Estimated Reflection Coefficients Research Articles

Accurate Estimation of Wave Reflection on a High Energy, Dissipative Beach

ABSTRACT Inch, K.; Davidson, M.; Masselink, G., and Russell, P., 2016. Accurate estimation of wave reflection on a high energy, dissipative beach. In: Vila-Concejo, A.; Bruce, E.; Kennedy, D.M., and McCarroll, R.J. (eds.), Proceedings of the 14th International Coastal Symposium (Sydney, Australia). Journal of Coastal Research, Special Issue, No. 75, pp. 877–881. Coconut Creek (Florida), ISSN 0749-0208. Noise induced error in estimated wave reflection coefficients using an array method is investigated using simulated time series of water surface elevation with known reflection coefficients and added uncorrelated noise. Reflection coefficients are found to be increasingly overestimated with the addition of noise and this positive bias is more significant for lower levels of true reflection. Coherence between the water surface elevation time series changes systematically with the bias and, along with the estimated reflection coefficients, is used to create a “look-up table” which serves as a function to corr...

Lidar and Pressure Measurements of Inner-Surfzone Waves and Setup

AbstractObservations of waves and setup on a steep, sandy beach are used to identify and assess potential applications of spatially dense lidar measurements for studying inner-surf and swash-zone hydrodynamics. There is good agreement between lidar- and pressure-based estimates of water levels (r2 = 0.98, rmse = 0.05 m), setup (r2 = 0.92, rmse = 0.03 m), infragravity wave heights (r2 = 0.91, rmse = 0.03 m), swell–sea wave heights (r2 = 0.87, rmse = 0.07 m), and energy density spectra. Lidar observations did not degrade with range (up to 65 m offshore of the lidar) when there was sufficient foam present on the water surface to generate returns, suggesting that for narrow-beam 1550-nm light, spatially varying spot size, grazing angle affects, and linear interpolation (to estimate the water surface over areas without returns) are not large sources of error. Consistent with prior studies, the lidar and pressure observations indicate that standing infragravity waves dominate inner-surf and swash energy at low frequencies and progressive swell–sea waves dominate at higher frequencies. The spatially dense lidar measurements enable estimates of reflection coefficients from pairs of locations at a range of spatial lags (thus spanning a wide range of frequencies or wavelengths). Reflection is high at low frequencies, increases with beach slope, and decreases with increasing offshore wave height, consistent with prior studies. Lidar data also indicate that wave asymmetry increases rapidly across the inner surf and swash. The comparisons with pressure measurements and with theory demonstrate that lidar measures inner-surf waves and setup accurately, and can be used for studies of inner-surf and swash-zone hydrodynamics.

Quality-factor and reflection-coefficient estimation using surface-wave ghost reflections from subvertical structures

Seismic interferometry can retrieve the Green's function between receivers from the cross-correlation and summation of recordings from a boundary of surrounding sources. Having the sources only along a boundary is sufficient if the medium is lossless. If the medium is dissipative, the retrieved result using cross-correlation contains non-physical (ghost) arrivals. When using receivers at the surface and transient sources in the subsurface for the retrieval of the reflection response in a dissipative medium, it has been shown that the retrieved ghost reflections are characteristic of the quality factor of the subsurface. The ghost reflections are caused by internal reflections inside subsurface layers. It has been shown with numerical examples for recordings in a borehole from a surface source that a ghost reflection can be discriminated from physical reflections and tied to a specific subsurface layer. After connecting the ghost reflection to a specific layer, the quality factor of the medium above this layer and the reflection coefficient at the layer interface can be estimated. In this article, we show how the above principles can be adapted and applied for surface waves. Due to intrinsic losses in the medium, surface-wave ghost reflections are retrieved from internal scattering between subvertical boundaries. We demonstrate the method on an ultrasonic dataset recorded on a sample composed of a PVC block and an aluminum block. The aluminum block has a groove parallel to the PVC/aluminum interface. Using a surface-wave ghost reflection between the groove and the PVC/aluminum interface, we estimate the quality factor of the PVC and the reflection coefficient at the PVC/aluminum interface. We also show that the ghost reflection can be identified and tied to the layer between the groove and the PVC/aluminum interface, thus confirming previous numerical findings.

