Propagation In Heterogeneous Media Research Articles

On the viscoelastic-electromagnetic-gravitational analogy

The analogy between electromagnetism and gravitation was achieved by linearizing the tensorial gravitational equations of general relativity and converting them into a vector form corresponding to Maxwell’s electromagnetic equations. On this basis, we use the equivalence with viscoelasticity and propose a theory of gravitational waves. We add a damping term to the differential equations, which is equivalent to Ohm’s law in electromagnetism and Maxwell’s viscosity in viscoelasticity, to describe the attenuation of the waves. The differential equations in viscoelasticity are those of cross-plane shear waves, commonly referred to as SH waves. A plane-wave analysis gives the phase velocity, the energy velocity, the quality factor and the attenuation factor of the field as well as the energy balance. To obtain these properties, we use the analogy with viscoelasticity; the properties of electromagnetic and gravitational waves are similar to those of shear waves. The presence of attenuation means that the transient field is generally a composition of inhomogeneous (non-uniform) plane waves, where the propagation and attenuation vectors do not point in the same direction and the phase velocity vector and the energy flux (energy velocity) are not collinear. The polarization of cross-plane field is linear and perpendicular to the propagation-attenuation plane, while the polarization of the field within the plane is elliptical. Transient wave fields in the space–time domain are analyzed with the Green function (in homogeneous media) and with a grid method (in heterogeneous media) based on the Fourier pseudospectral method for calculating the spatial derivatives and a Runge–Kutta scheme of order 4 for the time stepping. In the examples, wave propagation at the Sun-Earth and Earth-Moon distances using quadrupole sources is considered in comparison to viscoelastic waves. The Green and grid solutions are compared to test the latter algorithm. Finally, an example of propagation in heterogeneous media is presented.

Efficient modeling of fractional Laplacian viscoacoustic wave equation with fractional finite-difference method

The fractional viscoacoustic/viscoelastic wave equation, which accurately quantifies the frequency-independent anelastic effects, has been the focus of seismic industry in recent years. The pseudo-spectral (PS) method stands as one of the most widely used numerical methods for solving the fractional wave equation. However, the PS method often suffers from low accuracy and efficiency, particularly when modeling wave propagation in heterogeneous media. To address these issues, we propose a novel and efficient fractional finite-difference (FD) method for solving the wave equation with fractional Laplacian operators. This method develops an arbitrary high-order FD operator via the generating function of our fractional FD (F-FD) scheme, enhancing accuracy with L2-optimal FD coefficients. Similar to classic FD methods, our F-FD method is characterized by straightforward programming and excellent 3D extensibility. It surpasses the PS method by eliminating the need for Fast Fourier Transform (FFT) and inverse-FFT (IFFT) operations at each time step, offering significant benefits for 3D applications. Consequently, the F-FD method proves more adept for wave-equation-based seismic data processes like imaging and inversion. Compared with existing F-FD methods, our approach uniquely approximates the entire fractional Laplacian operator and stands as a local numerical algorithm, with an adjustable F-FD operator order based on model parameters for enhanced practicality. Accuracy analyses confirm that our method matches the precision of the PS method with a correctly ordered F-FD operator. Numerical examples show that the proposed method has good applicability for complex models. Finally, we have carried out reverse time migration on the Marmousi-2 model, and the imaging profiles indicate that the proposed method can be effectively applied to seismic imaging, demonstrating good practicability.

A quantum computing concept for 1-D elastic wave simulation with exponential speedup

SUMMARY Quantum computing has attracted considerable attention in recent years because it promises speedups that conventional supercomputers cannot offer, at least for some applications. Though existing quantum computers (QCs) are, in most cases, still too small to solve significant problems, their future impact on domain sciences is already being explored now. Within this context, we present a quantum computing concept for 1-D elastic wave propagation in heterogeneous media with two components: a theoretical formulation and an implementation on a real QC. The method rests on a finite-difference approximation, followed by a sparsity-preserving transformation of the discrete elastic wave equation to a Schrödinger equation, which can be simulated directly on a gate-based QC. An implementation on an error-free quantum simulator verifies our approach and forms the basis of numerical experiments with small problems on the real QC IBM Brisbane. The latter produce simulation results that qualitatively agree with the error-free version but are contaminated by quantum decoherence and noise effects. Complementing the discrete transformation to the Schrödinger equation by a continuous version allows the replacement of finite differences by other spatial discretization schemes, such as the spectral-element method. Anticipating the emergence of error-corrected quantum chips, we analyse the computational complexity of the best quantum simulation algorithms for future QCs. This analysis suggests that our quantum computing approach may lead to wavefield simulations that run exponentially faster than simulations on classical computers.

