Velocity Reconstruction Research Articles

Surface Quasi Geostrophic Reconstruction of Vertical Velocities and Vertical Heat Fluxes in the Southern Ocean: Perspectives for SWOT

AbstractMesoscale currents account for 80% of the ocean's kinetic energy, whereas submesoscale currents capture 50% of the vertical velocity variance. SWOT's first sea surface height (SSH) observations have a spatial resolution an order of magnitude greater than traditional nadir‐looking altimeters and capture mesoscale and submesoscale features. This enables the derivation of submesoscale vertical velocities, crucial for the vertical transport of heat, carbon and nutrients between the ocean interior and the surface. This work focuses on a mesoscale energetic region south of Tasmania using a coupled ocean‐atmosphere simulation at km‐scale resolution and preliminary SWOT SSH observations. Vertical velocities (w), temperature anomalies and vertical heat fluxes (VHF) from the surface down to 1,000 m are reconstructed using effective surface Quasi‐Geostrophic (sQG) theory. An independent method for reconstructing temperature anomalies, mimicking an operational gridded product, is also developed. Results show that sQG reconstructs 90% of the modeled w and VHF rms at scales down to 30 km just below the mixed layer and 50%–70% of the rms for scales larger than 70 km at greater depth, with a spatial correlation of 0.6. The reconstruction is spectrally coherent for scales larger than 30–40 km at the surface, slightly degrading ( 0.55) at depth. Two temperature anomaly data sets yield similar results, indicating the dominance of w on VHF. The RMS of sQG and VHF derived from SWOT are twice as large as those derived from conventional altimetry, highlighting the potential of SWOT for reconstructing energetic meso and submesoscale dynamics in the ocean interior.

Full-waveform ultrasonic imaging for bone

Abstract This paper suggests a full-waveform ultrasonic imaging strategy for bone. A novel forward wavefield propagation is performed in the frequency-domain. To improve the efficiency of full-waveform inversion bone imaging, all relative computations are also conducted in the frequency-domain. Additionally, a conjugate gradient algorithm is employed in the inversion procedure to accelerate the reconstruction of the bone acoustic velocity. Eventually, numerical experiments on different bone models are carried out to demonstrate the effectiveness of explored imaging strategy.

On the capability of high redshift kSZ measurement with galaxy surveys

The kinematic Sunyaev-Zel'dovich (kSZ) effect has been detected at z < 1 using various techniques and data sets. The ongoing and upcoming spectroscopic galaxy surveys such as DESI (Dark Energy Spectroscopic Instrument) and PFS (Prime Focus Spectrograph) will push the detection beyond z = 1, and therefore map the baryon distribution at high redshifts. Such detection can be achieved by both the kSZ stacking and tomography methods. While the two methods are theoretically equivalent, they differ significantly in the probed physics and scales, and required data sets. Taking the combination of PFS and ACT (Atacama Cosmology Telescope) as an example, we build mocks of kSZ and galaxies, quantify the kSZ detection S/N, and compare between the two methods. We segment the PFS galaxies into three redshift bins: 0.6 < z < 1.0, 1.0 < z < 1.6, and 1.6 < z < 2.4. For tomography method, our analysis reveals that the two higher redshift bins exhibit significantly higher S/N ratios, with values of 32 and 28, respectively, compared to the first redshift bin, which yielded an S/N of 8. This is attributed to not only the increasing of electron density with redshifts, but also the larger survey volume and the reduced non-linearity, facilitating velocity reconstruction at higher redshifts. Therefore, the capability of the PFS survey to measure high redshift kSZ effect stands as a substantial advantage over other spectroscopic surveys at lower redshift. The S/N of kSZ stacking largely depends on the number of galaxy groups available from another photometric survey. But in general, its S/N is lower than that of kSZ tomography, largely due to CMB instrument noise and error in galaxy group redshift. Incorporating next-generation CMB surveys like CMB-S4, characterized by significantly reduced instrument noise and improved angular resolution, is expected to enhance tomographic detection by a factor of ten and stacking detection by fivefold. This future high S/N detection holds the promise of not only providing precise constraints on the overall baryon abundance but also initiating a new insight into baryon distribution.

