Amplitude variation with offset inversion using the reflectivity method

It has been more than three years since The Leading Edge last published a special section on amplitude variation with offset (AVO) inversion, and interest in the subject remains strong. This past spring, SEG hosted a joint symposium in Houston, Texas, on the “Resurgence of seismic inversion,” and the body of talks and case studies demonstrated the method's continued relevance to making impactful drilling decisions. Despite this, and despite AVO inversion's position as a mature and well-established technique, there are an abundance of examples in which inaccurate AVO predictions have led to drastic failures at the drill bit. This highlights the challenges that still exist in the successful execution of such investigations and makes the subject occasionally controversial and certainly fraught with data-quality and best-practice considerations. In this vein, the special section presented here offers examples of the broad sweep of considerations and methods relevant to enabling successful AVO inversion and the interpretation of its products, as well as case studies that demonstrate how application of the technique can be impactful all the way through to appraisal and field development programs.

Seismic shear waves have been used in oil and gas exploration for decades. A 2D seismic shear wave inline was acquired in the Sanhu area, located in the Qaidam Basin in western China. Although the acquired shear wave data showed high resolution and comparable bandwidth to the compressional wave, it was contaminated by various types of noise, including linear noise, single-frequency noise, and especially internal multiples. Internal multiples seriously compromise the primary reflections at both near offset and far offset and are difficult to suppress. This paper presents a case study of noise attenuation for the seismic shear wave. First, single-frequency noise and linear noise are attenuated through filtering methods. Then, two methods (the Radon transform and the frequency-wavenumber (F-K) filtering) are evaluated for their effectiveness in multiple suppression and amplitude preservation. The results indicate that both methods successfully reduce long-period multiples at the far offset, enhancing the signal-to-noise ratio. We show that F-K filtering retains the characteristic ‘strong–weak–strong’ amplitude variation in the SV-SV-wave data gather, making it preferable for subsequent amplitude variation with offset analysis and inversion. Finally, a wave equation-based multiple suppression inversion method is used to suppress near-offset internal multiples. This involves iteratively predicting internal multiples and adaptively subtracting them from the original data. Stacked sections of different offsets are compared to demonstrate the de-multiple result, and the result is also validated by the improvement of well calibration with the seismic shear wave data.

Field records for small source-receiver offsets often contain intensive converted PS-waves that may be caused by the influence of anisotropy on either side of the reflector. Here, we study the small-angle reflection coefficients of the split converted [Formula: see text]- and [Formula: see text]-waves ([Formula: see text] and [Formula: see text]) for a horizontal interface separating two transversely isotropic (TI) media with arbitrary orientations of the symmetry axis. The normal-incidence reflection coefficients [Formula: see text] and [Formula: see text] vanish when both half-spaces have a horizontal symmetry plane, which happens if the symmetry axis is vertical or horizontal (i.e., if the medium is VTI or HTI). For a tilted symmetry axis in either medium, however, the magnitude of the reflection coefficients can reach substantial values that exceed 0.1, even if the anisotropy strength is moderate. To study the influence exerted by the orientation of the symmetry axis and the anisotropy parameters, we develop concise weak-contrast, weak-anisotropyapproximations for the PS-wave reflection coefficients and com-pare them with exact numerical results. In particular, the analytic solutions show that the contributions made by the Thomsen parameters [Formula: see text] and [Formula: see text] and the symmetry-axis tilt [Formula: see text] to the coefficients [Formula: see text] and [Formula: see text] can be expressed through the first derivative of the P-wave phase velocity at normal incidence. If the symmetry-axis orientation and anisotropy parameters do not change across the interface, the normal-incidence reflection coefficients are insignificant, regardless of the strength of the velocity and density contrast. The AVO (amplitude variation with offset) gradients of the PS-waves are influenced primarily by the anisotropy of the incidence medium that causes shear-wave splitting and determines the partitioning of energy between the [Formula: see text] and [Formula: see text] modes. Because of their substantial amplitude, small-angle PS reflections in TI media contain valuable information for anisotropic AVO inversion of multicomponent data. Our analytic solutions provide a foundation for linear AVO-inversion algorithms and can be used to guide nonlinear inversion that is based on the exact reflection coefficients.

Solutions to the amplitude variation with offset (AVO) inverse problem are inherently nonunique. Thus, estimating the range of potential solutions is crucial. For this reason, uncertainty inversion is more appropriate than deterministic AVO inversion. However, most studies on deep learning (DL)-based inversion focus on deterministic prediction. In general, there are few studies on uncertainty inversion, mainly focused on poststack seismic data. In this study, we propose a DL-based AVO uncertainty inversion method based on an improved variational Bayesian neural network (VBNN) for predicting multiple elastic parameters. Moreover, to mitigate the issue of insufficient labeled data in inversion tasks, we combine the improved VBNN with a semi-supervised learning framework. Synthetic data experiments demonstrate that the proposed method exhibits higher accuracy and robustness to noisy seismic data than the well-known traditional Bayesian linearized inversion (BLI) method. The proposed method also has slightly higher inversion accuracy than the state-of-the-art improved-hybrid-seismic-prior-guided neural network (IHGNN). Moreover, the uncertainty estimation confirms that the proposed method can explore potential solutions to the AVO inverse problem more effectively and reasonably than the comparison methods. Furthermore, field data AVO inverse experiments verify that the proposed method can obtain reasonable predicted results and effectively reveal uncertainty in the inversion results.

