Frequency Dependence Of Reflection Coefficient Research Articles

Enhanced wave transmission in random media with mirror symmetry

We present an analysis of enhanced wave transmission through random media with mirror symmetry about a reflecting barrier. The mathematical model is the acoustic wave equation, and we consider two setups, where the wave propagation is along a preferred direction: in a randomly layered medium and in a randomly perturbed waveguide. We use the asymptotic stochastic theory of wave propagation in random media to characterize the statistical moments of the frequency-dependent random transmission and reflection coefficients, which are scalar-valued in layered media and matrix-valued in waveguides. With these moments, we can quantify explicitly the enhancement of the net mean transmitted intensity, induced by wave interference near the barrier.

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.

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.

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

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.

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.

Field study of wave reflection from permeable rubble mound breakwater of Chabahar Port

The present study analyzes the field measurements of the reflective response of a permeable rubble mound breakwater encountered with a bimodal wave regime. The coexistence of sea and swell wind-driven waves during the measurement program provided directional spreading wave realizations for subsequent bulk and frequency-dependent wave reflection analysis. The directional wave data were acquired near the primary breakwater of Chabahar Port within 28 days, including 643 bursts using an AWAC wave recorder. The available formulae for wave reflection coefficient were evaluated against this data set. Results showed that the equations proposed by Postma (1989) and Zanuttigh and Van der Meer (2007) are in general agreement with the observations of the present study. However, the accuracy of reflection coefficient predictions was improved by developing two new alternative formulations. It was realized that the frequency reflective response differs between sea and swell prevailing conditions. The reflection coefficient decreases drastically within high sea wave predominant periods for the harmonics higher than peak frequency. However, reflection coefficients of high harmonics reduced slightly within swell domination periods. The frequency-dependent reflection coefficients can be even higher than unity due to energy transfer amongst other wave harmonics.

Modeling the effects of fracture infill on frequency-dependent anisotropy and AVO response of a fractured porous layer

In a fractured porous hydrocarbon reservoir, wave velocities and reflections depend on frequency and incident angle. A proper description of the frequency dependence of amplitude variations with offset (AVO) signatures should allow effects of fracture infills and attenuation and dispersion of fractured media. The novelty of this study lies in the introduction of an improved approach for the investigation of incident-angle and frequency variations-associated reflection responses. The improved AVO modeling method, using a frequency-domain propagator matrix method, is feasible to accurately consider velocity dispersion predicted from frequency-dependent elasticities from a rock physics modeling. And hence, the method is suitable for use in the case of an anisotropic medium with aligned fractures. Additionally, the proposed modeling approach allows the combined contributions of layer thickness, interbedded structure, impedance contrast and interferences to frequency-dependent reflection coefficients and, hence, yielding seismograms of a layered model with a dispersive and attenuative reservoir. Our numerical results show bulk modulus of fracture fluid significantly affects anisotropic attenuation, hence causing frequency-dependent reflection abnormalities. These implications indicate the study of amplitude versus angle and frequency (AVAF) variations provides insights for better interpretation of reflection anomalies and hydrocarbon identification in a layered reservoir with vertical transverse isotropy (VTI) dispersive media.

Rock Physical Modeling and Seismic Dispersion Attribute Inversion for the Characterization of a Tight Gas Sandstone Reservoir

Gas identification using seismic data is challenging for tight gas reservoirs with low porosity and permeability due to the complicated poroelastic behaviors of tight sandstone. In this study, the Chapman theory was used to simulate the dispersion and attenuation caused by the squirt flow of fluids in the complex pore spaces, which are assumed to consist of high aspect-ratio pores (stiff pores) and low aspect-ratio microcracks (soft pores). The rock physics modeling revealed that as the gas saturation varies, P-wave velocity dispersion and attenuation occurs at seismic frequencies, and it tends to move to high frequencies as the gas saturation increases. The velocity dispersion of the tight gas sandstone causes a frequency-dependent contrast in the P-wave impedance between the tight sandstone and the overlying mudstone, which consequently leads to frequency-dependent incidence reflection coefficients across the interface. In the synthetic seismic AVO modeling conducted by integrating the rock physics model and the propagator matrix method, the variations in the amplitudes and phases of the PP reflections can be observed for various gas saturations. The tests of the frequency-dependent AVO inversion of these synthetic data revealed that the magnitude of the inverted P-wave dispersion attribute can be used to indicate gas saturation in tight sandstone reservoirs. The applications of the frequency-dependent AVO inversion to the field pre-stacked seismic data revealed that the obtained P-wave dispersion attribute is positively correlated with the gas production from the pay zone at the well locations. Thus, the methods of the rock physics modeling and the frequency-dependent AVO inversion conducted in this study have good potential for the evaluation of the gas saturation in tight gas sandstone reservoirs.

