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.

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Seismic AVO statistical inversion incorporating poroelasticity

Petroleum Science ◽

10.1007/s12182-020-00483-5 ◽

2020 ◽

Vol 17 (5) ◽

pp. 1237-1258

Author(s):

Kun Li ◽

Xing-Yao Yin ◽

Zhao-Yun Zong ◽

Hai-Kun Lin

Keyword(s):

Monte Carlo Algorithm ◽

Inversion Method ◽

Probability Density Distribution ◽

Simultaneous Estimation ◽

Model Parameters ◽

Reflection Coefficients ◽

Rock Matrix ◽

Critical Porosity ◽

Avo Inversion ◽

Rock Porosity

Abstract Seismic amplitude variation with offset (AVO) inversion is an important approach for quantitative prediction of rock elasticity, lithology and fluid properties. With Biot–Gassmann’s poroelasticity, an improved statistical AVO inversion approach is proposed. To distinguish the influence of rock porosity and pore fluid modulus on AVO reflection coefficients, the AVO equation of reflection coefficients parameterized by porosity, rock-matrix moduli, density and fluid modulus is initially derived from Gassmann equation and critical porosity model. From the analysis of the influences of model parameters on the proposed AVO equation, rock porosity has the greatest influences, followed by rock-matrix moduli and density, and fluid modulus has the least influences among these model parameters. Furthermore, a statistical AVO stepwise inversion method is implemented to the simultaneous estimation of rock porosity, rock-matrix modulus, density and fluid modulus. Besides, the Laplace probability model and differential evolution, Markov chain Monte Carlo algorithm is utilized for the stochastic simulation within Bayesian framework. Models and field data examples demonstrate that the simultaneous optimizations of multiple Markov chains can achieve the efficient simulation of the posterior probability density distribution of model parameters, which is helpful for the uncertainty analysis of the inversion and sets a theoretical fundament for reservoir characterization and fluid discrimination.

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Multiparameter deblurring filter and its application to elastic migration and inversion

Geophysics ◽

10.1190/geo2017-0572.1 ◽

2018 ◽

Vol 83 (5) ◽

pp. S421-S435 ◽

Cited By ~ 7

Author(s):

Zongcai Feng ◽

Bowen Guo ◽

Gerard T. Schuster

Keyword(s):

Coupling Effect ◽

Seismic Inversion ◽

Single Type ◽

Inversion Method ◽

Model Parameters ◽

S Wave ◽

Different Types ◽

Iterative Inversion ◽

Local Filters ◽

And Inversion

Different types of model parameters, such as the P- and S-wave velocities, can be coupled to one another in multiparameter seismic inversion. This coupling effect is not taken into account by the conventional approximation to the Hessian inverse for a single type of parameter, and so it can lead to a slow rate of convergence by an iterative inversion method. To solve this problem, we have developed a multiparameter deblurring filter that approximates the Hessian inverse. This filter takes into account the coupling between different parameters by using stationary local filters to approximate the submatrices of the Hessian inverse for the different types of parameters. The filters are calculated by matching the reference multiparameter migration images to their reference reflectivity models. Numerical tests with elastic migration and inversion indicate that the multiparameter deblurring filter not only reduces the footprint noise, balances the amplitude, and increases the resolution of the elastic migration images, but it also mitigates the crosstalk artifacts caused by the coupling effect. When used as a preconditioner, it also accelerates the convergence rate for elastic inversion.

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A data-driven amplitude variation with offset inversion method via learned dictionaries and sparse representation

Geophysics ◽

10.1190/geo2017-0615.1 ◽

2018 ◽

Vol 83 (6) ◽

pp. R725-R748 ◽

Cited By ~ 11

Author(s):

Bin She ◽

Yaojun Wang ◽

Jiandong Liang ◽

Zhining Liu ◽

Chengyun Song ◽

...

