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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

Multiscale and Layer-Stripping Wave-Equation Dispersion Inversion of Rayleigh Waves

The iterative wave-equation dispersion inversion can suffer from the local minimum problem when inverting seismic data from complex Earth models. We develop a multiscale, layer-stripping method to alleviate the local minimum problem of wave-equation dispersion inversion of Rayleigh waves and improve the inversion robustness. We first invert the high-frequency and near-offset data for the shallow S-velocity model, and gradually incorporate the lower-frequency components of data with longer offsets to reconstruct the deeper regions of the model. We use a synthetic model to illustrate the local minima problem of wave-equation dispersion inversion and how our multiscale and layer-stripping wave-equation dispersion inversion method can mitigate the problem. Here, we demonstrate the efficacy of our new method using field Rayleigh-wave data.

58 GEOSCIENCES↗
DOE OSTI2023

Solving Seismic Wave Equations on Variable Velocity Models With Fourier Neural Operator

Here, in the study of subsurface seismic imaging, solving the acoustic wave equation is a pivotal component in existing models. The advancement of deep learning (DL) enables solving partial differential equations (PDEs), including wave equations, by applying neural networks to identify the mapping between the inputs and the solution. This approach can be faster than traditional numerical methods when numerous instances are to be solved. Previous works that concentrate on solving the wave equation by neural networks consider either a single velocity model or multiple simple velocity models, which is restricted in practice. Instead, inspired by the idea of operator learning, this work leverages the Fourier neural operator (FNO) to effectively learn the frequency domain seismic wavefields under the context of variable velocity models. We also propose a new framework paralleled FNO (PFNO) for efficiently training the FNO-based solver given multiple source locations and frequencies. Numerical experiments demonstrate the high accuracy of both FNO and PFNO with complicated velocity models in the OpenFWI datasets. Furthermore, the cross-dataset generalization test verifies that PFNO adapts to out-of-distribution velocity models. Finally, PFNO admits higher computational efficiency on large-scale testing datasets than the traditional finite-difference method. The aforementioned advantages endow the FNO-based solver with the potential to build powerful models for research on seismic waves.

58 GEOSCIENCES↗
DOE OSTI2019

Quantum algorithm for simulating the wave equation

We present a quantum algorithm for simulating the wave equation under Dirichlet and Neumann boundary conditions. The algorithm uses Hamiltonian simulation and quantum linear system algorithms as subroutines. It relies on factorizations of discretized Laplacian operators to allow for polynomially improved scaling in truncation errors and improved scaling for state preparation relative to general purpose quantum algorithms for solving linear differential equations. Relative to classical algorithms for simulating the D-dimensional wave equation, our quantum algorithm achieves exponential space savings and achieves a speedup which is polynomial for fixed D and exponential in D. Furthermore, we also consider using Hamiltonian simulation for Klein-Gordon equations and Maxwell's equations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Efficient 3-D velocity model building using joint inline and crossline plane-wave wave-equation migration velocity analyses

SUMMARY Wave-equation migration velocity analysis (WEMVA) is an image-domain inversion method for velocity model building. Automatic plane-wave WEMVA (PWEMVA) calculates the moveouts of plane-wave common-image gathers (CIGs) by searching a best-fitting parabola with semblance analysis and backprojects residual CIG moveouts into wavefield wave paths with a reflection tomographic kernel. However, 3-D PWEMVA is very computationally expensive because 3-D reflection tomographic inversion requires at least five 3-D reverse-time migrations per iteration and stores two types of source wavefields at model boundaries. We develop a joint inline and crossline PWEMVA method for efficient 3-D velocity model building. We alternatively implement the inline and crossline PWEMVAs with a constraint for each other, in which we iteratively construct the 3-D velocity model update through 1-D spline interpolation of 2-D gradients. The inline and crossline joint inversion is practical since PWEMVA only inverts for low-wavenumber velocity perturbations along wave paths, and the method can take less than 1 per cent of the computational cost of full 3-D PWEMVA. To construct unaliased plane waves for our joint inline and crossline PWEMVA, we develop a 3-D data interpolation method in the frequency–wavenumber (FK) domain to recover regularly and randomly missing traces. The method minimizes the misfit on sufficiently localized data subsets with iterative optimal step lengths and a gradient preconditioner that iteratively selects dominant dips along different azimuths. In numerical experiments, we use a 3-D synthetic seismic data set and a land 3-D field seismic data set acquired at the Farnsworth CO2-EOR (enhanced oil recovery) field to demonstrate the efficacy of our velocity model building and data interpolation methods.

Liu, Xuejian↗
DOE OSTI2019

Joint PP and PS plane-wave wave-equation migration-velocity analysis

Conventional joint PP and PS velocity analysis is based on ray tomography. We develop a joint PP and PS wave-equation migration-velocity-analysis method using plane-wave common-image gathers (CIGs) to produce accurate P- and S-wave velocity models. The objective function of our new method consists of three terms: The first and second terms penalize the moveout residuals computed from PP and PS plane-wave CIGs, respectively, and the third term constrains the nonzero relative depth shifts between the PP and PS migration images. The moveout of plane-wave CIGs is automatically picked using a semblance analysis method, and the relative depth shifts between the PP and PS images are automatically computed using dynamic warping or manually picking the depths of certain primary reflectors. The moveout residuals and the relative depth shifts are transformed into weighted image perturbations, and they are then projected into the velocity models to update the P- and S-wave velocity models using the scalar-wave equations and their linearized forms. Here, numerical tests with synthetic and multicomponent field data demonstrate that our method can simultaneously invert for accurate P- and S-wave velocity models for elastic migration.

