Amplitude Versus Offset Inversion Research Articles

Second-Order Approximate Reflection Coefficient of Thin Interbeds with Vertical Fractures

The horizontal fractures in the strata will close in the compaction effect of overlying strata, while the vertical cracks are widely developed, which can be equivalent to HTI (transverse isotropy with a horizontal axis of symmetry) medium. When an S-wave propagates into HTI media, the shear wave will divide into two types of waves: a fast S-wave and slow S-wave. When the strata of HTI are thin and overlapping, called the thin interbeds model, the wave field exhibits complex primary reflections, converted waves, and multiples. We introduce a new second-order approximation of the total reflection coefficient, with the incidence angle lower than the critical angle in thin-interbed HTI media using a recursive algorithm. We verify the effectiveness of the second-order approximation by analyzing the energy of multiples. Comparing the second-order approximate solution that degenerates the HTI medium into isotropic and Kennett’s exact solution, we find that our solution has an accuracy of over 99.9% in any azimuth, with the incidence angle lower than the critical angle under P-wave incidence. However, our solution of the SP wave field is suitable for incidence azimuth angles between 0–75° and 120–180°, with the lowest accuracy occurring at an incidence angle of 25° and a relative error of 6.4%. The approximate solution in the SS wave field has the same applicable range as the SP wave, with the maximum error of 6.3% occurring at the incident angle of 1°. This new second-order approximate formula for the total reflection coefficient of thin interbeds composed of HTI helps us to understand the reflection characteristics of complex thin interbeds. It also lays a theoretical foundation for the development of AVO (Amplitude Versus Offset) analysis and inversion techniques for lithological and stratigraphic oil and gas reservoirs.

An Exact Zoeppritz Based Prestack Inversion Using Whale Optimization Particle Filter Algorithm Under Bayesian Framework

Conventional AVO (Amplitude Versus Offset) inversion methods are mainly based on various Zoeppritz approximations. The assumptions of small contrast and linear relationship lead the most inversion methods being difficult to have high inversion accuracy. In this paper, the exact Zoeppritz equation is used to establish the prestack inversion method under the Bayesian framework. It integrates multi-source information to generate posterior distributions of P-, S-wave velocity and density. In the Bayesian theory, the prior model works as the regularization term which has a strong effect on the inversion results. The strategy to obtain a relatively accurate prior model can improve the inversion accuracy. Therefore, an exact Zoeppritz equation based nonlinear AVO inversion algorithm combing whale optimization particle filtering (WOPF) is proposed. The WOPF method can generate a relatively stable and accurate initial model for the Bayesian prestack inversion. We validate the new method through two synthetic models and field data. Comparisons are made with the conventional linear and nonlinear AVO inversion methods. The results show that the proposed method can provide much more accurate inverted elastic parameters in different geological conditions.

Frequency-dependent AVO inversion applied to physically based models for seismic attenuation

SUMMARYSeismic inversion of amplitude versus offset (AVO) data in viscoelastic media can potentially provide high-resolution subsurface models of seismic velocities and attenuation from offset/angle seismic gathers. P- and S-wave quality factors (Q), whose inverse represent a measure of attenuation, depend on reservoir rock and pore fluid properties, in particular, saturation, permeability, porosity, fluid viscosity and lithology; however, these quality factors are rarely taken into account in seismic AVO inversion. For this reason, in this work, we aim to integrate quality factors derived from physically based models in AVO inversion by proposing a gradient descent optimization-based inversion technique to predict the unknown model properties (P- and S-wave velocities, the related quality factors and density). The proposed inversion minimizes the non-linear least-squares misfit with the observed data. The optimal solution is iteratively obtained by optimizing the data misfit using a second-order limited-memory quasi-Newton technique. The forward model is performed in the frequency–frequency-angle domain based on a convolution of broad-band signals and a linearized viscoelastic frequency-dependent AVO (FAVO) equation. The optimization includes the adjoint-state-based gradients with the Lagrangian formulation to improve the efficiency of the non-linear seismic FAVO inversion process. The inversion is tested on synthetic seismic data, in 1-D and 2-D, with and without noise. The sensitivity for seismic quality factors is evaluated using various rock physics models for seismic attenuation and quality factors. The results demonstrate that the proposed inversion method reliably retrieves the unknown elastic and an-elastic properties with good convergence and accuracy. The stability of the inverse solution especially seismic quality factors estimation relies on the noise level of the seismic data. We further investigate the uncertainty of the solution as a function of the variability of the initial models.

