Frequency-dependent Reflection Research Articles

Finite-difference frequency-domain method with QR-decomposition-based complex-valued adaptive coefficients for 3D diffusive viscous wave modelling

Abstract The diffusive viscous (DV) model is a useful tool for interpreting low-frequency seismic attenuation and the influence of fluid saturation on frequency-dependent reflections. Among present methods for the numerical solution of the corresponding DV wave equation, the finite-difference frequency-domain (FDFD) method with complex-valued adaptive coefficients (CVAC) has the advantage of efficiently suppressing both numerical dispersion and numerical attenuation. In this research, the FDFD method with CVAC is first generalized to a 3D DV equation. In addition, the current calculation of CVAC involves the numerical integration of propagation angles, conjugate gradient (CG) iterative optimization, and the sequential selection of initial values, which is difficult and inefficient for implementation. An improved method is developed for calculating CVAC, in which a complex-valued least-squares problem is constructed by substituting the 3D complex-valued plane-wave solutions into the FDFD scheme. The QR-decomposition method is used to efficiently solve the least-squares problem. Numerical dispersion and attenuation analyses reveal that the FDFD method with CVAC requires ∼2.5 spatial points in a wavelength within a dispersion deviation of 1% and an attenuation deviation of 10% for the 3D DV equation. An analytic solution for 3D DV wave equation in homogeneous media is proposed to verify the effectiveness of the proposed method. Numerical examples also demonstrate that the FDFD method with CVAC can obtain accurate wavefield modelling results for 3D DV models with a limited number of spatial points in a wavelength, and the FDFD method with QR-based CVAC requires less computational time than the FDFD method with CG-based CVAC.

Electromagnetic and microwave properties of single-layer thermoplastic natural rubber (TPNR)/yttrium iron garnet (Y3Fe5O12)/magnetite (Fe3O4) composites backed by a perfect conductor

The use of a single-layer material for microwave applications continues to attract many researchers due to materials’ homogeneity in an acceptable range of thickness. This study outlines the microwave electromagnetic characteristics and interpretation of results based on a single-layer material backed by a perfect conductor. Data from three different laboratory prepared thermoplastic natural rubber (TPNR)/yttrium iron garnet (Y3Fe5O12)/magnetite (Fe3O4) composites were presented. The microwave relative complex dielectric permittivity (ε r*) and magnetic permeability (µ r*) were measured using a microwave vector network analyser (MVNA) in the frequency range of 0.1846–10.0104 GHz. The specular material model backed by a perfect conductor was used to obtain the frequency-dependent reflection loss (R L) assuming a normal incident of electromagnetic (EM) wave. The real and imaginary components of ε r* (ε r′ and ε r″) and µ r* (µ r′ and µ r″) for the three samples show a similar trend of frequency dependent. TPNR/Y3Fe5O12 reflected the EM wave less when its thickness (t) equals a quarter of the propagating wavelength (λ m/4) inside the material. Interestingly, in the presence of Fe3O4, multiple minimal reflections occur at smaller thicknesses (e.g. t = λ m/32). For both cases, this is the condition where the reflected wave at the surface of the material is in a 180°-phase difference from the wave reflected earlier at the material-conductor interface. Destructive interference occurs when these two waves meet and is visualized as the dip on the reflection loss (R L) vs. frequency plot. The number of dips increases with thickness. The lowest frequency dip occurs at a lower frequency for a thicker material. For TPNR/Y3Fe5O12/Fe3O4 and TPNR/Fe3O4, as the material gets thicker, the high-frequency dips on the R L plot become smaller and the use of the material in microwave application is no longer practical due to the increase in its weight and a smaller reflection loss.

