Pre-stack Inversion Method Research Articles

Quantitative interpretation using conventional and facies-based pre-stack inversion — A thin dolomite reservoir case study in Cabin Creek Field, Williston Basin

Cabin Creek Field, on the southwestern flank of the Williston Basin, is one of 14 hydrocarbon fields within Cedar Creek nticline. The field was initially discovered in May 1953 and developed by Shell starting with primary production followed by water flooding beginning in the late 1950s. In 1999, Encore purchased Shell’s interests and focused on infill drilling. In 2010, Denbury Resources acquired Encore giving it the potential to undertake enhanced oil recovery operations in the Rockies. Production is from the Ordovician Red River, Silurian Stony Mountain, Interlake, and Mississippian Mission Canyon Formations. The objective of the Cabin Creek reservoir characterization is to document reservoir heterogeneity within the target reservoirs and to facilitate development of the CO2 flood. The goal of this integrated case study is to generate a representative reservoir model that combines the structural framework and porosity prediction within the Red River Formation. This paper focuses on utilizing and comparing conventional and facies-based pre-stack inversion methods to characterize the porosity at the reservoir level.

Application of simultaneous prestack inversion in reservoir facies identification

Poststack inversion is purely acoustic because there is no mode conversion at normal incidence. Therefore, P-wave impedance is the only information that can be estimated from poststack inversion of P-wave data. In full prestack inversion, both the low- and high-frequency components of the P-wave acoustic impedance can be extracted from the seismic data. In addition to the P-wave acoustic impedance, S-wave information or Poisson's ratio can also be estimated from prestack data. This provides fluid information for the reservoirs; thus, prestack inversion has an advantage over poststack inversion. We determined k, KC, m, and mC which are, respectively, the slope of the natural logarithm of shear impedance against the natural logarithm of acoustic impedance, the intercept of the natural logarithm of shear impedance against the natural logarithm of acoustic impedance, the slope of the natural logarithm of density against the natural logarithm of acoustic impedance, and the intercept of the natural logarithm of shear impedance against the natural logarithm of acoustic impedance. We also needed a set of angle-dependent wavelets, which are derived from angle stacks. Hence, we built three angle stacks; the near-angle stack (0–11 degrees), middle-angle stack (11–20 degrees), and far-angle stack (20–29 degrees). Using these angle stacks, we built three statistical angle-dependent wavelets. Finally, with log information we built an initial model for acoustic impedance, and tried to solve the inversion matrix using the conjugate gradient method. By solving this, we could simultaneously derive the acoustic impedance, shear impedance, and density sections from prestack data. Simultaneous inversion used the assumption of a constant shear wave to compressional wave velocity ratio, and the generalized Garnder equation, which are only valid in clastic rocks. The simultaneous prestack inversion method was used for the identification of reservoir facies in one of the hydrocarbon fields in Iran. With this method, four facies were identified; these were confirmed by reservoir geological information and well data.

A new prestack three-parameter amplitude variation with offset inversion method

Prestack seismic inversion is an important method in reservoir prediction and fluid identification. In this paper, we develop a new strategy to carry out a prestack three-parameter AVO inversion to obtain P-wave velocity, S-wave velocity, and density. Using the Aki and Richards equation to calculate the PP reflection coefficients, which is the approximation to the Zoeppritz PP equation, we re-derive the relationship between reflection coefficients and their partial derivatives with respect to P-wave velocity, S-wave velocity, and density. We transform the objective function into the form of matrix multiplication and solve it using a damped least-squares method and Tikhonov regularization method. Then we directly obtain the inversion results, including P-wave velocity, S-wave velocity and density. To demonstrate the validity of the proposed prestack inversion method, we set up a 1D forward simulation model and add uniform noise into the synthetic seismic records. Then we test the proposed method on the overthrust model and field data. In order to demonstrate its high accuracy and the efficiency of the Tikhonov regularization method, we carry out a damped least-squares inversion method using the same models as a comparison. We find that the proposed prestack seismic data AVO inversion method has higher anti-noise capability, accuracy, and efficiency, both in synthetic records and field data using the Tikhonov regularization method.

A nonlinear multiparameter prestack seismic inversion method based on hybrid optimization approach

Multiparameter prestack seismic inversion is one of the most powerful techniques in quantitatively estimating subsurface petrophysical properties. However, it remains a challenging problem due to the nonlinearity and ill-posedness of the inversion process. Traditional regularization approach can stabilize the solution but at the cost of smoothing valuable geological boundaries. In addition, compared with linearized optimization methods, global optimization techniques can obtain better results regardless of initial models, especially for multiparameter prestack inversion. However, when solving multiparameter prestack inversion problems, the application of standard global optimization algorithms maybe limited due to the issue of high computational cost (e.g., simulating annealing) or premature convergence (e.g., particle swarm optimization). In this paper, we propose a hybrid optimization-based multiparameter prestack inversion method. In this method, we introduce a prior constraint term featured by multiple regularization functions, intended to preserve layered boundaries of geological formations; in particular, to address the problem of premature convergence existing in standard particle swarm optimization algorithm, we propose a hybrid optimization strategy by hybridizing particle swarm optimization and very fast simulating annealing to solve the nonlinear optimization problem. We demonstrate the effectiveness of the proposed inversion method by conducting synthetic test and field data application, both of which show encouraging results.

Comparison of model-based generalized regression neural network and prestack inversion in predicting Poisson's ratio in Heidrun Field, North Sea

Drilling wells in the oil and gas industry is a substantial process, whether they are appraisal wells drilled for reservoir-characteristic assessments at the exploration stage or production wells drilled following prior assessments. The challenge has always been to reduce drilling-related expenses and natural/environmental hazards by reducing the number of wells drilled, and to evaluate reservoir characteristics with as few calibration wells as possible. Physical and mathematical modeling of seismic data can help us understand the geologic and structural formations with minimal wells, and interpolate reservoir characteristics across large areas between a few drilled wells. In a new comparative approach, simultaneous prestack inversion and artificial neural network (ANN) methods are used to create 3D Poisson's ratio (PR) models built upon low-frequency initial models (IMs). Training the ANN on IMs similar to those used in the inversion has improved its performance while creating a valid base of comparison between the two methods. The inversion method was able to model the PR around four wells that had been used in creating the IMs. The generalized regression neural network that was trained on a PR IM, along with other seismic attributes, gave results that were consistent with the existing wells. The results of both methods confirm the existence of a strong relationship between PR and known hydrocarbon presence in these wells. However, examining the results with a blind well showed that the ANN was notably more successful than inversion in extrapolating the results beyond the logged sections in the wells and away from control wells. While this particular conclusion cannot be generalized, and the results obtained from the same methodology may vary from one reservoir to another, such results suggest that this procedure can become a robust part of a predrilling reservoir-evaluation phase in developing hydrocarbon fields.

Joint PP and PS AVA seismic inversion using exact Zoeppritz equations

The Zoeppritz equations describe the relationship between seismic properties that are useful for the interpretation of lithology and fluid properties. Various approximations to the Zoeppritz equations are often used in linear amplitude variation with offset and amplitude variation with angle inversions, assuming low-contrast boundaries. These approximations restrict the inversion method to not-too-large-angle cases and reduce the inversion accuracy. Therefore, it is necessary to develop joint PP and PS prestack inversion methods using the exact Zoeppritz equations. We have developed a method for nonlinear joint prestack inversion using the exact Zoeppritz equations. We established an objective function to combine PP and PS information based on a least-squares approach, and we used the Taylor expansion method to derive a model updating formula for the inversion. We also used a mean shift method to improve the accuracy of inversion results. We validated our inversion using synthetic and field seismic data. The model for calculating synthetic data contained high-contrast interfaces to match the reservoir layers, which included, for example, coal seams and unconsolidated sandstone. The outputs of the inversion were the elastic parameters (P- and S-wave velocities, as well as density), rather than the changes in elastic parameters. We found that the nonlinear joint prestack inversion achieved more accurate results than the linear joint prestack inversion, regardless of incidence angle size. Furthermore, if the prestack data were of high enough quality, it was possible to identify thin layers from the inversion result.