Three-term AVO inversion using group total variation regularization

The seismic amplitude-versus-offset (AVO) inversion based on the total variation (TV) regularization is used to estimate blocky solutions for elastic parameters. It is achieved by minimizing the l1-norm of the first-order difference for model parameters. As the parameters in the subsurface are highly correlated with each other, a group optimization strategy was applied to the TV regularized AVO inversion. A group TV-norm that is a composition of the TV-norm and the l2-norm was designed. In this way, the TV regularization is performed among groups to promote sparsity of the gradients for the model parameters. By contrast, l2 regularization is performed within each group to constrain uniformity. The new three-term AVO inversion algorithm based on group TV regularization helps estimate the elastic parameters with desired blocky structure. Also, this algorithm ensures correlated resulting solutions even when no covariance matrix is used. It has proved to obtain good results in numerical and field examples.

Uncertainty estimation in AVO inversion using Bayesian dropout based deep learning

Amplitude versus offset (AVO) inversion is the process of transforming seismic reflection into elastic properties such as P- and S- impedance to estimate the interval properties and thickness of underlying geology using well log and post- or prestack seismic data. Recent applications of AVO inversion based on deep learning have shown excellent results and practical applicability. However, traditional deep learning methods yield only prediction results without any associated predictive uncertainty. Two types of predictive uncertainty should be considered: aleatoric uncertainty, which occurs when noisy data are included; and epistemic uncertainty, which is caused by a lack of data. To estimate the impedances and their uncertainties, Bayesian approximation using Monte Carlo dropout is applied, which simply approximates a Bayesian neural network. From the proposed method, we can not only predict impedances but also estimate their predictive uncertainties in the seismic survey area and determine whether prediction results are reliable.

Bayesian Seismic AVO Inversion Using a Laterally Coupled Multimodal Prior Model

A Bayesian seismic amplitude versus offset (AVO) inversion scheme with a laterally coupled prior model for porosity, water saturation, and volume of clay is proposed. A 2-D section and a 3-D volume of an oil reservoir are studied. The oil reservoir is considered at the initial state, which entails gravitationally induced bimodality in the water saturations along vertical traces. A selection Gaussian random field (S-GRF) prior model, capable of representing this bimodality, is specified for porosity, water saturation, and volume of clay. The S-GRF is specified to have lateral correlation, which may reduce the impact of trace-unique signal errors in the seismic AVO data on the inversion results. The likelihood model is linear and Gaussian, for which the S-GRF prior model is conjugate; hence, the posterior model is also an S-GRF. The form of the posterior distribution is therefore known and its parameter values can be analytically computed. Real seismic AVO data from the 2-D section and the 3-D volume are inverted and the results appear to be reliable along validation wells and represent a geologically plausible reservoir design. Furthermore, a notable variance reduction in the laterally coupled posterior model relative to an alternative posterior model without lateral coupling is achieved.

Hydrocarbon Mapping on Reservoir Carbonate Using AVO Inversion Method

Amplitude Versus Offset (AVO) inversion has been applied for reservoir analysis focused on the horizon carbonate Peutu and Belumai. Simultaneous inversion analysis is used to determine gas anomaly inside carbonate-rocks and it’s spread laterally around target zones. It is based on the fact that small Vpand Vs value changes are going to show the better anomaly to identify reservoir fluid content. The AVO inversion method applies angle gather data as the input and then it is inverted to produce P impedance (Zp) and S impedance (Zs). Zp and Zs are derived to produce Lambda-Rho and Mu-Rho that are sensitive to fluid and lithology. Value of Mu-Rho between 44–65 Gpa gr/cc while value of Lambda-Rho smaller than 10 Gpa gr/cc (for carbonate-rock filled by fluid). This research found that Lambda-Rho is the best parameter to show the existence of hydrocarbon in the case of gas. While Mu-Rho is the best parameter to show the differences in lithology.