Keyword(s):

Sparse Representation ◽

Prior Information ◽

Data Driven ◽

Inversion Method ◽

Model Parameters ◽

Well Log ◽

Elastic Parameters ◽

Amplitude Variation ◽

Amplitude Variation With Offset ◽

Avo Inversion

Amplitude variation with offset (AVO) inversion is a typical ill-posed inverse problem. To obtain a stable and unique solution, regularization techniques relying on mathematical models from prior information are commonly used in conventional AVO inversion methods (hence the name model-driven methods). Due to the difference between prior information and the actual geology, these methods often have difficulty achieving satisfactory accuracy and resolution. We have developed a novel data-driven inversion method for the AVO inversion problem. This method can effectively extract useful knowledge from well-log data, including sparse dictionaries of elastic parameters and sparse representation of subsurface model parameters. Lateral continuity of subsurface geology allows for the approximation of model parameters for a work area using the learned dictionaries. Instead of particular mathematical models, a sparse representation is used to constrain the inverse problem. Because no assumption is made about the model parameters, we consider this a data-driven method. The general process of the algorithm is as follows: (1) using well-log data as the training samples to learn the sparse dictionary of each elastic parameter, (2) imposing a sparse representation constraint on the objective function, making the elastic parameters be sparsely represented over the learned dictionary, and (3) solving the objective function by applying a coordinate-descent algorithm. Tests on several synthetic examples and field data demonstrate that our algorithm is effective in improving the resolution and accuracy of solutions and is adaptable to various geologies.

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Two-step joint PP- and PS-wave three-term amplitude-variation with offset inversion

Interpretation ◽

10.1190/int-2016-0056.1 ◽

2016 ◽

Vol 4 (4) ◽

pp. T613-T625 ◽

Cited By ~ 1

Author(s):

Qizhen Du ◽

Bo Zhang ◽

Xianjun Meng ◽

Chengfeng Guo ◽

Gang Chen ◽

...

Keyword(s):

Reflection Coefficient ◽

Wave Reflection ◽

Coefficient Matrix ◽

P Wave ◽

Inversion Method ◽

S Wave ◽

Amplitude Variation ◽

Amplitude Variation With Offset ◽

Avo Inversion ◽

Pp Wave

Three-term amplitude-variation with offset (AVO) inversion generally suffers from instability when there is limited prior geologic or petrophysical constraints. Two-term AVO inversion shows higher instability compared with three-term AVO inversion. However, density, which is important in the fluid-type estimation, cannot be recovered from two-term AVO inversion. To reliably predict the P- and S-waves and density, we have developed a robust two-step joint PP- and PS-wave three-term AVO-inversion method. Our inversion workflow consists of two steps. The first step is to estimate the P- and S-wave reﬂectivities using Stewart’s joint two-term PP- and PS-AVO inversion. The second step is to treat the P-wave reflectivity obtained from the first step as the prior constraint to remove the P-wave velocity related-term from the three-term Aki-Richards PP-wave approximated reflection coefficient equation, and then the reduced PP-wave reflection coefficient equation is combined with the PS-wave reflection coefficient equation to estimate the S-wave and density reﬂectivities. We determined the effectiveness of our method by first applying it to synthetic models and then to field data. We also analyzed the condition number of the coefficient matrix to illustrate the stability of the proposed method. The estimated results using proposed method are superior to those obtained from three-term AVO inversion.

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Bayesian Time-lapse Difference Inversion Based on the exact Zoeppritz Equations with Blockiness Constraint

Journal of Environmental and Engineering Geophysics ◽

10.2113/jeeg19-045 ◽

2020 ◽

Vol 25 (1) ◽

pp. 89-100

Author(s):

Lin Zhou ◽

Jianping Liao ◽

Jingye Li ◽

Xiaohong Chen ◽

Tianchun Yang ◽

...

Keyword(s):

