Wavefield Reconstruction Research Articles

Phase shift migration with absorbing boundary condition for full-matrix imaging heterogenous medium with high quality

Ultrasonic imaging with phased array has been widely employed for nondestructive testing in various fields. Phase shift migration (PSM) is a significant imaging method and shows great advantages for multilayer structures. However, the artifact reflections at the edges of the calculation region emerge in the wavefield reconstruction process, which greatly deteriorate the imaging quality of PSM. To overcome this problem, two absorbing boundary conditions for the wavefield extrapolation of PSM are proposed in this paper. The first absorbing boundary condition renders elements in the boundary regions lower weights in frequency-space domain. The second one follows a nonstationary phase shift scheme and filters the incident waves in the boundary regions in frequency-wavenumber domain. The implementing schemes of the absorbing boundary conditions for both homogenous and heterogenous medium are developed, and the full-matrix imaging method with absorbing boundary conditions is proposed. According to the simulation and experiment, the proposed boundary conditions have strong ability to suppress the background artifacts, and they can improve the signal-to-noise ratio (SNR) and resolution by 2 times when imaging heterogenous medium. Further experiments indicate that the boundary conditions are insensitive to the window functions, and a width of one-sixteenth the length of the scan line is recommended for the absorbing boundary conditions.

Effective seismic force retrieval from surface measurement for SH-wave reconstruction

We present a new method to obtain dynamic body force at virtual interfaces to reconstruct shear wave motions induced by a source outside a truncated computational domain. Specifically, a partial differential equation (PDE)-constrained optimization method is used to minimize the misfit between measured motions at a limited number of sensors on the ground surface and their counterparts reconstructed from optimized forces. Numerical results show that the optimized forces accurately reconstruct the targeted ground motions in the surface and the interior of the domain. The proposed optimization framework yields a particular force vector among other valid solutions allowed by the domain reduction method (DRM). Per this optimized or inverted force vector, the reconstructed wave field is identical to its reference counterpart in the domain of interest but may differ in the exterior domain from the reference one. However, we remark that the inverted solution is valid and introduce a simple post-process that can modify the solution to achieve an alternative force vector corresponding to the reference wave field. We also study the desired sensor spacing to accurately reconstruct the wave responses for a given dominant frequency of interest. We remark that the presented method is omnidirectionally applicable in terms of the incident angle of an incoming wave and is effective for any given material heterogeneity and geometry of layering of a reduced domain. The presented inversion method requires information on the wave speeds and dimensions of only a reduced domain. Namely, it does not need any information on the geophysical profile of an enlarged domain or a seismic source profile outside a reduced domain. Thus, the computational cost of the method is compact even though it leads to the high-fidelity reconstruction of wave response in the reduced domain, allowing for studying and predicting ground and structural responses using real seismic measurements.

Speckle-free compact holographic near-eye display using camera-in-the-loop optimization with phase constraint.

We present a compact holographic near-eye display system with high-quality speckle-free optical reconstructions using camera-in-the-loop (CITL) optimization with phase constraint strategy. The CITL optimization with phase constraint is used to iteratively synthesize the computer-generated holograms (CGHs) based on the in-system optical feedback. The phase constraint embedded into the whole CGH optimization process can effectively smooth the phase profile of reconstructed wave field, which helps to suppress the speckle noise caused by the phase singularities in CGH reconstruction. Numerical and optical experiments have been performed to demonstrate that the proposed method can provide speckle-free optical reconstructions with excellent image fidelity for holographic near-eye display in a compact setup.

Seismic wavefield reconstruction based on compressed sensing using data-driven reduced-order model