In-depth analysis of ternary NaCuX (X = Se and Te) chalcogenides: Bridging structural elastic, electronic, and optical properties

This study employs density functional theory (DFT) using the full potential linearized augmented plane wave plus local orbital (FP-LAPW+1o) approach to investigate the structural, elastic, electronic, and optical properties of NaCuX (X = Se and Te) compounds. Additionally, the modified Becke-Johanson (TB-mBJ) potential is applied to ensure accurate band gap results. Both compounds exhibit semiconducting behavior with a direct band gap at the Γ point. The computed elastic constants confirm mechanical stability for NaCuSe and NaCuTe, as evidenced by their respective bulk modulus, Young modulus, shear modulus, Poisson's ratio, B/G ratio, and elastic anisotropy. The materials display ductile characteristics, indicated by their B/G ratio and Poisson's ratio. The Debye temperature (θD) reveals that NaCuSe possesses the highest thermal conductivity. A decrease in θD is observed from NaCuSe to NaCuTe due to declining elastic constants. Additionally, anisotropy in acoustic velocities is assessed and discussed. The study's equilibrium structural properties align well with experimental data. Optical properties, including frequency-dependent dielectric function, refractive index, extinction coefficient, absorption coefficient, reflectivity, and energy loss function, are calculated and comprehensively analyzed.

First-principles calculations to investigate structural, electronic, optical and elastic properties of α-Ca3N2

The optoelectronic industry, which has become a cornerstone, requires a semiconductor compound to function as a sustainable and green energy source. In this connection, the present study provides a systematic approach to examine the electronic and optical properties of α-Ca3N2 using the linear combination of atomic orbitals method. The xc-functional BECKE-PBE gives the best results for electronic properties by describing the band gap correctly. The dispersion curve shows that α-Ca3N2 is a semiconductor with an indirect band gap of 1.33 eV along the H-Γ direction. Effective masses of electrons and holes are calculated at the peak of the lowest conduction band and highest valence band, along the Γ- direction. Calculation for optical properties has been performed using coupled-perturbed Hartree-Fock scheme for static values and phonon spectrum calculations are performed for dynamic dielectric functions. Further, frequency dependent electron loss function and reflectivity are determined from the dielectric functions. The elastic constants are estimated and elastic moduli are determined. Bulk modulus of 80.6 GPa and Poisson’s ratio of 0.275 reveals that α-Ca3N2 is a hard and ductile material. The characteristic properties of α-Ca3N2 make it a suitable candidate for optoelectronic applications.

Frequency-dependent reflection of a misaligned beam by a Fabry–Pérot cavity

Gravitational-wave detectors, such as Virgo, LIGO, and KAGRA, are modified Michelson interferometers, with a system of coupled Fabry–Pérot cavities, to increase its sensitivity and bandwidth. In order to control the detector, several radio frequency sidebands, not resonant in the kilometric arm cavities but resonant in the central cavities of the interferometer, are added to the carrier frequency to extract longitudinal and alignment error signals. Misalignment of the laser in the Fabry–Pérot cavities causes sensitivity degradation through different mechanisms and results in non-superposition of carrier and sidebands. These relative misalignment between fields at different frequency contain clues to optimally align the interferometer, but the question of the direction of a reflected beam by a Fabry–Pérot cavity, as a function of the state of resonance of the incoming electromagnetic field, is neither straightforward nor intuitive. While numerical optical simulations used in the gravitational-wave detector community are able to answer the question, they do not give a qualitative and handy understanding of the observed phenomenon, useful for the commissioning and operation of the detectors. In this Letter, we present a model based on Gaussian beam first-order modal expansion to calculate analytically how misalignment on the input beam in a Fabry–Pérot cavity translates into misalignment of the reflected and circulating beams. We find a strong dependence not only on the beam resonance condition but also on the mirror geometry. Finally, we checked the consistency of our model by comparing its predictions with existing numerical simulators.