Wave Equations ◽

Oil And Gas ◽

Time Lapse ◽

Seismic Inversion ◽

Field Application ◽

Inversion Method ◽

S Wave ◽

Elastic Parameters ◽

Zoeppritz Equations ◽

Approximate Formulas

Accurately inverting changes in the reservoir elastic parameters that are caused by oil and gas exploitation is of great importance in accurately describing reservoir dynamics and enhancing recovery. Previously numerous time-lapse seismic inversion methods based on the approximate formulas of exact Zoeppritz equations or wave equations have been used to estimate these changes. However the low accuracy of calculations using approximate formulas and the significant calculation effort for the wave equations seriously limits the field application of these methods. However, these limitations can be overcome by using exact Zoeppritz equations. Therefore, we study the time-lapse seismic difference inversion method using the exact Zoeppritz equations. Firstly, the forward equation of time-lapse seismic difference data is derived based on the exact Zoeppritz equations. Secondly, the objective function based on Bayesian inversion theory is constructed using this equation, with the changes in elastic parameters assumed to obey a Gaussian distribution. In order to capture the sharp time-lapse changes of elastic parameters and further enhance the resolution of the inversion results, the blockiness constraint, which follows the differentiable Laplace distribution, is added to the prior Gaussian background model. All examples of its application show that the proposed method can obtain stable and reasonable P- and S-wave velocities and density changes from the difference data. The accuracy of estimation is higher than for existing methods, which verifies the effectiveness and feasibility of the new method. It can provide high-quality seismic inversion results for dynamic detailed reservoir description and well location during development.

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Seismic pre-stack AVA inversion scheme based on lithology constraints

Journal of Geophysics and Engineering ◽

10.1093/jge/gxaa001 ◽

2020 ◽

Vol 17 (3) ◽

pp. 411-428

Author(s):

Shuang Xiao ◽

Jing Ba ◽

Qiang Guo ◽

J M Carcione ◽

Lin Zhang ◽

...

Keyword(s):

Model Updating ◽

Optimal Solution ◽

Seismic Inversion ◽

Inversion Method ◽

Good Resolution ◽

S Wave ◽

Elastic Parameters ◽

Multivariate Gaussian Distribution ◽

Stability Performance ◽

The Stability

Abstract Seismic pre-stack AVA inversion using the Zoeppritz equation and its approximations as a forward engine yields P- and S-wave velocities and density. Due to the presence of seismic noise and other factors, the solution to seismic inversion is generally ill-posed and it is necessary to add constraints to regularize the algorithm. Moreover, since pre-stack inversion is a nonlinear problem, linearized optimization algorithms may fall into false local minima. The simulated annealing (SA) algorithm, on the other hand, is capable of finding the global optimal solution regardless of the initial model. However, when applied to multi-parameter pre-stack inversion, standard SA suffers from instability. Thus, a nonlinear pre-stack inversion method is proposed based on lithology constraints. Specifically, correlations among the elastic parameters are introduced to establish constraints based on a Bayesian framework, with special intention of mitigating the ill-posedness of the inversion problem as well as addressing the lithological characteristics of the formations. In particular, to improve the stability, a multivariate Gaussian distribution of elastic parameters is incorporated into the model updating the SA algorithm. We apply the algorithm to synthetic and field seismic data, indicating that the proposed method has a good resolution and stability performance.

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A high-resolution prestack AVO inversion method for P- and S-wave moduli

10.1190/segam2018-2996795.1 ◽

2018 ◽

Author(s):

Gan Zhang ◽

Jingye Li ◽

Lin Zhou ◽

Xiaohong Chen ◽

Chen Zhou ◽

...

Keyword(s):

High Resolution ◽

Inversion Method ◽

S Wave ◽

Avo Inversion

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Computation of dry-rock VP/VS ratio, fluid property factor, and density estimation from amplitude-variation-with-offset inversion

Geophysics ◽

10.1190/geo2017-0621.1 ◽

2018 ◽

Vol 83 (6) ◽

pp. R669-R679 ◽

Cited By ~ 1

Author(s):

Gang Chen ◽

Xiaojun Wang ◽

Baocheng Wu ◽

Hongyan Qi ◽

Muming Xia

Keyword(s):

Reservoir Characterization ◽

Synthetic Data ◽

Pore Fluid ◽

Inversion Method ◽

S Wave ◽

Amplitude Variation ◽

Amplitude Variation With Offset ◽

Fluid Identification ◽

Fluid Property ◽

Avo Inversion

Estimating the fluid property factor and density from amplitude-variation-with-offset (AVO) inversion is important for fluid identification and reservoir characterization. The fluid property factor can distinguish pore fluid in the reservoir and the density estimate aids in evaluating reservoir characteristics. However, if the scaling factor of the fluid property factor (the dry-rock [Formula: see text] ratio) is chosen inappropriately, the fluid property factor is not only related to the pore fluid, but it also contains a contribution from the rock skeleton. On the other hand, even if the angle gathers include large angles (offsets), a three-parameter AVO inversion struggles to estimate an accurate density term without additional constraints. Thus, we have developed an equation to compute the dry-rock [Formula: see text] ratio using only the P- and S-wave velocities and density of the saturated rock from well-logging data. This decouples the fluid property factor from lithology. We also developed a new inversion method to estimate the fluid property factor and density parameters, which takes full advantage of the high stability of a two-parameter AVO inversion. By testing on a portion of the Marmousi 2 model, we find that the fluid property factor calculated by the dry-rock [Formula: see text] ratio obtained by our method relates to the pore-fluid property. Simultaneously, we test the AVO inversion method for estimating the fluid property factor and density parameters on synthetic data and analyze the feasibility and stability of the inversion. A field-data example indicates that the fluid property factor obtained by our method distinguishes the oil-charged sand channels and the water-wet sand channel from the well logs.

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Bayesian linearized AVO inversion

Geophysics ◽

10.1190/1.1543206 ◽

2003 ◽

Vol 68 (1) ◽

pp. 185-198 ◽

Cited By ~ 450

Author(s):

Arild Buland ◽

Henning Omre

Keyword(s):

Wave Velocity ◽

Posterior Distribution ◽

Acoustic Impedance ◽

Velocity Ratio ◽

P Wave ◽

Inversion Method ◽

Inversion Algorithm ◽

S Wave ◽

Data Set ◽

Avo Inversion

A new linearized AVO inversion technique is developed in a Bayesian framework. The objective is to obtain posterior distributions for P‐wave velocity, S‐wave velocity, and density. Distributions for other elastic parameters can also be assessed—for example, acoustic impedance, shear impedance, and P‐wave to S‐wave velocity ratio. The inversion algorithm is based on the convolutional model and a linearized weak contrast approximation of the Zoeppritz equation. The solution is represented by a Gaussian posterior distribution with explicit expressions for the posterior expectation and covariance; hence, exact prediction intervals for the inverted parameters can be computed under the specified model. The explicit analytical form of the posterior distribution provides a computationally fast inversion method. Tests on synthetic data show that all inverted parameters were almost perfectly retrieved when the noise approached zero. With realistic noise levels, acoustic impedance was the best determined parameter, while the inversion provided practically no information about the density. The inversion algorithm has also been tested on a real 3‐D data set from the Sleipner field. The results show good agreement with well logs, but the uncertainty is high.

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AVO inversion and poroelasticity with P- and S-wave moduli

Geophysics ◽

10.1190/geo2011-0214.1 ◽

2012 ◽

Vol 77 (6) ◽

pp. N17-N24 ◽

Cited By ~ 76

Author(s):

Zhaoyun Zong ◽

Xingyao Yin ◽

Guochen Wu

Keyword(s):

Seismic Data ◽

Real Data ◽

P Wave ◽

Model Parameters ◽

Initial Model ◽

S Wave ◽

Data Set ◽

Statistical Probability ◽

Avo Inversion ◽

Poroelasticity Theory

The fluid term in the Biot-Gassmann equation plays an important role in reservoir fluid discrimination. The density term imbedded in the fluid term, however, is difficult to estimate because it is less sensitive to seismic amplitude variations. We combined poroelasticity theory, amplitude variation with offset (AVO) inversion, and identification of P- and S-wave moduli to present a stable and physically meaningful method to estimate the fluid term, with no need for density information from prestack seismic data. We used poroelasticity theory to express the fluid term as a function of P- and S-wave moduli. The use of P- and S-wave moduli made the derivation physically meaningful and natural. Then we derived an AVO approximation in terms of these moduli, which can then be directly inverted from seismic data. Furthermore, this practical and robust AVO-inversion technique was developed in a Bayesian framework. The objective was to obtain the maximum a posteriori solution for the P-wave modulus, S-wave modulus, and density. Gaussian and Cauchy distributions were used for the likelihood and a priori probability distributions, respectively. The introduction of a low-frequency constraint and statistical probability information to the objective function rendered the inversion more stable and less sensitive to the initial model. Tests on synthetic data showed that all the parameters can be estimated well when no noise is present and the estimated P- and S-wave moduli were still reasonable with moderate noise and rather smooth initial model parameters. A test on a real data set showed that the estimated fluid term was in good agreement with the results of drilling.

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