PP-wave Reflection Coefficient Research Articles

Amplitude variation with azimuth direct inversion for effective pressure-sensitivity parameters in horizontal transversely isotropic media

Effective pressure prediction is of great significance for fracturability evaluation in unconventional reservoirs. Quantitative characterization of effective pressure remains a great challenge in the inversion prediction of subsurface media. Our goal is to develop a novel Bayesian amplitude varying with azimuth (AVAZ) inversion method to estimate fracture weaknesses and effective pressure for a horizontal transversely isotropic (HTI) medium. Using Schoenberg’s linear slip model and pore space compressibility theory, an anisotropic saturated stiffness matrix directly characterized by effective pressure is derived based on a weak-contrast interface separating two weakly anisotropic half-spaces of HTI medium. Based on the perturbation stiffness matrix and scattering theory, we derive a PP-wave reflection coefficient approximation directly characterized by fracture weaknesses and effective pressure-sensitive parameters, which establishes a quantitative relationship between seismic reflection coefficient and effective pressure. The analysis of accuracy and sensitivity is performed to verify the reliability and applicability of the constructed reflection coefficient. And then, the azimuth-amplitude-difference forward solver is constructed based on seismic reflection coefficients to eliminate the influence of isotropic background perturbations on seismic reflection coefficients and reduce the condition number of the forward solver. Finally, we present a novel Bayesian azimuth-amplitude-difference AVAZ inversion method for transversely isotropic media constrained by Cauchy and Gaussian regularization to directly estimate the fracture weaknesses and effective pressure-sensitive parameters. The application of synthetic data and field data verifies that the inversion results are in good agreement with the actual data, indicating that the method can effectively realize the stable prediction of anisotropic parameters and effective pressure-sensitive parameters of complex media.

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]).

Horizontal transverse isotropy anisotropic parameter inversion via azimuthal seismic velocity anisotropy and its application to anisotropic 3D in-situ stress estimation

Anisotropic parameter inversion in horizontal transverse isotropy (HTI) media plays an important role in predicting the fracture density and the anisotropic in-situ stress for unconventional reservoirs. The current industry practice is to use the azimuthal PP-wave reflection coefficient to estimate the HTI anisotropic parameters. Based on the linear slip theory, we develop an innovative approach that uses azimuthal P-wave phase velocity to calculate HTI anisotropic parameters, which presents superiority over the conventional azimuthal PP-wave reflection coefficient inversion. Specifically, we first verify that the azimuthal P-wave phase velocity is for the HTI elliptical fitting than the azimuthal PP-wave reflection coefficient using the analytical formulations. Second, we sort the prestack wide-azimuth data into offset vector tile sectors and perform amplitude-variation-with-offset inversion at each azimuth. Third, we apply an elliptical fitting to the obtained azimuthal P-wave phase velocities to estimate the HTI anisotropic parameters, fracture density, and fracture direction. Fourth, based on the HTI mechanical earth model, we formulate a cost-effective 3D in-situ stress estimation method using the obtained elastic parameters and fracture compliance. Finally, field examples from the Zhaotong area, China, demonstrate that the estimated fracture density and anisotropic in-situ stress are more accurate and have higher resolution compared with conventional methods. The dominant stress regime in the study area is a strike-slip faulting regime with a governing orientation of northeast–southwest and presents good alignments with well logs, which demonstrates the reliability and accuracy of our method for predicting fracture density and anisotropic in-situ stress.

