Bayesian linearized petrophysical AVO inversion

Geophysics ◽  
2018 ◽  
Vol 83 (3) ◽  
pp. M1-M13 ◽  
Author(s):  
Xiaozheng Lang ◽  
Dario Grana
Keyword(s):  
Seismic Data ◽  
Elastic Moduli ◽  
Water Saturation ◽  
Forward Model ◽  
Inversion Method ◽  
Data Set ◽  
Critical Porosity ◽  
Explicit Analytical Solution ◽  
Fluid Properties ◽  
Model Linearization

Seismic reservoir characterization aims to provide a 3D model of rock and fluid properties based on measured seismic data. Petrophysical properties, such as porosity, mineral volumes, and water saturation, are related to elastic properties, such as velocity and impedance, through a rock-physics model. Elastic attributes can be obtained from seismic data through seismic modeling. Estimation of the properties of interest is an inverse problem; however, if the forward model is nonlinear, computationally demanding inversion algorithms should be adopted. We have developed a linearized forward model, based on a convolutional model and a new amplitude variation with offset approximation that combined Gray’s linearization of the reflectivity coefficients with Gassmann’s equation and Nur’s critical porosity model. Physical relations between the saturated elastic moduli and the matrix elastic moduli, fluid bulk modulus, and porosity are almost linear, and the model linearization can be obtained by computing the first-order Taylor series approximation. The inversion method for the estimation of the reservoir properties of interest is then developed in the Bayesian framework. If we assume that the distributions of the prior model and error term are Gaussian, then the explicit analytical solution of the posterior distribution of rock and fluid properties can be analytically derived. Our method has first been validated on synthetic seismic data and then applied to a 2D seismic section extracted from a real data set acquired in the Norwegian Sea.

scholarly journals Fast probabilistic petrophysical mapping of reservoirs from 3D seismic data

Geophysics ◽  
2012 ◽  
Vol 77 (3) ◽  
pp. O1-O19 ◽  
Author(s):  
Mohammad S. Shahraeeni ◽  
Andrew Curtis ◽  
Gabriel Chao
Keyword(s):  
Seismic Data ◽  
Water Saturation ◽  
Random Noise ◽  
Clay Content ◽  
Inversion Method ◽  
Model Parameters ◽  
Nonlinear Inversion ◽  
Desktop Computer ◽  
Data Set ◽  
Mixture Density

A fast probabilistic inversion method for 3D petrophysical property prediction from inverted prestack seismic data has been developed and tested on a real data set. The inversion objective is to estimate the joint probability density function (PDF) of model vectors consisting of porosity, clay content, and water saturation components at each point in the reservoir, from data vectors with compressional- and shear-wave-impedance components that are obtained from the inversion of seismic data. The proposed inversion method is based on mixture density network (MDN), which is trained by a given set of training samples, and provides an estimate of the joint posterior PDF’s of the model parameters for any given data point. This method is much more time and memory efficient than conventional nonlinear inversion methods. The training data set is constructed using nonlinear petrophysical forward relations and includes different sources of uncertainty in the inverse problem such as variations in effective pressure, bulk modulus and density of hydrocarbon, and random noise in recorded data. Results showed that the standard deviations of all model parameters were reduced after inversion, which shows that the inversion process provides information about all parameters. The reduction of uncertainty in water saturation was smaller than that for porosity or clay content; nevertheless the maximum of the a posteriori (MAP) of model PDF clearly showed the boundary between brine saturated and oil saturated rocks at wellbores. The MAP estimates of different model parameters show the lateral and vertical continuity of these boundaries. Errors in the MAP estimate of different model parameters can be reduced using more accurate petrophysical forward relations. This fast, probabilistic, nonlinear inversion method can be applied to invert large seismic cubes for petrophysical parameters on a standard desktop computer.

Seismic resolution enhancement in shale-oil reservoirs

Geophysics ◽  
2018 ◽  
Vol 83 (5) ◽  
pp. B281-B287 ◽  
Author(s):  
Xiwu Liu ◽  
Fengxia Gao ◽  
Yuanyin Zhang ◽  
Ying Rao ◽  
Yanghua Wang
Keyword(s):  
Seismic Data ◽  
Resolution Enhancement ◽  
Oil Reservoirs ◽  
Inversion Method ◽  
Shale Oil ◽  
Data Set ◽  
Extension Method ◽  
Seismic Resolution ◽  
Full Band ◽  
Shale Oil Reservoirs

We developed a case study of seismic resolution enhancement for shale-oil reservoirs in the Q Depression, China, featured by rhythmic bedding. We proposed an innovative method for resolution enhancement, called the full-band extension method. We implemented this method in three consecutive steps: wavelet extraction, filter construction, and data filtering. First, we extracted a constant-phase wavelet from the entire seismic data set. Then, we constructed the full-band extension filter in the frequency domain using the least-squares inversion method. Finally, we applied the band extension filter to the entire seismic data set. We determined that this full-band extension method, with a stretched frequency band from 7–70 to 2–90 Hz, may significantly enhance 3D seismic resolution and distinguish reflection events of rhythmite groups in shale-oil reservoirs.

Time-lapse acoustic impedance variations during CO2 injection in Weyburn oilfield, Canada

Geophysics ◽  
2019 ◽  
Vol 85 (1) ◽  
pp. M1-M13 ◽  
Author(s):  
Yichuan Wang ◽  
Igor B. Morozov
Keyword(s):  
Oil Recovery ◽  
Seismic Data ◽  
Acoustic Impedance ◽  
Time Lapse ◽  
Time Shift ◽  
Co2 Injection ◽  
Inversion Method ◽  
Data Sets ◽  
Storage Site ◽  
Data Set

For seismic monitoring injected fluids during enhanced oil recovery or geologic [Formula: see text] sequestration, it is useful to measure time-lapse (TL) variations of acoustic impedance (AI). AI gives direct connections to the mechanical and fluid-related properties of the reservoir or [Formula: see text] storage site; however, evaluation of its subtle TL variations is complicated by the low-frequency and scaling uncertainties of this attribute. We have developed three enhancements of TL AI analysis to resolve these issues. First, following waveform calibration (cross-equalization) of the monitor seismic data sets to the baseline one, the reflectivity difference was evaluated from the attributes measured during the calibration. Second, a robust approach to AI inversion was applied to the baseline data set, based on calibration of the records by using the well-log data and spatially variant stacking and interval velocities derived during seismic data processing. This inversion method is straightforward and does not require subjective selections of parameterization and regularization schemes. Unlike joint or statistical inverse approaches, this method does not require prior models and produces accurate fitting of the observed reflectivity. Third, the TL AI difference is obtained directly from the baseline AI and reflectivity difference but without the uncertainty-prone subtraction of AI volumes from different seismic vintages. The above approaches are applied to TL data sets from the Weyburn [Formula: see text] sequestration project in southern Saskatchewan, Canada. High-quality baseline and TL AI-difference volumes are obtained. TL variations within the reservoir zone are observed in the calibration time-shift, reflectivity-difference, and AI-difference images, which are interpreted as being related to the [Formula: see text] injection.

Simultaneous inversion of PP and PS seismic data

Geophysics ◽  
2006 ◽  
Vol 71 (3) ◽  
pp. R1-R10 ◽  
Author(s):  
Helene Hafslund Veire ◽  
Martin Landrø
Keyword(s):  
Seismic Data ◽  
Reservoir Characterization ◽  
Model Building ◽  
Joint Inversion ◽  
P Wave ◽  
Inversion Method ◽  
System Of Equations ◽  
S Wave ◽  
Data Set ◽  
Simultaneous Inversion