A Vortex Particle-on-Mesh Method for Soap Film Simulation

This paper introduces a novel physically-based vortex fluid model for films, aimed at accurately simulating cascading vortical structures on deforming thin films. Central to our approach is a novel mechanism decomposing the film's tangential velocity into circulation and dilatation components. These components are then evolved using a hybrid particle-mesh method, enabling the effective reconstruction of three-dimensional tangential velocities and seamlessly integrating surfactant and thickness dynamics into a unified framework. By coupling with its normal component and surface-tension model, our method is particularly adept at depicting complex interactions between in-plane vortices and out-of-plane physical phenomena, such as gravity, surfactant dynamics, and solid boundary, leading to highly realistic simulations of complex thin-film dynamics, achieving an unprecedented level of vortical details and physical realism.

Coastal current convergence structures in the Bay of Biscay from optimized high-frequency radar and satellite data

The southeastern Bay of Biscay has been described as a “dead end” for floating marine litter, often accumulating along small-scale linear streaks. Coastal Current Convergence Structures (CCS), often associated with vertical motions at river plume edges, estuarine fronts, or other physical processes, can be at the origin of the accumulation. Understanding the formation of CCS and their role in the transport of marine litter is essential to better quantify and to help mitigate marine litter pollution. The Lagrangian framework, used to estimate the absolute dispersion, and the finite-size Lyapunov exponents (FSLE), have proved very effective for identifying CCS in the current velocity field. However, the quality of CCS identification depends strongly on the Eulerian fields. Two surface current velocity data sets were used in the analysis: the remotely sensed velocities from the EuskOOS High-Frequency Radar (HFR) network and velocities from three-dimensional model outputs. They were complemented by drifting buoy velocity measurements. An optimization method, involving the fusion of drifting buoys and HFR velocities is proposed to better reconstruct the fine-scale structure of the current velocity field. Merging these two sources of velocity data reduced the mean Lagrangian error and the Root Mean Square Error (RMSE) by 50 % and 30 % respectively, significantly improving velocity reconstruction. FSLE ridgelines obtained from the Lagrangian analysis of optimized velocities were compared with remotely sensed concentrations of Chlorophyll-a. It was shown that ridgelines control the spatial distribution of phytoplankton. They fundamentally represent the CCS which can potentially affect marine litter aggregation. Analysis of the absolute dispersion revealed large stirring in the alongshore direction which was also confirmed by spatial distribution of FSLE ridgelines. The alignment between FSLE ridgelines and patterns of high Chlorophyll-a concentration was observed, often determining the limits of river plume expansion in the study area.

Peculiar Velocity Reconstruction from Simulations and Observations Using Deep Learning Algorithms

In this paper, we introduce a U-Net model of deep learning algorithms for reconstructions of the 3D peculiar velocity field, which simplifies the reconstruction process with enhanced precision. We test the adaptability of the U-Net model with simulation data under more realistic conditions, including the redshift space distortion effect and halo mass threshold. Our results show that the U-Net model outperforms the analytical method that runs under ideal conditions, with a 16% improvement in precision, 13% in residuals, 18% in correlation coefficient, and 27% in average coherence. The deep learning algorithm exhibits exceptional capacities to capture velocity features in nonlinear regions and substantially improve reconstruction precision in boundary regions. We then apply the U-Net model trained under Sloan Digital Sky Survey (SDSS) observational conditions to the SDSS Data Release 7 data for observational 3D peculiar velocity reconstructions.

Inversion strategies for Q estimation in viscoacoustic full-waveform inversion

Estimation of an attenuation parameter, represented by the quality factor Q, holds paramount importance in seismic exploration. One of the main challenges in Q estimation through viscoacoustic full-waveform inversion (FWI) is effectively decoupling Q from velocity. In this study, our objective is to enhance Q inversion by addressing critical aspects, such as gradient preconditioning, workflow, and misfit design. By developing a new preconditioner that approximates the diagonal of the Hessian, we facilitate automatic parameter tuning across different classes, ensuring comparable magnitudes of preconditioned gradients for velocity and Q. Moreover, our investigations confirm the efficacy of the two-stage hierarchical strategy in mitigating velocity- Q trade-offs, enabling more accurate Q estimation by first focusing on velocity reconstruction before jointly estimating velocity and Q. The analysis and numerical examples also highlight the importance of broadband data and long-offset acquisition for a reliable Q estimation. In addition, leveraging amplitude information can improve Q estimation to some extent, but careful consideration of frequency band and noise effects is necessary. We explore two misfit functions that capture amplitude variation with frequency in the time-frequency domain, noting their sensitivity to noise. To address this, we develop a differential strategy that can effectively mitigate the effects of low-frequency noise. This comprehensive study on enhancing Q estimation in viscoacoustic FWI offers valuable insights for multiparameter inversion in realistic scenarios.