PP-Wave Reflection Coefficient Equation for HTI Media Incorporating Squirt Flow Effect and Frequency-Dependent Azimuthal AVO Inversion for Anisotropic Fluid Indicator

PP-Wave Reflection Coefficient Equation for HTI Media Incorporating Squirt Flow Effect and Frequency-Dependent Azimuthal AVO Inversion for Anisotropic Fluid Indicator

Direct inversion for shale brittleness index using a delayed rejection adaptive Metropolis-Markov chain Monte Carlo method

The reservoir brittleness index can characterize the relative brittleness of shale oil and gas reservoirs, which provides guidance for hydraulic fracturing in the later stage of oil and gas exploration and development. It is a significant index to evaluate the sweet spot of oil and gas reservoirs. Most research on the brittleness index involves laboratory measurements and petrophysical quantitative analysis, but few studies directly predict the reservoir brittleness index from prestack seismic data. The Markov chain Monte Carlo (MCMC) probabilistic algorithm incorporating the delayed rejection adaptive Metropolis (DRAM) strategy has been developed to invert the reservoir brittleness index directly. The different brittleness indexes are analyzed and compared by using the constructed rock-physics model of the shale gas exploration area to select the most sensitive one. Based on the chosen brittleness index, the approximate equation of the PP-wave reflection coefficient for the brittleness index is deduced, and the correctness and achievability of the modeling operator are indicated by theoretical analysis. To analyze the uncertainty of the brittleness index and enhance computational efficiency, an improved MCMC probabilistic inversion algorithm is introduced, which aims to optimize the sampling process of the general MCMC algorithm by delayed rejection and adaptive Metropolis strategies. Our study finds that the DRAM strategy improves the efficiency of the algorithm by nearly 30%. Synthetic examples and field seismic data verify the applicability and effectiveness of our inversion method.

Estimating two groups of fracture weaknesses using azimuthal differences in partially incidence-angle-stacked seismic amplitudes

Geophysical and geologic data, e.g., results obtained using rock cores, outcrops, and borehole images, reveal the presence of multiple sets of fractures in rock. To analyze how fracture interactions affect seismic anisotropy and dispersion, we consider an effective model that contains two sets of orthogonal fractures. In seismic amplitude analysis, we focus on the case of subsurface target zones containing a fracture network composed of primary and secondary fracture sets. Focusing on gas-bearing rocks with small fracture densities, we formulate simplified stiffness parameters in terms of two groups of fracture weaknesses, which are related to the primary and secondary fractures, respectively. Using the simplified stiffness parameters, we derive the PP-wave reflection coefficient and the azimuthal elastic impedance (AEI) as functions of the two groups of normal and tangential fracture weaknesses. Based on the derived PP-wave reflection coefficient and AEI, we propose a method and workflow in which the azimuthal variations of the partial incidence-angle-stacked seismic data are used to estimate the AEI and differences in AEI (which we refer to as DEI) is input to a nonlinear inversion for two groups of fracture weaknesses. In the nonlinear inversion, the initial values of fracture weaknesses are obtained based on a two-term approximation of the PP-wave reflection coefficient. First- and second-order derivatives of DEI with respect to fracture weakness parameters are calculated to generate the update in the unknown parameter vector. Synthetic seismic gathers with varying signal-to-noise ratios are used to validate the robustness of the estimation. Applying the inversion method to a real data set, we obtain what we interpret to be reliable fracture weakness estimates that produce azimuthal amplitude differences matching those extracted from real seismic data. The results provide a potential tool for determining if two sets of fractures have developed in a reservoir.

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

PP-wave reflection coefficient for vertically cracked media: Single set of aligned cracks

The main goal is to analyze the influence of cracks on the azimuthal variations of amplitude. We restrict our investigation to a single set of vertical, circular, and flat cavities aligned along a horizontal axis. Such cracks are embedded in either transversely isotropic background with a vertical symmetry axis (VTI) or isotropic surroundings. We employ the effective medium theory to obtain either orthotropic or VTI homogenised medium, respectively. To consider the amplitudes, we focus on a Vavrycuk-Psencik approximation of the PP-wave reflection coefficient. We assume that cracks are situated in one of the halfspaces only.Azimuthal variations depend on the background stiffnesses, incidence angle, and crack density parameter. Upon analytical analysis, we indicate which factors (such as background’s saturation) cause the reflection coefficient to have maximum absolute value in the direction parallel or perpendicular to cracks. We discuss the irregular cases, where such extreme values appear in the other than the aforementioned directions.Due to the support of numerical simulations, we propose graphic patterns of two-dimensional amplitude variations with azimuth. The patterns consist of a series of shapes that change with the increasing value of the crack density parameter. Schemes appear to differ depending on the incidence angle and the saturation. Finally, we extract these shapes that are characteristic of gas-bearing rocks. They may be treated as gas indicators. We support the findings and verify our patterns using real values of stiffnesses extracted from the sedimentary rocks’ samples.

