Amplitude Variation With Offset Inversion Research Articles

Bayesian joint residual moveout and amplitude-variation-with-offset inversion

Residual moveout (RMO) can have a severe impact on seismic amplitude-variation-with-offset (AVO) analysis. It is, therefore, common practice to quality control and correct the processed seismic data for RMO before AVO analysis. However, a complicating factor is that AVO effects and tuning may result in up- or down-dipping events that are easily mistaken for events with RMO, e.g., AVO Class 2p response. Flattening these events will lead to an incorrect AVO estimation. We present a new Bayesian joint RMO and AVO inversion to estimate the RMO time shifts and the AVO intercept and gradient. The joint inversion corrects the seismic data based on the RMO and AVO prior models rather than explicitly assuming that the data should be flattened. The prior models will typically guide toward flat gathers but will also allow for up- and down-dipping events when these are possible within the prior model. The method is illustrated on synthetic and real seismic data. For cases wherein flat events are correct, the results are similar to sequential methods with RMO correction before AVO analysis, but in situations wherein dipping seismic reflectors may be misinterpreted as events with RMO, the joint inversion provides better results by evaluating RMO and AVO simultaneously. The inversion results include the posterior covariance matrix, which represents uncertainties for the AVO intercept and gradient, the RMO time shifts, and the correlations between these at all samples. The uncertainty of the RMO time shift varies within seismic gathers and depends on the seismic quality and how clear and well determined the seismic events are. The uncertainty of the RMO is lower for clear and continuous events but increases in the zones with weaker and noisy events. The uncertainty of the RMO time shifts has a low impact on the uncertainty of the AVO intercept but increases the uncertainty of the AVO gradient significantly.

Quantitative inversion of the elastic parameters outside the borehole based on exact Zoeppritz equations

The acoustic remote detecting method in the borehole has developed rapidly in the past few decades. It uses the reflected waves recorded by array receivers based on monopole or dipole sources in the fluid filled borehole to image geological structures outside the well. The result can provide guidance on the exploration and evaluation of oil and gas reservoirs and mineral resources. However, the present structure imaging results lack of the elastic information, which limit the quantitative evaluation of the resources. The AVO (amplitude variation with offset) inversion theory is introduced into the analysis of borehole waves. The interested interfaces (fractures or minor faults) with a generally larger wave impedance difference makes the widely used approximate equation in the surface exploration no longer applicable. Therefore, the exact Zoeppritz equations are used as the forward equations in the inversion. To reduce the nonlinearity of inversion, the initial model combining structure tensor and mode wave velocity analysis is constructed. The simultaneous inversion of the wave velocity and density of the reflector provides a theoretical basis for quantitatively evaluating the elastic parameters of the reservoir outside the borehole. [Work supported by the National Natural Science Foundation of China (42004117 and 42127807).]

Spherical-wave elastic inversion in transversely isotropic media with a vertical symmetry axis

SUMMARY Although subsurface media are usually assumed to be isotropic, anisotropy is ubiquitous in crustal rocks and leads to the variation of seismic response with direction. Transversely isotropic media with a vertical symmetry axis (VTI media) are widely found in the real world, such as in textured shale reservoirs. Plane-wave reflection coefficients (PRCs) in VTI media have been widely exploited in amplitude variation with offset (AVO) inversion to estimate the elastic and anisotropy parameters of subsurface media. However, the PRCs in VTI media meet some fundamental problems, especially at near-critical or post-critical incidence angles where the spherical-wave effect is significant. To consider the wave front curvature, a complex spherical-wave reflection coefficient (SRC) in VTI media is derived. To better understand the spherical-wave seismic response in VTI media, we investigate the dependence of the complex SRC on frequency, reflector depth and Thomsen anisotropy parameters ($\varepsilon $ and $\delta $). Based on a complex convolution model, a spherical-wave AVO inversion approach in VTI media is proposed to estimate the vertical (symmetry-axis) compressional and shear wave velocities (P and S waves), density and Thomsen anisotropy parameters from observed seismic data with different incidence angle and frequency components. Synthetic data with Gaussian random noise are used to verify the robustness of the spherical-wave AVO inversion approach in VTI media. Field data examples show that the proposed approach can produce reasonable inversion results that match well with the well-logging data.