Reflection dispersion of seismic waves at the ocean bottom due to mesoscopic-flow loss

Seismic reflections at the interface of heterogeneous porous media are significantly affected by the multi-scale fluid-flow losses. In this work, we study the seismic reflection dispersion from the ocean bottom separating seawater and heterogeneous porous seabed, described by the effective Biot theory where the mesoscopic loss is present. The analytical reflection coefficient is obtained based on the displacement potentials and suitable boundary conditions. Two reflection scenarios, including the water/water-bearing medium contact and water/gas-saturated medium interface, are considered. The shear-wave attenuation is also considered by using a Cole-Cole complex shear modulus. Numerical results showing the variation in reflection magnitude versus frequency and incidence angle are presented, revealing that the P-wave mesoscopic attenuation, complex shear modulus, boundary conditions and permeability can significantly affect the frequency and angle dependence of the reflection coefficients. Reflections at the water/gas-saturated medium interface exhibit quite different behaviors from those at the water/water-bearing medium contact. The open-pore interface gives frequency-dependent reflections, whereas in sealed-pore case, the reflection magnitudes remain unchanged for all frequencies, due to the fact that the interface degrades into a water/elastic solid one. The study can be relevant for reservoir prediction and fluid identification based on the reflected marine data.

Characteristics of the far-field source signature and its ghost effect of a marine single air gun

The estimation of the air gun source signature is a crucial topic in marine seismic. Typical approaches such as numerical modelling or near-field measurement-based inversion normally work in practice, but suffer from lack of knowledge on the varying sea surface reflection coefficient, the signature directional consistency and the dynamically changed source geometry. For better understanding of the above uncertainties, real far-field air gun source signatures were acquired. A customized approach combined with sparse f-k transformation and adaptive subtraction is applied to deblend the source signature from the sea-floor reflections. Characteristic of the ghost notch distribution and bubble oscillation period indicate an overall good match to the simulated results, except the latter part due to the unexpected air-leakage. Amplitude decay with incidence-angle increase is observed, indicating that the point-source spherical theory for directional signature estimation may be questionable. The sea-surface reflection coefficient appears time-variant and frequency-dependent which challenges the assumption of flat sea surface in signature estimation. An innovative notional source inversion workflow is adapted to the frequency-dependent reflection coefficient. The notional signature inversed through the adapted approach results in less ghost residuals and weaker spectral notch effect comparing with the normal inversion result, i.e., based on a constant reflection coefficient.

Analysis and Hermite Spectral Approximation of Diffusive-Viscous Wave Equations in Unbounded Domains Arising in Geophysics

The diffusive-viscous wave equation (DVWE) is widely used in seismic exploration since it can explain frequency-dependent seismic reflections in a reservoir with hydrocarbons. Most of the existing numerical approximations for the DVWE are based on domain truncation with ad hoc boundary conditions. However, this would generate artificial reflections as well as truncation errors. To this end, we directly consider the DVWE in unbounded domains. We first show the existence, uniqueness, and regularity of the solution of the DVWE. We then develop a Hermite spectral Galerkin scheme and derive the corresponding error estimate showing that the Hermite spectral Galerkin approximation delivers a spectral rate of convergence provided sufficiently smooth solutions. Several numerical experiments with constant and discontinuous coefficients are provided to verify the theoretical result and to demonstrate the effectiveness of the proposed method. In particular, We verify the error estimate for both smooth and non-smooth source terms and initial conditions. In view of the error estimate and the regularity result, we show the sharpness of the convergence rate in terms of the regularity of the source term. We also show that the artificial reflection does not occur by using the present method.

Frequency-Dependent Nonlinear AVO Inversion for Q-Factors in Viscoelastic Media

Viscoelastic theory-based frequency-dependent amplitude variation with offset (AVO) inversions are a useful tool for identifying fluids based on their dispersion properties. When used to identify reservoir oil and gas qualities, the quality factors ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula> -factors) derived from the inversion have produced good results. But currently, the majority of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula> -factor inversions are linear inversions based on linear approximations, whereas nonlinear inversions based on exact equations with higher precision and fewer assumptions are only occasionally carried out. Meanwhile, in broadband seismic inversion, the low-frequency model estimated by complex frequency inversion can fully utilize seismic data’s low-frequency information and provide improved robustness and rationality for inversion. Therefore, we derive a frequency-dependent reflection coefficient equation that varies with angle by replacing the nearly constant <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula> model suggested by Aki and Richards into the exact Zoeppritz equation and simplifying. Additionally, using the Bayesian framework as a foundation, we created a novel two-stage broadband frequency-dependent nonlinear inversion approach for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula> -factors that can estimate <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula> -factors, produce accurate fluid identification results, and serve as a solid foundation for oil and gas exploration and reservoir identification. Utilizing examples from both synthetic and real-world data, we verify the applicability of oil and gas indicators.

