Scalar Acoustic Wave Research Articles

Geometric Phase in Twisted Topological Complementary Pair.

Geometric phase enabled by spin-orbit coupling has attracted enormous interest in optics over the past few decades. However, it is only applicable to circularly-polarized light and encounters substantial challenges when applied to wave fields lacking the intrinsic spin degree of freedom. Here, a new paradigm is presented for achieving geometric phase by elucidating the concept of topological complementary pair (TCP), which arises from the combination of two compact phase elements possessing opposite intrinsic topological charge. Twisting the TCP leads to the generation of a linearly-varying geometric phase of arbitrary order, which is quantified by the intrinsic topological charge. Notably distinct from the conventional spin-orbit coupling-based theories, the proposed geometric phase is the direct result of the cyclic evolution of orbital-angular-momentum transformation in mode space, thereby exhibiting universality across classical wave systems. As a proof of concept, the existence of this geometric phase is experimentally demonstrated using scalar acoustic waves, showcasing the remarkable ability in the precise manipulation of acoustic waves at subwavelength scales. These findings engender a fresh understanding of wave-matter interaction in compact structures and establish a promising platform for exploring geometric phase, offering significant opportunities for diverse applications in wave systems.

Explicit finite-difference modeling for the acoustic scalar wave equation in tilted transverse isotropic media with optimal operators

We have developed an explicit finite-difference modeling scheme for the scalar acoustic wave equation in tilted transverse isotropic (TTI) media, which is computationally efficient in terms of speed and memory and can be used for reverse time migration. Our method uses local spatial operators optimized in the least-squares sense by matching the discrete operator in the wavenumber domain. The calculated operator is applied locally to the wavefield in the space-time domain when the medium is TTI and turns into a conventional finite-difference operator when the medium is isotropic. Our wavefield modeling is stable with no limits such as [Formula: see text] on anisotropic parameters and does not generate S-wave artifacts. The accuracy and the efficiency of our modeling scheme are demonstrated for homogeneous, two half-space TTI, and the BP 2007 TTI models.

Phase-preserving theory and its linearization approximation for forward scattering field of scalar acoustic wave equation

The conventional wave-equation linearization methods, such as the first-order Born or Rytov approximation, always implicitly imply a weak-scattering assumption, making it valid only for weak perturbation models. To extend the wave-equation linearization theory to strong perturbation models, we consider a scenario that the reference model is smooth within the scale of the incident wave length, and propose a phase-preserving method which can predict the phase perturbation of forward scattering wave field. First, we introduce the WKBJ approximation to the scattered- and incident wave fields so that the integral of the unknown solution (i.e. the scattered field) in the nonlinear Ricatti integral equation can be replaced by the integral of scattering-angle and model perturbation, yielding an explicit expression of the scattered field. Theoretical derivation shows that the proposed phase-preserving method can accurately predict the phase-perturbation of forward scattered wave field regardless of the strength of velocity perturbations for one-dimensional wave propagation problem. To apply the phase-preserving approximation to the inverse problem, we further consider a scenario of small-angle forward propagation. In this case, the phase-preserving approximation can be linearized by neglecting the influence of scattering angles, leading to a linear relation between the scattered field and the model perturbation, which we refer to as the generalized Rytov approximation. Numerical experiments demonstrate that the generalized Rytov approximation can predict the phase perturbation of the scattered field with higher accuracy for small-angle forward propagation, and is suitable for strong model perturbations. The generalized Rytov approximation extends the validity and the scope of application of the traditional Rytov approximation. In specific application fields such as the seismic traveltime tomography or medical ultrasonic transmission imaging, a new traveltime/phase sensitivity kernel can be derived by replacing the conventional Rytov approximation with the proposed method, which can increase the inversion accuracy and speed up the convergence.

Accurately Stable Q-Compensated Reverse-Time Migration Scheme for Heterogeneous Viscoelastic Media

The development of multi-component seismic acquisition technology creates new possibilities for the high-precision imaging of complex media. Compared to the scalar acoustic wave equation, the elastic wave equation takes the information of P-waves, S-waves, and converted waves into account simultaneously, enabling accurate description of actual seismic propagation. However, inherent attenuation is one of the important factors that restricts multi-component high-precision migration imaging. Its influence is mainly reflected in the following three ways: first, the attenuation of the amplitude energy makes the deep structure display unclear; second, phase distortion introduces errors to the positioning of underground structures; and third, the loss of high frequency components reduces imaging resolution. Therefore, it is crucial to fully consider the absorption and attenuation characteristics of the real Earth during seismic modeling and imaging. This paper aims to develop an accurate attenuation compensation reverse-time migration scheme for complex heterogeneous viscoelastic media. We first utilize a novel viscoelastic wave equation with decoupled fractional Laplacians to depict the Earth’s attenuation behavior. Then, an adaptive stable attenuation compensation operator is developed to realize high-precision attenuation compensation imaging. Several synthetic and field data analyses verify the effectiveness of the proposed method.