Bayesian linearized rock-physics amplitude-variation-with-offset inversion for petrophysical and pore-geometry parameters in carbonate reservoirs

Rock-physics amplitude-variation-with-offset (AVO) inversion aims at directly predicting reservoir properties from prestack seismic data. However, carbonate reservoir rocks often develop complex pore structures, which limits the application of conventional inversion methods with fixed pore-geometry parameters. We derive a PP-wave reflectivity equation in terms of porosity, water saturation, and pore-aspect ratio and we develop a rock-physics AVO inversion method to jointly estimate the petrophysical and pore-geometry parameters in carbonates. The reflectivity equation is obtained by linearizing the rock-physics model based on the differential effective medium model and Gassmann’s equation using Taylor series approximation, and we combine the linearization with the Aki-Richards equation. Thanks to the linearized model, the analytical solution to the inverse problem is derived using Bayesian linear theory. Our solution combines simulated annealing to estimate the prior information of the pore geometry and the iterative Bayesian inversion to update the posterior model. The method is tested on a benchmark data set and compared with conventional methods with a fixed aspect ratio. The results show that our method improves the petrophysical results. The method is also compared with two-step and nonlinear inversion methods to demonstrate its advantages. The method is applied to a field seismic section from a carbonate reservoir with a complex pore structure to demonstrate its advantages in terms of prediction accuracy.

Spectral decomposition and multifrequency joint amplitude-variation-with-offset inversion based on the neural network

The conventional amplitude-variation-with-offset (AVO) inversion method based on the amplitude attribute of prestack gathers calculates the elastic parameters of underground media through the variation of amplitude with offset. However, when the underground medium is a thin interlayer, the tuning effect will occur, which is the aliasing phenomenon of amplitude at the reflection interface. The tuning effect makes the conventional AVO inversion method based on amplitude attributes difficult to solve the problem of thin interlayer recognition. In addition, the same reflection interface will have different AVO characteristics at different frequencies, whereas the frequency factor is not included in conventional AVO inversion methods. Two-stage neural network approaches based on deep learning are combined to improve the resolution of thin interlayers and to accurately invert the elastic parameters. For the first-stage neural network, a fully connected network is used to solve the inversion spectral decomposition problem. It can eliminate the thin interlayer tuning effect, effectively improve the resolution, and obtain reflection coefficients at different frequencies. For the second-stage neural network, a multichannel convolutional neural network is used to establish the mapping relationship between multifrequency reflection coefficients and elastic parameters, so that the multifrequency joint inversion of the elastic parameters could be realized. This procedure is applied to synthetic data (with and without noise) to indicate the resistance to noise interference of the two-stage deep-learning method. Compared with the method of directly predicting elastic parameters using seismic data and the conventional AVO inversion method, the two-stage deep-learning method can describe the elastic parameters of thin interbeds more accurately. The same procedure is applied to the field data, and the inversion results indicate that they can well match with the well-logging data. Hence, it is promising for practical applications.

Information-based seismic amplitude inversion

Amplitude variation with offset (AVO) inversion, particularly for more than two model parameters, is a highly ill-posed problem and, hence, regularization is indispensable. For common regularization such as norm-regularization, learning can be forged ahead via gradient descent. Alternatively, learning can be achieved by performing gradient descent on the objective and projects the result back into the space of the regularizer; this allows the use of atypical regularization functions. Here, we propose a regularized inverse problem to mitigate the Ill-posedness of the amplitude inversion. The regularization is added to measure the difference in information between the a priori probability density function and the predicted probability density of the inverted parameters, and therefore enhances the consistency between the inversion results and the a priori geological information. Information theory provides a collection of contrast functions which quantify the divergence from one probability distribution to another, such as the relative entropy. The a priori density is approximated by a Gaussian mixture model, obtained from well logs and rock physics data. The mixture model is a density estimator, providing the statistical properties of the model parameters of interest. The likelihood of the data and the divergence are combined in an augmented Lagrangian scheme, to obtain a stable solution that best generate the recorded seismic data and satisfy the geological constraints conveyed by the a priori probability density function. The proposed inversion scheme is applied to the anisotropy AVO inversion, for estimating the elastic and seismic anisotropy parameters of shale formations. Compared to the unconstrained minimization, the P- and S-wave velocity, and ε are better recovered, moreover, density and Thomsen's δ are well-constrained.