A time-domain SGFD-FK hybrid method for 2D teleseismic elastic wave modeling and inversion

AbstractFull waveform inversion (FWI) has proved to be a reliable tool for high-resolution imaging of lithospheric structures at various depths down to the upper mantle. However, when the size of the model is large, the computational burden is significative and applications are restricted to low frequencies. To tackle this issue, we developed a new 2D time-domain hybrid method to simulate high-frequency teleseismic body waves propagating through a local heterogeneous elastic Earth model: The frequency-wavenumber (FK) integration method is coupled with the staggered grid finite difference method (SGFD). The FK method is used to compute the wavefield due to obliquely incident plane P and SV waves in a 1D multilayered half space that excites a local heterogeneous region. Inside this region, the velocity-stress staggered grid FD method (SGFD) is used to accurately deal with wave propagation in heterogeneous media. Spurious waves that might be generated at the boundaries of the local region are avoided using convolutional perfectly matched layers (CPML). This new hybrid method inherits the low-memory requirements of the FK method and the accuracy, efficiency and easy implementation of the SGFD. The new hybrid method is benchmarked against the analytical FK method for some canonical models and shows good agreement with analytical solutions. Subsequently, our modeling tool is incorporated into a full waveform inversion algorithm adapted for teleseismic configurations to invert the incident P wave and its coda. The inversion is carried out using a gradient approach that is efficiently implemented via the adjoint-state method. The results suggest that our hybrid method and FWI algorithm represent a valuable tool for 2D forward and inverse regional applications using teleseismic data sets.

Single and multiple scattering quantitative ultrasound methods in muscle

Increased intramuscular fat—or fatty infiltration (FI)—often develops as a consequence of various musculoskeletal and neuromuscular disorders. FI is an important factor for the assessment and intervention of surgical candidacy. Therefore, there is a need for an accessible, non-invasive quantitative, and objective evaluation of FI in muscle. We can exploit the complexity of ultrasound wave propagation in heterogeneous media to extract quantitative features of the fat distribution in muscle. From finite-difference time-domain simulations conducted with maps created from magnetic resonance imaging scans of healthy and injured shoulders, we acquire radiofrequency (RF) ultrasound data. Single and multiple scattering (SS and MS) components of the RF data are separated by using singular value decomposition and eigenvalue thresholding. Spectral and envelope quantitative ultrasound (QUS) parameters are computed from the SS component. MS-based QUS parameters are obtained by extracting the diffusion constant and tracking the SS intensity decay rate. We investigate the relationship between SS and MS-based QUS parameters and an increasing FI, because more FI will lead to more multiple scattering and modified ultrasonic signatures.

A Hybrid Chebyshev Pseudo-Spectral Finite-Difference Time-Domain Method for Numerical Simulation of 2D Acoustic Wave Propagation

In this study, a hybrid Chebyshev pseudo-spectral finite-difference time-domain (CPS-FDTD) algorithm is proposed for simulating 2D acoustic wave propagation in heterogeneous media, which is different from the other traditional numerical schemes such as finite element and finite difference. This proposed hybrid method integrates the efficiency of the FDTD approach in the time domain and the high accuracy of the CPS technique in the spatial domain. We present the calculation formulas of this novel approach and conduct simulation experiments to test it. The biconjugate gradient is solved by combining the large symmetric sparse systems stabilized algorithm with an incomplete LU factorization. Three numerical experiments are further presented to illustrate the accuracy, efficiency, and flexibility of the hybrid CPS-FDTD algorithm.

A theragnostic HIFU transducer and system for inherently registered imaging and therapy.

One big challenge with high intensity focused ultrasound (HIFU) is the difficulty in accurate prediction of focal location due to the complex wave propagation in heterogeneous medium even with imaging guidance. This study aims to overcome this by combining therapy and imaging guidance with one single HIFU transducer using the vibro-acoustography (VA) strategy. Based on the VA imaging method, a HIFU transducer consisting of 8 transmitting elements was proposed for therapy planning, treatment and evaluation. Inherent registration between the therapy and imaging created unique spatial consistence in HIFU transducer's focal region in the above three procedures. Performance of this imaging modality was first evaluated through in-vitro phantoms. In-vitro and ex-vivo experiments were then designed to demonstrate the proposed dual-mode system's ability in conducting accurate thermal ablation. Point spread function of the HIFU-converted imaging system had a full wave half maximum of about 1.2 mm in both directions at a transmitting frequency of 1.2 MHz, which outperformed the conventional ultrasound imaging (3.15 MHz) in in-vitro situation. Image contrast was also tested on the in-vitro phantom. Various geometric patterns could be accurately 'burned out' on the testing objects by the proposed system both in vitro and ex vivo. Implementation of imaging and therapy with one HIFU transducer in this manner is feasible and it has potential as a novel strategy for addressing the long-standing problem in the HIFU therapy, possibly pushing this non-invasive technique forward towards wider clinical applications.