Gravitational tensor and acoustic waves in a radiation dominated universe: Weyl curvature and polarization patterns

We provide evidence that gravitational radiation in a 4D radiation-dominated universe, with equation-of-state $w=1/3$, consists of two components: helicity-2 gravitons and massless scalar acoustic waves. On physical grounds, we would expect the homogeneous solution of the Weyl tensor components to be a good approximation to its inhomogeneous counterparts, whenever the observer is located well in the far zone of an isolated astrophysical source of cosmological gravitational radiation. We show explicitly that these homogeneous and inhomogeneous solutions both receive contributions from the gauge-invariant tensor {\it and} the two Bardeen (acoustic) scalars. Comparison of these Weyl tensor computations thus allows us to not only identify, in the high frequency limit, the corresponding gravitational tensor and scalar radiation; but also their oscillatory polarization patterns.

Effective anisotropy of periodic acoustic and elastic composites

The propagation of acoustic or elastic waves in artificial crystals, including the case of phononic and sonic crystals, is inherently anisotropic. As is known from the theory of periodic composites, anisotropy is directly dictated by the space group of the unit cell of the crystal and the rank of the elastic tensor. Here, we examine effective velocities in the long wavelength limit of periodic acoustic and elastic composites as a function of the direction of propagation. We derive explicit and efficient formulas for estimating the effective velocity surfaces based on the second-order perturbation theory, generalizing the Christoffel equation for elastic waves in solids. We identify strongly anisotropic sonic crystals for scalar acoustic waves and strongly anisotropic phononic crystals for vector elastic waves. Furthermore, we observe that under specific conditions, quasi-longitudinal waves can be made much slower than shear waves propagating in the same direction.

Performance of the Double Absorbing Boundary Method when Applied to the 3D Acoustic Wave Equation

SUMMARY The double absorbing boundary (DAB) is a new highorder absorbing boundary condition for the scalar acoustic wave equation. It suppresses scattered waves at the edge of a boundary layer in computational domain boundary by using destructive interference analogous to a noise-cancelling headphone. This method has advantages in that it addresses some of the shortfalls in existing boundary conditions, such as the need for tuning in Perfectly Matched Layers or complex formulations at corners such as in high-order absorbing boundary conditions. We extend the original formulation of the DAB to three dimensions and higher-order stencils. Through numerical simulation we test the performance of the DAB by comparison with a reflecting boundary. We find that the DABC is a broadband attenuator with a power attenuation of 20-30dB using only six boundary cells. Increasing the order of the method improves accuracy for wavelengths less than 10 cells, whereas increasing the layer width does not improve accuracy. The method shows promise as a robust and computationally efficient boundary condition for seismic applications.

Transformation devices: Event carpets in space and space-time

Here we extend the theory of space-time or event cloaking into that based on the carpet or ground-plane reflective surface. Further, by recasting and generalizing a scalar acoustic wave model into a new mathematically covariant form, we also show how transformation theories for optics and acoustics can be combined into a single prescription. The single prescription, however, still respects the fundamental differences between electromagnetic and acoustic waves, which then provide us with an existence test for any desired transformation device -- are the required material properties (the required constitutive parameters) physically permitted by the wave theory being designed for? Whilst electromagnetism is a flexible theory permitting almost any transformation device (T-device) design, we show that the acoustic model used here is more restricted.

Rapid expansion and pseudo spectral implementation for reverse time migration in VTI media

In isotropic media, we use the scalar acoustic wave equation to perform reverse time migration (RTM) of the recorded pressure wavefield data. In anisotropic media, P- and SV-waves are coupled, and the elastic wave equation should be used for RTM. For computational efficiency, a pseudo-acoustic wave equation is often used. This may be solved using a coupled system of second-order partial differential equations. We solve these using a pseudo spectral method and the rapid expansion method (REM) for the explicit time marching. This method generates a degenerate SV-wave in addition to the P-wave arrivals of interest. To avoid this problem, the elastic wave equation for vertical transversely isotropic (VTI) media can be split into separate wave equations for P- and SV-waves. These separate wave equations are stable, and they can be effectively used to model and migrate seismic data in VTI media where |ε - δ| is small. The artifact for the SV-wave has also been removed. The independent pseudo-differential wave equations can be solved one for each mode using the pseudo spectral method for the spatial derivatives and the REM for the explicit time advance of the wavefield. We show numerically stable and high-resolution modeling and RTM results for the pure P-wave mode in VTI media.