AVO Inversion Based on Closed-Loop Multitask Conditional Wasserstein Generative Adversarial Network

Neural networks are commonly used for post-stack and pre-stack seismic inversion. With sufficient labelled data, the neural network-based seismic inversion results are more accurate than that use traditional seismic inversion methods. However, in the case of insufficient labeled data, the accuracy of neural networks-based seismic inversion results decreases and is even lower than those based on traditional inversion methods. In addition, the seismic inversion results based on neural networks generally suffer from lateral discontinuity. It further reduces the accuracy of the inversion results. To tackle these problems, we propose a pre-stack seismic amplitude variation with offset (AVO) inversion method based on Closed-Loop Multi-task conditional Wasserstein Generative Adversarial Network (CMcWGAN), which is a GAN-based AVO inversion method. CMcWGAN enables simultaneous and accurate inversion of P-wave velocity ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V_p</i> ), S-wave velocity ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V_s</i> ), and density ( ρ ). Moreover, it uses the low-frequency information of elastic parameters as a conditional input to alleviate the problem of lateral discontinuity in inversion results. Experimental results of simulated data show that the inversion results based on CMcWGAN have higher accuracy than those based on traditional AVO inversion methods. In addition, when the seismic angle gather is noisy, CMcWGAN has better robustness than the traditional methods. CMcWGAN can also obtain reasonable AVO inversion results in field seismic angle gather data.inversion results. Experimental results of simulated data show that the inversion results based on CMcWGAN have higher accuracy than those based on traditional AVO inversion method. In addition, when the seismic angle gather is noisy, CMcWGAN has better robustness than traditional method. CMcWGAN can also get reasonable AVO inversion results in field seismic angle gather data.

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.

Characterizing Gas Hydrate-Bearing Marine Sediments Using Elastic Properties—Part 2: Seismic Inversion Based on a Pore-Filling–Solid Matrix Decoupling Scheme

Characterizing gas hydrate-bearing marine sediments using seismic methods is essential for locating potential hydrate resources. However, most existing pre-stack seismic inversion methods estimate the properties of sediments containing gas hydrates without considering specific characteristics associated with gas hydrate occurrences. In the present study, a pore-filling–solid matrix decoupling amplitude variation with offset (AVO) formula is proposed to represent seismic reflectivity in terms of properties associated with gas hydrates. Based on the rock physics relationships of solid substitution, the parameters introduced into the decoupling AVO equation estimate the concentration of gas hydrates with different occurrences, including pore fillings mixed with water and solid components forming part of the dry sediment frame. A theoretical model test indicates that seismic attributes obtained with the decoupling AVO inversion are superior to the conventional wave velocities-related properties in predicting gas hydrate saturations. A realistic model test further validates the applicability of the proposed method in characterizing a gas hydrate system with varying concentrations and layer thickness. By adjusting the tuning parameters, the configurations and concentrations of the gas hydrate system can be identified using the obtained attributes. Therefore, the presented method provides a useful tool for the characterization of gas hydrate-bearing sediments.

Model-data-driven seismic inversion method based on small sample data

As sandstone layers in thin interbedded section are difficult to identify, conventional model-driven seismic inversion and data-driven seismic prediction methods have low precision in predicting them. To solve this problem, a model-data-driven seismic AVO (amplitude variation with offset) inversion method based on a space-variant objective function has been worked out. In this method, zero delay cross-correlation function and F norm are used to establish objective function. Based on inverse distance weighting theory, change of the objective function is controlled according to the location of the target CDP (common depth point), to change the constraint weights of training samples, initial low-frequency models, and seismic data on the inversion. Hence, the proposed method can get high resolution and high-accuracy velocity and density from inversion of small sample data, and is suitable for identifying thin interbedded sand bodies. Tests with thin interbedded geological models show that the proposed method has high inversion accuracy and resolution for small sample data, and can identify sandstone and mudstone layers of about one-30th of the dominant wavelength thick. Tests on the field data of Lishui sag show that the inversion results of the proposed method have small relative error with well-log data, and can identify thin interbedded sandstone layers of about one-15th of the dominant wavelength thick with small sample data.

Nonlinear petrophysical amplitude variation with offset inversion with spatially variable pore aspect ratio

Petrophysical amplitude variation with offset (AVO) inversion, which combines a rock-physics model and prestack inversion, aims at effectively quantifying reservoir-property parameters from prestack seismic data. However, for a reservoir with complex pore structures, this approach may suffer from difficulties in rock-physics modeling, which hinders solving the relevant inverse problem. We have proposed a petrophysical AVO inversion method that considers the complex pore structures within reservoir rocks. The method integrates a differential effective medium model, the Gassmann equation, and the exact Zoeppritz equation as the forward operator. In particular, the pore complexity is addressed by favoring the spatial variation of pore type. Differing from conventional sequential inversion methods, the pore-type variation is introduced by updating the aspect ratio together with the reservoir parameters during the inversion process. To enhance the stability of the results, the estimation of aspect ratio and reservoir parameters is jointly conditioned to seismic and elastic data under a Bayesian framework, which leads to the objective function with joint data misfit terms. The objective function is optimized with a simulated annealing algorithm that includes the full nonlinearity of the forward operator. The proposed method is demonstrated by testing and applying on a carbonate reservoir. It generally outperforms methods that are either purely conditioned on the seismic data or based on a constant aspect ratio.

Robust data-driven AVO inversion algorithm based on generalized nonconvex dictionary learning

In recent years, a dictionary learning and sparse representation based data-driven amplitude variation with offset (AVO) inversion algorithm has achieved desirable performance. However, in this data-driven inversion (DDI) method, sparse coefficients sequence generated by K-SVD may not always be convergent. Furthermore, the convergence of the data-driven AVO inversion results cannot be guaranteed. On the other hand, using L2 norm as a loss function in the DDI algorithm will lead to a robustness problem when seismic data contains outlier noise. In this paper, we propose a robust AVO inversion algorithm based on generalized nonconvex dictionary learning. The generalized nonconvex dictionary learning algorithm utilizes a family of nonconvex functions as the sparsity-inducing function for accurate estimation and a convergent sparse coefficient sequence. To deal with outlier noise, a smoothed L1 norm is utilized as the loss function. Meanwhile, a new spectral Polak–Ribière–Polyak (PRP) conjugate gradient algorithm is used to optimize the entire robust AVO inversion problem. Furthermore, the convergence analysis of the proposed algorithm is provided. In comparison with the conventional DDI algorithm, the proposed algorithm is robust, convergent, and computationally efficient. Results of synthetic data and field data experiments verify the superior performance of the proposed algorithm.

Inversion of low- to medium-frequency velocities and densities from AVO data using invertible neural networks

Amplitude-variation-with-offset (AVO) inversion and neural networks (NN) are widely used to invert elastic parameters. With more constraints from well-log data, neural network-based inversion may estimate elastic parameters with greater precision and resolution than traditional AVO inversion; however, neural network approaches necessitate a massive number of reliable training samples. Furthermore, because the lack of low-frequency information in seismic gathers leads to multiple solutions of the inverse problem, both inversions rely heavily on proper low-frequency initial models. To mitigate the dependence of inversions on accurate training samples and initial models, we have adopted solving inverse problems with the recently developed invertible neural networks (INNs). Unlike conventional neural networks, which address the ambiguous inverse issues directly, INNs learn definite forward modeling and use additional latent variables to increase the uniqueness of solutions. Motivated by the newly developed neural networks, we adopt an INN-based AVO inversion method, which can reliably invert low- to medium-frequency velocities and densities with randomly generated easy-to-access data sets rather than trustworthy training samples or well-prepared initial models. Tests on synthetic and field data indicate that our method is feasible, antinoise capable, and practicable.

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.

Estimation of porosity, fluid bulk modulus, and stiff-pore volume fraction using a multitrace Bayesian amplitude-variation-with-offset petrophysics inversion in multiporosity reservoirs

The estimation of petrophysical and fluid-filling properties of subsurface reservoirs from seismic data is a crucial component of reservoir characterization. Seismic amplitude-variation-with-offset (AVO) inversion driven by rock physics is an effective approach to characterize reservoir properties. In general, PP-wave reflection coefficients, elastic moduli, and petrophysical parameters are nonlinearly coupled, especially in multiple-type pore-space reservoirs, which makes seismic AVO petrophysics inversion ill-posed. We have developed a new approach that combines Biot-Gassmann’s poroelasticity theory with Russell’s linear AVO approximation, to estimate the reservoir properties including elastic moduli and petrophysical parameters based on multitrace probabilistic AVO inversion algorithm. We first derive a novel PP-wave reflection coefficient formulation in terms of porosity, stiff-pore volume fraction, rock-matrix shear modulus, and fluid bulk modulus to incorporate the effect of pore structures on elastic moduli by considering the soft and stiff pores with different aspect ratios in sandstone reservoirs. Through the analysis of the four types of PP-wave reflection coefficients, the approximation accuracy and inversion feasibility of the derived formulation are verified. Our stochastic inversion method aims to predict the posterior probability density function in a Bayesian setting according to a prior Laplace distribution with vertical correlation and prior Gaussian distribution with lateral correlation of model parameters. A Metropolis-Hastings stochastic sampling algorithm with multiple Markov chains is developed to simulate the posterior models of porosity, stiff-pore volume fraction, rock-matrix shear modulus, and fluid bulk modulus from seismic AVO gathers. The applicability and validity of our inversion method is illustrated with synthetic examples and a real data application.

Lithology, porosity and saturation joint prediction using stochastic rock physics modelling and litho-petro-elastic inversion

In this paper we present the application of a single-loop litho-petro-elastic (LPE) inversion, which is a data assimilation algorithm that uses nonlinear Zoeppritz reflectivity operators with sequential filtering. It integrates rock physics models with seismic amplitude variation with offset (AVO) inversion and Bayesian inversion to define lithology, elastic, and petrophysical properties in a single loop, thus, combining several steps of the conventional reservoir characterization workflow. In the conventional multistep approach, the lithology and petrophysical properties are generated sequentially from elastic properties after AVO inversion is performed, which can add prediction uncertainty at each step and produce results that are not correlated with each other. The LPE inversion ensures that the predicted properties maintain the relationships defined by the rock physics model. The LPE inversion was tested on data from offshore Australia with three wells, for a faulted reservoir zone containing oil with a gas cap. It provided robust predictions for lithology, porosity, and water saturation, which matched acceptably at the three wells. The algorithm also accounted for subsurface uncertainties as it produced prediction probabilities of facies, porosity, and water saturation using multidimensional probability density functions. This approach can be effectively used to classify reservoir properties in a single-loop workflow.

Amplitude-variation-with-offset inversion based on group sparse regularization

Seismic amplitude-variation-with-offset (AVO) inversion from prestack seismic data plays a significant role in estimating elastic parameters and characterizing reservoir properties. In general, sparse regularization is widely used to solve ill-posed inverse problems by reducing the solution space of subsurface parameters, which makes seismic AVO inversion more stable. However, the traditional sparse constraint inversion only focuses on the vector sparsity of reflectivity, instead of the structural sparse characteristics of the estimated parameters. Consequently, various elastic parameters demonstrate different formation structural features in the same location of stratum. In this study, we have developed a novel approach that combines the structural sparsity and the vector sparsity of the model reflectivity to establish the posterior probability density distribution and solve the objective function of the model parameters. Based on the relationship among multiple elastic parameters, we divide the model parameters to be inverted into several groups according to intrinsic structural sparse characteristics of elastic parameters. In this case, all of the model parameters at the same sampling point are classified into the identical group, which ensures that different estimated parameters indicate the same characteristic in terms of stratigraphic structure. From the perspective of Bayesian inference, we use the modified Cauchy probability density function (PDF) to characterize the group sparsity and describe the relationship among model parameters in the same group by Gaussian PDF. Furthermore, we estimate the optimum solution corresponding to the maximum a posteriori probability under Bayesian inference. Synthetic experiments on a Marmousi model prove that the estimated P-velocity, S-velocity, and density are consistent with those of the real models, and the application of field data confirms the availability and feasibility of group sparse inversion.