Anisotropic Nonlinear Inversion Based on a Novel PP Wave Reflection Coefficient for VTI Media

Anisotropic Nonlinear Inversion Based on a Novel PP Wave Reflection Coefficient for VTI Media

Direct hydrocarbon identification in shale oil reservoirs using fluid dispersion attribute based on an extended frequency-dependent seismic inversion scheme

The identification of hydrocarbons using seismic methods is critical in the prediction of shale oil reservoirs. However, delineating shales of high oil saturation is challenging owing to the similarity in the elastic properties of oil- and water-bearing shales. The complexity of the organic matter properties associated with kerogen and hydrocarbon further complicates the characterization of shale oil reservoirs using seismic methods. Nevertheless, the inelastic shale properties associated with oil saturation can enable the utilization of velocity dispersion for hydrocarbon identification in shales. In this study, a seismic inversion scheme based on the fluid dispersion attribute was proposed for the estimation of hydrocarbon enrichment. In the proposed approach, the conventional frequency-dependent inversion scheme was extended by incorporating the PP-wave reflection coefficient presented in terms of the effective fluid bulk modulus. A rock physics model for shale oil reservoirs was constructed to describe the relationship between hydrocarbon saturation and shale inelasticity. According to the modeling results, the hydrocarbon sensitivity of the frequency-dependent effective fluid bulk modulus is superior to the traditional compressional wave velocity dispersion of shales. Quantitative analysis of the inversion results based on synthetics also reveals that the proposed approach identifies the oil saturation and related hydrocarbon enrichment better than the above-mentioned conventional approach. Meanwhile, in real data applications, actual drilling results validate the superiority of the proposed fluid dispersion attribute as a useful hydrocarbon indicator in shale oil reservoirs.

PP-wave reflection coefficient in stress-induced anisotropic media and amplitude variation with incident angle and azimuth inversion

The PP-wave reflection coefficient (i.e., the ratio of the amplitude of reflected P wave to the amplitude of incident P wave) has crucial practical applications in many field scenarios, such as seismic inversion and in-situ stress monitoring. However, the effect of biaxial stress, frequently encountered in the earth’s interior, on the PP-wave reflection coefficient is seldom studied. To fill this gap, we first formulate the P- and S-wave moduli and density in a biaxial-stress-induced anisotropic medium based on the acoustoelasticity theory. Then, the stress-dependent anisotropy parameters and normal/tangential rock weaknesses are proposed in the context of the stress-induced anisotropy model to obtain the corresponding effective elastic stiffness tensor and its spatial perturbation. Two stress-induced anisotropy factors (SIAF) are established to quantify the magnitude of anisotropy in a stress-induced anisotropic medium. The media with large SIAF tend to demonstrate strong anisotropy when stressed and tend to be more easily fractured from the perspective of engineering application. Furthermore, an approximate formula for the PP-wave reflection coefficient for biaxial-stress-induced anisotropic media is developed with the scattering theory. Numerical results illustrate how the reflection coefficients are affected by horizontal biaxial stress and demonstrate the feasibility and accuracy of our formula. Modeled and field inversion examples illustrate that SIAF can be reasonably inverted with our amplitude variation with incident angle and azimuth inversion method from azimuthal seismic data. Our results help to better understand the effect of biaxial stress on anisotropy and wave propagation in stress-induced anisotropic media.