58 GEOSCIENCES↗
DOE OSTI2021

Decoupled Fréchet kernels based on a fractional viscoacoustic wave equation

We formulate the Fréchet kernel computation using the adjoint-state method based on a fractional viscoacoustic wave equation. We first numerically prove that both the 1/2- and the 3/2-order fractional Laplacian operators are self-adjoint. Using this property, we show that the adjoint wave propagator preserves the dispersion and compensates the amplitude, while the time-reversed adjoint wave propagator behaves identically as the forward propagator with the same dispersion and dissipation characters. Without introducing rheological mechanisms, this formulation adopts an explicit Q parameterization, which avoids the implicit Q in the conventional viscoacoustic/viscoelastic full waveform inversion (Q-FWI). In addition, because of the decoupling of operators in the wave equation, the viscoacoustic Fréchet kernel is separated into three distinct contributions with clear physical meanings: lossless propagation, dispersion, and dissipation. Here, we find that the lossless propagation kernel dominates the velocity kernel, while the dissipation kernel dominates the attenuation kernel over the dispersion kernel.

58 GEOSCIENCES↗
DOE OSTI2019

On the Cauchy Problem for the Wave Equation with Data on the Boundary

The Cauchy problem for the wave equation in Ω × ℝ with data given on some part of the boundary ∂Ω × ℝ is considered. A reconstruction algorithm for this problem based on analytic expressions is given. This result is applicable to the problem of determining a nonstationary wave field arising in geophysics, photoacoustic tomography, tsunami wave source recovery.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Hermite Methods for the Scalar Wave Equation

Arbitrary order dissipative and conservative Hermite methods for the scalar wave equation are presented here. Both methods use $(m+1)^d$ degrees of freedom per node for the displacement in $d$ dimensions; the dissipative and conservative methods achieve orders of accuracy $(2m-1)$ and $2m$, respectively. Stability and error analyses as well as implementation strategies for accelerators are also given.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Fréchet kernels based on a fractional viscoacoustic wave equation

Incorporating the seismic attenuation into the waveform inversion framework could not only improve the accuracy of the velocity model but also provide an additional Q model. Recently, we proposed a viscoacoustic wave equation assisted by the fractional Laplacian operators to accurately model the wave propagation in heterogeneous attenuating media with computational efficiency. The explicit presence of Q as a coefficient in this equation suggests the potential to conveniently develop its full waveform inversion scheme. In this study, we utilize the adjoint-state method to formulate the computation of the Fréchet kernels with respect to both velocity and attenuation based on this wave equation. These kernels will play a fundamental role in the viscoacoustic multiparameter waveform inversion.

Xing, Guangchi↗
DOE OSTI2025

The Parabolic Wave Equation Generalized to a Spatially Varying Plasma in a Vertical Magnetic Field

This report walks through the process of deriving the wave equation for a vertical wave being propagated through a spatially varying plasma in a vertical magnetic field. Additionally, this report shows how to derive the index of refraction of the plasma corresponding to three different modes of the vertical magnetic field. Finally, this paper briefly explores the next steps planned to successfully simulate and test the equations in a pre-existing phase screen scintillation code.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

An implementation of a high-order generalized finite difference method for solving the time-harmonic cold plasma wave equation in toroidal geometry

A high-order physics-informed meshless finite difference numerical technique is introduced for solving the time-harmonic cold plasma wave equation in toroidal geometries, presenting a novel application of the generalized finite difference (GFD) method to plasma wave simulations. The algorithm employs an irregular distribution of computational points, with local point density informed by the shortest wavelength derived from the cold plasma dispersion relation. Numerical stability and robustness are addressed using regularization techniques. The algorithm, implemented for two spatial dimensions, solves for the wave electric field and is demonstrated to achieve convergence rates of $\mathcal{O}$($\mathcal{h}$ $\mathcal{P}$ )⁠. Verification tests reproduce plane wave solutions, and example simulations of ion cyclotron resonance heating and electron cyclotron resonance heating demonstrate its capability, approaching realistic tokamak plasma scenarios. This work contributes to laying a foundation for the GFD method to be used in more sophisticated, optimized, and physically realistic full-wave simulations in time-harmonic plasma wave research.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Energy conservative SBP discretizations of the acoustic wave equation in covariant form on staggered curvilinear grids

