Elastic Impedance Simultaneous Inversion for Multiple Partial Angle Stack Seismic Data with Joint Sparse Constraint

ABSTRACTThe transformation of elastic impedance (EI) from partial‐angle‐stacked seismic data is a crucial technique in the domains of reservoir modelling. Conventionally, EI inversion is performed on a per‐angle basis, leading to significant discrepancies in EI values across different angles, which may not accurately represent actual conditions. When the signal‐to‐noise ratio (SNR) of seismic data is low, the inverted EI tends to be unstable, resulting in poor‐quality inversion outcomes. This research proposes a novel method that allows for enabling the derivation of EI for various angles simultaneously inverted from multiple partial angle‐stack seismic datasets in one process. The aim of simultaneous inversion is to potentially ensure consistent EI results. To obtain this aim, we utilize an advanced regularization method called the Gramian constraint. Consequently, the objective function for the simultaneous inversion of multiple EIs is developed. Results from both synthetic and field data demonstrate improved stability in EI inversion, especially for the case of low SNR.

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

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.

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 …

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.

Seismic Reservoir Characterization, also known as reservoir geophysics, has evolved over the past several years into a multi-disciplinary, business-critical function in most ED&P organizations. Sheriff defines reservoir geophysics as "The use of geophysical methods to assist in delineating or describing a reservoir or monitoring the changes in a reservoir as it is produced." Reservoir geophysics is applied across a wide spectrum of the oilfield life cycle from discovery and early development to tertiary recovery. One critical part of this process is careful analysis and understanding of petrophysical properties from well logs and core data (seismic petrophysics). The purpose of this paper is to illustrate why seismic petrophysics is so important and to show how carefully constructed synthetic models can help the geoscientist interpret acoustic and elastic impedance inversion from seismic data. Introduction Well logs are sometimes viewed by geophysicists as "hard data" and not subjected to the same level of scrutiny as the seismic data. This can be a mistake because well logs are susceptible to errors from a number of sources. In this presentation we will examine some of the processes and procedures that allow well logs to be correctly used in Seismic Reservoir Characterization. The basic steps in seismic petrophysics analysis are:Collect and organize input dataPerform geophysical log interpretation for volume minerals, porosity, and fluidsDetermine fluid properties (oil API, brine salinity, etc.) and reservoir pressuretemperaturePerturb reservoir properties using rock physics effective medium models (pseudo-well modeling)Compute synthetic seismic tracesGenerate trend curves and crossplotsCreate graphics and digital output files. Geophysical Well Log Analysis Well log analysis for geophysics differs in several important ways from standard log analysis. In most cases well logs are obtained for the purpose of estimating recoverable hydrocarbon volumes. Therefore the zone of interest is mainly the producing interval(s). For geophysics, well logs form the basis for relating seismic properties to the reservoir. While we are still concerned about producing intervals, we also need good information about all of the rock through which the seismic waves have passed. Therefore our zone of interest is much larger and encompasses basically everything from the surface to total depth. In all cases the log data will require some editing, normalization, and interpretation before they can be used in a reservoir study. Several specific analysis steps will be followed:De-spike and filter to remove or correct anomalous data pointsNormalize logs from all of the selected wells to determine the appropriate ranges and cutoffs for porosity, clay content, water resistivity, etc.Compute the volumetric curves such as total porosity, Vclay, and SwCalibrate the volumetric curves to core data if availableCorrect sonic and density logs for mud filtrate invasion if neededCompute Vshear on all wells. Missing log curves can often be computed with a reasonable degree of certainty. There are two major ways this is done. The first is through application of modern rock physics principles.

We present a deterministic methodology for mapping the lithology, pore fluid, and porosity from seismic data. The input is the P- and S-wave data volumes that may come, e.g., from acoustic and elastic impedance inversion or cross-well measurements. The output is the pore fluid type (hydrocarbon versus water), total porosity, and clay content. The key element of this methodology is a site-specific rock physics model that provides the needed transforms from the elastic rock properties to the reservoir properties. The model is established by comparing model-based predictions, such as impedance versus porosity, to the relations present in well log data. Once selected, the model is used to identify the presence of hydrocarbons from a combination of the P-wave impedance and Poisson’s ratio. Then the P-wave impedance is used to map porosity and clay content assuming that a deterministic relation exists between the latter two properties. All deterministic equations are calibrated at a well. These equations subsequently are applied to up-scaled well log data to confirm their validity at the seismic scale.

Chapter 7 - Geophysical Techniques

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.

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.

Deep learning (DL) applications of seismic reservoir characterization often require the generation of synthetic data to augment available sparse labeled data. An approach for generating synthetic training data consists of specifying probability distributions modeling prior geologic uncertainty on reservoir properties and forward modeling the seismic data. A prior falsification approach is critical to establish the consistency of the synthetic training data distribution with real seismic data. With the help of a real case study of facies classification with convolutional neural networks (CNNs) from an offshore deltaic reservoir, we have highlighted several practical nuances associated with training DL models on synthetic seismic data. We highlight the issue of overfitting of CNNs to the synthetic training data distribution and propose regularization strategies to address it. We demonstrate the efficacy of our proposed strategies by training the CNN on synthetic data and making robust predictions with real 3D partial stack seismic data.