Normal incidence measurement in a subaqueous sand dune field in the South China Sea.

Regions with subaqueous sand dunes have been discovered on the upper continental slope of the northern South China Sea. These large subaqueous sand dunes are expected to cause errors in the measurement of normal incidence reflection. This letter presents experiment results of two normal incidence survey tracks conducted in 2013, and the errors in reflection coefficient estimation and the resulting sediment properties induced by sand dune bedforms. The results demonstrate that the reflected energy is focused and scattered by different parts of sand dune bedforms and that they produce significant variation in the estimated reflection coefficients and the inverted geoacoustic properties.

Tight gas detection based on the reflectivity dispersion technology

Abstract The study focuses on the reflectivity dispersion caused by velocity dispersion related to pore fluid and its application to identify tight gas reservoirs. Seismic attenuation in viscoelastic media has two effects: (1) the change in frequency content and amplitude of a pulse propagating through attenuating media; (2) reflection coefficients are frequency dependent. Based on linear viscoelastic theory of velocity dispersion and the linearization of Zoeppritz equations, a new approximate reflection coefficient is presented considering P & S wave velocity dispersion, which adds the effects of frequencies and quality factors in reflection coefficient formula, representing the characteristics of reflection coefficient dependent by frequency, incident angle, quality factor etc. Based on the relationship between P-wave velocity and gas saturation, the reflected energy changes induced by reflectivity dispersion can be calculated and used to directly detect gas reservoirs, combining with seismic velocity, amplitude and energy attenuation mechanism caused by gas, such as squirt flow mechanism. This method has been successfully applied to characterize the distribution of tight gas sands in the GA101 well area of Sichuan Basin, and the results offer reliable foundations for seismic prospecting and well designing.

A Novel Time-Domain Reflection Coefficient Function: TM Case

In determining electromagnetic transient response of structure placed above the half space, the half space properties can be taken into account via the reflection coefficient (RC) approximation. The choice of an RC function used in RC approximation is often important with regards to accuracy and computational efficiency of the overall method. In this paper, a new time-domain RC function for the case of TM polarization is presented. The function is derived using Gaver-Stehfest algorithm for numerical inverse Laplace transform and does not require the use of Bessel functions. The resulting formulation is rather simple, and, as the results indicate, accurate and computationally efficient.

Improving seismic interpretation: a high-contrast approximation to the reflection coefficient of a plane longitudinal wave

Linearized approximations of reflection and transmission coefficients set a foundation for amplitude versus offset (AVO) analysis and inversion in exploration geophysics. However, the weak properties contrast hypothesis of those linearized approximate equations leads to big errors when the two media across the interface vary dramatically. To extend the application of AVO analysis and inversion to high contrast between the properties of the two layers, we derive a novel nonlinearized high-contrast approximation of the PP-wave reflection coefficient, which establishes the direct relationship between PP-wave reflection coefficient and P-wave velocities, S-wave velocities and densities across the interface. (A PP wave is a reflected compressional wave from an incident compressional wave (P-wave).) This novel approximation is derived from the exact reflection coefficient equation with Taylor expansion for the incident angle. Model tests demonstrate that, compared with the reflection coefficients of the linearized approximations, the reflection coefficients of the novel nonlinearized approximate equation agree with those of the exact PP equation better for a high contrast interface with a moderate incident angle. Furthermore, we introduce a nonlinear direct inversion method utilizing the novel reflection coefficient equation as forward solver, to implement the direct inversion for the six parameters including P-wave velocities, S-wave velocities, and densities in the upper and lower layers across the interface. This nonlinear inversion algorithm is able to estimate the inverse of the nonlinear function in terms of model parameters directly rather than in a conventional optimization way. Three examples verified the feasibility and suitability of this novel approximation for a high contrast interface, and we still could estimate the six parameters across the interface reasonably when the parameters in both media across the interface vary about 50%.

해저지층 탐사를 위한 Schur 알고리즘

본 논문은 송신신호와 다층의 해수층 및 해저지층으로 구성된 매질의 퇴적물의 배치 및 형태에 의해 반사된 수신 신호를 이용하여 매질 각층의 특성을 계산 할 수 있는 알고리즘을 제안한다. 제안된 알고리즘은 이종의 다층 매질로 구성되어 있는 해수층 및 해저지층의 구조 특성을 추정하는 것으로, 일반적으로 Schur 알고리즘이라 부른다. 제안된 알고리즘은 주어진 역산란(inverse scattering) 문제를 matrix factorization을 수행하여 효율적으로 매질의 반사계수(reflection coefficient)를 추정한다. 본 논문에서는 제안된 알고리즘의 성능을 분석하기 위하여 해수층 및 해저지층의 이종 다층 매질 구조를 고려한 lattice 필터 모델을 구성하였고, 이 필터 모델로부터 얻어진 송신 및 반사 신호를 이용하여 다양한 컴퓨터 모의실험을 수행한 결과, 제안된 알고리즘이 효율적으로 매질을 추정함을 확인하였다.

Generalized approximations of reflection coefficients in orthorhombic media

Reflection coefficients of qP- (quasi-P) and qS- (quasi-S) incident waves in orthorhombic media can be explicitly expressed by means of impedance matrices. In this paper, we extend previous studies and derive the generalized and linearized equations of reflectivity for all four types of waves in the symmetry-axis plane. These approximations have sufficient accuracy over a wide range of angles, therefore they are suitable for characterizing the seismic amplitude responses of unconventional resources. For example, they can be applied to represent the amplitude variation with offset for shale gas or coalbed methane reservoirs with strong anisotropy and complicated symmetry. Reduced equations are then derived in a transverse isotropic medium with a vertical symmetry axis (VTI) or a horizontal axis (HTI) for the anisotropic amplitude inversion. They retain higher accuracy than the corresponding previously published expressions at a strongly anisotropic interface, because they include the second-order terms of anisotropic parameters contrast. Numerical analyses on the inverse problem using different linearized expressions show the practical value of the new derived expressions in the joint inversion of the qPqP- and qPqS-waves for elastic parameters and anisotropic parameters.

Perfectly matched layer-absorbing boundary condition for finite-element time-domain modeling of elastic wave equations

The perfectly matched layer (PML) is a highly efficient absorbing boundary condition used for the numerical modeling of seismic wave equation. The article focuses on the application of this technique to finite-element time-domain numerical modeling of elastic wave equation. However, the finite-element time-domain scheme is based on the second-order wave equation in displacement formulation. Thus, the first-order PML in velocity-stress formulation cannot be directly applied to this scheme. In this article, we derive the finite-element matrix equations of second-order PML in displacement formulation, and accomplish the implementation of PML in finite-element time-domain modeling of elastic wave equation. The PML has an approximate zero reflection coefficients for bulk and surface waves in the finite-element modeling of P-SV and SH wave propagation in the 2D homogeneous elastic media. The numerical experiments using a two-layer model with irregular topography validate the efficiency of PML in the modeling of seismic wave propagation in geological models with complex structures and heterogeneous media.

A three-microphone acoustic reflection technique using transmitted acoustic waves in the airway

The acoustic reflection technique noninvasively measures airway cross-sectional area vs. distance functions and uses a wave tube with a constant cross-sectional area to separate incidental and reflected waves introduced into the mouth or nostril. The accuracy of estimated cross-sectional areas gets worse in the deeper distances due to the nature of marching algorithms, i.e., errors of the estimated areas in the closer distances accumulate to those in the further distances. Here we present a new technique of acoustic reflection from measuring transmitted acoustic waves in the airway with three microphones and without employing a wave tube. Using miniaturized microphones mounted on a catheter, we estimated reflection coefficients among the microphones and separated incidental and reflected waves. A model study showed that the estimated cross-sectional area vs. distance function was coincident with the conventional two-microphone method, and it did not change with altered cross-sectional areas at the microphone position, although the estimated cross-sectional areas are relative values to that at the microphone position. The pharyngeal cross-sectional areas including retropalatal and retroglossal regions and the closing site during sleep was visualized in patients with obstructive sleep apnea. The method can be applicable to larger or smaller bronchi to evaluate the airspace and function in these localized airways.

Performance evaluation of a semicircular breakwater with truncated wave screens

A semicircular breakwater model with rectangular perforations and with truncated wave screen(s) of different porosities has been developed in this study which could act as an anti-reflection wave barrier, providing wave protection to coastal and marine infrastructures. The hydrodynamic performance of the breakwater model is evaluated through wave measurements in a wave flume under irregular waves. The experiments are undertaken with three setups; (i) a wave screen is attached to the front curved wall of the semicircular breakwater and none at the rear wall, (ii) a wave screen is attached at the rear curved wall of the semicircular breakwater and none at the front wall and (iii) wave screens one each is attached to the front and rear walls of the semicircular breakwater. The wave surface elevations are measured at different locations upstream and downstream of the breakwater model and the coefficients of wave transmission, reflection and energy dissipation are determined. Wave climate in the vicinity of the breakwater and the horizontal wave force on the model are also measured and analysed. The results show that the semicircular breakwater with double screens of 25% porosity is the most viable design that offers reasonably good hydraulic performance as this acts as an energy dissipater rather than a wave reflector. Further, empirical models developed using a multi-regression method for estimation of reflection, transmission and energy loss coefficients as well as the normalised wave force coefficients, correlates well with the experimental data.

Shot-profile true amplitude crosscorrelation imaging condition

The U/D imaging condition for shot profile migration can be used to estimate the angle dependent reflection coefficient, but is difficult to implement numerically because of the spectral division involved. Most techniques for stabilizing the division require a damping factor which might be difficult to estimate and which also introduces bias into the final result. A stable result can be achieved by approximating the imaging condition with a crosscorrelation of the up- and downgoing wavefields at zero time lag, but this will lead to incorrect amplitude-versus-angle (AVA) behavior of the estimated reflection coefficient. We use a simple model for wave propagation of primary reflections in the wavenumber frequency domain and invert the model with respect to the reflection coefficient. By using the properties of wavefield extrapolators it can then be shown that the reflection coefficients can be estimated by crosscorrelation of the upgoing wavefield and a downgoing wavefield where the initial wavefield is the inverse of the wavefield generated by a point source. The new imaging condition gives the correct AVA behavior for horizontal reflectors. For dipping reflectors it is shown that a postmigration correction factor can be used to recover the correct angle behavior of the reflection coefficient. The new imaging condition is numerically stable, does not involve damping factors, is simple to implement numerically, and is a simple modification of the classical crosscorrelation imaging condition. Numerical examples confirm the correct AVA behavior of the new imaging condition.

Research on micro-feature extraction algorithm of target based on terahertz radar

Micro-Doppler motion of a target is an important characteristic in high-resolution radar observation. The target feature extraction of micro motion has already been applied to many aspects of radar research. In this article, general model is established for the echo signal of a target with micro-motion. Combination of time-frequency analysis method, a method using Radon transformation to detect the parameters of lines and sinusoidal curves to estimate motion parameters of target is proposed, and the estimation of reflection coefficients of scatterers is completed through nonlinear least squares and CLEAN algorithm. The simulation result shows that this method of Radon transformation has the advantages of high precision and strong anti-noise and can extract the parameters well. The model of echo signal and method of parameter estimation are useful for radar target detection and identification.

PP and PS joint AVO inversion and fluid prediction

Abstract The technique of amplitude variation with offset or angle (AVO or AVA) can be used to extract fluid and lithology information from prestack seismic data. Based on three-term AVO equations, three elastic parameters can be inverted for by linear AVO inversion. However, many theoretical and numerical studies have demonstrated that by using offset limited data, a three-term AVO inversion may have problems of instability and inaccuracy while inverting for the density term. We have searched for an elastic parameter that contains density information and inverted this parameter in a more stable manner using offset limited data. First, we test the sensitivity of elastic parameters to hydrocarbon reservoirs and select the optimal fluid factor ( ρf ) that contains density information and has an excellent performance as an inversion parameter used to detect hydrocarbons. Then, we derive approximate PP and PS reflection coefficient equations in terms of the fluid factor. The derived equations allow us to directly estimate the fluid factor of the reservoir. Finally, we apply these equations to synthetic data by employing a joint AVO inversion technique. The results show that the method is stable and unambiguous.

Time-Domain Generalized Telegrapher's Equations for the Electromagnetic Field Coupling to Finite Length Wires Above a Lossy Ground

In this paper, a time-domain variant of the generalized telegrapher's equations for transient electromagnetic field coupling to a finite-length wire above a lossy half-space is derived. The approach is fully based on the thin-wire antenna theory. The lossy ground effects are taken into account by means of the reflection coefficient approximation. The obtained equations are handled numerically via the Galerkin-Bubnov indirect boundary element method. Computational examples are presented for the case of a single-wire line excited by an electromagnetic pulse excitation source. The obtained results for the induced current along the line are compared with those obtained using 1) the method of moments solution of the electric field integral equation implemented in the numerical electromagnetics code (NEC-4), and 2) the transmission line (TL) theory. It is shown that the results obtained by the proposed method are in excellent agreement with those of NEC-4. It is also shown that the TL approximation yields in general results which are in reasonably good agreement with the full-wave results, especially for the early time response and even beyond the limits of the accuracy of the TL theory. The TL theory can, however, give accurate results only for times before the arrival of the first reflection from the TL terminations and it fails to reproduce accurately the dispersion effects occurring after the first reflection.

Accounting for Antenna in Half-Space Fresnel Coefficient Estimation

The problem of retrieving the Fresnel reflection coefficients of a half-space medium starting from measurements collected under a reflection mode multistatic configuration is dealt with. According to our previous results, reflection coefficient estimation is cast as the inversion of linear operator. However, here, we take a step ahead towards more realistic scenarios as the role of antennas (both transmitting and receiving) is embodied in the estimation procedure. Numerical results are presented to show the effectiveness of the method for different types of half-space media.

Introduction to this special section: Land acquisition, vibroseis

How many of us have chosen to become geophysicists after an undergraduate course in which programming vibroseis correlation was one of the assignments? The first time a student understands the mathematical foundation of vibroseis is often an epiphany. The topic is a microcosm of seismology, requiring knowledge of the Fourier transform, convolution, reflection coefficient series, correlation, amp-litude and phase spectra, all aimed at the final unlikely goal of recovering a band-limited estimate of subsurface reflection coefficients by injecting a long, slowly varying signal into the ground with a truck the size of a bus. But it worked, and we went from explosive sources with only two crude control levers (shot depth and charge size) to a source with a dashboard of fine-tuning control knobs (number of vibes, source array, sweep length, up- or down-sweep, and so on).

AVO approximation for PS-wave and its application in PP/PS joint inversion

Multi-component exploration has many advantages over ordinary P-wave exploration. PP/PS joint AVO analysis and inversion are useful and powerful methods to discriminate between reservoir and non-productive lithology. In this paper, we derive a new PS-wave reflection coefficient approximation equation which is more accurate at larger incidence angles. The equation is simplified for small incidence angles, which makes AVO analysis clearer and easier for angles less than 30 degrees. Based on this approximation, a PP/PS joint inversion is introduced. A real data example shows that oil sands, brine sands and shales can be differentiated based on the P- to S-wave velocity ratio from the PP/PS joint inversion. Fluid factors and Poisson’s ratio also indicate an anomaly in the target zone at the oil well location.

The reflection of the fundamental torsional guided wave from multiple circular holes in pipes

Localised corrosion is a major concern in the petrochemical industry, and often occurs as clusters of pits. A study of the reflection from two and three small circular holes in pipes with the fundamental torsional guided wave incident is presented. FE analyses with both part and through thickness holes at different relative positions are presented, and are a step towards estimation of the scattering behaviour of multiple and random defects. The validity of employing the superposition technique in estimating reflection coefficients is assessed. Results show that the reflection coefficient for the T(0,1) mode is dependent on absolute frequency and axial separation, and independent of circumferential position. Employing superposition is found to be valid down to defect centre to centre separation distances of two diameters in the worst case, with improved validity with shallower defects. Results from the FE analyses are validated experimentally.