In this work, we develop a numerical method for solving the acoustic wave equation in covariant form on staggered curvilinear grids in an energy conserving manner. The use of a covariant basis decomposition leads to a rotationally invariant scheme that outperforms a Cartesian basis decomposition on rotated grids. The discretization is based on high order Summation-By-Parts (SBP) operators and preserves both symmetry and positive definiteness of the contravariant metric tensor. To improve accuracy and decrease computational cost, we also derive a modified discretization of the metric tensor that leads to a conditionally stable discretization. Bounds are derived that yield a point-wise condition that can be evaluated to check for stability of the modified discretization. This condition shows that the interpolation operators should be constructed such that their norm is close to one.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Sparse Approximate Multifrontal Factorization with Butterfly Compression for High-Frequency Wave Equations

In this work, we present a fast and approximate multifrontal solver for large-scale sparse linear systems arising from finite-difference, finite-volume or finite-element discretization of high-frequency wave equations. The proposed solver leverages the butterfly algorithm and its hierarchical matrix extension for compressing and factorizing large frontal matrices via graph-distance guided entry evaluation or randomized matrix-vector multiplication-based schemes. Complexity analysis and numerical experiments demonstrate $\mathcal{O}(N\log^2 N)$ computation and $\mathcal{O}(N)$ memory complexity when applied to an $N\times N$ sparse system arising from 3D high-frequency Helmholtz and Maxwell problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Fourth Order Finite Difference Methods for the Wave Equation with Mesh Refinement Interfaces

In this work, we analyze two types of summation-by-parts finite difference operators for approximating the second derivative with variable coefficient. The first type uses ghost points, while the second type does not use any ghost points. A previously unexplored relation between the two types of summation-by-parts operators is investigated. By combining them we develop a new fourth order accurate finite difference discretization with hanging nodes on the mesh refinement interface. We take the model problem as the two-dimensional acoustic wave equation in second order form in terms of acoustic pressure, and we prove energy stability for the proposed method. Compared to previous approaches using ghost points, the proposed method leads to a smaller system of linear equations that needs to be solved for the ghost point values. Another attractive feature of the proposed method is that the explicit time step does not need to be reduced relative to the corresponding periodic problem. Numerical experiments, both for smoothly varying and discontinuous material properties, demonstrate that the proposed method converges to fourth order accuracy. A detailed comparison of the accuracy and the time-step restriction with the simultaneous-approximation-term penalty method is also presented. (An erratum is attached.)

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

D1-D5-P superstrata in 5 and 6 dimensions: separable wave equations and prepotentials

We construct the most general single-mode superstrata in 5 dimensions with ambipolar, two centered Gibbons Hawking bases, via dimensional reduction of superstrata in 6 dimensions. Previously, asymptotically AdS 3 × $\mathbb{S}$ 2 5-dimensional superstrata have been produced, giving microstate geometries of black strings in 5 dimensions. Our construction produces asymptotically AdS 2 × $\mathbb{S}$ 3 geometries as well, the first instances of superstrata describing the microstate geometries of black holes in 5 dimensions. New examples of superstrata with separable massless wave equations in both 5 and 6 dimensions are uncovered. A $\mathbb{Z}$ 2 symmetry which identifies distinct 6-dimensional superstrata when reduced to 5 dimensions is found. Finally we use the mathematical structure of the underlying hyper-Kähler bases to produce prepotentials for the superstrata fluxes in 5 dimensions and uplift them to apply in 6 dimensions as well.l.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

A WKB based preconditioner for the 1D Helmholtz wave equation

Frequency-domain full-wave solutions to the cold-plasma problem have become ubiquitous in the study of radio frequency power in fusion plasmas. However, recent efforts at extreme levels of geometric fidelity have revealed fundamental limits in the problem size that can be solved by typical sparse direct solver based methods. These limits are of particular importance in the 3D study of RF launchers, where the number of degrees of freedom required can exceed 100 million. In such cases, it would be advantageous to solve the system via iterative means, but due to the large null space of the curl-curl operator, the convergence properties of algorithms like GMRES are poor. Here we present a physics-based preconditioner in the form of a WKB solution and demonstrate the iterative solution to the frequency-domain Helmholtz problem in 1D for several cases ranging from satisfying the WKB approximation to strongly violating it.

Green, David↗
DOE OSTI2019

Integer-squared laws for global vortices in the Born–Infeld wave equations

A series of quantization identities are established for static vortex solutions governed by the Born–Infeld type actions. These identities are of a universal nature which are indifferent to the details of the models and provide refined descriptions of divergent energetic quantities.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Two body relativistic wave equations

The relativistic quantum mechanics of two interacting particles is considered. We first present a covariant formulation of kinematics and of reduced phase space, giving a short outline of the classical results. We then quantize the systems for the scalar–scalar, fermion–scalar and fermion–fermion cases. We study the spectrum and the spherical waves solutions of the free case. The interaction with central scalar and vector potentials is introduced and the explicit equations are deduced. The one particle and the non relativistic limits are recovered and the general lines for the solution of the boundary value problems are given. We make a numerical analysis of the first two cases with Coulomb interaction. For the two fermions we largely revisit the model we had previously derived in order to uniformize the description for all the three cases. In order to give a complete review we report in the Appendix some of the most interesting results obtained for atomic and mesonic systems with Coulomb and Cornell potential interactions respectively.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