SUMMARYReconstruction of the distribution of ground motion due to an earthquake is one of the key technologies for the prediction of seismic damage to infrastructure. Particularly, the immediate reconstruction of the spatially continuous wavefield is valuable for decision-making of disaster response decisions in the initial phase. For a fast and accurate reconstruction, utilization of prior information is essential. In fluid mechanics, full-state recovery, which recovers the full state from sparse observation using a data-driven model reduced-order model, is actively used. In this study, the framework developed in the field of fluid mechanics is applied to seismic wavefield reconstruction. A seismic wavefield reconstruction framework based on compressed sensing using the data-driven reduced-order model (ROM) is proposed and its characteristics are investigated through numerical experiments. The data-driven ROM is generated from the data set of the wavefield using the singular value decomposition. The spatially continuous seismic wavefield is reconstructed from the sparse and discrete observation and the data-driven ROM. The observation sites used for reconstruction are effectively selected by the sensor optimization method for linear inverse problems based on a greedy algorithm. The proposed framework was applied to simulation data of theoretical waveform with the subsurface structure of the horizontally stratified three layers. The validity of the proposed method was confirmed by the reconstruction based on the noise-free observation. Since the ROM of the wavefield is used as prior information, the reconstruction error is reduced to an approximately lower error bound of the present framework, even though the number of sensors used for reconstruction is limited and randomly selected. In addition, the reconstruction error obtained by the proposed framework is much smaller than that obtained by the Gaussian process regression. For the numerical experiment with noise-contaminated observation, the reconstructed wavefield is degraded due to the observation noise, but the reconstruction error obtained by the present framework with all available observation sites is close to a lower error bound, even though the reconstructed wavefield using the Gaussian process regression is fully collapsed. Although the reconstruction error is larger than that obtained using all observation sites, the number of observation sites used for reconstruction can be reduced while minimizing the deterioration and scatter of the reconstructed data by combining it with the sensor optimization method. Hence, a better and more stable reconstruction of the wavefield than randomly selected observation sites can be realized, even if the reconstruction is carried out with a smaller number of observations with observation noise, by combining it with the sensor optimization method.

Deep learning super-resolution for the reconstruction of full wavefield of Lamb waves

Scanning laser Doppler vibrometer is a popular tool for the acquisition of the full wavefield of propagating guided waves, in particular Lamb waves. Signal processing of such a wavefield enables us to reveal damage in the inspected structure. However, the process of acquiring the full wavefield of guided waves is time-consuming. One possible solution to tackle this problem is to acquire the Lamb waves in a low-resolution form and then apply a compressive sensing (CS) or deep learning-based super-resolution approach to that low-resolution form of full wavefield data. In this work, we applied two deep learning-based super-resolution approaches on a large synthetic low-resolution dataset of full wavefields of propagating Lamb waves in a plate of CFRP. The developed deep learning approaches are elaborated, and the results obtained from both models are compared with the conventional CS approach. Furthermore, the validation of the proposed deep learning models in a real-world scenario is performed by an experiment on a CFRP plate with embedded Teflon inserts simulating delaminations. It is concluded that the performance of both models outperforms the conventional CS approach.

Full reconstruction of acoustic wavefields by means of pointwise measurements

A novel method for full wavefield reconstruction from pointwise measurements data collected by a vertical receiver array is proposed for geoacoustic waveguides of a shallow sea. This method is based on a generalization of the Whittaker–Shannon interpolation formula to the case of a waveguide cross-section. The generalization is obtained by means of the so-called discrete variable representation. The method can be implemented both for tonal and pulse signals. It is shown that the method is robust against array distortions and ambient noise of moderate amplitude. Efficiency of reconstruction is verified by means of numerical simulation with a model of a shallow-sea waveguide. It is shown that the presence of sound attenuation in the seabottom results in the possibility to accurately reconstruct the field using a relatively sparse receiver array.

Source wavefield reconstruction based on an implicit staggered-grid finite-difference operator for seismic imaging

Reverse time migration and full waveform inversion involve the crosscorrelation of two wavefields, propagated in the forward- and reverse-time directions, respectively. As a result, the forward-propagated wavefield needs to be stored, and then accessed to compute the correlation with the backward-propagated wavefield. Boundary-value methods reconstruct the source wavefield using saved boundary wavefields and can significantly reduce the storage requirements. However, the existing boundary-value methods are based on the explicit finite-difference (FD) approximations of the spatial derivatives. Implicit FD methods exhibit greater accuracy and thus allow for a smaller operator length. We develop two (an accuracy-preserving and a memory-efficient) wavefield reconstruction schemes based on an implicit staggered-grid FD (SFD) operator. The former uses boundary wavefields at M layers of grid points and the spatial derivatives of wavefields at one layer of grid points to reconstruct the source wavefield for a (2 M + 2)th-order implicit SFD operator. The latter applies boundary wavefields at N layers of grid points, a linear combination of wavefields at M – N layers of grid points, and the spatial derivatives of wavefields at one layer of grid points to reconstruct the source wavefield (0 ≤ N < M ). The required memory of accuracy-preserving and memory-efficient schemes is ( M +1)/ M and ( N +2)/ M times, respectively, that of the explicit reconstruction scheme. Numerical results reveal that the accuracy-preserving scheme can achieve accurate reconstruction at the cost of storage. The memory-efficient scheme with N = 2 can obtain plausible reconstructed wavefields and images, and the storage amount is 4/( M +1) of the accuracy-preserving scheme.