Roughness correction method for the measurement of attenuation coefficient using contact transducers

The surface quality of a material significantly affects the accurate measurement of the ultrasonic attenuation coefficient. In this research, a roughness correction method for experimental calculation of the attenuation coefficient using contact transducers is proposed. Firstly, the losses due to the scattering from a rough interface are analysed. According to the mechanism of ultrasonic waves reflected from a thin layer between two solid media, the frequency-dependent reflection coefficient of the coupling interface involving a roughness parameter is derived based on the phase-screen approximation theory. Then, a compensation model is established to correct the error caused by the surface roughness. 304 stainless steel and 45 steel specimens with different levels of surface roughness are prepared and ultrasonic measurements are implemented using both the through-transmission and pulse-echo methods. The experimental results show that the proposed correction method can effectively eliminate the losses caused by surface roughness and improve the measurement accuracy of the attenuation coefficient.

Implications of the quantum nature of the black hole horizon on the gravitational-wave ringdown

Motivated by capturing putative quantum effects at the horizon scale, we model the black hole horizon as a membrane with fluctuations following a Gaussian profile. By extending the membrane paradigm at the semiclassical level, we show that the quantum nature of the black hole horizon implies partially reflective boundary conditions and a frequency-dependent reflectivity. This generically results into a modified quasi-normal mode spectrum and the existence of echoes in the postmerger signal. On a similar note, we derive the horizon boundary condition for a braneworld black hole that could originate from quantum corrections on the brane. This scenario also leads to a modified gravitational-wave ringdown. We discuss general implications of these findings for scenarios predicting quantum corrections at the horizon scale.

Designing variable reflection coefficient for upstream and downstream terminations to study their effect on flame thermoacoustics

In this paper, the design, construction and results of experiments performed on a generic combustion system are presented. The setup is supplemented by various weakly frequency-dependent variable reflection coefficient (RC) devices as upstream and downstream acoustic terminations. The main objective of building such terminations is to provide a method to study burner/flame stability when it is placed between various acoustic configurations (RC: 0.1-0.9) and to determine the figure of merit of a burner based on the evaluation of its map of (in-)stability. Furthermore, burner design parameters such as the burner perforation pattern (holes diameter, pitch, perforation area, etc.) which will provide combustion stability for the widest range of burner's acoustic embedding conditions are identified. The experimental setup comprises of an upstream acoustic termination, a telescopic tube with adjustable length is placed after the upstream termination followed by the burner and the quartz tube. On the top of the quartz tube, the replaceable downstream terminations are installed. Nine downstream terminations are constructed by stacking plates of 0.25 mm thickness separated by spacers ranging from 0.1 to 1 mm thickness. Particularly, for the burners tested in this setup, the smallest hole diameter burner (with the largest perforation area) results in the largest stable region on the stability map in the parameter space. An increase in the flow velocity leads to an increase in the frequency of instability and makes a stable system tend to become unstable, while an increase in the equivalence ratio contributes to stabilizing system instability

Optical study on topological superconductor candidate Sr-doped Bi2Se3

Utilizing infrared spectroscopy, we study the charge dynamics of the topological superconductor candidate Sr x Bi2Se3. The frequency-dependent reflectivity R(ω) demonstrates metallic feature and the scattering rate of the free carriers decreases with temperature decreasing. The plasma edge shows a slight blue shift upon cooling, similar to the behavior of Cu x Bi2Se3. As the carrier concentration n obtained by Hall resistivity increases slightly with the decreasing temperature, the effective mass is proved to increase as well, which is in contrast with that of Cu x Bi2Se3. We also perform the ultrafast pump-probe study on the Sr0.2Bi2Se3 compounds. Resembling its parent compound Bi2Se3, three distinct relaxation processes are found to contribute to the transient reflectivity. However, the deduced relaxation times are quite different. In addition, the electron-optical-phonon coupling constant is identified to be λ = 0.88.