Elastic parameters derived from seismic data are valuable input for reservoir characterization because they can be related to lithology and fluid content of the reservoir through empirical relationships. The relationship between physical properties of rocks and fluids and P-wave seismic data is nonunique. This leads to large uncertainties in reservoir models derived from P-wave seismic data. Because S- waves do not propagate through fluids, the combined use of P-and S-wave seismic data might increase our ability to derive fluid and lithology effects from seismic data, reducing the uncertainty in reservoir characterization and thereby improving 3D reservoir model-building. We present a joint inversion method for PP and PS seismic data by solving approximated linear expressions of PP and PS reflection coefficients simultaneously using a least-squares estimation algorithm. The resulting system of equations is solved by singular-value decomposition (SVD). By combining the two independent measurements (PP and PS seismic data), we stabilize the system of equations for PP and PS seismic data separately, leading to more robust parameter estimation. The method does not require any knowledge of PP and PS wavelets. We tested the stability of this joint inversion method on a 1D synthetic data set. We also applied the methodology to North Sea multicomponent field data to identify sand layers in a shallow formation. The identified sand layers from our inverted sections are consistent with observations from nearby well logs.

Integrated reservoir characterization of a Utica Shale field

2018 ◽  
Vol 37 (9) ◽  
pp. 656-661
Author(s):  
Jinming Zhu
Keyword(s):  
Seismic Data ◽  
Reservoir Characterization ◽  
Water Saturation ◽  
Clay Content ◽  
Seismic Inversion ◽  
Data Set ◽  
Utica Shale ◽  
Multidisciplinary Study ◽  
3D Seismic Data

We performed an integrated multidisciplinary study for reservoir characterization of a Utica Shale field in eastern Ohio covered by a multiclient 3D seismic data set acquired in 2015. Elastic seismic inversion was performed in-house for effective reservoir characterization of the Utica Shale, which covers the interval from the top of Upper Utica (UUTIC) to the top of Trenton Limestone. Accurate, high-fidelity inversion results were obtained, including acoustic impedance, shear impedance, density, and VP/VS. These consistent inversion results allow for the reliable calculation of geomechanical and petrophysical properties of the reservoir. The inverted density clearly divides the Point Pleasant (PPLS) interval as low density from the overlying UUTIC Shale interval. Both Poisson's ratio (PR) and brittleness unmistakably separate the underlying PPLS from the overlying Utica interval. The PPLS Formation is easier to hydraulically fracture due to its much lower PR. Sequence S4 is the best due to its higher Young's modulus to sustain the open fractures. The calculated petrophysical volumes indisputably delineate the traditional Utica Shale into two distinctive sections. The upper section, the UUTIC, can be described as having 1%–2% total organic carbon (TOC), 3.5%–4.8% porosity, 10%–24% water saturation, and 40%–58% clay content. The lower section, PPLS, can be described as having 3%–4.5% TOC, 5%–9% porosity, 2%–10% water saturation, and about 15%–35% clay content. Both sections exhibit spatial variation of the properties. Nevertheless, the underlying PPLS is obviously a significantly better reservoir and operationally easier to produce.

Combined simulation and inversion of SP and resistivity logs for the estimation of connate-water resistivity and Archie’s cementation exponent

Geophysics ◽  
2008 ◽  
Vol 73 (3) ◽  
pp. E107-E114 ◽  
Author(s):  
Jesús M. Salazar ◽  
Gong Li Wang ◽  
Carlos Torres-Verdín ◽  
Hee Jae Lee
Keyword(s):  
Water Saturation ◽  
Estimation Method ◽  
Inversion Method ◽  
Initial Water ◽  
Data Set ◽  
Spontaneous Potential ◽  
Connate Water ◽  
Resistivity Logs ◽  
Combined Simulation ◽  
Water Resistivity

Knowledge of initial water saturation is necessary to estimate original hydrocarbon in place. A reliable assessment of this petrophysical property is possible when rock-core measurements of Archie’s parameters, such as saturation exponent [Formula: see text] and cementation exponent [Formula: see text], are available. In addition, chemical analysis of formation water is necessary to measure connate-water resistivity [Formula: see text]. Such measurements are seldom available in most applications; if they are available, their reliability may be questionable. We describe a new inversion method to estimate [Formula: see text] and Archie’s cementation exponent from the combined use of borehole spontaneous-potential (SP) and raw array-induction resistivity measurements acquired in water-bearing depth intervals. Combined inversion of resistivity and SP measurements is performed assuming a piston-like invasion profile. In so doing, the reservoiris divided into petrophysical layers to account for vertical heterogeneities. Inversion products are values of invaded and virgin formation resistivity, radius of invasion, and static spontaneous potential (SSP). Connate-water resistivity is calculated by assuming membrane and diffusion potentials as the main contributors to the SSP. Archie’s or dual-water equations enable the estimation of [Formula: see text]. The new combined estimation method has been successfully applied to a data set acquired in a clastic formation. Data were acquired in a high permeability and moderately high-salt-concentration reservoir. Values of [Formula: see text] and [Formula: see text] yielded by the inversion are consistent with those obtained with a traditional interpretation method, thereby confirming the reliability of the estimation. The method is an efficient, rigorous alternative to conventional interpretation techniques for performing petrophysical analysis of exploratory and appraisal wells wherein rock-core measurements may not be available.

scholarly journals Optimal trace selection for AVA processing of shale-sand reservoirs

Geophysics ◽  
2010 ◽  
Vol 75 (4) ◽  
pp. C37-C47 ◽  
Author(s):  
Thomas Guest ◽  
Andrew Curtis
Keyword(s):  
Seismic Data ◽  
Data Sets ◽  
Statistical Experimental Design ◽  
Data Set ◽  
Optimal Processing ◽  
Fluid Properties ◽  
Reservoir Porosity ◽  
Selection For ◽  
Amplitude Variation With Angle ◽  
Rock Parameters

When processing data, a principal aim is to maximize information inferred from a data set by minimizing the expected postprocessing uncertainties on parameters of interest. Nonlinear statistical experimental design (SED) methods can be used to find optimal trace profiles for processing amplitude-variation-with-angle (AVA) surveys that account for all prior petrophysical information about the target reservoir. Optimal selections change as prior knowledge of rock parameters and reservoir fluid content changes, and which of the prior parameters have the greatest effect on selected traces can be assessed. The results show that optimal profiles are far more sensitive to prior information about reservoir porosity than to information about saturating fluid properties. By applying ray-tracing methods, AVA results can be used to design optimal processing profiles from seismic data sets for multiple targets, each with different prior-model uncertainties.

Joint seismic and petrophysical nonlinear inversion with Gaussian mixture-based adaptive regularization

Geophysics ◽  
2021 ◽  
pp. 1-57
Author(s):  
Qiang Guo ◽  
Jing Ba ◽  
Li-Yun Fu ◽  
Cong Luo
Keyword(s):  
Inverse Problem ◽  
Seismic Data ◽  
Simulated Annealing Algorithm ◽  
Gaussian Mixture ◽  
Forward Model ◽  
Inversion Method ◽  
Model Parameters ◽  
Adaptive Regularization ◽  
Petrophysical Parameters ◽  
Highly Nonlinear

The estimation of reservoir parameters from seismic observations is one of the main objectives in reservoir characterization. However, the forward model relating petrophysical properties of rocks to observed seismic data is highly nonlinear, and solving the relevant inverse problem is a challenging task. We present a novel inversion method for jointly estimating elastic and petrophysical parameters of rocks from prestack seismic data. We combine a full rock-physics model and the exact Zoeppritz equation as the forward model. To overcome the ill-conditioning of the inverse problem and address the complex prior distribution of model parameters given lithofacies variations, we introduce a regularization term based on the prior Gaussian mixture model under Bayesian framework. The objective function is optimized by the fast simulated annealing algorithm, during which the Gaussian mixture-based regularization terms are adaptively and iteratively adjusted by the maximum likelihood estimator, allowing the posterior distribution to be more consistent with the observed seismic data. The adaptive regularization method improves the accuracy of petrophysical parameters compared to the sequential inversion and non-adaptive regularization methods, and the inversion result can be used for indicating gas-saturated areas when applied to field data.