A frequency-decomposed nonstationary convolutional model for amplitude-versus-angle-and-frequency forward waveform modeling in attenuative media

The conventional convolutional model (CCM) is widely applied to generate synthetic seismic data for numerous applications including amplitude variation with offset forward modeling, seismic well tie, and inversion. This approach assumes frequency-independent reflection coefficients and time-invariant seismic wavelets in laterally homogeneous elastic media. We have extended CCM to heterogeneous poroelastic media in which reflection coefficients are frequency dependent and the seismic wave is attenuated as it propagates. First, we decompose the seismic wavelet into monofrequency components through the Fourier transform. Then, to account for the attenuation effects at the reflection interfaces, we multiply the frequency-dependent reflection coefficients series with an attenuation function of frequency-variant quality factor [Formula: see text]. Finally, we convolve this product results with a monofrequency wavelet and sum all of the frequencies together to obtain the synthetic seismograms. The advantage of the proposed frequency-decomposed nonstationary convolutional model is that it takes into account the effects of attenuation on the wave reflections and propagation in attenuative media. In addition, it uses the frequency-dependent [Formula: see text] instead of the constant [Formula: see text] that is used by the traditional nonstationary convolutional model. The technique has been applied to amplitude-versus-angle-and-frequency forward waveform modeling in attenuative media, and it shows good agreement between synthetic and real data on seismic well ties.

Matching pursuit-based sparse spectral analysis: Estimating frequency-dependent anomalies from nonstationary seismic data

Spectral decomposition has been widely used to detect frequency-dependent anomalies associated with hydrocarbons. By ignoring the time-variant feature of the frequency content of individual reflected wavelets, we have adopted a sparse time-frequency spectrum and developed a matching pursuit-based sparse spectral analysis (MP-SSA) method to estimate the sparse time-frequency representation of the seismic data. Further, we evaluate a generalized nonstationary convolution model concerning propagation attenuation and frequency-dependent reflectivity, and we mathematically evaluate the sparse time-frequency spectrum of the nonstationary seismic data as being equal to the product of the Fourier spectrum of the source wavelet, frequency-dependent reflection coefficient, and the cumulative attenuation during seismic wave propagation. Therefore, the reflectivity spectrum, which is a combination of the frequency-dependent reflectivity and the propagation attenuation, can be determined by dividing the sparse time-frequency spectrum of the seismic data by the Fourier spectrum of the source wavelet. Application of the matching pursuit-based decomposition methods to synthetic nonstationary convolutional data illustrates that the adopted MP-SSA spectrum shows a higher time resolution than the matching pursuit-based Wigner-Ville distribution and the matching pursuit-based instantaneous spectral analysis spectra. Notably, the MP-SSA method can avoid spectral smearing, which may introduce distortions to the frequency-dependent anomaly estimation. Application of the amplitude versus frequency analysis based on MP-SSA to field data illustrates the potential of using the sparse reflectivity spectral intercept and gradient to detect the hydrocarbon reservoirs.

Contactless Characterization of Metals’ Thermal Expansion Coefficient by a Free-Space RF Measurement

In this communication, a novel method to characterize the thermal dilatation of metals using a contactless measurement of the frequency-dependent reflection coefficient of a resonator is introduced. This wireless technique allows extracting the thermal expansion coefficient of the material without the need of any calibration. Two antennas, a VNA, and a scatterer fabricated with the under-test material are required. All the measurements have been achieved using a climatic chamber with absorbers to control the scatterer's temperature. The measured values for thermal expansion coefficients are in good agreement with the values provided by the manufacturer which is confirmed by a sensibility study.