Direct depth-domain Bayesian amplitude-variation-with-offset inversion

We have developed a new approach to perform Bayesian linearized amplitude-variation-with-offset (AVO) inversion in the depth domain using nonstationary wavelets. Bayesian linearized AVO inversion, a hybrid approach combining physics-based models with statistical learning, has gained immense popularity because of its superior computational speed and ability to estimate uncertainties in inverted model parameters. Bayesian linearized AVO inversion is performed on time-domain seismic data; therefore, depth-imaged seismic cannot be inverted directly using this method and would require depth-to-time conversion before AVO inversion can be done. Subsequently, time-to-depth conversion of the inverted volumes would be required for reservoir modeling and well placement. Domain conversions introduce additional uncertainty in geophysical workflows. In conventional AVO inversion, the seismic wavelet is assumed to be stationary, and this assumption leads to a restriction in the length of the time window over which the inversion can be performed. Therefore, AVO inversion is usually restricted to a narrow time window around the target of interest, and if multiple targets are present at different depths, multiple inversions must be run on the same volume. Depth-domain amplitude inversion is a recent development and has been previously presented in an iterative formulation. Implementing linearized Bayesian inversion directly in the depth domain using nonstationary wavelets is a convenient new approach that takes advantage of superior computational speed and uncertainty quantification without compromising the accurate spatial location that depth imaging provides. Combining these two ideas creates a novel, unique, and powerful seismic inversion technique that can be useful for quantitative interpretation and reservoir characterization.

Bayesian seismic amplitude variation with offset inversion for reservoir variables with bimodal spatial histograms

We consider seismic amplitude variation with offset (AVO) inversion for prediction of the reservoir properties porosity and water saturation. An oil reservoir at the initial state is studied; hence, gravitational effects dominate and keep hydrocarbons from mixing with water. Histograms of observations of water saturation along wells are consequently clearly bimodal, which is challenging to model. The seismic AVO inversion is cast into a Bayesian framework. The prior spatial model for porosity and water saturation is specified to be a selection Gaussian random field (S-GRF), which is capable of representing spatial variables with multimodal histograms. By using linear models for the seismic and rock-physics likelihoods, the posterior model is also an S-GRF. Hence, the Bayesian seismic inversion can be solved analytically, and the bimodal characteristics of water saturation can be reproduced. The methodology is defined and demonstrated on two synthetic cases inspired by real data from an oil reservoir, and thereafter applied to the real case. The well observations are fairly accurately reproduced and the inversion results are considered to be substantial improvements compared to standard spatial Gaussian models.

AVO Inversion in Orthotropic Media Based on SA-PSO

The seismic inversion of anisotropic media is a popular research direction. Orthotropic media closely approximate real strata, but their inversion remains difficult because of their many parameters and large variations. In this article, particle swarm optimization (PSO) and simulated annealing (SA) are combined to invert prestack amplitude variation with offset (AVO) data in orthotropic media. PSO is a stochastic algorithm that easily falls into local minima and has a poor global search ability. Integrating SA into PSO adds the probabilistic jump-out mechanism of SA, modifying the global optimization of PSO by adjusting the temperature. The hybrid SA-PSO algorithm can overcome premature phenomena, avoids easily falling into local minima, and fissures stronger global optimization. With the P-wave reflection coefficient formula, we establish an objective function for the anisotropic parameters of orthotropic media and use SA-PSO to invert prestack AVO data in orthotropic media. The inversion process is stable, and the inversion error is small. The proposed method is applied to the partial Marmousi2 model, and seven anisotropic parameters of orthotropic media are inverted. According to the relationships between anisotropic and fracture weakness parameters, profiles of the weakness parameters are obtained, and the fracture infill materials are predicted. The prediction results are consistent with the actual model, verifying the correctness of the method. The difference between the reservoir and surrounding rock is significant in the inversion profiles, benefiting reservoir identification. These results will provide a basis for reservoir identification and prediction and provide theoretical support for AVO inversion in anisotropic media.