods was systematically assessed using normalized root mean squared error (NRMSE), structural similarity index measure (SSIM), and peak signal-to-noise ratio (PSNR). For tumor detection performance, receiver operating characteristic analysis was employed. The dual-channel IILR method was also tested on clinical human breast data. Ensemble average of the NRMSE, SSIM, and PSNR evaluated on this clinical dataset were 0.2355, 0.8845, and 28.33 dB, respectively.

Bayesian time‐lapse full waveform inversion using Hamiltonian Monte Carlo

AbstractTime‐lapse images carry out important information about dynamic changes in Earth's interior, which can be inferred using different full waveform inversion schemes. The estimation process is performed by manipulating more than one seismic dataset, associated with the baseline and monitors surveys. The time‐lapse variations can be so minute and localized that quantifying the uncertainties becomes fundamental to assessing the reliability of the results. The Bayesian formulation of the full waveform inversion problem naturally provides confidence levels in the solution, but evaluating the uncertainty of time‐lapse seismic inversion remains a challenge due to the ill‐posedness and high dimensionality of the problem. The Hamiltonian Monte Carlo can effectively sample over high‐dimensional distributions with affordable computational efforts. In this context, we explore the sequential approach in a Bayesian fashion for time‐lapse full waveform inversion using the Hamiltonian Monte Carlo method. The idea relies on integrating the baseline survey information as prior knowledge to the monitor estimation. We compare this methodology with a parallel scheme in perfect and a simple perturbed acquisition geometry scenario considering the Marmousi and a typical Brazilian pre‐salt velocity model. We also investigate the correlation effect between baseline and monitor samples on the propagated uncertainties. The results show that samples between different surveys are weakly correlated in the sequential case, while the parallel strategy provides time‐lapse images with lower dispersion. Our findings demonstrate that both methodologies are robust in providing uncertainties even in non‐repeatable scenarios.

Variational prior replacement in Bayesian inference and inversion

SUMMARY Many scientific investigations require that the values of a set of model parameters are estimated using recorded data. In Bayesian inference, information from both observed data and prior knowledge is combined to update model parameters probabilistically by calculating the posterior probability distribution function. Prior information is often described by a prior probability distribution. Situations arise in which we wish to change prior information during the course of a scientific project. However, estimating the solution to any single Bayesian inference problem is often computationally costly, as it typically requires many model samples to be drawn, and the data set that would have been recorded if each sample was true must be simulated. Recalculating the Bayesian inference solution every time prior information changes can therefore be extremely expensive. We develop a mathematical formulation that allows the prior information that is embedded within a solution, to be changed using variational methods, without recalculating the original Bayesian inference. In this method, existing prior information is removed from a previously obtained posterior distribution and is replaced by new prior information. We therefore call the methodology variational prior replacement (VPR). We demonstrate VPR using a 2-D seismic full waveform inversion example, in which VPR provides similar posterior solutions to those obtained by solving independent inference problems using different prior distributions. The former can be completed within minutes on a laptop computer, whereas the latter requires days of computations using high-performance computing resources. We demonstrate the value of the method by comparing the posterior solutions obtained using three different types of prior information: uniform, smoothing and geological prior distributions.

Envelope Inversion with Source encoding for Ultrasound Computed Tomography

Abstract 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.

Deep-learning optimization using the gradient of a custom objective function: A full-waveform inversion example study on the convolutional objective function

The integration of conventional high-performance full-waveform inversion (FWI) algorithms with deep-learning frameworks is an innovative and promising research direction with the potential to enhance and broaden the application prospects of this field significantly. Automatic differentiation with backpropagation techniques can derive the gradients of model parameters in an equivalent manner to that of adjoint methods; however, it requires a substantial amount of computer memory, particularly when considering the time-step layers. In addition, some excellent objective functions suitable for FWI are not available in deep-learning frameworks. In comparison, the adjoint method, based on effective boundary storage technology, offers greater practicality for calculating the gradients of various objective functions. Therefore, this paper develops a novel approach toward FWI that integrates deep-learning optimization with high-performance gradient computation. In particular, our method inputs model parameter gradients from a custom objective function into the deep-learning framework. Herein, we use the acoustic equation with variable density as an example to demonstrate how a convolutional objective function, along with its corresponding velocity and density gradients, can be used for optimized inversion, multiscale inversion, and deep network parameterization-based multiscale inversion within the deep-learning framework. This approach provides a paradigm for deep-learning-optimized FWI, which we apply to synthetic and field data scenarios.

Full Waveform Inversion Based on Dynamic Time Warping and Application to Reveal the Crustal Structure of Western Yunnan, Southwest China

AbstractWe develop a 3D full waveform inversion (FWI) method based on dynamic time warping (DTW) to address the issue of cycle‐skipping, which can prohibit the convergence of conventional FWI methods. DTW globally compares data samples at different time steps in 2D matrices against the time shifts of waveforms. We introduce the concept of shape descriptors into softDTW, creating a soft‐shapeDTW objective function within our waveform inversion process to improve alignment accuracy. Additionally, including constraints from Sakoe‐Chiba bands in the inversion further enhances efficiency and overall performance. A synthetic test has shown that the soft‐shapeDTW inversion outperforms conventional waveform inversions in overcoming the cycle‐skipping challenges that arise from poor initial models. This method was applied to fit observed seismograms to reveal western Yunnan's crustal structure. Seismic waveforms were recorded by 88 broadband stations from 10 local earthquakes, which were then denoised using a continuous wavelet transform method. Generalized cut and paste waveform inversions were used to determine the source parameters of these seismic events. Our inversion well‐aligned various seismic phases in the selected time windows of seismograms, and the resolved velocity models well associate with local geological structure. Results suggest that the soft‐shapeDTW inversion offers a robust alternative to FWI, reducing the reliance on accurate starting models.

Truncated Newton full waveform inversion method for the human brain imaging

Abstract It has been shown that full-waveform inversion (FWI) method can be a competitive alternative for medical imaging problems. It offers high-resolution results while delivering the advantages of being fast, safe, portable, and affordable, compared to magnetic resonance imaging (MRI) and x-ray computed tomography. However, to the best of our knowledge, FWI applications in medical imaging only use the first-order derivative information. In this case, the high parameter contrasts between different tissues of human body and multi-scatterings problems may lead FWI to local minima. Thus, we present a competitive truncated Newton method for high-resolution imaging of the human brain. This truncated Newton method, based on the efficient linear solver MINRES-QLP, can make full use of multiple scattering wavefield information. Compared with the truncated Newton method based on conjugate gradient, the MINRES-QLP iterative method presents various advantages when solving linear systems, such as the capacity to handle both non-singular and singular systems, less computational cost, and efficiency even for ill-conditioned systems. Numerical experiments for imaging the brain with and without the skull are conducted. Numerical results indicate that, compared with the truncated Newton method based on conjugate gradient, the truncated Newton method based on MINRES-QLP exhibits computational efficiency while maintaining the same level of accuracy.