Geostatistical inversion of prestack seismic data for the joint estimation of facies and impedances using stochastic sampling from Gaussian mixture posterior distributions

Geophysics ◽  
2017 ◽  
Vol 82 (4) ◽  
pp. M55-M65 ◽  
Author(s):  
Xiaozheng Lang ◽  
Dario Grana
Keyword(s):  
Elastic Properties ◽  
Posterior Distribution ◽  
Seismic Data ◽  
Gaussian Mixture ◽  
Seismic Inversion ◽  
Joint Estimation ◽  
Inversion Method ◽  
Inversion Algorithm ◽  
Data Set ◽  
Geostatistical Approach

We have developed a seismic inversion method for the joint estimation of facies and elastic properties from prestack seismic data based on a geostatistical approach. The objectives of our inversion methodology are to sample from the posterior distribution of seismic properties and to simultaneously classify the lithology conditioned by seismic data. The inversion algorithm is a sequential Gaussian mixture inversion based on Bayesian linearized amplitude variation with offset inverse theory and sequential geostatistical simulations. The stochastic approach to the inversion allows generating multiple elastic models that match the seismic data. To mathematically represent the multimodal behavior of elastic properties due to their variations within different lithologies, we adopt a Gaussian mixture distribution for the prior model of the elastic properties and we use the prior probability of the facies as weights of the Gaussian components of the mixture. The solution of the inverse problem is achieved by deriving the explicit analytical expression of the posterior distribution of the elastic properties and facies and by sampling from this distribution according to a spatial correlation model. The inversion methodology has been validated using well logs and synthetic seismic data with different noise levels, and it is then applied to a real 3D seismic data set in North Sea.

Time-lapse difference inversion based on the modified reflectivity method with differentiable Hyper-Laplacian blocky constraint

Geophysics ◽  
2021 ◽  
pp. 1-121
Author(s):  
Wei Tang ◽  
Jingye Li ◽  
Wenbiao Zhang ◽  
Jian Zhang ◽  
Weiheng Geng ◽  
...  
Keyword(s):  
Seismic Data ◽  
Time Lapse ◽  
Inversion Method ◽  
Transmission Losses ◽  
Bayesian Theorem ◽  
Reflectivity Method ◽  
Fluid Properties ◽  
Internal Multiples ◽  
Fine Tune

Time-lapse (TL) seismic has great potential in monitoring and interpreting time-varying variations in reservoir fluid properties during hydrocarbon exploitation. Obtaining the disparities of reservoir elastic parameters by inversion is essential for TL reservoir monitoring. Conventional TL inversion is carried out by stages without coupling processing and leads to inaccuracy of the results. We directly use the differences in seismic data responses from different vintages, namely difference inversion, to improve the results credibility. It may reduce the deviations of the subtraction of base and monitor inversions in traditional methods. Moreover, most existing studies involving pre-stack inversion methods use the Zoeppritz equation or its approximants, which failed to consider the wave propagation effects. Here, we propose a new TL difference inversion based on the modified reflectivity method (MRM), the internal multiples and transmission losses are taken into consideration to fine-tune the characterization of the seismic wave propagating underground. The new method is modified on the basis of reflectivity method (RM) making it feasible in TL difference inversion, and derived from the Bayesian theorem. For further delineating the boundaries between layers, the differentiable Hyper-Laplacian blocky constraint (DHLBC) is introduced into the prior information of Bayesian framework, which heightens the sparseness in the vertical gradients of inversion results and leads to sharp interlayer boundaries of difference parameters. The synthetic and field data examples demonstrate that the proposed TL difference inversion method has clear advantages in accuracy and resolution compared to Zoeppritz method and MRM without DHLBC.

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