Bayesian Frequency-Dependent AVO Inversion Using an Improved Markov Chain Monte Carlo Method for Quantitative Gas Saturation Prediction in a Thin Layer

One of the main objectives in the hydrocarbon reservoir characterization is determining rock and fluid properties that rely extensively on inference from seismic observations. In this letter, we present a novel Bayesian prestack inversion method using frequency-dependent amplitude versus offset (AVO) analysis with the goal to directly estimate gas saturation and porosity of a target thin reservoir zone. The proposed methodology is based on an improved Markov chain Monte Carlo (MCMC) sampling algorithm, which is computationally very coefficient due to its satisfactory acceptance probability and the convergence speed of Markov chains. Using a nonlinear rock physics model (RPM), properly calibrated for the investigating area, and a seismic forward operator based on the frequency-domain propagator matrix approach in the Bayesian inversion framework, we then evaluate the full posterior probability distribution of petrophysical parameters conditioned to seismic data and available prior information, using the MCMC algorithm in which we iteratively sample within the petrophysical property space. The proposed inversion approach is validated through applications to a synthetic reservoir model and the real seismic data from gas-bearing reservoirs with strong velocity dispersion.

Determining the petroleum potential of sandstone reservoir GX field based on AVO analysis

Amplitude Versus Offset (AVO) is an effectively used seismic method in O&G exploration and production. Many studies indicated that the combination of AVO and seismic inversion allows reducing risks in the identification of gas-bearing sandstone reservoirs. Based on the input data including Pre-stack Time Migration, Post-stack Depth Migration and well logging at well 2X, the paper presents the method and procedure of analyzing AVO properties at GX field, block 05-2, Nam Con Son basin. The paper showed the process of building synthetic seismograms with common depth points, sketching graphs to analyze the behavior of AVO properties using intercept A and gradient B values calculated from the well logging data at a defined well, and predicting AVO’s behavior when the lithological and fluid properties in the reservoir change. Therefore, the abnormal section of the reservoir is constructed to determine the lithological features of the reservoir as well as the fluid within the GX field. The interpreted results reveal that the research object is a gas-bearing sandstone reservoir with the boundary in the time domain of 2920ms - 2936ms (or depth 3582.9m - 3616.1m), which is the foundation for determining the reservoir's potential scale.

Integration of new interpretation, attribute analysis and inversion results for the Dampier Sub-basin, North West Shelf of Australia

The Davros-Typhon Multi-Client 3D surveys are located approximately 70km from the north-west coast of Australia, largely covering the NE trending Dampier Sub-basin and straddling the Rankin Trend within the Northern Carnarvon Basin. The basins within the North West Shelf formed as a result of seafloor spreading, associated with the breakup of the North West margin of East Gondwana. The combined, contiguous Davros-Typhon survey areas cover a number of significant discoveries and producing fields, which include both oil and gas accumulations. The key objective of the survey was to enhance the imaging of Triassic to Lower Cretaceous reservoir units and to develop a new interpretation framework, made possible by the modern broadband acquisition parameters and advanced processing techniques. Challenges associated with imaging and interpretation include the effects of high velocity carbonate overburden, steeply dipping structures, fault shadow and structural complexity at depth, which is critical for evaluation of reservoir targets. A major reprocessing effort was undertaken to further mitigate these issues, which included Davros and a number of adjacent existing 3D surveys, resulting in the Typhon Multi-Client 3D. CGG Multi-client and New Ventures geoscientists, in collaboration with CGG Seismic Imaging, have undertaken new interpretation and amplitude versus offset (AVO) inversion analysis using subsets of the Typhon 3D. The resulting volume-based attribute analysis and integration of new AVO inversion results demonstrates enhanced attribute quality for the reprocessed data and provides a platform for quantitative analysis over a large area of the Northern Carnarvon Basin.