Zoeppritz equation-based prestack inversion and its application in fluid identification

Prestack seismic inversion methods adopt approximations of the Zoeppritz equations to describe the relation between reflection coefficients and P-wave velocity, S-wave velocity, and density. However, the error in these approximations increases with increasing angle of incidence and variation of the elastic parameters, which increases the number of inversion solutions and minimizes the inversion accuracy. In this study, we explore a method for solving the reflection coefficients by using the Zoeppritz equations. To increase the accuracy of prestack inversion, the simultaneous inversion of P-wave velocity, S-wave velocity, and density by using prestack large-angle seismic data is proposed based on generalized linear inversion theory. Moreover, we reduce the ill posedness and increase the convergence of prestack inversion by using the regularization constraint damping factor and the conjugate gradient algorithm. The proposed prestack inversion method uses prestack large-angle seismic data to obtain accurate seismic elastic parameters that conform to prestack seismic data and are consistent with logging data from wells.

Prestack seismic inversion versus neural-network analysis: A case study in the Scarab field offshore Nile Delta, Egypt

In clastic depositional systems such as those encountered in the Nile Delta Basin, simultaneous prestack seismic-amplitude inversion is an effective method for detecting and appraising gas-bearing sandstone reservoirs. However, the method has limitations concerning the requirement of a reliable set of wavelets, suitable wireline logs, and a sufficiently dense initial model. The neural-network analysis method is an alternative technique which sometimes can provide similar or better results and does not require significant volumes of data. Simultaneous prestack inversion was applied over the Scarab field, West Delta Deep Marine concession, offshore Egypt. The field comprises submarine channel-based gas reservoirs that extend laterally over 20 km2. Six wells were analyzed in a rock-physics study prior to performing inversion. Three angle gathers (near: 0–15°; mid: 15–30°; far: 30–45°) were inverted for P-wave impedance (ZP), S-wave impedance (ZS), P-wave velocity (VP), S-wave velocity (VS), VP/VS, and density (ρ) using the prestack inversion method. Neural-network analysis was performed using full-stack seismic data along with well logs in the training stage, followed by cross-validation of results and rendering of VP, VS, VP/VS, and density volumes. The VP/VS volumes produced from the two methods were used to infer water saturation (Sw). Direct comparisons were made between neural-network and prestack inversion results at a blind-well location to assess the relative quality of each method. Results suggest that application of the proposed neural-network method leads to reliable inferences. Hence, using the neural-network method alone or along with the prestack inversion method has a positive impact on reserves growth and increased production.

Converted-wave time domain registration using the inverted pseudo-PS-wave attribute section

The main aim of the event registration of PP- and PS-waves in multicomponent seismic exploration is to provide the same time/depth domain data for further interpretation and application to reservoir characterization and hydrocarbon detection. Most registration methods are based on waveform similarity and phase consistency by correlating the stacked records, which may cause serious errors due to differences in PP- and PS-wave reflectivity. Our motivation was to develop a time matching workflow to improve the event registration of multicomponent seismic data and enhance joint interpretation techniques. In this paper, we present a prestack inversion method to obtain a pseudo-PS-wave (PPS) section based on prestack PP-wave gathers, and establish an attributes matching workflow based on the waveform similarity comparison of PP-, PS- and PPS-wave sections. We investigate the PP-wave prestack inversion method and the waveform similarity comparison of PP-, PS- and PPS-wave sections using synthetic data. The test on synthetic data clearly shows that the PPS-wave section has much better waveform similarity to the PS-wave section than the PP-wave due to the phase consistency of the reflectivity, increasing the correlation coefficient of waveform similarity to over 90% for PPS- and PS-waves from about 50% for PP- and PS-waves. The application to field data shows a very good improvement in the event registration, especially due to the partial nonexistence of events in the PP-wave section. The benefits for the time matching are also made evident by comparing the correlation sections of PPS- and PS-waves with PP- and PS-waves. The improved accuracy in event registration leads to better joint inversion and interpretation for the stratigraphic features and hydrocarbon detection in the subsequent applications.