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.

Seismic characterization of in situ stress in orthorhombic shale reservoirs using anisotropic extended elastic impedance inversion

Seismic characterization of anisotropic in situ stress is of great importance in improving the success of planning drilling and hydraulic fracturing treatment. Shales generally exhibit orthorhombic elastic symmetry due to the presence of vertical fractures and horizontal fine layering. We propose a novel anisotropic extended elastic impedance (AEEI) inversion approach for in situ stress estimates in shale gas reservoirs with weakly orthorhombic symmetry. Considering an orthorhombic model formed by a system of aligned vertical fractures embedded in a vertical transverse isotropic (VTI) background rock, we first derive the in situ stress expression by combining poroelastic Hooke’s law and linear slip theory. Next, we deduce a linearized PP-wave reflection coefficient as a function of fluid bulk modulus, vertical effective stress-sensitive parameter, dry-rock P- and S-wave moduli, density, dry normal and tangential weaknesses of the VTI background, and dry normal and tangential weaknesses of vertical fractures. To estimate in situ stress from the observed seismic data, we derive the AEEI and Fourier coefficients (FCs) expression and establish a three-step AEEI inversion workflow involving (1) Bayesian seismic inversion for intercept impedance, gradient impedance, and curvature impedance estimates; (2) estimating model parameters using the FCs of AEEI; and (3) estimating in situ stress using the inverted model parameters. The synthetic examples demonstrate that in situ stress can be reliably estimated even with moderate noise. Test on a real data set implies that the proposed method can generate reasonable results of in situ stress that are helpful for optimizing the horizontal drilling and hydraulic fracture stimulations of shale gas reservoirs.

Second-order approximate expressions of P- and SV-plane-wave reflection coefficients at the solid/solid media interface

To completely use large incident angle seismic data and improve the accuracy of amplitude-variation-with-offset inversion, especially for density information, we have derived second-order approximate expressions of the P- and SV-wave reflection coefficients at the solid/solid media interface. Vectors and Hessian matrices are used to describe the first- and second-order terms of the approximate expressions. The second-order approximations are then rewritten in a simple form. Furthermore, different pseudosecond-order approximations with different power series of the ray parameter p are derived based on the Taylor expansion of the second-order approximation of the P-wave reflection coefficient for the incident P wave (PP-wave reflection coefficient) according to the ray parameter p. By establishing four different single-phase medium models, we have verified that the accuracies of the second-order approximate expressions were remarkably higher than those of the first-order approximations. Furthermore, the pseudo p2 second-order approximation of the PP-wave reflection coefficient is highly consistent with the exact analytical expression.

Bayesian amplitude variation with angle and azimuth inversion for direct estimates of a new brittleness indicator and fracture density

Estimates of natural fractures or fracture-prone brittleness sweet spots are of great importance for the seismic characterization of fracability and successful commercial production of a shale play. Young’s modulus is commonly considered as a measure of brittleness. However, Young’s modulus may be unsuitable to characterize the brittleness of the organic-rich shale gas reservoirs because it exhibits an inverse relationship to porosity, total organic carbon, and gas saturation. The [Formula: see text] attribute (the ratio of Young’s modulus E to the first Lamé constant [Formula: see text]) is more sensitive than the commonly used Young’s modulus to the organic-rich shale gas reservoirs, making it a sensitive brittleness indicator. We have proposed a novel inversion technique of amplitude variation with angle and azimuth (AVAZ) for direct estimates of the new brittleness indicator [Formula: see text] and fracture density in shale gas reservoirs. Considering a horizontally transverse isotropic model formed by a system of rotationally invariant vertical fractures embedded in an isotropic background, we first derive a linearized PP-wave reflection coefficient as a function of Young’s modulus, new brittleness indicator, density, and fracture density. The new linearized approximation allows us to estimate the brittleness and fracture properties of the reservoir in a more direct manner. Next, we present a Bayesian AVAZ inversion incorporating Cauchy-sparse and smoothing-model constraint regularization to directly estimate these model parameters from azimuthal seismic data. Finally, we apply the proposed inversion approach to a synthetic example and a real data set of a shale gas reservoir from the southern Sichuan Basin to illustrate its potential in the seismic characterization of brittleness and natural fractures.

Detection of Natural Tilted Fractures From Azimuthal Seismic Amplitude Data Based on Linear-Slip Theory

Tilted transverse isotropy (TTI) is common for naturally fractured reservoir when the fractures exist a tilted axis of symmetry. Seismic characterization of natural tilted fractures from observable azimuthal reflected amplitude data, however, is quite difficult. We focus on the detection of natural tilted fractures from azimuthal seismic amplitude data, especially for low- and high-angle tilted fractures. Using the linear-slip theory, we first express the effective elastic stiffness matrix of a TTI medium as a function of background elastic moduli, fracture density, and three angles, including the incident angle, the azimuth angle, and the tilt angle. Based on the scattering function and the first-order perturbations in stiffness components across a weak-contrast reflection interface separating two weak-anisotropy TTI media, we then derive a weak-anisotropy and linearized PP-wave reflection coefficient containing the tilt angle and fracture density. For low- and high-angle aligned fracture sets, we formulate the low- and high-angle approximate PP-wave reflection coefficient equations, respectively, and propose a Bayesian seismic inversion approach to estimate the tilt angle and the corresponding fracture densities using the azimuthal differences in seismic reflected amplitude data. Synthetic and real datasets are used to demonstrate the feasibility and reliability of the proposed inversion approach. Test results make us believe that our proposed inversion approach allow us to obtain the tilted fracture properties of hydrocarbon reservoirs in a more accurate manner than previous cases of vertically transverse isotropy (VTI) or horizontally transverse isotropy (HTI).

Inversion Method of Elastic and Fracture Parameters of Shale Reservoir With a Set of Inclined Fractures

The inversion of reservoir elastic parameters and fracture parameters is of great significance to oil and gas production. In shale reservoirs with inclined fractures, using the reflection coefficient equation of vertical fractures or horizontal fractures under the vertical transverse isotropy (VTI) background has certain limitations. For this reason, based on the linear-slip model, this article establishes the approximate stiffness matrix of the monoclinic medium with a set of inclined fractures under the background of VTI and combines the Born scattering theory to further derive the PP-wave linear reflection coefficient equation of the monoclinic medium. The equation includes parameters, such as Young’s modulus, Poisson’s ratio, density, fracture weaknesses, and bedding weaknesses. Then, a rock physics model that comprehensively considers horizontal bedding and inclined fractures is established, and the influence of the inclination of the fractures on the reflection coefficient is analyzed. Finally, taking the advantage of Bayesian theory, the fracture weakness inversion method based on the azimuth amplitude difference is established, and the inversion accuracy is improved by adding Cauchy constraints and smoothing model regularization terms. Then, take the fracture weaknesses as inputs to invert the parameters, such as Young’s modulus, Poisson’s ratio, density, and bedding weaknesses. The inversion results of theoretical data show that the method can invert the fracture information well, and it can also be effectively applied to low-to-medium signal-to-noise ratio (SNR) data. The inversion results of theoretical and actual data prove that the inversion equation derived in this article can be used to obtain more accurate elastic and fracture parameters in fractured shale reservoirs.