Surface velocity reconstruction of a vibrating structure based on dictionary learning and sparse sampling

The sparse regularization has been successfully applied to near-field acoustic holography to provide the reconstruction accuracy of sound field with limited number of measurements. However, most of the applications are concentrated on the reconstruction of the sound pressure and the corresponding sparse bases are designed for the sound pressure. In this study, dictionary learning is introduced and K-SVD is utilized to generate a sparse basis for the velocity. Then the reconstruction of surface velocity of a vibrating structure can be realized in a sparse framework to improve the reconstruction accuracy with limited number of measurements. In the process of data sample selection, the equivalent source method is used to generate the velocity samples according to the feature of the sound field and samples can be obtained by numerical simulations. The results of numerical simulations and experiment demonstrate the validity of the learned dictionary and the advantage of the proposed method.

Kinematic Sunyaev-Zel′dovich pairwise velocity reconstruction with machine learning

Kinematic Sunyaev-Zel′dovich pairwise velocity reconstruction with machine learning

Identifiability of spatiotemporal tissue perfusion models

Objective. Standard models for perfusion quantification in DCE-MRI produce a bias by treating voxels as isolated systems. Spatiotemporal models can remove this bias, but it is unknown whether they are fundamentally identifiable. The aim of this study is to investigate this question in silico using one-dimensional toy systems with a one-compartment blood flow model and a two-compartment perfusion model. Approach. For each of the two models, identifiability is explored theoretically and in-silico for three systems. Concentrations over space and time are simulated by forward propagation. Different levels of noise and temporal undersampling are added to investigate sensitivity to measurement error. Model parameters are fitted using a standard gradient descent algorithm, applied iteratively with a stepwise increasing time window. Model fitting is repeated with different initial values to probe uniqueness of the solution. Reconstruction accuracy is quantified for each parameter by comparison to the ground truth. Main results. Theoretical analysis shows that flows and volume fractions are only identifiable up to a constant, and that this degeneracy can be removed by proper choice of parameters. Simulations show that in all cases, the tissue concentrations can be reconstructed accurately. The one-compartment model shows accurate reconstruction of blood velocities and arterial input functions, independent of the initial values and robust to measurement error. The two-compartmental perfusion model was not fully identifiable, showing good reconstruction of arterial velocities and input functions, but multiple valid solutions for the perfusion parameters and venous velocities, and a strong sensitivity to measurement error in these parameters. Significance. These results support the use of one-compartment spatiotemporal flow models, but two-compartment perfusion models were not sufficiently identifiable. Future studies should investigate whether this degeneracy is resolved in more realistic 2D and 3D systems, by adding physically justified constraints, or by optimizing experimental parameters such as injection duration or temporal resolution.

Velocity reconstruction in the era of DESI and Rubin/LSST. II. Realistic samples on the light cone

Velocity reconstruction in the era of DESI and Rubin/LSST. II. Realistic samples on the light cone

Velocity reconstruction in the era of DESI and Rubin/LSST. I. Exploring spectroscopic, photometric, and hybrid samples

Velocity reconstruction in the era of DESI and Rubin/LSST. I. Exploring spectroscopic, photometric, and hybrid samples

A low-cost, penalty parameter-free, and pressure-robust enriched Galerkin method for the Stokes equations

This paper proposes a low-cost, penalty parameter-free, and pressure-robust Stokes solver based on the enriched Galerkin (EG) method with a discontinuous velocity enrichment function. The EG method employs the interior penalty discontinuous Galerkin (IPDG) formulation to weakly impose the continuity of the velocity function. However, despite its advantage of symmetry, the symmetric IPDG formulation requires a lot of computational effort to choose an optimal penalty parameter and compute different trace terms. To reduce such effort, we replace the derivatives of the velocity function with its weak derivatives computed by the geometric data of elements. Therefore, our modified EG (mEG) method is a penalty parameter-free numerical scheme that has reduced computational complexity and conserves the optimal convergence orders. Moreover, we achieve pressure robustness for the mEG method by employing a velocity reconstruction operator on the load vector on the right-hand side of the discrete system. The theoretical results are confirmed through numerical experiments with two- and three-dimensional examples.