AVO inversion based on generalized extreme value distribution with adaptive parameter estimation

Amplitude variation with offset (AVO) inversion is a typical ill-posed inverse problem. To obtain a stable and unique solution, regularization techniques relying on mathematical models from prior information are commonly used in conventional AVO inversion methods (hence the name model-driven methods). Due to the difference between prior information and the actual geology, these methods often have difficulty achieving satisfactory accuracy and resolution. We have developed a novel data-driven inversion method for the AVO inversion problem. This method can effectively extract useful knowledge from well-log data, including sparse dictionaries of elastic parameters and sparse representation of subsurface model parameters. Lateral continuity of subsurface geology allows for the approximation of model parameters for a work area using the learned dictionaries. Instead of particular mathematical models, a sparse representation is used to constrain the inverse problem. Because no assumption is made about the model parameters, we consider this a data-driven method. The general process of the algorithm is as follows: (1) using well-log data as the training samples to learn the sparse dictionary of each elastic parameter, (2) imposing a sparse representation constraint on the objective function, making the elastic parameters be sparsely represented over the learned dictionary, and (3) solving the objective function by applying a coordinate-descent algorithm. Tests on several synthetic examples and field data demonstrate that our algorithm is effective in improving the resolution and accuracy of solutions and is adaptable to various geologies.

SUMMARY In this paper, we investigate the use of artificial neural networks (ANN) for amplitude variation with offset (AVO) analysis. Prospecting using AVO is dependent on the fact that the difference between near-offset and far-offset responses can be a hydrocarbon indicator. Neural networks are good at “learning” and “predicting” such relationships and can thus be trained to learn the relationship between, for example, a near-offset partially stacked trace and a far-offset partially stacked trace for background (non-hydrocarbon bearing rocks). Far traces can then be predicted by this learned relationship and the difference between observed and ANN predicted traces can potentially be used as a hydrocarbon indicator. An advantage of this method over conventional cross-plotting techniques is that it can be made insensitive to incorrect normal moveout corrections.

An improved artificial immune algorithm is proposed for geophysical P-wave amplitude variation with offset (AVO) inversion. In this paper, the algorithm is described and implemented. The orthogonal crossover is used to generate the initial population and the elitist-crossover is adopted to add the good patterns of the population. The hybrid mutation method is presented to increase the ability of local and global optimization. The improved immune algorithm is then applied to earth interface models of Mexican gulf for AVO inversion. The experimental results show that the improved algorithm is of high precision than the traditional immune algorithm.

In 2008, WesternGeco acquired the 5000 sq/km Keystone multi-client survey located offshore between the giant Io/Jansz and Scarborough gas fields on Australia’s NW shelf, in order to image potential gas reservoir’s at multiple stratigraphic levels within complex geology. Searching for leads and prospects within such a large volume using seismic data alone is traditionally a time-consuming process. An efficient prospect screening tool has been produced in the form of a well log-calibrated gas sand probability cube derived from amplitude variation with offset (AVO) inversion outputs. Using advanced visualisation techniques the data can then be rapidly interrogated highlighting a number of direct hydrocarbon indicators (DHI's) and potential prospects. AVO and quantitative interpretation have played a key role in a number of discoveries in this area, particularly within the Triassic.

Improving seismic interpretation: a high-contrast approximation to the reflection coefficient of a plane longitudinal wave

The [Formula: see text] of hydrocarbon‐bearing sediments normally deviates from the [Formula: see text] trend of the background rocks. This causes anomalous reflection amplitude variation with offset (AVO) in the seismic data. The estimation of these AVOs is inevitably affected by wave propagation effects and inversion algorithm limitations, such as thin‐bed tuning and migration stretch. A logical point is to determine the minimum [Formula: see text] change required for an anomalous AVO to be detectable beyond the background tuning and stretching effects. Assuming Ricker wavelet for the seismic data, this study addresses this point by quantifying the errors in the intercept/slope estimate. Using these results, two detectability conditions are derived. Denoting the background [Formula: see text] by γ and its variation by δγ, the thin‐bed parameter (thickness/wavelength) by ξ, the maximum background intercept closest to the AVO by |A|max, and the thin‐bed intercept value by |A|thinthe two conditions are [Formula: see text] [Formula: see text] for detectability against stretching and tuning plus stretching, respectively. Tests on synthetic data confirm their validity and accuracy. These conditions provide a quantitative guideline for evaluating AVO applicability and effectiveness in seismic exploration. They can eliminate some of the subjectivity when interpreting AVO results in different attribute spaces. To improve AVO detectability, a procedure is suggested for removing the tuning and stretching effects.

PreviousNext No AccessSEG Technical Program Expanded Abstracts 1998AVO detectability against tuning and stretching artifactsAuthors: Wenjie DongWenjie DongMobil E&P Technical Centerhttps://doi.org/10.1190/1.1820387 SectionsAboutPDF/ePub ToolsAdd to favoritesDownload CitationsTrack CitationsPermissions ShareFacebookTwitterLinked InRedditEmail Permalink: https://doi.org/10.1190/1.1820387FiguresReferencesRelatedDetailsCited By4. Chapter 4: Development GeophysicsColin MacBeth, