Nonlinear amplitude-variation-with-offset inversion for Lamé parameters using a direct inversion method

2017 ◽  
Vol 5 (3) ◽  
pp. SL57-SL67 ◽  
Author(s):  
Guangsen Cheng ◽  
Xingyao Yin ◽  
Zhaoyun Zong
Keyword(s):  
Nonlinear Equation ◽  
Real Data ◽  
Seismic Inversion ◽  
Inversion Method ◽  
Nonlinear Inversion ◽  
Reservoir Prediction ◽  
Amplitude Variation ◽  
Linear Inversion ◽  
Amplitude Variation With Offset ◽  
Avo Inversion

Prestack seismic inversion is widely used in fluid indication and reservoir prediction. Compared with linear inversion, nonlinear inversion is more precise and can be applied to high-contrast situations. The inversion results can be affected by the parameters’ sensitivity, so the parameterization of nonlinear equations is very significant. Considering the poor nonlinear amplitude-variation-with-offset (AVO) inversion results of impedance and velocity parameters, we adjust the parameters of the nonlinear equation, avoid the inaccuracy caused by parameters sensitivity and get the ideal nonlinear AVO inversion results of the Lamé parameters. The feasibility and stability of the nonlinear equation based on the Lamé parameters and method are verified by the model and the real data examples. The resolution and the lateral continuity of nonlinear inversion results are better compared with the linear inversion results.

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

2016 ◽  
Vol 4 (4) ◽  
pp. T613-T625 ◽  
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.

Reservoir-oriented wave-equation-based seismic amplitude variation with offset inversion

2017 ◽  
Vol 5 (3) ◽  
pp. SL43-SL56 ◽  
Author(s):  
Dries Gisolf ◽  
Peter R. Haffinger ◽  
Panos Doulgeris
Keyword(s):  
Wave Equation ◽  
Elastic Wave ◽  
Time Lapse ◽  
Background Model ◽  
Nonlinear Inversion ◽  
Elastic Wave Equation ◽  
Amplitude Variation ◽  
Amplitude Variation With Offset ◽  
Avo Inversion ◽  
Object Domain

Wave-equation-based amplitude-variation-with-offset (AVO) inversion solves the full elastic wave equation, for the properties as well as the total wavefield in the object domain, from a set of observations. The relationship between the data and the property set to invert for is essentially nonlinear. This makes wave-equation-based inversion a nonlinear process. One way of visualizing this nonlinearity is by noting that all internal multiple scattering and mode conversions, as well as traveltime differences between the real medium and the background medium, are accounted for by the wave equation. We have developed an iterative solution to this nonlinear inversion problem that seems less likely to be trapped in local minima. The surface recorded data are preconditioned to be more representative for the target interval, by redatuming, or migration. The starting model for the inversion is a very smooth (0–4 Hz) background model constructed from well data. Depending on the data quality, the nonlinear inversion may even update the background model, leading to a broadband solution. Because we are dealing with the elastic wave equation and not a linearized data model in terms of primary reflections, the inversion solves directly for the parameters defining the wave equation: the compressibility (1/bulk modulus) and the shear compliance (1/shear modulus). These parameters are much more directly representative for hydrocarbon saturation, porosity, and lithology, than derived properties such as acoustic and shear impedance that logically follow from the linearized reflectivity model. Because of the strongly nonlinear character of time-lapse effects, wave-equation based AVO inversion is particularly suitable for time-lapse inversion. Our method is presented and illustrated with some synthetic data and three real data case studies.

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

Geophysics ◽  
2018 ◽  
Vol 83 (6) ◽  
pp. R669-R679 ◽  
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.

Joint anisotropic amplitude variation with offset inversion of PP and PS seismic data

Geophysics ◽  
2018 ◽  
Vol 83 (2) ◽  
pp. N31-N50 ◽  
Author(s):  
Jun Lu ◽  
Yun Wang ◽  
Jingyi Chen ◽  
Ying An
Keyword(s):  
Seismic Data ◽  
Local Minimum ◽  
Synthetic Data ◽  
Inversion Method ◽  
Amplitude Variation ◽  
Amplitude Variation With Offset ◽  
Avo Inversion ◽  
Time Migration ◽  
Amplitude Variation With Angle ◽  
Two Stages

With the increase in exploration target complexity, more parameters are required to describe subsurface properties, particularly for finely stratified reservoirs with vertical transverse isotropic (VTI) features. We have developed an anisotropic amplitude variation with offset (AVO) inversion method using joint PP and PS seismic data for VTI media. Dealing with local minimum solutions is critical when using anisotropic AVO inversion because more parameters are expected to be derived. To enhance the inversion results, we adopt a hierarchical inversion strategy to solve the local minimum solution problem in the Gauss-Newton method. We perform the isotropic and anisotropic AVO inversions in two stages; however, we only use the inversion results from the first stage to form search windows for constraining the inversion in the second stage. To improve the efficiency of our method, we built stop conditions using Euclidean distance similarities to control iteration of the anisotropic AVO inversion in noisy situations. In addition, we evaluate a time-aligned amplitude variation with angle gather generation approach for our anisotropic AVO inversion using anisotropic prestack time migration. We test the proposed method on synthetic data in ideal and noisy situations, and find that the anisotropic AVO inversion method yields reasonable inversion results. Moreover, we apply our method to field data to show that it can be used to successfully identify complex lithologic and fluid information regarding fine layers in reservoirs.

Azimuthal amplitude variation with offset parameterization and inversion for fracture weaknesses in tilted transversely isotropic media

Geophysics ◽  
2020 ◽  
Vol 86 (1) ◽  
pp. C1-C18
Author(s):  
Xinpeng Pan ◽  
Lin Li ◽  
Shunxin Zhou ◽  
Guangzhi Zhang ◽  
Jianxin Liu
Keyword(s):  
Tilt Angle ◽  
Stiffness Matrix ◽  
Incidence Angle ◽  
Fractured Reservoirs ◽  
Seismic Inversion ◽  
Inversion Method ◽  
Amplitude Variation ◽  
Amplitude Variation With Offset ◽  
Pp Wave ◽  
And Inversion

The characterization of fracture-induced tilted transverse isotropy (TTI) seems to be more suitable to actual scenarios of geophysical exploration for fractured reservoirs. Fracture weaknesses enable us to describe fracture-induced anisotropy. With the incident and reflected PP-wave in TTI media, we have adopted a robust method of azimuthal amplitude variation with offset (AVO) parameterization and inversion for fracture weaknesses in a fracture-induced reservoir with TTI symmetry. Combining the linear-slip model with the Bond transformation, we have derived the stiffness matrix of a dipping-fracture-induced TTI medium characterized by normal and tangential fracture weaknesses and a tilt angle. Integrating the first-order perturbations in the stiffness matrix of a TTI medium and scattering theory, we adopt a method of azimuthal AVO parameterization for PP-wave reflection coefficient for the case of a weak-contrast interface separating two homogeneous weakly anisotropic TTI layers. We then adopt an iterative inversion method by using the partially incidence-angle-stacked seismic data with different azimuths to estimate the fracture weaknesses of a TTI medium when the tilt angle is estimated based on the image well logs prior to the seismic inversion. Synthetic examples confirm that the fracture weaknesses of a TTI medium are stably estimated from the azimuthal seismic reflected amplitudes for the case of moderate noise. A field data example demonstrates that geologically reasonable results of fracture weaknesses can be determined when the tilt angle is treated as the prior information. We determine that the azimuthal AVO inversion approach provides an available tool for fracture prediction in a dipping-fracture-induced TTI reservoir.

Seismic inversion based on proximal objective function optimization algorithm

Geophysics ◽  
2016 ◽  
Vol 81 (5) ◽  
pp. R237-R246 ◽  
Author(s):  
Ronghuo Dai ◽  
Fanchang Zhang ◽  
Hanqing Liu
Keyword(s):  
Objective Function ◽  
Optimization Algorithm ◽  
Computational Efficiency ◽  
Real Data ◽  
Cauchy Distribution ◽  
Critical Issue ◽  
Seismic Inversion ◽  
Function Optimization ◽  
Inversion Method ◽  
Reservoir Prediction

Seismic impedance inversion has become a common approach in reservoir prediction. At present, the critical issue in the application of seismic inversion is its low computational efficiency, especially in 3D. To improve the computational efficiency, we have developed an inversion method derived from the proximal objective function optimization algorithm. Our inversion method calculates each unknown parameter in the model vector, one by one during iteration. Compared with routine gradient-dependent inversion algorithms, such as the iteratively reweighted least-squares (IRLS) algorithm, our inversion method has lower computational complexity as well as higher efficiency. In addition, to obtain a sparse reflectivity series, a long-tailed Cauchy distribution is used as the a priori constraint. The weak nonlinear problem owing to the introduction of Cauchy sparse constraint is addressed by taking advantage of reweighting strategy. Results of synthetic and real data tests illustrate that the proposed inversion method has higher computational efficiency than IRLS algorithm, and its inversion accuracy remains the same.

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

Geophysics ◽  
2018 ◽  
Vol 83 (6) ◽  
pp. R725-R748 ◽  
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.

Meet West Africa deep exploration challenge with geomorphology and targeted amplitude variation with offset inversion

2020 ◽  
Vol 8 (1) ◽  
pp. SA25-SA33
Author(s):  
Ellen Xiaoxia Xu ◽  
Yu Jin ◽  
Sarah Coyle ◽  
Dileep Tiwary ◽  
Henry Posamentier ◽  
...  
Keyword(s):  
West Africa ◽  
Critical Role ◽  
Reservoir Quality ◽  
Quality Prediction ◽  
Reservoir Prediction ◽  
Amplitude Variation ◽  
Amplitude Variation With Offset ◽  
Simultaneous Inversion ◽  
Seismic Amplitude ◽  
Class 1

Seismic amplitude has played a critical role in the exploration and exploitation of hydrocarbon in West Africa. Class 3 and 2 amplitude variation with offset (AVO) was extensively used as a direct hydrocarbon indicator and reservoir prediction tool in Neogene assets. As exploration advanced to deeper targets with class 1 AVO seismic character, the usage of seismic amplitude for reservoir presence and quality prediction became challenged. To overcome this obstacle, (1) we used seismic geomorphology to infer reservoir presence and precisely target geophysical analysis on reservoir prone intervals, (2) we applied rigorous prestack data preparation to ensure the accuracy and precision of AVO simultaneous inversion for reservoir quality prediction, and (3) we used lateral statistic method to sum up AVO behavior in regions of contrasts to infer reservoir quality changes. We have evaluated a case study in which the use of the above three techniques resulted in confident prediction of reservoir presence and quality. Our results reduced the uncertainty around the biggest risk element in reservoir among the source, charge, and trap mechanism in the prospecting area. This work ultimately made a significant contribution toward a confident resource booking.

Linearized amplitude variation with offset (AVO) inversion with supercritical angles

Geophysics ◽  
2006 ◽  
Vol 71 (5) ◽  
pp. E49-E55 ◽  
Author(s):  
Jonathan E. Downton ◽  
Charles Ursenbach
Keyword(s):  
Reflection Coefficient ◽  
Critical Angle ◽  
Waveform Inversion ◽  
Phase Variation ◽  
Reflection Coefficients ◽  
Amplitude Variation ◽  
Amplitude Variation With Offset ◽  
Zoeppritz Equations ◽  
Avo Inversion ◽  
Angle Data

Contrary to popular belief, a linearized approximation of the Zoeppritz equations may be used to estimate the reflection coefficient for angles of incidence up to and beyond the critical angle. These supercritical reflection coefficients are complex, implying a phase variation with offset in addition to amplitude variation with offset (AVO). This linearized approximation is then used as the basis for an AVO waveform inversion. By incorporating this new approximation, wider offset and angle data may be incorporated in the AVO inversion, helping to stabilize the problem and leading to more accurate estimates of reflectivity, including density reflectivity.

scholarly journals An Accurate Jacobian Matrix with Exact Zoeppritz for Elastic Moduli of Dry Rock

2019 ◽  
Vol 9 (24) ◽  
pp. 5485
Author(s):  
Xiaobo Liu ◽  
Jingyi Chen ◽  
Fuping Liu ◽  
Zhencong Zhao
Keyword(s):  
Jacobian Matrix ◽  
Incidence Angle ◽  
Inversion Method ◽  
Seismic Velocities ◽  
Amplitude Variation ◽  
Amplitude Variation With Offset ◽  
Shear Moduli ◽  
Partial Derivatives ◽  
Solid Matrices ◽  
Derivatives Of

Seismic velocities are related to the solid matrices and the pore fluids. The bulk and shear moduli of dry rock are the primary parameters to characterize solid matrices. Amplitude variation with offset (AVO) or amplitude variation with incidence angle (AVA) is the most used inversion method to discriminate lithology in hydrocarbon reservoirs. The bulk and shear moduli of dry rock, however, cannot be inverted directly using seismic data and the conventional AVO/AVA inversions. The most important step to accurately invert these dry rock parameters is to derive the Jacobian matrix. The combination of exact Zoeppritz and Biot–Gassmann equations makes it possible to directly calculate the partial derivatives of seismic reflectivities (PP-and PS-waves) with respect to dry rock moduli. During this research, we successfully derive the accurate partial derivatives of the exact Zoeppritz equations with respect to bulk and shear moduli of dry rock. The characteristics of these partial derivatives are investigated in the numerical examples. Additionally, we compare the partial derivatives using this proposed algorithm with the classical Shuey and Aki–Richards approximations. The results show that this derived Jacobian matrix is more accurate and versatile. It can be used further in the conventional AVO/AVA inversions to invert bulk and shear moduli of dry rock directly.

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