Estimated Reflection Coefficients Research Articles

Seismic amplitude inversion based on a new PP-wave reflection coefficient approximation equation for vertical transversely isotropic media

We develop a method for the simultaneous amplitude-variation-with-offset or -angle inversion of anisotropic parameters for transversely isotropic media with vertical axis of symmetry (VTI media). First, we introduce a nonlinear PP-wave reflection coefficient approximation equation in terms of only P- and S-wave impedances for isotropic elastic media. Then, by replacing the isotropic part of Rüger’s equation with this equation, we obtain a new PP-wave reflection coefficient approximation equation called the ASI Rüger equation for VTI media. To invert the parameters for VTI media based on the ASI Rüger equation, we adopt the Bayesian generalized linear inversion (GLI) method, a combination of GLI and Bayesian linear inversion, in which the noise and model perturbation are assumed to conform to the zero-mean Gaussian distribution. Compared with Rüger’s equation, the ASI Rüger equation decreases the trade-off between the parameters and reduces the ill-posedness of the inverse problem. The synthetic and field data tests demonstrate the feasibility of our method for inverting VTI media parameters (the vertical P-wave impedance, the vertical S-wave impedance, and Thomsen’s parameters [Formula: see text] and [Formula: see text]).

Characterization and analysis of attenuation anisotropy in viscoelastic vertical transverse isotropic media

AbstractDue to the intrinsic attenuation of the earth, the study of wave propagation characteristics, considering seismic attenuation plays an important role in high‐precision reservoir prediction. Therefore, we investigate the propagation and reflection characteristics of seismic waves in viscoelastic vertical transverse isotropic media in the complex frequency domain. Specifically, we analyse the response characteristics of velocity, propagation vector and attenuation vector with respect to viscosity media with different attenuation intensities. Furthermore, based on the quasi‐Zoeppritz equation, the variation of reflection coefficient amplitude with offset at different attenuation angles and different attenuation intensities is studied. We also compare the trends in the amplitude variation of reflection coefficients with offset in elastic isotropic, elastic anisotropic and viscoelastic anisotropic media. Due to the complexity of the exact reflection coefficient expression, we first propose the approximate expression of the attenuation–anisotropy parameters and then derive the approximate expression of the reflection coefficient. The numerical simulation results show that the approximate expression of the reflection coefficient is still accurate, even in media with strong anisotropy. Finally, the accuracy evaluations of the reflection coefficient formulas using four typical theory models demonstrate that the approximate reflection coefficient formulas are highly accurate in both weak and strong anisotropic media.

Simultaneous prediction of the geofluid and permeability of reservoirs in prestack seismic inversion

Geofluid discrimination and permeability prediction are indispensable steps in reservoir evaluation. From the perspective of prestack seismic inversion, predicting fluid indicators is an effective method for obtaining fluid properties directly from seismic data. In contrast, the direct prediction of permeability from observed seismic gathers is constrained by the difficulty in establishing a link between permeability and elastic parameters. However, we show that the pore structure parameters in seismic petrophysical theory are highly related to permeability, providing a new solution for predicting permeability using seismic data. Therefore, the correlation between the shear flexibility factor and permeability is first verified based on logging curves and laboratory data, and the results demonstrate that the shear flexibility factor can be an indicator of reservoir permeability. Second, an approximate reflection coefficient equation is derived for the direct characterization of the shear flexibility factor. In the developed equation, a novel fluid indicator, expressed as the ratio of Russell’s fluid indicator to the square of the shear flexibility factor, is defined for the simultaneous prediction of fluid types and permeability. With the validated response of the novel fluid indicator to geofluid types, we achieve simultaneous predictions of fluid types and reservoir permeability characteristics from prestack seismic data, using a boundary-constrained Bayesian inversion strategy. The model tests and the application of field data from a clastic reservoir confirm the effectiveness and applicability of the method.

A Reflection Coefficient Estimation Method for Power Cable Defects Based on Three-Point Interpolated FFT

A Reflection Coefficient Estimation Method for Power Cable Defects Based on Three-Point Interpolated FFT

Normal incidence reflection coefficient approximation at an isotropic–poroelastic interface

AbstractSeismic response from porous sediments can be used in reservoir characterization and fluid detection. Reflection coefficient at the isotropic/poroelastic interface is essential to reveal seismic response from the fluid‐saturated deposits. The exact normal incidence reflection coefficient is given by complex mathematic expression and not very clear relations with solid and fluid properties. Therefore, we derive the reflection coefficient approximate formula in series with respect to the square root of the imaginary unit multiplying by the ratio between angular frequency and the characteristic angular frequency. Compared to the exact reflection coefficient, the proposed approximate formula has a more concise mathematical form and clearer relationship with the moduli and densities. Meanwhile, there is no need to calculate the complex wavenumbers of poroelastic media from the dispersion equation as the exact reflection coefficient. When the frequency tends to zero, the approximate formula is consistent with reflection coefficient for the isotropic/isotropic interface. The proposed formula's applicability is verified through two models with an interface separating the mudstone and fully fluid‐saturated sandstone with pore fluids as water or carbon dioxide.

A Decoupled Fracture- and Stress-Induced PP-wave Reflection Coefficient Approximation for Azimuthal Seismic Inversion in Stressed Horizontal Transversely Isotropic Media

A Decoupled Fracture- and Stress-Induced PP-wave Reflection Coefficient Approximation for Azimuthal Seismic Inversion in Stressed Horizontal Transversely Isotropic Media

Seismic pre-stack inversion for physical and anisotropic parameters in fractured shale reservoirs

AbstractThe estimation of physical and anisotropic parameters is of great importance for the characterization of fractured reservoirs. Vertical fractures developing in a laterally isotropic (VTI) setting are equivalent to orthotropic anisotropic (OA) media common in stratified fractured shale reservoirs. To obtain independent anisotropic and physical information, a novel reflection coefficient approximation containing physical and anisotropic parameters is derived to improve the stability of the inversion for orthotropic media. To simplify the equation for the reflection coefficient, an approximate rock physics model is constructed using the approximate theory of rock modulus. The estimated parameters are reduced from nine to six. The accuracy analysis reveals that the new reflection coefficient is appropriate and suitable for inversion. In addition, a stepwise Bayesian amplitude versus angle and azimuth (AVAZ) inversion method with smooth background constraints is developed to estimate the anisotropic and physical parameters from the azimuthal seismic data. The smooth background constraint improves the robustness of the inversion. And the stepwise inversion strategy solves the problem that the contribution of the fracture parameter to the reflection coefficient is smaller than the other parameters. Synthetic cases show that the proposed stepwise Bayesian AVAZ inversion method is feasible in estimating the anisotropic parameters for OA media even when the signal-to-noise ratio is 2. The field cases show that the proposed inversion method has good stability and robustness in predicting shale reservoirs with vertical or near-vertical fractures.

Reflection Coefficient Estimation of Femtosecond Laser Surface Processing Using Support Vector Regression

An image analysis-based Reflection Coefficient (RC) estimation method of femtosecond laser surface processing for the blackening of X-ray imaging sensor shell is proposed. The Support Vector Regression (SVR) is used for RC computation and both an offline and an online steps are considered in this method. Regarding offline step, the typical laser process parameters are set to perform surface processing and Scanning Electron Microscope (SEM) images are recorded. Then a series of image features are computed and both the computed image features and typical laser parameters are used to train SVR: the training dataset includes the laser line space, laser beam diameter, natural logarithm of laser power divided by laser frequency, and image features of Gray-Level Co-occurrence Matrix (GLCM); the supervising data are laser ablation diameters. As for online step, when SEM image data are recorded after laser processing, the trained SVR is used to predict laser ablation diameter and then the RC can be computed by laser ablation model. Many experiment results have verified the effectiveness of our proposed method, and the RC estimation accuracy can be better than 90.0%.

Seismic inversion and fracture prediction in tilted transversely isotropic media

Abstract The conventional Amplitude variation with offset (AVO) inversion has been mainly developed for the isotropic media and therefore it is generally inapplicable to the anisotropic fractured formations. A set of tilted fractures in isotropic medium can be regarded as a transversely isotropic (TTI) medium. The reflection coefficient equation in TTI media contains many parameters such as anisotropic parameters, velocities, azimuth and dip angles. The selection of objective functions can significantly affect its performance in searching for the optimal solution. The seismic inversion of the TTI medium remains challenging because of its many parameters, and is very complicated after conversion into solving function problems. The genetic algorithm (GA) provides a universal framework to solve the optimization problem in complex systems, and it is independent of the types and disciplines of problems. In this study, the GA-based seismic prestack inversion of the TTI medium is implemented by constructing the objective functions of anisotropic parameters based on the TTI medium reflection coefficient approximation. The inversion performance is shown to be satisfactory on the one-dimensional well logging model, modified Hess model and the field datum. Furthermore, fracture filling materials are well predicted according to the theories of the equivalent medium for fractured materials and fracture weakness. The inversion results demonstrate the proposed method to be feasible and robust. The findings of this research are expected to provide theoretical guidance for the inversion of elastic parameters of anisotropic media and fracture type identification in hydrocarbon reservoirs.

A matrix-fracture-fluid decoupled PP reflection coefficient approximation for seismic inversion in tilted transversely isotropic media

Fracture-induced azimuthal anisotropy of seismic waves has useful applications in the characterization of hydrocarbon reservoirs as well as the overburden. Existing theories face problems estimating the fracture-weakness parameters, identifying the saturating fluid, and constraining the depth model building. To overcome these problems, we have adopted an azimuthal amplitude variation with angle/offset inversion for the estimation of these parameters and identification of the fluid. First, we define more intuitive fracture and fluid indicators based on rock physics, identifying the fluid by decoupling the fracture weakness parameters. Then, we derive a “rock matrix-fracture-fluid” decoupled PP-wave reflection coefficient approximation of a weakly tilted transversely isotropic medium by using a perturbation matrix and scattering theory. Compared with the conventional fracture weakness-based approximation, our method incorporates the fracture density and the fluid indicator. The inversion test finds that our approximation is effective.

Joint PP-PS seismic prestack inversion of thin-bed reservoirs

Abstract Thin beds are significant targets in seismic exploration of lithological reservoirs. The conventional Amplitude Versus Offset/Angle (AVO/AVA) inversion methods are based on Zoeppritz equations and their approximate formulas under single-interface assumptions, which are not suitable for thin-bed problems. Therefore, AVO/AVA inversion methods for thin-bed reservoirs are needed in high-resolution seismic exploration. Based on approximate reflection coefficients of a thin bed, this paper proposes a joint PP-PS prestack inversion method of thin-bed reservoirs using a least-squares approach. The method directly predicts elastic properties, including P-wave velocities, S-wave velocities and densities, as well as thin-bed thickness. In this study, four typical thin-bed models and an actual thin coal seam were used to prove applicability and superiority of the given inversion procedure. Compared to prestack inversion methods using exact Zoeppritz equations, our inversion method reveals thin-bed existence precisely, gives higher estimation accuracy and has better noise robustness. Future applications of the proposed inversion method are expected to advance seismic reflectivity techniques of thin-bed reservoirs, making it possible to detect potential source reservoirs with higher precision and accuracy.

Approximate reflection and transmission coefficients at an interface between two contrasting viscoelastic anisotropic half-spaces

SUMMARY We present and compare two new methods to calculate the reflection and transmission coefficients of qP, qSV and qSH waves at a flat interface between two contrasting viscoelastic anisotropic half-spaces. The first method is a new version of the real ray tracing method that extends the traditional real ray tracing method to tackle the triplications of the qSV wave. This new version is valid for computing the reflection and transmission coefficients of the qP and qSV waves for all pre- and post-critical angles of incidence, which cannot be handled by the previous approach. The second method employs the real slowness direction and Snell's law to provide approximate reflection and transmission coefficients for such wave modes. This approximate method has attractive advantages which are not only the avoidance of the searching process inherent in the real ray tracing method but also offers competitive economical solutions to the first method. Many viscoelastic VTI models are utilized to validate the two methods. The numerical results show that (1) the ray angles, ray velocities, ray Q-factors, and the magnitudes of the reflection and transmission coefficients obtained by the two methods closely agree with each other, except in the vicinity of the critical angles and (2) the phase angles of the reflected and transmitted waves exhibit complexities due to the existence of some reverse phenomena between the approximate and the real ray tracing solutions. However, such phase discrepancies do not affect the magnitudes of the reflection and transmission coefficients. Moreover, the energy ratios of the different wave modes satisfy the energy conservation criterion at the interface.

Investigation of ultrasonic soft tissue-bone reflection coefficients correlating with curve severity in children with adolescent idiopathic scoliosis.

Adolescent idiopathic scoliosis (AIS) is a three-dimensional curvature of spine. Children with AIS and low bone quality have higher chance to get curve progression leading to bigger spinal curvature. In addition, bone quality affects acoustic impedance of bone, thus influencing the reflection coefficient of ultrasound signal from the soft tissue–bone interface. This study aimed to estimate the bone quality of AIS patients based on the reflection coefficients to determine the correlation of the bone quality with curve severity. A simple bone model was used to develop an equation to calculate the reflection coefficient value. Experiments were conducted on five different phantoms. Acrylic was used to design a vertebral shape to study the effect of surface roughness and inclination, including: smooth flat surface (SFS), smooth curved surface (SCS), rough curved surface (RCS), and the rough curved inclined surface (RCIS). A clinical study with 37 AIS patients were recruited. The estimated reflection coefficient values of plate phantoms agreed well with the predicted values and the maximum error was 6.7%. The reflection coefficients measured from the acrylic-water interface for the SFS, SCS, RCS, RCIS (3° and 5°) were 0.37, 0.33, 0.28, (0.23 and 0.12), respectively. The surface roughness and inclination increased the reflection loss. From the clinical data, the average reflection coefficients for children with AIS were 0.11 and 0.07 for the mild curve group and the moderate curve group, respectively. A moderate linear correlation was found between the reflection coefficients and curve severity ( = 0.3). Patients with lower bone quality have observed to have larger spinal curvature.

A Bayesian Method for ViSAR Image Fusion Using Effective Reflection Coefficient

Since the isotropic scattering assumption does not hold in a wide-angle synthetic aperture radar, the video synthetic aperture radar (ViSAR), a new sensing mode by sequentially forming SAR images on a series of contiguous or overlapping sub-apertures, has the promising capability to capture aspect-dependent scattering behavior of objects. In this paper, a new Bayesian method for fusing ViSAR images is proposed. First, the notion of effective reflection coefficient is defined to characterize aspect-dependent scattering behavior of objects. Based on the ViSAR images sequence, the spatial effective reflection coefficient in the area of interest (AOI) when observing at different aspect angles are estimated. A Bayesian hypothesis testing is then derived to fuse the obtained effective reflection coefficient estimates for detecting scatterers in the AOI. The performance of the proposed method is evaluated and compared with that of the conventional GLRT-based ViSAR image fusion method in a simulated scenario. Numerical results demonstrate the superiority of the proposed method in capturing the aspect-dependent scattering characteristics as well as the spatial structure of objects.

Seismic AVA inversion of elastic and attenuative parameters in viscoelastic media using the Zoeppritz equations

When seismic wave passes through oil-gas bearing reservoir, it will cause relatively large attenuation effect due to energy dissipation. Two constants characterizing attenuation strength, P- and S-wave inverse quality factors, are widely used in seismic prediction. Although various attenuation-related petrophysical models have been introduced into the approximate reflection coefficient equations to describe a viscoelastic medium, the low accuracy of the approximation in the range of moderate to large incident angle limits the approximation-based amplitude variation with angle (AVA) inversion methods in estimation of attenuation factors. To avoid the impact caused by the uncertainty of the linear factors in the attenuation model, we propose an AVA inversion based on Zoeppritz equations to directly estimate elastic properties (P- and S-wave velocity, and density) and attenuation factors (P- and S-wave inverse quality factors). First, we introduce the complex velocity model into the Zoeppritz equations to decouple the viscoelastic velocity into elastic velocity and inverse quality factors. Under the generalized linear inversion framework, we then derive the Jacobian matrices and establish a joint PP- and PS-wave inversion to improve the stability and accuracy. Tests on both synthetic and real multi-component seismic data sets verify the elastic properties and attenuation factors can be reasonably and stably predicted. It can be concluded that the established approach is an effective tool in attenuation factors estimation, and the predicted attenuation factors appear as an additional proof for the identification of gas-bearing reservoirs.

Second-order approximate reflection coefficients of vertical transversely isotropic thin beds

Second-order approximate reflection coefficients of vertical transversely isotropic thin beds

Combined fluid factor and brittleness index inversion for coal‐measure gas reservoirs

ABSTRACTGas content and brittleness characteristics, which are mostly quantified using the fluid factor and brittleness index, are the key factors in the evaluation of coal‐measure gas reservoirs, which are similar to traditional unconventional gas reservoirs. However, most previous seismic inversion research and evaluations only focused on one of the parameters. Therefore, in this study, we performed a combined inversion of the fluid factor and brittleness index based on pre‐stack seismic records collected from a typical coal‐measure gas block in the Sichuan Basin. First, a new P–P wave reflection coefficient approximation based on both parameters was derived, and the precision and sensitivity of the inversion parameters were analysed. We then constructed a new inversion equation based on Bayes’ theorem. The logging curves obtained for a typical coal‐measure gas well and through pre‐stack seismic profile were used to evaluate the inversion method. The results of the model test and profile inversion at the well location were in good agreement with the original logging values. Finally, we analysed and discussed the results of the inversion of both parameters for the evaluation of the gas content and brittleness characteristics of the target reservoirs.

Weak-anisotropy approximation of P-wave reflection coefficient in anisotropic media of arbitrary symmetry and tilt

Applicability of the approximate expression for the P-wave reflection coefficient at a weak-contrast reflector separating two weakly anisotropic half-spaces of arbitrary symmetry is extended to media of arbitrary symmetry and tilt. The reflection coefficient consists of the approximate P-wave reflection coefficient at a weak-contrast interface separating two reference isotropic half-spaces and a correction term due to anisotropy. Along an arbitrarily chosen profile, the “isotropic” term depends on the density and P- and S-wave contrasts, and the correction term depends linearly on the contrasts of four profile weak-anisotropy (WA) parameters specifying anisotropy along the profile. In addition, both terms depend on the polar angle of incidence. In each half-space, the four profile WA parameters can be expressed as a linear combination of 12 of 21 global WA parameters specifying anisotropy of the half-space. Coefficients of this linear combination are functions of the azimuth of the profile. WA parameters are a generalization of Thomsen parameters to arbitrary anisotropy and represent an alternative to 21 independent elements of the stiffness tensor. WA parameters can be used for the approximation of other related concepts such as the reflection moveout or the geometric spreading. Presented tests illustrate high accuracy and flexibility of the proposed formula for the P-wave reflection coefficient. They also show that very accurate results can be obtained for contrasts and anisotropy, which cannot be considered weak.

Approximate equations of PP-, PS1- and PS2-wave reflection coefficients in fluid-filled monoclinic media

SUMMARY Studying the seismic reflection characteristics of fractured strata can provide a theoretical basis for the exploration of unconventional oil and gas reservoirs. When several (more than 1) sets of oblique vertical fractures that are rotationally non-invariant are embedded in an isotropic or vertical transversely isotropic (VTI) background, the stratum exhibits equivalent monoclinic anisotropy. However, the exact algorithm of the reflection and transmission coefficients of monoclinic media is algebraically complicated and difficult to use in theoretical analysis and application. In this paper, under the assumption that fractures are filled with fluid, based on the linear-slip theory, we solve the phase velocities of monoclinic media from the Christoffel equations by using the first-order perturbation method and then derive the recursive equations of the PP-, PS1-, and PS2-wave reflection coefficients. The theoretical analysis results show that for an interface of monoclinic media, when setting a series of fracture densities for the lower medium, the relative error of the proposed approximate reflection coefficient of the PS2 wave is less than 5.7 per cent, and those of the PP and PS1 waves are generally less than 2.5 per cent for a wide range of anisotropy strength and impedance contrast; when setting a series of fracture densities for the upper medium, the relative error of the proposed approximate reflection coefficients of the PP, PS1 and PS2 waves are generally less than 6.4, 5.1 and 4.5 per cent, respectively. When degenerated to the horizontal transversely isotropic model, compared with Rüger's approximation, at incidence angles of 1–30°, the two results are almost coincident, but the proposed approximations are closer to the exact solutions.

Reconstruction of half-space boundary impedance and sound source direct radiation based on reflection coefficient estimation

When implementing the reconstruction of the sound field directly radiated from a source located in a half-space, the half-space basis functions with boundary impedance as a parameter, need to be formulated. And the boundary impedance is usually obtained via <i>in situ</i> sound impedance measurement techniques. In the reconstruction method based on the expansion in half-space spherical wave basis functions, a hologram surface and a single reference microphone placed in the near-field are used to collect sound pressures. The sound pressure at the reference microphone is first reconstructed and the error of the reconstructed pressure relative to the measured pressure is then calculated. The sound pressure reflection coefficient corresponding to the minimum error is chosen as the measure of the reflection coefficient at the measurement point. Thus, this method is applicable to reconstructing the directly radiated sound pressures without the knowledge of boundary impedance, free from the in situ sound impedance measurement techniques necessary for conventional methods. The purpose of this work is to discuss the various parameters affecting the accuracy of reconstruction. Moreover, the boundary impedance is reconstructed based on the estimation of the reflection coefficient, so that a sound impedance measurement technique implemented via the near-field acoustical holography is proposed. By taking the spherical source for example, numerical simulations are conducted to verify the proposed method of reconstructing the boundary impedance and the directly radiated sound pressures. The influences of reference microphone coordinate, the effective flow resistivity of the boundary, and the rate of decrease of porosity with depth of the boundary on the accuracy of reconstruction are quantitatively analyzed.