Seismic pre-stack AVA inversion scheme based on lithology constraints

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.

Anisotropic total variation pre-stack multitrace inversion based on Lp norm constraint

A geostatistical seismic pre-stack inversion was carried out over a producing gas and condensate field in the Gulf of Thailand, North Malay basin. As the main reservoirs are thin-bedded stacked fluvial deltaic sands of Miocence age, detailed mapping of reservoir distribution was challenging due to limited seismic resolution. To overcome such challenges, a pre-stack geostatistical inversion was initiated. The input dataset consisted of six wells and 250 km2 of 3D seismic data. The well log data passed through rigorous QC and rock physics analysis, while the seismic data were subject to preconditioning to ensure improved CDP gather flatness and signal-to-noise ratio. Starting from geostatistical modeling, the inversion generated multiple detailed realizations of lithology and elastic properties based on Bayesian Inference and Markov-Chain Monte Carlo methods. Statistic of multiple resulting realizations also implied a range of possible solutions of this non-unique inverse problem. In addition, petrophysical properties were simulated by using statistical relationships between inverted elastic and petrophysical properties. By integrating high frequency well logs with low frequency seismic, the geostatistical inversion process provided high vertical resolution and captured spatial variations of the various lithology types and their respective elastic properties. Since a majority of the stacked gas sand reservoirs in the area were below the tuning thickness, the geostatistic inversion results provided significantly improved insight to facies distribution. According to blind well results, precision of net pay estimation provided by the geostatistical inversion improved from 40% to 83%, compared to predrilled prognosis; while, pay estimation uncertainty was reduced by 30%. The generated petrophysical volumes also showed more detailed spatial variation, and can be used to improve in-place volumetric calculations and support field development planning.

AVO/AVA (amplitude variation with an offset or angle) inversion is one of the most practical and useful approaches to estimating model parameters. So far, publications on AVO inversion in the Fourier domain have been quite limited in view of its poor stability and sensitivity to noise compared with time-domain inversion. For the resolution and stability of AVO inversion in the Fourier domain, a novel robust Bayesian pre-stack AVO inversion based on the mixed domain formulation of stationary convolution is proposed which could solve the instability and achieve superior resolution. The Fourier operator will be integrated into the objective equation and it avoids the Fourier inverse transform in our inversion process. Furthermore, the background constraints of model parameters are taken into consideration to improve the stability and reliability of inversion which could compensate for the low-frequency components of seismic signals. Besides, the different frequency components of seismic signals can realize decoupling automatically. This will help us to solve the inverse problem by means of multi-component successive iterations and the convergence precision of the inverse problem could be improved. So, superior resolution compared with the conventional time-domain pre-stack inversion could be achieved easily. Synthetic tests illustrate that the proposed method could achieve high-resolution results with a high degree of agreement with the theoretical model and verify the quality of anti-noise. Finally, applications on a field data case demonstrate that the proposed method could obtain stable inversion results of elastic parameters from pre-stack seismic data in conformity with the real logging data.

Prestack inversion identification of organic reef gas reservoirs of Permian Changxing Formation in Damaoping area, Sichuan Basin, SW China

Shale oil reservoir characterization is conducted in Western Depression of Liaohe Oilfieid of China. The major storage space is fracture which is preferably developed in shale with high content of silica, calcite or dolomite. A workflow of integrating rock physics models, amplitude preserved processing, and pre-stack inversions is developed and implemented which provides elastic parameters such as Young's modulus, Poisson's ratio and fracture density and orientation. These parameters are used to characterize brittleness of shale and preferable drilling locations for such kind of reservoir. In order to accurately estimate velocity in shale, a better rock physics model called AS-Xu-White is integrated in the workflow especially for guidance of interpretation, which is modified from Xu-white model. Fluid discrimination in fracture with newly developed anisotropic rock physics model is also employed in this work. Introduction Shale constitutes about 75% of sedimentary rocks (Vernik and Liu, 1996). It is not only the major source and seal, but also serves as reservoirs. A large amount of shale gas/oil has been discovered since last century. The rapid development of exploiting techniques increases the unconventional shale gas/oil output greatly, which also lead to growing proportion in hydrocarbon yield. Thus, shale reservoirs exploration has drawn more and more attention. In this paper shale oil reservoir characterization is conducted in Western Depression of Liaohe Oilfieid of China. The hydrocarbon-rich shale in Sha3 member of Shahejie formation in Chenjia sag is selected for the case study (the location is shown in Figure 1). The dark shale in Sha3 member is deposited in semideep-deep lacustrine sedimentary environment, which is very thick and has high ability to generate hydrocarbon with abundant organic matter. The major applications of 3D seismic data in the study of shale reservoir focus on the following three aspects:identifying the faults and karst to direct drilling (Norton et al, 2011);predicting natural fractures indirectly by geometric attributes such as coherence and curvature calculated from post-stack data (Guo et al, 2010), and directly by anisotropic inversion of AVAZ and VVAZ (Ruger, 1998; Goodway et al, 2007);mapping geo-mechanical brittleness and horizontal stress directions for effective hydraulic fracture stimulation (Goodway et al, 2010; Sena et al, 2011). In this paper the shale oil in the target member is not from tight rocks but mainly from natural fractures. Thus the study should focus on identifying fracture-prone zones. An integrated and comprehensive workflow for shale oil reservoir prediction is implemented which provides elastic parameters such as Young's modulus, Poisson's ratio and fracture density and orientation. Before pre-stack inversion, a modified Xu-white model is introduced to simulate the complex fracture system of shale, which leads to better estimate velocity. Since brittleness and fractures are two major factors that control reservoir quality, reservoir prediction could be accessed by identifying fracture-prone brittle areas and detecting the natural fractures, where the isotropic and anisotropic inversion are both used. As a result, the brittle shale distribution determined by crossploting Erho (i.e. a parameter constructed by Young's modulus and density) and Poisson's ratio is in a good agreement with both the well production data and the latest drilling data. On the other hand, fractures predicted by improved anisotropic inversion using limited azimuthal data coincide well with that from the FMI, and are proven to be reasonable from geologic analysis. Fluid discrimination in fracture with newly developed anisotropic rock physics model is also employed in this work. Combining the results with geological analysis, the favorable area is proposed finally.

The Sulige is the largest discovered gas field in China. The reservoir is characterized by low porosity, low permeability and strong heterogeneity. Meanwhile single sand body is superimposed each other and the composite sand bodies are contiguous, whereas the distribution of gas reservoirs is dispersed. Consequently, traditional method for sand body prediction is difficult to meet the need for gas reservoir prediction that is the one of key problems of reservoir prediction in Sulige area. P-wave seismic technology has played an important role in exploration and development of Sulige gas field. But with the expanding edge of exploration and the fineness of development, using PP seismic data alone has shortcoming for the prediction of effective thin reservoir and spatial distribution of gas and water reservoirs. Beginning with the first full digital 3D3C seismic data acquisition in Sulige area in 2003, it gradually sets up a work flow and related methods of using multicomponent seismic data to identify gas reservoir. In this paper, we present a practical application of using 3D3C seismic data. Considering the feature of tight gas reservoir in Sulige area, characteristics of rock physics parameters being sensitive to gas reservoir are set up on the basis of rock physics analysis. Through the co-analysis of seismic modeling and joint PP/PS pre-stack inversion, elastic parameters including P-impedance, S-impedance and Vp/Vs ratio etc are got from joint PP/PS pre-stack inversion. Finally, the methods of elastic parameters crossplot and facies/fluid probability analysis are employed to interpret the inversion result, thus improving the accuracy of gas reservoir prediction.

Economic shale gas production requires hydraulic fracture stimulation to increase the formation permeability. Hydraulic fracturing strongly depends on geomechanical parameters such as Young’s modulus and Poisson’s ratio. Fracture-prone sweet spots can be predicted by prestack inversion, which is an ill-posed problem; thus, regularization is needed to obtain unique and stable solutions. To characterize gas-bearing shale sedimentary bodies, elastic parameter variations are regarded as an anisotropic Markov random field. Bayesian statistics are adopted for transforming prestack inversion to the maximum posterior probability. Two energy functions for the lateral and vertical directions are used to describe the distribution, and the expectation–maximization algorithm is used to estimate the hyperparameters of the prior probability of elastic parameters. Finally, the inversion yields clear geological boundaries, high vertical resolution, and reasonable lateral continuity using the conjugate gradient method to minimize the objective function. Antinoise and imaging ability of the method were tested using synthetic and real data.

Summary S-wave velocity plays an important role in both reservoir prediction and pre-stack inversion. However, the current deep learning-based S-wave velocity prediction methods have certain limitations. In order to solve the problems of insufficient training samples in real field areas and poor generalization of the deep learning model, we combine DNN and theoretical rock physics model to predict the S-wave velocity of limestone reservoir. Firstly, four parameters (P-wave velocity, crack-density, density, porosity) affecting the prediction of S-wave velocity are selected according to the synthetic data generated by the theoretical rock physics model of limestone reservoir and DNN, and then the selected parameters are used as the input features of the neural network and synthetic data are utilized to train the neural network. The results show that the neural network trained by the synthetic data has strong robustness and high prediction accuracy, the R2 of the the synthetic data prediction results is 0.9689, the prediction error is less than 3%, and the prediction performance is better than the empirical formula. Meanwhile, the prediction results of the real data show that the approach can be applied to real field work areas.

Young’s modulus and Poisson ratio are essential parameters for rock brittleness evaluation. At present, prestack inversions of these parameters mostly adopt linear approximation, whereas the nonlinear inversion methods that are based on the exact Zoeppritz equation are seldomly conducted. Nevertheless, in the case of large incident angles and high-impedance contrast, the nonlinear equation has higher accuracy than the linear approximation. It is more in line with the nature of geophysical inversion problems, and it describes the variation of formations’ elastic parameters better than the linear approximation does. Therefore, based on the exact solution of the Zoeppritz equation, we have parameterized and derived a new nonlinear reflection coefficient equation using nonlinear Young’s modulus, Poisson ratio, and density (YPD) as variables. Subsequently, by combining the inverse operator algorithm with the YPD equation, we develop a new nonlinear amplitude-variation-with-offset inversion scheme. This approach can robustly extract Young’s modulus and Poisson ratio from seismic data and identify shale-gas sweet spot locations within the reservoir, as well as predict reservoir fluid properties. We have tested the accuracy and applicability of this approach with synthetic and real data examples.

Sensitivity parameters of tight sand gas: A case study of Lower Cretaceous Yingcheng Formation of Yingtai gas field in Songliao Basin, NE China

Predicting gas content in high-maturity marine shales using artificial intelligence based seismic multiple-attributes analysis: A case study from the lower Silurian Longmaxi Formation, Sichuan Basin, China

A fluid discrimination approach incorporating linearized poroelasticity theory and pre-stack seismic reflection inversion with Bayesian inference is proposed to identify the fluid underground. The fluid modulus is defined as the fluid indicator which is mainly affected by the fluid contained in reservoirs. A novel linearized P-wave reflectivity equation coupling the fluid modulus is derived to avoid the complicated nonlinear relationship between the fluid modulus with seismic data. Convoluting this linearized P-wave reflectivity with seismic wavelets as the forward solver, a practical pre-stack Bayesian seismic inversion method is presented to estimate the fluid modulus directly. Cauchy and Gaussian distribution are utilized for prior probability distribution of the model parameters and the likelihood function to enhance the inversion resolution. The preconditioned conjugate gradient method is coupled in the optimization of the inversion objective function to weaken the strong degree of correlation among the four model parameters and enhance the stability of multiple parameters estimation simultaneously. The synthetic test demonstrates the feasibility and stability of the proposed novel seismic coefficient equation and inversion approach. Test on a real data set illustrates the efficiency and success of the proposed approach in differentiating the fluid filled reservoirs.

Geofluid discrimination plays an important role in the fields of hydrogeology, geothermics, and exploration geophysics. A geofluid discrimination approach incorporating linearized poroelasticity theory and pre-stack seismic reflection inversion with Bayesian inference is proposed in this study to identify the types of geofluid underground. Upon the review of the development of different geofluid indicators, the fluid modulus is defined as the geofluid indicator mainly affected by the fluid contained in reservoirs. A novel linearized P-wave reflectivity equation coupling the fluid modulus is derived to avoid the complicated nonlinear relationship between the fluid modulus and seismic data. Model examples illustrate the accuracy of the proposed linearized P-wave reflectivity equation comparing to the exact P-wave reflectivity equation even at moderate incident angle, which satisfies the requirements of the parameter estimations with P-wave pre-stack seismic data. Convoluting this linearized P-wave reflectivity equation with seismic wavelets as the forward solver, a pragmatic pre-stack Bayesian seismic inversion method is presented to estimate the fluid modulus directly. Cauchy and Gaussian probability distributions are utilized for prior information of the model parameters and the likelihood function, respectively, to enhance the inversion resolution. The preconditioned conjugate gradient method is coupled in the optimization of the objective function to weaken the strong degree of correlation among the four model parameters and enhance the stability of those parameter estimations simultaneously. The synthetic examples demonstrate the feasibility and stability of the proposed novel seismic coefficient equation and inversion approach. The real data set illustrates the efficiency and success of the proposed approach in differentiating the geofluid filled reservoirs.

Summary S-wave velocity plays an important role in both reservoir prediction and pre-stack inversion. However, the prediction methods based on empirical formulas, rock physics models, and fully connected neural networks have some limitations. To overcome the limitations of poor generalization and low prediction accuracy of these methods, we introduce the LSTM network into S-wave velocity prediction, which can learn logging sequence information better than the back-propagation neural networks. Six logging curve features (Porosity, GR, Vp, CAL, VSH, DEN) which are highly correlated with S-wave velocity are selected using intersection analysis as the input features of the LSTM network to establish an S-wave velocity prediction network. The average relative error is less than 2% and the average absolute error is less than 46m/s using the test results of two wells in Sichuan area, which is much lower than the prediction effect of the common empirical formula and rock physics model. At the same time, the prediction accuracy is higher than that of the DNN prediction method, which indicates that the method has a good application prospect in the real field areas.