Laser-induced shock wave two-dimensional extraction technology based on a beam deflection method

This paper introduces a method for analyzing the spatiotemporal progression of laser-induced shock waves using the beam deflection technique. This method allows for the accurate measurement of the shock wave evolution and can replace high-speed cameras. The results demonstrate the detection signals at various distances and energies, as well as the extraction and reconstruction of the shock wave velocities and propagation trajectories. The characteristic velocities of the shock waves propagating in air from various metals and energetic materials were measured and compared with the results obtained from high-speed cameras. The study also predicts the macroscopic detonation velocity of energetic materials based on the characteristic velocity. Overall, this approach offers a reliable and cost-effective method for studying the shock waves and has potential applications in various fields.

Recent advances in multimodal imaging in tetralogy of fallot and double outlet right ventricle.

In the ever-evolving field of medical imaging, this review highlights significant advancements in preoperative and postoperative imaging for Tetralogy of Fallot (TOF) and double outlet right ventricle (DORV) over the past 18 months. This review showcases innovations in echocardiography such as 3D speckle tracking echocardiography (3DSTE) for assessing right ventricle-pulmonary artery coupling (RVPAC) and Doppler velocity reconstruction (DoVeR) for intracardiac flow fields evaluation. Furthermore, advances in assessment of cardiovascular anatomy using computed tomography (CT) improve the integration of imaging in ablation procedures. Additionally, the inclusion of cardiac magnetic resonance (CMR) parameters as risk score predictors for morbidity, and mortality and for timing of pulmonary valve replacement (PVR) indicates its significance in clinical management. The utilization of 4D flow techniques for postoperative hemodynamic assessment promises new insights into pressure mapping. Lastly, emerging technologies such as 3D printing and 3D virtual reality are expected to improve image quality and surgical confidence in preoperative planning. Developments in multimodality imaging in TOF and DORV are poised to shape the future of clinical practice in this field.

Enhanced echocardiographic assessment of intracardiac flow in congenital heart disease.

4D flow magnetic resonance imaging (4D flow MRI) can assess and measure the complex flow patterns of the right ventricle (RV) in congenital heart diseases, but its limited availability makes the broad application of intracardiac flow assessment challenging. Color Doppler imaging velocity reconstruction from conventional echocardiography is an emerging alternative, but its validity against 4D flow MRI needs to be established. To compare intracardiac flow parameters measured by color Doppler velocity reconstruction (DoVeR) against parameters measured from 4D flow MRI. We analyzed 20 subjects, including 7 normal RVs and 13 abnormal RVs (10 with repaired Tetralogy of Fallot, and 3 with atrial-level shunts). Intracardiac flow parameters such as relative pressure difference, vortex strength, total kinetic energy, and viscous energy loss were quantified using DoVeR and 4D flow MRI. The agreement between the two methods was determined by comparing the spatial fields and quantifying the cross-correlation and normalized difference between time-series measurements. The hemodynamic parameters obtained from DoVeR and 4D flow MRI showed similar flow characteristics and spatial distributions. The time evolutions of the parameters were also in good agreement between the two methods. The median correlation coefficient between the time-series of any parameter was between 0.87 and 0.92, and the median L2-norm deviation was between 10% to 14%. Our study shows that DoVeR is a reliable alternative to 4D flow MRI for quantifying intracardiac hemodynamic parameters in the RV.

Reconstruction of Electron Vortex in Space Plasmas

Space plasmas are turbulent and maintain different types of critical points or flow nulls. Electron vortex, as one type of flow null structure, is crucial in the energy cascade in turbulent plasmas. However, due to the limited time resolution of the spacecraft observations, one can never analyze the three-dimensional properties of the electron vortex. In the present study, with the advancement of the FOTE-V method and the unprecedented high-resolution measurements from four Magnetospheric Multiscale spacecraft, we successfully identify the electron vortex and then reconstruct its three-dimensional topology of the surrounding electron flow field. The results of the reconstruction show that the configuration of the electron vortex is elliptical. Comparison between the observation and reconstruction scales of the vortex indicates the reliable reconstruction of the flow velocity. Our study sheds light on the understanding of the topology and property of the electron vortex and its relationship with kinetic-scale magnetic holes.