Frequency-dependent spherical-wave reflection coefficient inversion in acoustic media: Theory to practice

As an approximation of the spherical-wave reflection coefficient (SRC), the plane-wave reflection coefficient does not fully describe the reflection phenomenon of a seismic wave generated by a point source. The applications of SRC to improve analyses of seismic data have also been studied. However, most of the studies focus on the time-domain SRC and its benefit to using the long-offset information instead of the dependency of SRC on frequency. Consequently, we have investigated and accounted for the frequency-dependent spherical-wave reflection coefficient (FSRC) and analyzed the feasibility of this type of inversion. Our inversion strategy requires a single incident angle using reflection data for inverting the density and velocity ratios, which is distinctly different from conventional inversion methods using amplitude variation with offset. Hence, this investigation provides an alternative approach for estimating media properties in some contexts, especially when the range of aperture of the reflection angles is limited. We apply the FSRC theory to the inversion of noisy synthetic and field data using a heuristic algorithm. The multirealization results of the inversion strategy are consistent with the feasibility analysis and demonstrate the potential of the outlined method for practical application.

Analysis of wave dispersion and attenuation effects on seismic low-frequency reflections of a poroelastic layer

We investigated reflection dispersion characteristics of a poroelastic layer with patchy saturations in seismic low-frequency range. Frequency-dependent attenuation and dispersion of phase velocity were determined with varying fluid saturation, porosity, permeability and heterogeneity size, using analytical solutions of a generalised 1D White’s model proposed here, obtained by incorporating capillary forces into the patchy saturation model. Numerical predictions were employed in combinations with an approximation for the complex and frequency-dependent reflection coefficient from an attenuating thin layer embedded in a dissipative background medium, so as to give a deep insight into the impacts of velocity dispersion and tuning, as well as acoustic impedance contrast, on the seismic low-frequency reflections. Results from this study suggest that wave-induced fluid flow in poroelastic media might account for low-frequency reflection signature anomalies that are associated with fluid saturation in the pore space. We also observed that seismic reflection coefficients of a partially saturated layer can vary strongly versus frequencies, especially in low-frequency range where high attenuation and dispersion can take place due to fluid partial saturation. Analysis of the crossplots of the magnitude for reflection coefficients and dispersion showed that attenuation, dispersion and tuning are more sensitive to gas saturation, porosity, and heterogeneity size. Thus the crossplot provides a useful means for detecting changes in fluid saturation and rock properties.

Effect of local fluid flow on the reflection and transmission of elastic waves at an interface between an elastic solid and a double-porosity medium

We have studied the reflection and transmission of elastic waves incident on an interface separating an elastic solid and a double-porosity medium described by the Biot-Rayleigh model that considers the effect of local fluid flow (LFF). The P1- and SV-wave incidence generates two reflected elastic waves in the elastic solid and four transmitted inhomogeneous waves in the double-porosity medium, represented by Helmholtz potential functions. The reflection and transmission coefficients are derived in closed form based on the boundary conditions at the interface. Energy ratios are then derived, and energy conservation at the interface is verified. The contribution of fluid flow to the three transmitted longitudinal waves in the double-porosity medium is expressed as a function of frequency, the transmission coefficient, and the corresponding slowness vector. Numerical examples indicate that LFF predicts significant compressional-wave velocity dispersion in the seismic band, and frequency-dependent reflection and transmission coefficients. For the case in which the incidence angle is larger than the critical angle, the transmitted P1-wave shows a nonzero energy flux in the vertical direction, whereas it does not if LFF is absent.

Estimating elastic properties and attenuation factor from different frequency components of observed seismic data

SUMMARY Based on an attenuation model, we first express frequency-dependent P- and S-wave attenuation factors as a function of P-wave maximum attenuation factor, and then we re-express P- and S-wave velocities in anelastic media and derive frequency-dependent stiffness parameters in terms of P-wave maximum attenuation factor. Using the derived stiffness parameters, we propose frequency-dependent reflection coefficient in terms of P- and S-wave moduli at critical frequency and P-wave maximum attenuation factor for the case of an interface separating two attenuating media. Based on the derived reflection coefficient, we establish an approach to utilize different frequency components of observed seismic data to estimate elastic properties (P- and S-wave moduli and density) and attenuation factor, and following a Bayesian framework, we construct the objective function and an iterative method is employed to solve the inversion problem. Tests on synthetic data confirm that the proposed approach makes a stable and robust estimation of unknown parameters in the case of seismic data containing a moderate noise/error. Applying the proposed approach to a real data set illustrates that a reliable attenuation factor is obtained from observed seismic data, and the ability of distinguishing oil-bearing reservoirs is improved combining the estimated elastic properties and P-wave attenuation factor.