Data-driven method for an improved linearised AVO inversion

Abstract Linearised approximations of the Zoeppritz equation are widely used for amplitude versus offset (AVO) forward modelling and prestack seismic inversion. However, current linearised approximations typically exhibit large errors for strong-contrast media and large incidence angles (even for those less than the critical angle), leading to poor quality estimation of elastic parameters. We therefore develop a data-driven method to improve the linearised AVO approximation, based on the concept that the inaccuracy of the conventional linearised AVO forward operator is solely responsible for generating residuals of the PP reflection coefficients calculated by the conventional linearised approximation compared with using the Zoeppritz equation. Therefore, if true model parameters from well-logging data are known, the residuals of the PP reflection coefficients can be used to estimate linear modifications of the inaccurate linearised AVO forward operators at well sites. We apply estimated linear modifications to original inaccurately linearised forward operators to obtain an improved linear AVO operator (ILAO). Because ILAOs can only be estimated at the well sites by the data-driven method, we construct spatially variant ILAOs using structure-guided interpolation for those at a distance from the well sites. Numerical example results reveal that the improved linear AVO approximation is more accurate than the Aki–Richards approximation for strong-contrast media and large incident angles. Moreover, the accuracy and resolution of the inverted P- and S-wave velocities and density using ILAOs are higher than those using the conventional Aki–Richards operators. Finally, application to the field data successfully demonstrates the feasibility and effectiveness of the improved linearised AVO inversion method.

Application of constrained AVO inversion: 2-D modelling of gas hydrates and free gas in Mahanadi basin, India

We present an application of Constrained Amplitude versus Offset (AVO) inversion for 2-D modelling of gas hydrates and free gas saturation in the Mahanadi offshore basin. In order to reliably model gas hydrate distribution, it is essential to derive both the P- and S-wave velocities (VP and VS). Hence, we use the method of Constrained AVO inversion, in which we obtain both the VP and VS using a combination of travel time and amplitude inversion. We employ this exercise on the 2-D seismic reflection data in the Mahanadi offshore basin and have derived 2-D sections for both VP and VS. Information about porosity has been derived from the model-based inversion by utilizing a porosity wavelet. The 2-D sections of VP, VS and porosity are then utilized in rock physics modelling for the saturation estimation of gas hydrates and free gas respectively. We have estimated gas hydrates saturation using Three-Phase Weighted equation (WE) and free gas saturation using Gassmann equations for fluid substitution. Further, we have used the Effective Medium Modelling (EMM) for gas hydrates saturation and understanding their distribution by considering two cases: (a) gas hydrates cementing the grain contact and (b) gas hydrates occurring away from the grain contact. We obtain an average gas hydrates saturation as 7% and 10% from EMM and WE modelling respectively, and free-gas saturation in between 1 and 3%. The base of gas hydrate stability zone is found gently dipping down from the Common Depth Point (CDP) 2200 to CDP 2900 at the depth range of 1840–1970 m. Cross plot of velocity versus saturation and validation with the well log saturation suggests that the latter model or uncemented nature of gas hydrate distribution holds good in the study area.

Combining CSEM or gravity inversion with seismic AVO inversion, with application to monitoring of large-scale CO2 injection

A sequential inversion methodology for combining geophysical data types of different resolutions is developed and applied to monitoring of large-scale CO2 injection. The methodology is a two-step approach within the Bayesian framework where lower resolution data are inverted first, and subsequently used in the generation of the prior model for inversion of the higher resolution data. For the application of CO2 monitoring, the first step is done with either controlled source electromagnetic (CSEM) or gravimetric data, while the second step is done with seismic amplitude-versus-offset (AVO) data. The Bayesian inverse problems are solved by sampling the posterior probability distributions using either the ensemble Kalman filter or ensemble smoother with multiple data assimilation. A model-based parameterization is used to represent the unknown geophysical parameters: electric conductivity, density, and seismic velocity. The parameterization is well suited for identification of CO2 plume location and variation of geophysical parameters within the regions corresponding to inside and outside of the plume. The inversion methodology is applied to a synthetic monitoring test case where geophysical data are made from fluid-flow simulation of large-scale CO2 sequestration in the Skade formation. The numerical experiments show that seismic AVO inversion results are improved with the sequential inversion methodology using prior information from either CSEM or gravimetric inversion.