Магнитное поле многовитковой цилиндрической катушки с ферромагнитным сердечником в непосредственной близости от металлических конструкций в задаче поиска людей под завалами в шахтах

Some aspects of the low-frequency magnetic field propagation in heterogeneous medium in mines are discussed in the paper. The theoretical model for calculation of magnetic field distribution in case of the parallel axis of transmitting antenna and bulk metal is developed. Metal structures are rail tracks, magnetic antenna is multiturn cylindrical coil with ferromagnetic core. Magnetic field according to proposed models principle in several stages using the method of integral equations was numerical calculated. This method of calculation of magnetic field in considered inhomogeneous space is based. The calculations of magnetic field strength of the multiturn cylindrical coil with ferromagnetic core in nearby proximity and at various distances from bulk metal were carried out. The possibility of use of low-frequency magnetic field attenuation for people search under avalanches was proved.

P-SV-wave propagation in heterogeneous media: Velocity-stress distributional finite-difference method

We have developed a 2D distributional-finite-difference (DFD) algorithm for modeling the propagation of seismic waves in heterogeneous media in the time domain. We revisit the classic staggered finite-difference algorithm by substituting the standard finite-difference operators with the recently introduced DFD operators with the methodological differences we underline. We find that the DFD operators improve the simulation accuracy while maintaining the simple structure of the finite-difference algorithm. Thanks to its weak formalism, the newly developed algorithm accurately and naturally accounts for the free surface, which is a substantial improvement for finite-difference approaches. Moreover, we develop an efficient factorization for the DFD operators. It limits the computational cost of the proposed algorithm to twice that of the finite-difference algorithm. Numerical examples demonstrate that the extra computational burden is well compensated by the superior accuracy of the DFD operators.

A Novel Coupled Meshless Model for Simulation of Acoustic Wave Propagation in Infinite Domain Containing Multiple Heterogeneous Media

This study presents a novel coupled meshless model for simulating acoustic wave propagation in heterogeneous media, based on the singular boundary method (SBM) and Kansa’s method (KS). In the proposed approach, the SBM was used to model the homogeneous part of the propagation domain, while KS was employed to model a heterogeneity. The interface compatibility conditions associated with velocities and pressures were imposed to couple the two methods. The proposed SBM–KS coupled approach combines the respective advantages of the SBM and KS. The SBM is especially suitable for solving external sound field problems, while KS is attractive for nonlinear problems in bounded non-homogeneous media. Moreover, the new methodology completely avoids grid generation and numerical integration compared with the finite element method and boundary element method. Numerical experiments verified the accuracy and effectiveness of the proposed scheme.

Numerical simulation of anti-plane wave propagation in heterogeneous media

This paper formulates a semi-analytical boundary meshless method, the singular boundary method (SBM), to simulate the anti-plane wave motion in the heterogeneous media. Two different continuous inhomogeneity variations are studied, and the corresponding fundamental solutions are derived by means of a simple variable transformation. The derivation reveals that the fundamental solutions are determined by the wavenumbers of the resulted governing equations after the variable transformation. The source singularities of these fundamental solutions are overcome by the novel origin intensity factors (OIFs). The fundamental solutions and OIFs make the SBM applicable for the simulation of the anti-plane wave scattering and diffraction in nonhomogeneous media. Numerical experiments, including the finite and semi-infinite cases with different variations and boundary conditions, are presented to illustrate the convergence, accuracy and effectiveness of the proposed SBM.