3D reconstruction of horizontal and vertical quasi-geostrophic currents in the North Atlantic Ocean

Abstract. In this paper we introduce a new high-resolution (1/10°) data-driven dataset of 3D ocean currents developed by the National Research Council of Italy in the framework of the European Space Agency World Ocean Circulation project: the WOC-NATL3D dataset. The product domain extends over a wide portion of the North Atlantic Ocean from the surface down to 1500 m depth, and the dataset covers the period between 2010 and 2019. To generate this product, a diabatic quasi-geostrophic diagnostic model is applied to data-driven 3D temperature and salinity fields obtained through a deep learning technique, along with ERA5 fluxes and empirical estimates of the horizontal Ekman currents based on input provided by the European Copernicus Marine Service. The assessment of WOC-NATL3D currents is performed by direct validation of the total horizontal velocities with independent drifter estimates at various depths (0, 15 and 1000 m) and by comparing them with existing reanalyses that are obtained through the assimilation of observations into ocean general circulation numerical models. Our estimates of the ageostrophic components of the flow improve the total horizontal velocity reconstruction, being more accurate and closer to observations than model reanalyses in the upper layers, also providing an indirect proof of the reliability of the resulting vertical velocities. The reconstructed WOC-NATL3D currents are freely available at https://doi.org/10.12770/0aa7daac-43e6-42f3-9f95-ef7da46bc702 (Buongiorno Nardelli, 2022).

Self-supervised, active learning seismic full-waveform inversion

A novel recursive, self-supervised machine-learning (ML) inversion scheme is developed. It is applied for fast and accurate full-waveform inversion of land seismic data. ML generalization is enhanced by using virtual super gathers (VSGs) of field data for training. These are obtained from midpoint-offset sorting and stacking after applying surface-consistent corrections from the decomposition of the transmitted wavefield. The procedure implements reinforcement learning concepts by adopting an inversion agent to interact with the environment and explore the model space under a data misfit optimization policy. The generated parameter distributions and related forward responses are used as new training samples for supervised learning. The active learning (AL) paradigm is further embedded in the procedure, for which queries on data diversity and uncertainty are used to generate fully informative reduced sets for training. The procedure is recursive. At each cycle, the physics-based inversion is coupled to the ML predictions via penalty terms that promote a long-term data misfit reduction. The resulting self-supervised, AL, physics-driven deep-learning inversion generalizes well with field data. The method is applied to perform full-waveform inversion (FWI) of a complex land seismic data set characterized by transcurrent faulting and related structures. High signal-to-noise VSGs are inverted with a 1.5D Laplace-Fourier FWI scheme. The AL inversion procedure uses a small fraction of data for training while achieving sharper velocity reconstructions and a lower data misfit when compared with previous results. AL FWI is highly generalizable and effective for land seismic velocity model building and for other inversion scenarios.

Natural surface floaters in image-based river surface velocimetry: Insights from a case study

This study focuses on utilizing image techniques for river velocity measurement, with a specific emphasis on natural surface floating patterns. Employing a multi-camera system, we conducted 3D measurements on river surfaces, including surface velocity and water surface reconstruction. A pattern-based tracking approach has been adopted to improve the performance of image measurements on different types of natural floating tracers. The study employs the following approaches: 3D Lagrangian Pattern Tracking Velocimetry (3D-LPTV), 2D Lagrangian Pattern Velocimetry (2D- LPTV), and Large-scale Particle Image Velocimetry (LSPIV), for surface velocity estimation. The outcomes revealed that all three approaches yielded consistent results in terms of averaged velocity. However, the LSPIV method produced about two times higher uncertainty in measured velocities compared to the other methods. A strategy to assess the quality of river surface patterns in velocity estimation is presented. Specifically, the sum of squared interrogation area intensity gradient (SSIAIG) was found to be strongly correlated with measurement uncertainty. Additionally, a term related to the peak sidelobe ratio (PSR) of the cross-correlation map was found as an effective constraint, ensuring the image-tracking process achieves high reliability. The precision of measurements increases corresponding to the increase of image intensity gradient and PSR.