Nonlinear joint PP-PS AVO inversion based on improved Bayesian inference and LSSVM

Multiwave seismic technology promotes the application of joint PP-PS amplitude versus offset (AVO) inversion; however conventional joint PP-PS AVO inversioan is linear based on approximations of the Zoeppritz equations for multiple iterations. Therefore the inversion results of P-wave, S-wave velocity and density exhibit low precision in the faroffset; thus, the joint PP-PS AVO inversion is nonlinear. Herein, we propose a nonlinear joint inversion method based on exact Zoeppritz equations that combines improved Bayesian inference and a least squares support vector machine (LSSVM) to solve the nonlinear inversion problem. The initial parameters of Bayesian inference are optimized via particle swarm optimization (PSO). In improved Bayesian inference, the optimal parameter of the LSSVM is obtained by maximizing the posterior probability of the hyperparameters, thus improving the learning and generalization abilities of LSSVM. Then, an optimal nonlinear LSSVM model that defines the relationship between seismic reflection amplitude and elastic parameters is established to improve the precision of the joint PP-PS AVO inversion. Further, the nonlinear problem of joint inversion can be solved through a single training of the nonlinear inversion model. The results of the synthetic data suggest that the precision of the estimated parameters is higher than that obtained via Bayesian linear inversion with PP-wave data and via approximations of the Zoeppritz equations. In addition, results using synthetic data with added noise show that the proposed method has superior anti-noising properties. Real-world application shows the feasibility and superiority of the proposed method, as compared with Bayesian linear inversion.

Gas hydrate elastic properties inversion by AVO Technology in Shenhu Area of the South China Sea

Amplitude versus offset (AVO) contains abundant information of sediment elastic properties. Some of these properties are sensitive to the saturation of gas hydrate or free gas accumulated in the sediments. Here, AVO inversion is performed to the seismic data of Shenhu Area, South China Sea. Based on the accurate Zoeppritz equation, P wave velocity and S wave velocity are obtained. Based on elastic impedance equation, P wave impedance, S wave impedance, and fluid factor are obtained. The inverted elastic parameters show that there are gas hydrate and free gas in this area. Moreover, the conception of elastic parameters relative variation rates was proposed and applied here, and the results show that they can be used to identify the top of gas hydrate zone.

A Novel Hydrocarbon Detection Approach via High-Resolution Frequency-Dependent AVO Inversion Based on Variational Mode Decomposition

Amplitude-versus-offset (AVO) inversion always plays an important role in reservoir fluid identification, which allows the estimation of various rock and fluid properties from prestack seismic data. In this paper, we propose a new method for discrimination of hydrocarbon accumulation that combines frequency-dependent AVO inversion scheme and variational mode decomposition (VMD). VMD is a recently developed algorithm for adaptive signal decomposition that is able to nonrecursively decompose a multicomponent signal into a number of quasi-orthogonal intrinsic mode functions and avoid mode mixing effectively. VMD is superior to other state-of-the-art approaches in obtaining high-resolution and high-fidelity local time–frequency depiction performance. Two synthetic signals are employed to illustrate that VMD achieves higher temporal and frequency resolution than the conventional continuous wavelet transform (CWT) decomposition. Other synthetic examples, elastic and dispersive, are utilized to demonstrate that the proposed method is more reliable for the detection of hydrocarbon saturation and a comparison is made with the CWT-based inverted results. Application on field data has further shown that the proposed approach has the potential in identifying the reservoir related to hydrocarbon.

Time-lapse joint AVO inversion using generalized linear method based on exact Zoeppritz equations

The conventional method of time-lapse AVO (Amplitude Versus Offset) inversion is mainly based on the approximate expression of Zoeppritz equations. Though the approximate expression is concise and convenient to use, it has certain limitations. For example, its application condition is that the difference of elastic parameters between the upper medium and lower medium is little and the incident angle is small. In addition, the inversion of density is not stable. Therefore, we develop the method of time-lapse joint AVO inversion based on exact Zoeppritz equations. In this method, we apply exact Zoeppritz equations to calculate the reflection coefficient of PP wave. And in the construction of objective function for inversion, we use Taylor series expansion to linearize the inversion problem. Through the joint AVO inversion of seismic data in baseline survey and monitor survey, we can obtain the P-wave velocity, S-wave velocity, density in baseline survey and their time-lapse changes simultaneously. We can also estimate the oil saturation change according to inversion results. Compared with the time-lapse difference inversion, the joint inversion doesn't need certain assumptions and can estimate more parameters simultaneously. It has a better applicability. Meanwhile, by using the generalized linear method, the inversion is easily implemented and its calculation cost is small. We use the theoretical model to generate synthetic seismic records to test and analyze the influence of random noise. The results can prove the availability and anti-noise-interference ability of our method. We also apply the inversion to actual field data and prove the feasibility of our method in actual situation.