Implementing a non-local lattice particle method in the open-source large-scale atomic/molecular massively parallel simulator

Using conventional continuum-based simulation frameworks to model crack initiation and extension can be computationally challenging. As an alternative to continuum-based approaches, particle-based simulation methods are well-suited to handle the discontinuities present during fracture propagation. A well-known particle-based method is the lattice particle method (LPM), which discretizes the system into a set of interconnected particles ollowing a periodic arrangement. Discontinuities can be handled simply by removing bonds between particles. For this reason, LPM-based simulations have been employed to simulate fracture propagation in heterogeneous media, notably in civil engineering and biomaterials applications. However, a practical limitation of this method is the absence of implementation within a commonly-used software platform. This work describes such an implementation of a non-local LPM within the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS). Specifically, we implemented a new LAMMPS bond style with a many-body term to tune Poisson’s ratios. In order to validate the nonlocal formalism and our implementation of this method within LAMMPS, simulated elastic properties are compared to analytical solutions reported in the literature. Good agreement between simulated and analytical values is found for systems with positive Poisson’s ratios. The computational and parallel efficiency of the LPM-LAMMPS implementation is also benchmarked. Finally, we compare the elastic response of a 3D porous structure and an aircraft wing as calculated using the LPM and finite-element analysis.

Features of the Propagation of Long Waves in Phononic Crystals, the Influence of the Concentration and Polydispersity of the Components

The relevance of the research is determined by the need to simulate wave propagation in heterogeneous media based on phononic crystals. These studies are necessary for the tasks of flaw detection, the development of non-destructive testing methods, geophysics, engineering geophysics and other methods of acoustic research. During the study, it was determined that the fragmentation of the components of two-component phononic crystals into 2, 3, … N equal parts in the unit cell leads to a catastrophic rearrangement of the dispersion relations and the appearance of new elementary wave packets for acoustic waves. Using numerical-analytical methods, it is shown that in two-component phononic crystals, the polydispersity of the components can significantly affect the average characteristics of the propagation of long acoustic waves when the polydisperse crystal is close to monodisperse with a smaller unit cell size. For polydisperse crystals close to monodisperse with the same period (unit cell size), their averaged characteristics for long waves coincide.

An innovative inverse analysis based on the Bayesian inference for concrete material

Nondestructive tests and evaluations are robust techniques for inspecting different attributes of concrete configuration. However, most nondestructive techniques focused on an aspect of concrete configuration based on comparison to other samples. In this paper, an innovative inverse analysis technique was developed to inspect different attributes of concrete configuration simultaneously. The methodology was based on the scattering feature of the ultrasonic waves during propagation in heterogeneous media. The transition matrix method was employed to determine the scattered wavefield. This method considers the shape of objects, unlike most other numerical methods. Furthermore, a novel algorithm was presented to establish a realistic space in three-dimensional for concrete. The Voronoi diagram and shrinking process established the framework of the algorithm. The inverse model conducted observation data from media to concrete configuration through the direct model. The inverse procedure extracted vast information from the medium. Statistical theory provided statistical inference based on Bayesian statistics for this procedure. The introduced inverse analysis technique then scrutinized the concrete specimens. For this aim, geopolymer concrete with different configurations was nominated as a sample of concrete material. In the end, the precision, accuracy, and validity of the inverse model solution were assayed in the light of statistics. The assessments demonstrated that the proposed method provided a comprehensive description of the overall concrete configuration.

Dynamic formulation of phase field fracture in heterogeneous media with finite thickness cohesive interfaces

Robust numerical prediction of crack propagation in heterogeneous media has been a matter of relevant importance in many engineering applications. In this study, a modelling framework for triggering dynamic fracture events in heterogeneous media, like layered materials, with internal finite thickness cohesive interfaces is proposed through the exploitation of the combined use of the phase field approach to fracture and the interface cohesive zone model to simulate the interplay between bulk and interface cracking. The proposed formulation is constructed via a consistent variational formalism leading to a coupled system of equations, which are solved using a staggered solution scheme. Representative applications examine the robustness of the computational approach, exhibiting results consistent with experimental evidences available in the literature.

Propagation and reaction–diffusion models with free boundaries

In this short survey, we describe some recent developments on the modeling of propagation by reaction-differential equations with free boundaries, which involve local as well as nonlocal diffusion. After the pioneering works of Fisher, Kolmogorov–Petrovski–Piskunov (KPP) and Skellam, the use of reaction–diffusion equations to model propagation and spreading speed has been widely accepted, with remarkable progresses achieved in several directions, notably on propagation in heterogeneous media, models for interacting species including epidemic spreading, and propagation in shifting environment caused by climate change, to mention but a few. Such models involving a free boundary to represent the spreading front have been studied only recently, but fast progress has been made. Here, we will concentrate on these free boundary models, starting with those where spatial dispersal is represented by local diffusion. These include the Fisher–KPP model with free boundary and related problems, where both the one space dimension and high space dimension cases will be examined; they also include some two species population models with free boundaries, where we will show how the long-time dynamics of some competition models can be fully determined. We then consider the nonlocal Fisher–KPP model with free boundary, where the diffusion operator [Formula: see text] is replaced by a nonlocal one involving a kernel function. We will show how a new phenomenon, known as accelerated spreading, can happen to such a model. After that, we will look at some epidemic models with nonlocal diffusion and free boundaries, and show how the long-time dynamics can be rather fully described. Some remarks and comments are made at the end of each section, where related problems and open questions will be briefly discussed.