Elastic impedance variation with angle inversion for elastic parameters

Elastic impedance (EI) and amplitude variation with offset or angle (AVO/AVA) inversion are two cardinal methods to estimate elastic parameters underground with reflection seismic data. Conventional EI inversion as a kind of pre-stack and post-stack joint inversion method has been widely applied in the industry because of its high efficiency and high stability of wavelet extraction; however, the robustness of extracting elastic parameters in conventional EI inversion is still controversial. The robustness of three-term AVO inversion has improved a lot; however, it is still challenging to extract reasonable space variant wavelets for each offset or incident angle. In this paper, a robust three-parameter estimation method, named elastic impedance variation with angle (EVA) inversion, is proposed in the Bayesian framework, which can estimate elastic parameters directly from EI. This method supposes that the parameters to be inverted are Cauchy distributed and it is implemented based on a normalized EI equation in a logarithmic domain which can reduce the nonlinearity of inversion. Application of a covariance matrix to decorrelate the parameters and constraint of well log curves introduced in an objective function enhances the robustness of EVA inversion. A model test shows that the proposed EVA inversion method enables one to estimate reasonable elastic parameters with extremely smooth initial models and moderate Gaussian noise. A real data example shows that the inverted P-wave velocity, S-wave velocity and density are identical to well log interpretation results, which shows the validity of the proposed method.

A Study of the Three‐Term Non‐Gaussian Pre‐Stack Inversion Method

AbstractIn view of the wide use of the “Gaussian distribution hypothesis of noise” in geophysical inversion problems, we study the non‐Gaussian distribution characteristics of the noise in pre‐stack seismic data. Upon this analysis, the concept of non‐Gaussian inversion of pre‐stack three‐term inversion is put forward, in which the mixed‐norm is proposed for suppressing both the Gaussian and non‐Gaussian noises. In view of the non‐derivable feature of the objective function, the Powell algorithm is used to solve the objective function. Model test and real seismic data inversion results show the correctness and reliability of the algorithm.

Reservoir prediction using pre-stack inverted elastic parameters

This is a case study of the application of pre-stack inverted elastic parameters to tight-sand reservoir prediction. With the development of oil and gas exploration, pre-stack data and inversion results are increasingly used for production objectives. The pre-stack seismic property studies include not only amplitude verse offset (AVO) but also the characteristics of other elastic property changes. In this paper, we analyze the elastic property parameters characteristics of gas- and wet-sands using data from four gas-sand core types. We found that some special elastic property parameters or combinations can be used to identify gas sands from water saturated sand. Thus, we can do reservoir interpretation and description using different elastic property data from the pre-stack seismic inversion processing. The pre-stack inversion method is based on the simplified Aki-Richard linear equation. The initial model can be generated from well log data and seismic and geologic interpreted horizons in the study area. The input seismic data is angle gathers generated from the common reflection gathers used in pre-stack time or depth migration. The inversion results are elastic property parameters or their combinations. We use a field data example to examine which elastic property parameters or combinations of parameters can most easily discriminate gas sands from background geology and which are most sensitive to pore-fluid content. Comparing the inversion results to well data, we found that it is useful to predict gas reservoirs using λ, λρ, λ/µ, and K/µ properties, which indicate the gas characteristics in the study reservoir.

Some practical aspects of prestack waveform inversion using a genetic algorithm: An example from the east Texas Woodbine gas sand

In this paper, a prestack inversion method using a genetic algorithm (GA) is presented, and issues relating to the implementation of prestack GA inversion in practice are discussed. GA is a Monte‐Carlo type inversion, using a natural analogy to the biological evolution process. When GA is cast into a Bayesian framework, a priori information of the model parameters and the physics of the forward problem are used to compute synthetic data. These synthetic data can then be matched with observations to obtain approximate estimates of the marginal a posteriori probability density (PPD) functions in the model space. Plots of these PPD functions allow an interpreter to choose models which best describe the specific geologic setting and lead to an accurate prediction of seismic lithology. Poststack inversion and prestack GA inversion were applied to a Woodbine gas sand data set from East Texas. A comparison of prestack inversion with poststack inversion demonstrates that prestack inversion shows detailed stratigraphic features of the subsurface which are not visible on the poststack inversion.