Reconstruction of nearshore wave fields based on physics-informed neural networks

This paper focuses on utilizing physics-informed neural networks (PINNs) to model nearshore wave transformation. The nearshore wave nets (NWnets), which integrate the prior knowledge of wave mechanics (i.e., the wave energy balance equation and dispersion relation) and fully connected neural networks, are developed to reconstruct nearshore wave fields with scarce wave measurements. The performance of the NWnets is examined by comparing the PINN outputs with numerical solutions from XBeach and experimental data over a two-dimensional alongshore uniform barred beach and a three-dimensional circular shoal, respectively. It is found that the test errors are reasonably small with wave height measurements at only three locations applied as the training data for the alongshore uniform barred beach. Moreover, the NWnets are able to reconstruct the entire wave field and capture the focusing and defocusing of wave energy with sufficient accuracy over the circular shoal when a small amount of wave height measurements from the laboratory experiment are employed as the training data. The influence of network sizes, collocation points, training points, and the resolution of wave directional spreading on the performance of the NWnets is investigated. The adaptive learning rate annealing algorithm is utilized to calculate weighting coefficients for balancing the interplay between different loss terms in the total loss functions. Several illustrative examples of transfer learning are also provided, which can accelerate the training of NWnets for modeling waves under different boundary and bathymetric conditions. Our results show that the physics-guided deep learning method is a promising tool for studying nearshore processes.

Wavefield reconstruction of pseudo-spectral reverse time migration using a one-point wide-based minimum boundary saving scheme

Wavefield reconstruction of pseudo-spectral reverse time migration using a one-point wide-based minimum boundary saving scheme

Non-Parametric Simultaneous Reconstruction and Denoising via Sparse and Low-Rank Regularization

Spatial irregular sampling and random noise are two important factors that restrict the accuracy of seismic imaging. Seismic wavefield reconstruction and denoising based on sparse representation are two popular antidotes to these two inevitable issues, respectively. This article presents a non-parametric simultaneous reconstruction and denoising via sparse and low-rank regularization that dealt with the prestack gathers efficiently and automatically. The proposed method makes no additional prior assumptions on original data other than that the seismic signal is compressible. The key parameters estimation adopts a data-driven framework without person-dependent intervention. The basic idea of the approach is to combine the two related algorithms. Thus, the sparse decomposition needs to be performed only once. We first extract the solution matrix via Fourier dictionary and then perform the reconstruction and denoising successively in the sparse domain. Obtaining a perfect interpolation result requires that the seismic data satisfy the Shannon–Nyquist sampling theorem. However, data with steep-dip events or gaps, which cannot be adequate for the procedure, are a challenge that must be faced. This work proposes to deal with the common-offset gathers, which is characterized by flat, even approximate horizontal events, to handle the under-sampling obstacle. Another excellent property of the common-offset gathers is the simple and periodic repetitive texture structure, which can be represented sparsely and accurately by the Fourier dictionary. Thus, the computational complexity of the sparse representation is reduced. Both synthetic and practical applications indicate that our algorithm is efficient and effective.

Wave-field prediction based on radar snapshots taken on a moving vessel

This paper presents a framework that is capable of producing phase-resolved wave-field prediction in real-time based on radar measurements taken off a moving vessel. Phase-resolved wave prediction capability is essential in providing the operating environment that an autonomous vessel would encounter in order to plan for maneuvering and pathway. We use Higher Order Spectral (HOS) method to generate synthetic short-crested wave-field. Based on the snapshots of wave-field as would be obtained by an X-band radar mounted on a moving vessel, we perform wave-field reconstruction and propagation using a predictive model based on linear wave theory to produce predictions of encountered wave-field in real-time. Comparisons are made between the predicted encountered wave-field and the underlying synthetic wave-field, and reasonably good agreement can be achieved considering the use of low-order model. The wave prediction capability can be further evolved into the prediction of vessel motion and structural response.