Corrections to "mSOUND: An Open Source Toolbox for Modeling Acoustic Wave Propagation in Heterogeneous Media".

In the above article [1]>, the authors regret that there were some mistakes pertaining to (1)-(3) and (5).

Hybrid High-Order Methods for the Acoustic Wave Equation in the Time Domain

We devise hybrid high-order (HHO) methods for the acoustic wave equation in the time domain. We first consider the second-order formulation in time. Using the Newmark scheme for the temporal discretization, we show that the resulting HHO-Newmark scheme is energy-conservative, and this scheme is also amenable to static condensation at each time step. We then consider the formulation of the acoustic wave equation as a first-order system together with singly-diagonally implicit and explicit Runge-Kutta (SDIRK and ERK) schemes. HHO-SDIRK schemes are amenable to static condensation at each time step. For HHO-ERK schemes, the use of the mixed-order formulation, where the polynomial degree of the cell unknowns is one order higher than that of the face unknowns, is key to benefit from the explicit structure of the scheme. Numerical results on test cases with analytical solutions show that the methods can deliver optimal convergence rates for smooth solutions of order $$\mathcal{O}(h^{k+1})$$ in the $$H^1$$ -norm and of order $$\mathcal{O}(h^{k+2})$$ in the $$L^2$$ -norm. Moreover, test cases on wave propagation in heterogeneous media indicate the benefits of using high-order methods.

3D Seismic-Wave Modeling with a Topographic Fluid–Solid Interface at the Sea Bottom by the Curvilinear-Grid Finite-Difference Method

ABSTRACTThe curvilinear-grid finite-difference method (FDM), which uses curvilinear coordinates to discretize the nonplanar interface geometry, is extended to simulate acoustic and seismic-wave propagation across the fluid–solid interface at the sea bottom. The coupled acoustic velocity-pressure and elastic velocity-stress formulation that governs wave propagation in seawater and solid earth is expressed in curvilinear coordinates. The formulation is solved on a collocated grid by alternative applications of forward and backward MacCormack finite difference within a fourth-order Runge–Kutta temporal integral scheme. The shape of a fluid–solid interface is discretized by a curvilinear grid to enable a good fit with the topographic interface. This good fit can obtain a higher numerical accuracy than the staircase approximation in the conventional FDM. The challenge is to correctly implement the fluid–solid interface condition, which involves the continuity of tractions and the normal component of the particle velocity, and the discontinuity (slipping) of the tangent component of the particle velocity. The fluid–solid interface condition is derived for curvilinear coordinates and explicitly implemented by a domain-decomposition technique, which splits a grid point on the fluid–solid interface into one grid point for the fluid wavefield and another one for the solid wavefield. Although the conventional FDM that uses effective media parameters near the fluid–solid interface to implicitly approach the boundary condition conflicts with the fluid–solid interface condition. We verify the curvilinear-grid FDM by conducting numerical simulations on several different models and compare the proposed numerical solutions with independent solutions that are calculated by the Luco-Apsel-Chen generalized reflection/transmission method and spectral-element method. Besides, the effects of a nonplanar fluid–solid interface and fluid layer on wavefield propagation are also investigated in a realistic seafloor bottom model. The proposed algorithm is a promising tool for wavefield propagation in heterogeneous media with a nonplanar fluid–solid interface.

RBF-FD analysis of 2D time-domain acoustic wave propagation in heterogeneous media

Radial Basis Function-generated Finite Differences (RBF-FD) is a popular variant of local strong-form meshless methods that do not require a predefined connection between the nodes, making it easier to adapt node-distribution to the problem under consideration. This paper investigates an RBF-FD solution of time-domain acoustic wave propagation in the context of seismic modeling in the Earth's subsurface. Through a number of numerical tests, ranging from homogeneous to highly-heterogeneous velocity models including non-smooth irregular topography, we demonstrate that the present approach can be further generalized to solve large-scale seismic modeling and full waveform inversion problems in arbitrarily complex models enabling more robust interpretations of geophysical observations.