Elastic Impedance Inversion With Gramian Constraint for Simultaneously Inverting Multiple Partial Angle Stack Seismic Data

Elastic impedance (EI) inversion for partial angle stack seismic data is a key technology in seismic reservoir prediction within the oil and gas industry. EI inversion provides a consistent framework to invert partial angle stack seismic data, just as the AI inversion does for post-stack data. The commonly used EI inversion process is angle by angle. Hence, the inverted EI for different angles may be nonconforming, especially for the seismic data with a low signal-to-noise ratio. This paper proposes to simultaneously invert multiple partial angle stack seismic data to obtain EI for different angles at once. To obtain conformable EI, we used the joint sparse constraint on the reflection coefficients for different angles. Then, the objective function for simultaneous EI inversion was constructed. Next, synthetic seismic data profiles with three different angles were used to show the superiority of the proposed EI inversion method compared to the conventional method. At last, a real seismic data line was used to test the feasibility of the proposed method in practice. The inversion results of synthetic data and real data showed that it provides an effective new alternative method to estimate EI from partial stack seismic data.

The classical elastic impedance (EI) inversion method, however, is based on the L2-norm misfit function and considerably sensitive to outliers, assuming the noise of the seismic data to be the Guassian-distribution. So we have developed a more robust elastic impedance inversion based on the L1-norm misfit function, and the noise is assumed to be non-Gaussian. Meanwhile, some regularization methods including the sparse constraint regularization and elastic impedance point constraint regularization are incorporated to improve the ill-posed characteristics of the seismic inversion problem. Firstly, we create the L1-norm misfit objective function of pre-stack inversion problem based on the Bayesian scheme within the sparse constraint regularization and elastic impedance point constraint regularization. And then, we obtain more robust elastic impedances of different angles which are less sensitive to outliers in seismic data by using the IRLS strategy. Finally, we extract the P-wave and S-wave velocity and density by using the more stable parameter extraction method. Tests on synthetic data show that the P-wave and S-wave velocity and density parameters are still estimated reasonable with moderate noise. A test on the real data set shows that compared to the results of the classical elastic impedance inversion method, the estimated results using the proposed method can get better lateral continuity and more distinct show of the gas, verifying the feasibility and stability of the method.

This paper compares the results of hybrid inversion, elastic impedance inversion, and prestack waveform inversion on a single data set. The method used for prestack inversion is a Monte-Carlo-based optimization method called genetic algorithm (GA). GA performs a full waveform inversion of normal moveout (NMO) uncorrected prestack seismic data, giving a detailed elastic earth model. In hybrid inversion, elastic models from GA inversion and/or well information are used to construct low-frequency background trends for the Pand the S-wave impedance values. These background trends are then used in the poststack inversion of the amplitude variation with offset (AVO) intercept and pseudoS-wave sections to generate the Pand the S-wave impedance sections. In elastic impedance inversion, elastic models from GA and/or well information are used to generate the low-frequency background trends for the elastic impedance for a range of incidence angles. These background trends are then used in the poststack inversion for the same range of angle stacks to generate the elastic impedance values for those angles. Once obtained, the elastic model is extracted from a linear fit to the logarithm of the elastic impedance.

Elastic impedance (EI) inversion is one of the prestack seismic inversion methods, which can obtain P-wave and S-wave velocity, density, Poisson ratio, Lame coefficients and other elastic parameters. But there have been many EI formulas nowadays, so which formula should be used in inversion is an urgent problem. This paper divides these formulas into two categories, and use several forward modeling to test the accuracy of these EI formulas. It shows that using the first kind of EI formulas in near offset seismic data can get high precision results.

Seismic fracture characterization in tight sand reservoirs: A case study of the Xujiahe Formation, Sichuan Basin, China

Up till now the EI (Elastic Impedance) and EEI (Extended Elastic Impedance) approaches have been applied exclusively to CI (Coloured Inversion) data of pairs of angle stacks or an intercept and gradient stack. This paper introduces a simple re-casting of the EI and EEI methods that allows the procedure to be applied directly to calibrated model based pre-stack seismic inversion data. A key advantage of the approach is that it only requires Zp and Zs as inputs (density is not required) and can therefore be applied to the vast majority of pre-stack inversion data volumes that have already been created. Additionally log and elastic impedance values are directly comparable as the seismic data is in the impedance domain whereas CI volumes are still in the reflectivity domain.

It is well known that if we are able to estimate acoustic impedance (AI) and a parameter related to shear-wave velocity from seismic data, our ability to discriminate between different lithologies and fluid phases will increase. Prestack inversion on individual CDP gathers and inverting directly for VP , VS , and density have been tested in several ways, but the estimated parameters are often poorly determined. A more robust approach is to apply poststack inversion on partial stacks. For inversion of the near-offset stack, AI can be calculated directly from well logs. However, for the far-offset stack, we need to derive an equivalent of the acoustic impedance that can be used to calibrate the non-zero-offset seismic reflectivity. Connolly (1998, 1999) derived such an equivalent—elastic impedance (EI)—and demonstrated how, by using elastic impedance logs (which requires shear-wave logs), he was able to perform well calibration and inversion of far-offset data. This article describes a new function—shear-wave elastic impedance (SEI)—for linking converted-wave stacks to wells using a linearization of the Zoeppritz equations. SEI is similar to EI but adapted to P-S converted seismic data. It can be computed from acoustic log data ( P - and S -wave velocities and density) and used for well calibration, wavelet estimation, and inversion of P-S reflectivity data leading to improved interpretability of converted wave data. (Equation 4 in Appendix 1 is the key mathematical formula in this approach to SEI). To test the SEI technique, we used a 3-D four-component (4-C) ocean-bottom cable (OBC) survey acquired in 1997 that covers approximately 10 km2 of the Statfjord Field (Rogno et al., 1999). Both P -wave and converted-wave data were 3-D prestack time-migrated. The hydrophone ( P ) and the vertical geophone ( Z ) component were summed to attenuate receiver side water-layer reverberations and both data sets ( PZ …

Summary In this case study we explore the use of both PP elastic impedance (EI) and PS elastic impedance (PSEI) inversion on ocean bottom cable (OBC) data from the West Cameron area in the Gulf of Mexico (GOM), where PS data has higher S/N ratio. We show the advantages of PS data and describe a workflow for joint PP and PS inversion to extract elastic properties from seismic data. A comparison between separate PP and PS data and joint PP-PS data in PP time shows that in this case PS data critically improve subsurface characterization.

Seismic inversion has been widely practiced in the oil and gas industry because it generates broad bandwidth of impedance data which maximizes vertical resolution and minimizes tuning effects. The lack of accurate prediction of lithology and fluid content of subtle features identified in seismic data acquired over the Sandfish field, Niger Delta, Nigeria necessitated the use of seismic inversion. In this paper, simultaneous seismic inversion is adopted to integrate seismic and well data for quantitative interpretation and uncertainty assessment of the subsurface reservoirs in the Sandfish field. Three Sandfish (Sfn) wells with the required petrophysical logs, check-shot data, high quality 3D seismic data of five angle stacks (6–12°, 12–18°, 18–26°, 26–32°, and 32–42°) were used for the analysis. A feasibility study including cross-plots of petrophysical and elastic properties from well data was first carried out to establish rock property relationships in the interval of interest. Biot-Gassmann fluid substitution analysis was also used to reveal sensitivity of rock properties to pore-fill type. Low frequency (0–2 Hz) models were generated from interpolation of high-cut-filtered P-sonic, S-sonic, and density logs guided by interpreted seismic horizons. The low frequency models were used to broaden the spectrum to estimate elastic volumes. The five partial angle stacks were simultaneously inverted using Jason’s Rock-Trace® inversion software which iterated trial inversions until the model sufficiently matched the seismic data. The inverted P-impedance (ZP), Simpedance (ZS), and density (ρ) were used to derive Poisson’s ratio (σ), volume of sand (Vsand), lambda-rho (λρ), and mu-rho (µρ). The cross-plot of λρ with µρ from well data looks similar to that from inverted results. Sands and shales are discriminated on the basis of sands having low values of µρ. Hydrocarbon-bearing sands are differentiated from water-bearing sands and shales on the basis of having lowest values of λρ. The Biot-Gassmann fluid substitution analysis at reservoir N-01 reveals typical class III amplitude variation with angle (AVA) responses for low-impedance hydrocarbon sands. The lithology and fluid prediction maps extracted from Vsand and σ at the N-01 seismic horizon show variation in lithology and fluid types for the entire volume. The inversion products reveal heterogeneities in the reservoirs away from well control validated by a blind well test. Hence, the study shows that rock-property model from a simultaneous inversion is an effective predictive tool for lithology and fluid types which in turn can guide well placement and predict reservoir development in the field of study.

PP-wave azimuthal elastic impedance (EI) data inverted from azimuthal prestack seismic reflection data can be theoretically and practically used for fluid- and fracture-property discrimination in naturally porous and fluid-saturated fractured reservoirs within the exploration seismic frequency band. From the perspective of the low-frequency Biot-Gassmann theory, Russell’s fluid indicator can be stably applied to fluid identification in hard-rock fractured reservoirs. Based on the low-frequency anisotropic poroelasticity theory, we first derive an azimuthal PP-wave reflection coefficient and an azimuthal EI equation in terms of Russell’s fluid indicator (a combination of acoustic impedances and dry-rock velocity ratio without the effect of squirt flow in the seismic frequency range) and two fracture indicators (i.e., normal and tangential fracture weaknesses). Using azimuthal differences in EI data, we then develop a three-step inversion method of EI difference versus angle and azimuth. It can be used accurately to estimate the fluid and fracture indicators and characterize the sensitive properties of saturated fractured porous reservoirs. Noisy synthetic data are used to verify the stability and robustness of the proposed hierarchical impedance inversion approach. A real data set acquired over a gas-bearing fractured reservoir is also used to obtain the sensitive indicators of the fluid and fracture properties, which agree well with the well-log data. Thus, our hierarchical inversion approach provides a more straightforward and efficient manner to characterize the porous and fluid-saturated fractured reservoirs.

Summary Deep learning have led to a certain extent breakthrough in seismic facies analysis(SFA). The greatest challenge in the SFA domain is how to cope with large seismic datasets and the limited amount of annotated samples, especially when employing supervised machine learning algorithms that require labelled data and larger training sample. we develop a supervised seismic facies analysis via an improved Auxiliary Classifier Generative Adversarial Network(ACGAN).To solve the problem of imbalanced seismic facies class distribution, and limited training data with labels, we used an improved ACGAN to generate synthetic seismic data sets, and then train Convolutional Neural Networks(CNN) using theses generated synthetic data. Fault data and seismic facies data test demonstrated that generated seismic data via the improved ACGAN can be used for synthetic data augmentation as for increased the performance of CNN and avoided overfitting compared to original seismic data training set. Therefore, we believe that the proposed method can effectively alleviate the problems of insufficient and imbalanced seismic data in SFA, and also can generalize to other seismic data classification applications.

Chapter 7 - Geophysical Techniques

Identification and prediction of fracture and its developmental zone is meaningful to reservoir exploration and development. According to solid mechanics ,fracture strata is anisotropic media . Previous formulation for S-wave elastic impedance neglects seismic anisotropic. In order to incorporate anisotropic , we use an approximation of converted PS-wave reflection coefficients to deduce converted wave elastic impedance in weakly anisotropic media for the first time. Through numerical simulation, the effect of Thomsen parameter, incident angle and azimuthal angle on the formulation are described in detail. At the same time, we analyze the precision of new approximation formulation and compare the hydrocarbon detection effect of PP wave and converted wave elastic impedance. The future work is to select the newest nonlinear inversion algorithm and realize elastic impedance inversion in anisotropic media.On the basis of sensitive fluid identification factor in isotropic media,we construct the new fluid identification factor in weakly anisotropic media, which is composed of PP wave and converted wave elastic impedance. The advantage of new fluid identification factor is to allow investigating AVO anomalies with the effect of anisotropic parameters .Then ,we can analyze the difference of fluid identification factor with azimuthal angle and anisotropic parameters in 3D space .Adding Thomsen parameter to the 25 formation models gived by Castagna and Smith, we analyze the identification effect. Numerical simulation results show that the new fluid factor can identify the gas sand and brine sand effectively.

It is well known that time-lapse seismic has been taken as a powerful tool for reservoir management and repeatability is the key factor of time-lapse seismic. In this paper, the author introduces a time-lapse seismic inversion method based on time-lapse seismic difference data. Based on the difference of time-lapse seismic data, elastic parameters variation can be obtained by elastic impedance inversion. Using this method, the inversion process will reduce the computation amount, simplifies the inversion process and improve the repeatability.

The study aims to implement a high-resolution Extended Elastic Impedance (EEI) inversion to estimate the petrophysical properties (e.g., porosity, saturation and volume of shale) from seismic and well log data. The inversion resolves the pitfall of basic EEI inversion in inverting below-tuning seismic data. The resolution, dimensionality and absolute value of basic EEI inversion are improved by employing stochastic perturbation constrained by integrated energy spectra attribute in a Bayesian Markov Chain Monte Carlo framework. A general regression neural network (GRNN) is trained to learn and memorize the relationship between the stochastically perturbed EEI and the associated well petrophysical log data. The trained GRNN is then used to predict the petrophysical properties of any given stochastic processed EEI. The proposed inversion was successfully conducted to invert the volume of shale, porosity and water saturation of a 4.0 m thick gas sand reservoir in Sarawak Basin, Malaysia. The three petrophysical geobodies were successfully built using the discovery wells cut-off values, showing that the inverted petrophysical properties satisfactorily reconstruct the well petrophysical logs with sufficient resolution and an accurate absolute value at the well site and are laterally conformable with seismic data. Inversion provides reliable petrophysical properties prediction that potentially helps further reservoir development for the study field.