Wavefield reconstruction inversion with weak-total-variation constraint based on first arrival traveltime tomography

Wavefield reconstruction inversion with weak-total-variation constraint based on first arrival traveltime tomography

Efficient least-squares reverse time migration using local cross-correlation imaging condition

Abstract The data-domain least-squares reverse time migration (LSRTM), a promising imaging method for obtaining a high-resolution reflectivity image, can be implemented by matching the de-migrated data to the observed one. However, LSRTM requires expensive computational costs in its implementation due to tremendous memory usage (direct storage on disk/memory) for saving source wavefields and repeatable forward/backward wavefield simulations with iterations compared to conventional RTM. Although the source wavefield reconstruction technique can be used to reduce the memory usage, additional computational cost is inevitable because it is implemented during backward wavefield simulation. To alleviate the computational burden, we have developed an efficient LSRTM scheme with local cross-correlation imaging condition (LSRTM-LC), which can use pre-saved source wavefields according to the window size. Because the window size is much shorter than the total recording time for wavefield extrapolation, storing source wavefields into computer memory can be feasible. In addition, the procedure for storing source wavefields is implemented only at the first iteration because the background velocity is fixed during iterations of LSRTM. To validate the feasibility of the LSRTM-LC scheme, we have carried out several numerical tests with synthetic datasets. Numerical tests demonstrated that LSRTM-LC can provide us with equivalent de-migrated data from saved source wavefields and the gradient vector obtained from LSRTM-LC compared to those obtained from the conventional LSRTM. As a result, LSRTM-LC can generate the same quality of reflectivity models as conventional LSRTM, however, it requires less computational costs compared to conventional LSRTM.

Lensfree on-chip microscopy based on single-plane phase retrieval.

We propose a novel single-plane phase retrieval method to realize high-quality sample reconstruction for lensfree on-chip microscopy. In our method, complex wavefield reconstruction is modeled as a quadratic minimization problem, where total variation and joint denoising regularization are designed to keep a balance of artifact removal and resolution enhancement. In experiment, we built a 3D-printed field-portable platform to validate the imaging performance of our method, where resolution chart, dynamic target, transparent cell, polystyrene beads, and stained tissue sections are employed for the imaging test. Compared to state-of-the-art methods, our method eliminates image degradation and obtains a higher imaging resolution. Different from multi-wavelength or multi-height phase retrieval methods, our method only utilizes a single-frame intensity data record to accomplish high-fidelity reconstruction of different samples, which contributes a simple, robust, and data-efficient solution to design a resource-limited lensfree on-chip microscope. We believe that it will become a useful tool for telemedicine and point-of-care application.

Wavefield Reconstruction Inversion Based on the Multi-Scale Cumulative Frequency Strategy for Ground-Penetrating Radar Data: Application to Urban Underground Pipeline

High-precision detection of the underground pipelines is an indispensable part of the development and construction of cities. At present, the inversion technology for ground-penetrating radar (GPR) data is an effective means of realizing shallow-underground-space visualization in the field of geophysical exploration. However, the traditional full-waveform inversion (FWI) method usually faces the problems of strong nonlinearity of the objective function, high dependence on the initial model, and huge calculation cost. For improving the accuracy and efficiency of GPR data inversion, a wavefield reconstruction inversion (WRI) strategy is used for GPR data imaging to reduce the nonlinearity of the inversion problem and the dependence on the initial model. Then, the frequency weighting strategy and the multi-scale method are adopted to avoid the high-frequency component data dominating the optimization process and enhance the stability of inversion. In this paper, two numerical experiments of pipeline models with different materials and spacing or buried depths verified that the proposed method can effectively reconstruct the subsurface pipelines, and further performance of our algorithm on the field data verified the reliability of high-precision imaging of urban underground pipelines, which shows great potential of application in the field of high-precision detection of the urban underground pipelines.

Wavefield reconstruction and wave equation inversion for seismic surface waves

SUMMARY Surface waves are a particular type of seismic wave that propagate around the surface of the Earth, but which oscillate over depth ranges beneath the surface that depend on their frequency of oscillation. This causes them to travel with a speed that depends on their frequency, a property called dispersion. Estimating surface wave dispersion is of interest for many geophysical applications using both active and passive seismic sources, not least because the speed–frequency relationship can be used to infer the subsurface velocity structure at depth beneath the surface. We present an inversion scheme that exploits spatial and temporal relationships in the scalar Helmholtz (wave) equation to estimate dispersion relations of the elastic surface wave data in both active and passive surveys, while also reconstructing the wavefield continuously in space (i.e. between the receivers at which the wavefield was recorded). We verify the retrieved dispersive phase velocity by comparing the results to dispersion analysis in the frequency-slowness domain, and to the local calculation of dispersion using modal analysis. Synthetic elastic examples demonstrate the method under a variety of recording scenarios. The results show that despite the scalar approximation made to represent these intrinsically elastic waves, the proposed method reconstructs both the wavefield and the phase dispersion structure even in the case of strong aliasing and irregular sampling.