Fracture Detection With Azimuthal Seismic Amplitude Difference Inversion in Weakly Monoclinic Medium

The rock with a vertical group of aligned fractures in the tilted transverse isotropy (TTI) background medium is regarded as an effective monoclinic medium. Thomsen parameters and fracture weaknesses can reflect the development degree of TTI background anisotropy and vertical fractures, respectively. Thus, this paper first establishes the approximate stiffness matrix of the monocline medium through the Bond transformation from Thomsen weak anisotropy theory and effective medium theory. Moreover, considering the Born scattering theory, a linearized approximate formula of PP wave reflection coefficient is further deduced. This approximate formula contains the parameters of incident angle, azimuth, tilted angle, compressional and shear moduli, density, fracture weaknesses, and Thomsen parameters. Then, the contribution of each parameter on the reflection coefficient by numerical simulation is analyzed respectively. Finally, from the perspective of Bayesian inference, an azimuthal seismic amplitude difference inversion approach incorporating Cauchy prior information and low-frequency regularization of model parameters is proposed to realize the simultaneous estimation of fracture weaknesses and Thomsen parameters. The synthetic test demonstrates that the inversion approach proposed in this article can obtain information on vertical fractures and TTI background medium and can be applied to azimuthal seismic data with moderate noise well. Furthermore, the inversion results of the synthetic test and field data illustrate the stability and feasibility of the inversion approach and also confirm the fracture weaknesses and Thomsen parameters of the monoclinic medium can be reasonably estimated by the inversion equation derived in this paper.

Seismic Characterization of Decoupled Orthorhombic Fractures Based on Observed Surface Azimuthal Amplitude Data

Commonly-used seismic fracture characterization method assumes one single fracture set, and this article aims to relax the limitation and demonstrate the feasibility of seismic characterization for two sets of orthorhombic fractures. Elastic properties of orthorhombic fractures can be studied using a model of horizontal and vertical fractures as linear-slip interfaces embedded in an isotropic background. High fracture density in hydrocarbon reservoirs is the “sweet spot” of effective permeability for fluid flow, and seismic characterization of orthorhombic fractures using the variations in reflection amplitude versus offset and azimuth (AVOAz) helps to optimize the production of naturally fractured reservoirs. Based on an effective orthorhombic linear-slip model, we first construct the effective elastic stiffness matrix in terms of elastic moduli and decoupled horizontal and vertical fracture densities under the assumption of weak anisotropy (WA) or small fracture densities. Using the scattering function and first-order perturbation in effective elastic stiffness components, we derive a WA and linearized PP-wave reflection coefficient containing decoupled orthorhombic fracture densities to describe the characteristics of horizontal and vertical fracture sets. We then propose an efficient AVOAz inversion method to perform the seismic characterization of decoupled orthorhombic fracture densities based on observed surface azimuthal amplitude data in a Bayesian framework. We finally apply the inversion approach to synthetic and field datasets to demonstrate its feasibility and reasonability in orthorhombic fracture characterization.

Hierarchical Bayesian Probabilistic Seismic AVO Inversion Using Gibbs Sampling With IA2RMS Algorithm

From the observed seismic data, the estimation of elastic parameters and lithofacies of subsurface layers with seismic amplitude variation with offset (AVO) inversion plays an important role in reservoir characterization. The sequential estimation of elastic parameters and lithofacies in AVO inversion usually affect the prediction accuracies of model parameters without considering the prior information related to lithofacies. We propose a novel probabilistic AVO inversion approach in hierarchical Bayesian framework that combines a hierarchical iterative strategy with Gibbs-IA2RMS sampling, to estimate elastic parameters and lithofacies simultaneously. From the exact PP-wave reflection coefficient, we first derive the posterior distribution of model parameters involving a Bayesian hyper-parameter of lithofacies through the hierarchical prior probability distributions and the likelihood distribution of observed data. Based on Monte Carlo Markov chain approximation, we then introduce an iterative Gibbs-IA2RMS sampling to achieve the high sampling stability of the high-dimensional posterior PDF in AVO inversion. The algorithm realizes the adaptive construction of proposal distribution, and has a higher acceptance rate than the generic Metropolis-Hastings algorithm. The numerical results show that the approach effectively simulates the posterior distributions and inversion uncertainties of model parameters, and improves the computational efficiency of probabilistic AVO inversion. The applicability and validity of the proposed approach are also demonstrated with a field data application.