Reflection dispersion signatures due to wave-induced pressure diffusion in heterogeneous poroelastic media

ABSTRACTWe have studied the reflection dispersion signatures of a heterogeneously patchy saturated reservoir exhibiting attenuation and velocity dispersion in a seismic range of frequency. A modified patchy saturation model is employed to predict velocity dispersion and intrinsic attenuation behaviour associated with wave-induced pressure diffusion due to the presence of both mesoscopic and microscopic heterogeneities. Understanding the combined effects of microscopic squirt flow and wave-induced fluid flow related to mesoscopic heterogeneities on wave attenuation and associated dispersion would be important for determining the relative contribution of both of the interdependent energy loss mechanisms. The acoustic properties from the modified patchy saturation model were then employed in combination with an approximate expression for the frequency-dependent normal-incidence reflection coefficient of a dispersive reservoir rock, to give insights into the impacts of attenuation (and its associated velocity dispersion) and acoustic impedance contrast on the reflection dispersion characteristics. Analysis of the results indicates that the dispersion attribute of reflection coefficients and the associated cross-plot are more sensitive to fluid saturation and porosity than the magnitude of the reflection coefficient, and hence provide a promising approach to characterise fluid saturation and porosity in heterogeneous hydrocarbon reservoirs.

Method for low frequency sound reflection coefficient measurements in a compact space

Here, we present a method to measure the quasi-normal reflection coefficients of sound absorbing materials in a compact space. A short incident sound pulse (length < 3ms) is generated by a deconvolution method with the source speaker. Then, a stage-mounted microphone moves across the material surface and records the total (incident + scattered) sound field. By comparing the sound field with and without the presence of the sound absorbing material, the frequency-dependent reflection coefficients can be derived by extracting the corresponding frequency components from the sound pulse. Using this method, we can calculate the reflection coefficients of a 2 ft. by2 ft acoustic panel from 300 Hz to 2500 Hz within a 2 m by2 m by3 m lab space without anechoic coatings. Moreover, this method enables us to investigate the spatial inhomogeneity of the sound absorbing material by studying the amplitude/phase variation of reflection coefficients across the material surface. Compared with conventional measurement techniques for reflection/absorption coefficients, our method has the advantages of low cost, minimal requirements for the measurement environment and the ability to measure the reflection coefficients at different locations. The proposed method can be favorable for measuring reflection coefficients of two-dimensional acoustic panels/metamaterials at low frequencies.

Prestack Stochastic Frequency-Dependent Velocity Inversion With Rock-Physics Constraints and Statistical Associated Hydrocarbon Attributes

Previous studies have demonstrated that P-wave velocity dispersion at seismic frequencies is often related to hydrocarbons, which results in frequency-dependent P-wave reflection coefficients. This effect is neglected in the conventional amplitude-versus-angle (AVA) inversion, or reduced in most AVA inversion involving seismic dispersion due to the linearization of either the forward modeling or the inversion objective function. As a consequence, there are times when nonnegligible error exists in the inverted dispersion-associated result, which is probably nonnegligible in some cases. In this letter, we adopt the propagator matrix forward modeling derived from the wave equation and the particle swarm optimization (PSO)-based inversion to solve the uncollapsed objective function to avoid any linearization operator at the cost of probably more computational complexity and inversion ill-posedness. To address the ill-posedness, in both the forward modeling and inversion, we introduce rock-physics constraints of frequency-independent S-wave velocity and limited variations of P-wave velocity with frequency. Furthermore, we statistically derive the average frequency-dependent P-wave velocity attribute, the P-wave velocity dispersion intensity attribute, and the characteristic frequency attribute corresponding to the maximum velocity dispersion gradient from multiple experimental inverted dispersive P-wave velocity results. These attributes can be directly applied to detect hydrocarbons. A synthetic data example and a real data example through a drilling well are used to demonstrate that PSO-based prestack stochastic inversion method with rock-physics constraints is effective, and that the statistical attributes derived from the multiple inverted dispersive P-wave velocities can be utilized to favorably indicate gas reservoirs.