PP and PS joint inversion with a posterior constraint and with particle filtering

The Bayesian framework works well in amplitude versus offset (AVO) inversion, which merges multi-information together to generate posterior distributions of P-wave velocity, S-wave velocity and density. Most existing AVO inversion methods utilize PP reflection seismic data to predict the three elastic parameters. These methods are not usually sensitive to S-wave velocity and density, which make the inversion methods inaccurate and unstable. One way of solving these problems is to perform PP and PS joint inversion by incorporating PS seismic data. Another way is to provide a relatively accurate prior model. In this paper, we apply a particle filtering technique to produce a prior model for the PP and PS joint inversion. In the Bayesian inversion setting, the prior model works as the regularization term. Particle filtering is a Bayesian recursive method that combines prior information with observed data to provide a posterior constraint to reduce the joint inversion's uncertainty. We generate synthetic models with different signal-to-noise ratios to validate our new method. Comparisons are provided with the traditional joint inversion, which adopts the Gaussian prior model. The inversion results show that the three elastic parameters are retrieved well when the signal-to-noise ratios are high. As the signal-to-noise ratio reduces, our new method can depict more detailed changes than the traditional inversion method, and improves the inversion accuracy apparent in the target layers.

Bayesian AVO inversion with consistent angle parameters

Amplitude versus offset (AVO) inversion has been extensively used in seismic exploration. Many different elastic parameters can be inverted by incorporating corresponding reflection coefficient approximations. Although efforts have been made to improve the accuracy of AVO inversions for years, there is still one problem that has long been ignored. In most methods, the angle in the approximation and the angle used in seismic angle gather extractions are not the same one. This inconsistency leads to inaccurate inversion results. In this paper, a Bayesian AVO inversion method with consistent angles is proposed to solve the problem and improve inversion accuracy. Firstly, a linearized P-wave reflection coefficient approximation with consistent angles is derived based on angle replacements. The equivalent form of the approximation in terms moduli and density is derived so that moduli can be inverted for reservoir characterization. Then, by convoluting it with seismic wavelets as the forward solver, a probabilistic prestack seismic inversion method with consistent angles is presented in a Bayesian scheme. The synthetic test proves that the accuracy of this method is higher than the traditional one. The real data example shows that the inversion result fits better with well log interpretation data, which verifies the feasibility of the proposed method.

Zoeppritz-based AVO inversion using an improved Markov chain Monte Carlo method

The conventional Markov chain Monte Carlo (MCMC) method is limited to the selected shape and size of proposal distribution and is not easy to start when the initial proposal distribution is far away from the target distribution. To overcome these drawbacks of the conventional MCMC method, two useful improvements in MCMC method, adaptive Metropolis (AM) algorithm and delayed rejection (DR) algorithm, are attempted to be combined. The AM algorithm aims at adapting the proposal distribution by using the generated estimators, and the DR algorithm aims at enhancing the efficiency of the improved MCMC method. Based on the improved MCMC method, a Bayesian amplitude versus offset (AVO) inversion method on the basis of the exact Zoeppritz equation has been developed, with which the P- and S-wave velocities and the density can be obtained directly, and the uncertainty of AVO inversion results has been estimated as well. The study based on the logging data and the seismic data demonstrates the feasibility and robustness of the method and shows that all three parameters are well retrieved. So the exact Zoeppritz-based nonlinear inversion method by using the improved MCMC is not only suitable for reservoirs with strong-contrast interfaces and long-offset ranges but also it is more stable, accurate and anti-noise.