Separate P- And Sv-Wave Equations for Vti Media

In isotropic media we use the scalar acoustic wave equation to perform reverse time migration (RTM) of the recorded pressure wavefield data. In anisotropic media P- and SV-waves are coupled and the elastic wave equation should be used for RTM. However, an acoustic anisotropic wave equation is often used instead. This results in significant shear wave energy in both modeling and RTM. To avoid this undesired SV-wave energy, we propose a different approach to separate P- and SV-wave components for vertical transversely isotropic (VTI) media. We derive independent pseudo-differential wave equations for each mode. The derived equations for P- and SVwaves are stable and reduce to the isotropic case. The equations presented here can be effectively used to model and migrate seismic data in VTI media where je Ie-δI is small. The SV-wave equation we develop is now well-posed and triplications in the SV wavefront are removed resulting in stable wave propagation. We show modeling and RTM results using the derived pure P-wave mode in complex VTI media and use the rapid expansion method (REM) to propagate the wavefields in time.

Acoustic cloaking transformations from attainable material properties

We propose a general methodology and a set of practical recipes for the construction of ultra-broadband acoustic cloaks—structures that can render themselves and a concealed object undetectable by means of acoustic scattering. The acoustic cloaks presented here are designed and function analogously to electromagnetic cloaks. However, acoustic cloaks in a fluid medium do not suffer the bandwidth limitations imposed on their electromagnetic counterparts by the finite speed of light in vacuum. In the absence of specific metamaterials having arbitrary combinations of quasi-static speed of sound and mass density, we explore the flexibility of continuum transformations that produce approximate cloaking solutions. We show that an imperfect, eikonal acoustic cloak (that is, one which is not impedance matched but is valid in the geometrical optics regime) with negligible dispersion can be designed using a simple layered geometry. Since a practical cloaking device will probably be composed of combinations of solid materials rather than fluids, it is necessary to consider the full elastic properties of such media, which support shear waves in addition to the compression waves associated with the acoustic regime. We perform a systematic theoretical and numerical investigation of the role of shear waves in elastic cloaking devices. We find that for elastic metamaterials with Poisson's ratio ν>0.49, shear waves do not alter the cloaking effect. Such metamaterials can be built from nearly incompressible rubbers (with ν≈0.499) and fluids. We expect this finding to have applications in other acoustic devices based on the form-invariance of the scalar acoustic wave equation.

Downward and upward continuation of 2-D seismic data to eliminate ocean bottom topography’s effect

In order to eliminate the effect of ocean bottom topography on seismic wave field, we transformed curved (x, z) coordinate system grids into rectangular (ξ, η) coordinate system grids and derived a 2-D scalar acoustic wave equation in the ξ, η domain. The seismic wave field collected at the sea surface was downward continued to the ocean bottom by the inverse finite difference method with the water velocity and then was reversely continued to the ocean surface by the finite difference method using the layer velocity from just below the ocean bottom in the (ξ, η) domain. Simulation calculations and practical application show that this method can not only remove the reflection travel time distortion but also correct the dynamic parameter changes caused by the ocean bottom topography. The inverted velocity after wave field continuation is much more accurate than before continuation and the image section was greatly improved compared to the original wave field.

Reverse time migration in tilted transversely isotropic (TTI) media

Reverse time migration (RTM) exhibits great advantages over other imaging methods because it is based on computing numerical solutions to a two-way wave equation. It does not suffer from dip limitation like one-way downward continuation techniques do, thus enabling overturned reflections to be imaged. As well as correctly handling multipathing, RTM has the potential to image internal multiples when the boundaries responsible for generating the multiples are present in the model. In isotropic media, one can use a scalar acoustic wave equation for RTM of pressure data. In anisotropic media, P- and SV-waves are coupled together so, formally, elastic wave equations must be used for RTM. A new wave equation for P-waves is proposed in tilted transversely isotropic (TTI) media that can be solved as part of an acoustic anisotropic RTM algorithm, using standard explicit finite differencing. If the shear velocity along the axis of symmetry is set to zero, stable numerical solutions can be computed for media with a vertical axis of symmetry and [Formula: see text] not less than [Formula: see text]. In TTI media with rapid variations in the direction of the axis of symmetry, setting the shear velocity along the axis of symmetry to zero can cause numerical solutions to become unstable. A solution to this problem is proposed that involves using a small amount of nonzero shear velocity. The amount of shear velocity added is chosen to remove triplications from the SV wavefront and to minimize the anisotropic term of the SV reflection coefficient. We show modeling and high-quality RTM results in complex TTI media using this equation.

Weak localization of acoustic waves in strongly scattering media.

We report the first direct measurement of coherent backscattering of scalar acoustic waves by disordered scattering medium. In two and three dimensions an excellent agreement between experimental data and the predictions of simple diffusion theory is found. These measurements have been done for the time dependent and independent cases.