Eigenfunction non-orthogonality factors and the shape of CPA-like dips in a single-channel reflection from lossy chaotic cavities

Motivated by the phenomenon of coherent perfect absorption, we study the shape of the deepest dips in the frequency-dependent single-channel reflection of waves from a cavity with spatially uniform losses. We show that it is largely determined by non-orthogonality factors O nn of the eigenmodes associated with the non-selfadjoint effective Hamiltonian. For cavities supporting chaotic ray dynamics we then use random matrix theory to derive, fully non-perturbatively, the explicit distribution of the non-orthogonality factors for systems with both broken and preserved time reversal symmetry. The results imply that O nn are heavy-tail distributed. As a by-product, we derive an explicit non-perturbative expression for the resonance density in a single-channel chaotic systems in a much simpler form than available in the literature.

Resonantly enhanced polariton wave mixing and parametric instability in a Floquet medium.

We introduce a new theoretical approach for analyzing pump and probe experiments in non-linear systems of optical phonons. In our approach, the effect of coherently pumped polaritons is modeled as providing time-periodic modulation of the system parameters. Within this framework, propagation of the probe pulse is described by the Floquet version of Maxwell's equations and leads to phenomena such as frequency mixing and resonant parametric production of polariton pairs. We analyze light reflection from a slab of insulating material with a strongly excited phonon-polariton mode and obtain analytic expressions for the frequency-dependent reflection coefficient for the probe pulse. Our results are in agreement with recent experiments by Cartella et al. [Proc. Natl. Acad. Sci. U. S. A. 115, 12148 (2018)], which demonstrated light amplification in a resonantly excited SiC insulator. We show that, beyond a critical pumping strength, such systems should exhibit Floquet parametric instability, which corresponds to resonant scattering of pump polaritons into pairs of finite momentum polaritons. We find that the parametric instability should be achievable in SiC using current experimental techniques and discuss its signatures, including the non-analytic frequency dependence of the reflection coefficient and the probe pulse afterglow. We discuss possible applications of the parametric instability phenomenon and suggest that similar types of instabilities can be present in other photoexcited non-linear systems.

Radar Absorber Fabric Design Based on Periodic Arrays of Circular Shaped Conductive Patches

In this study, the design and electrical tests of radar absorber fabric containing an array of circular shaped conductive patches positioned on a neoprene fabric are presented. In the designs, electrical performance of the radar absorber fabric is numerically studied in both planar and conformal structures. Furthermore, the two-dimensional (2D) surface current distribution at the resonant frequency is examined to better understand the operating principles of the proposed structure. Finally, the prototype of the radar absorber fabric is manufactured, and the frequency dependent reflection parameter values are measured by using the free space measurement technique to validate the numerical results. A good agreement between the measurement and numerical results is obtained.

A New Fluid Mobility Calculation Method Based on Frequency-Dependent AVO Inversion

Fluid mobility (i.e., permeability to viscosity ratio) is a key parameter that can evaluate the reservoir permeability and delineate the fluid characteristic in hydrocarbon-saturated reservoirs. Based on the asymptotic representation for the frequency-dependent reflections in the fluid-saturated pore-elastic media and frequency-dependent AVO inversion, we propose a novel method for estimating fluid mobility from poststack seismic data. First, we establish the relationship between fluid mobility and frequency-dependent AVO analysis. Then, the fluid mobility is estimated using the theory of frequency-dependent AVO inversion. Tests on synthetic data reveal that the fluid mobility shows excellent imageability for the fluid-saturated reservoirs and can accurately delineate the spatial distribution shape of the gas-saturated reservoir. The application of field data examples demonstrates that the fluid mobility calculated by the proposed method produces less background interferences caused by elastic layers compared with the conventional frequency-dependent fluid indicator. The frequency-dependent fluid mobility takes into account the dispersion features associated with hydrocarbon reservoirs, and it provides a new way to detect the location of hydrocarbon reservoirs and characterize their spatial distribution.