Time-Domain Wavefield Reconstruction Inversion Based on Unbalanced Optimal Transport

Wavefield Reconstruction Inversion (WRI) is a novel seismic inversion method with a more expansive search space and reduced non-linearity and is more robust than other conventional techniques (e.g., full waveform inversion, FWI) in terms of local minima. Most of the modifications and applications of WRI are generally employed in the frequency domain, while the current time-domain solutions for WRI are either based on rough approximations, which lead to inaccurate inversion results, or are computationally expensive due to the data-domain Hessian. Here, we will provide another perspective to address time-domain WRI and maintain its effectiveness, namely reducing non-linearity and the effects of “cycle-skipping” while ignoring the data-domain Hessian. On the basis of iteratively solving the inversion problem, the time-domain augmented wave equation is solved by approximating the reconstructed wavefield on the right as the current wavefield. Due to this approximation and the traditional <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> measurement, the reconstructed wavefield based on the poor model will be inaccurate away from the receivers, which will affect the subsequent model inversion. To alleviate this problem, we incorporate the unbalanced optimal transmission (UOT) distance measurement into the inversion. This distance measurement method can accurately obtain the best misfit between two unbalanced signals. Moreover, the accurately measured misfit with low-frequency and long-wavelength acts as an extended source of the subsequent wavefield reconstruction, ensuring the reconstructed wavefield’s accuracy based on the defective initial model without excessive additional computation. The numerical results demonstrate the accuracy and applicability of the proposed method.

An improved adjoint-based ocean wave reconstruction and prediction method

We propose an improved adjoint-based method for the reconstruction and prediction of the nonlinear wave field from coarse-resolution measurement data. We adopt the data assimilation framework using an adjoint equation to search for the optimal initial wave field to match the wave field simulation result at later times with the given measurement data. Compared with the conventional approach where the optimised initial surface elevation and velocity potential are independent of each other, our method features an additional constraint to dynamically connect these two control variables based on the dispersion relation of waves. The performance of our new method and the conventional method is assessed with the nonlinear wave data generated from phase-resolved nonlinear wave simulations using the high-order spectral method. We consider a variety of wave steepness and noise levels for the nonlinear irregular waves. It is found that the conventional method tends to overestimate the surface elevation in the high-frequency region and underestimate the velocity potential. In comparison, our new method shows significantly improved performance in the reconstruction and prediction of instantaneous surface elevation, surface velocity potential and high-order wave statistics, including the skewness and kurtosis.

Full Reconstruction of Acoustic Wavefields by Means of Pointwise Measurements

Sound propagation in the ocean is considered. We demonstrate a novel algorithm for full wavefield reconstruction using pointwise measurements by means of a vertical array. The algorithm is based on the so-called discrete variable representation and can be implemented both for tonal and pulse signals. It is shown that the algorithm is robust against array distortions and ambient noise of moderate amplitude. Efficiency of reconstruction is verified by means of numerical simulation with a model of a shallow-sea waveguide. It is found that the effect of bottom sound attenuation enables accurate reconstruction with arrays having relatively low density of hydrophones.

Wavefield Reconstruction Inversion via Physics-Informed Neural Networks

Wavefield reconstruction inversion (WRI) formulates a PDE-constrained optimization problem to reduce cycle skipping in full-waveform inversion (FWI). WRI is often implemented by solving for the frequency-domain representation of the wavefield using the finite-difference method. The approach requires matrix inversions and affords limited flexibility to accommodate irregular model geometries. On the other hand, the physics-informed neural network (PINN) uses the underlying physical laws as loss functions to train the neural network (NN) to provide flexible continuous functional approximations of the solutions without matrix inversions. By including a data-constrained term in the loss function, the trained NN can reconstruct a wavefield that simultaneously fits the recorded data and satisfies the Helmholtz equation for a given initial velocity model. Using the predicted wavefields, we rely on a small-size NN to predict the velocity using the reconstructed wavefield. In this velocity prediction NN, spatial coordinates are used as input data to the network, and the scattered Helmholtz equation is used to define the loss function. After we train this network, we are able to predict the velocity in the domain of interest. We develop this PINN-based WRI method and demonstrate its potential using a part of the Sigsbee2A model and a modified Marmousi model. The results show that the PINN-based WRI is able to invert for a reasonable velocity with very limited iterations and frequencies, which can be used in a subsequent FWI application.