A finite-element algorithm with a perfectly matched layer boundary condition for seismic modelling in a diffusive-viscous medium

AbstractSeismic numerical modelling involved in each stage of seismic exploration process is aimed at predicting seismograms in an assumed subsurface medium. The energies and phases of waves vary with the presence of fluids, while the frequency-dependent seismic reflections in a reservoir with hydrocarbons was explained using the diffusive-viscous wave (DVW) equation. We proposed a Galerkin finite-element method (FEM) to numerically study the propagation properties of the DVW in fluid-filled media to ascertain the influences of saturated fluids on characteristics of the wavefield. We also theoretically analysed the numerical dispersion and stability condition of the FEM algorithm, which indicated that a minimum of six nodes per wavelength is recommended to achieve more accurate results. In numerical simulation, we presented a non-split perfectly matched layer (NPML) boundary condition for the DVW equation to absorb the artificial reflections in finite-element modelling, using a homogeneous model to demonstrate the effectiveness of the NPML boundary condition through comparisons with the results without the PML condition. Moreover, we modelled the DVW propagation in a fluid-saturated (gas, oil and water) medium with sharp edges and curved interfaces using the proposed method and compared the results with those pertaining to acoustic waves. The numerical results indicated significant amplitude damping and phase variation in the DVW when it propagates across the fluid-saturated layers compared with those of acoustic waves. Furthermore, we compared the numerical results in the fluid-saturated model calculated via the FEM with those calculated via FCT-FDM (flux corrected transport-finite-difference method) to demonstrate the validity of the former.

Linearized Frequency-Dependent Reflection Coefficient and Attenuated Anisotropic Characteristics of Q-VTI Model

Seismic wave exhibits the characteristics of anisotropy and attenuation while propagating through the fluid-bearing fractured or layered reservoirs, such as fractured carbonate and shale bearing oil or gas. We derive a linearized reflection coefficient that simultaneously considers the effects of anisotropy and attenuation caused by fractures and fluids. Focusing on the low attenuated transversely isotropic medium with a vertical symmetry axis (Q-VTI) medium, we first express the complex stiffness tensors based on the perturbation theory and the linear constant Q model at an arbitrary reference frequency, and then we derive the linearized approximate reflection coefficient of P to P wave. It decouples the P- and S-wave inverse quality factors, and Thomsen-style attenuation-anisotropic parameters from complex P- and S-wave velocity and complex Thomsen anisotropic parameters. By evaluating the reflection coefficients around the solution point of the interface of two models, we analyze the characteristics of reflection coefficient vary with the incident angle and frequency and the effects of different Thomsen anisotropic parameters and attenuation factors. Moreover, we realize the simultaneous inversion of all parameters in the equation using an actual well log as a model. We conclude that the derived reflection coefficient may provide a theoretical tool for the seismic wave forward modeling, and again it can be implemented to predict the reservoir properties of fractures and fluids based on diverse inversion methods of seismic data.

Pressure-Induced Excitations in the Out-of-Plane Optical Response of the Nodal-Line Semimetal ZrSiS.

The anisotropic optical response of the layered, nodal-line semimetal ZrSiS at ambient and high pressure is investigated by frequency-dependent reflectivity measurements for the polarization along and perpendicular to the layers. The highly anisotropic optical conductivity is in very good agreement with results from density-functional theory calculations and confirms the anisotropic character of ZrSiS. Whereas the in-plane optical conductivity shows only modest pressure-induced changes, we found strong effects on the out-of-plane optical conductivity spectrum of ZrSiS, with the appearance of two prominent excitations. These pronounced pressure-induced effects can neither be attributed to a structural phase transition according to our single-crystal x-ray diffraction measurements, nor can they be explained by electronic correlation and electron-hole pairing effects, as revealed by theoretical calculations. Our findings are discussed in the context of the recently proposed excitonic insulator phase in ZrSiS.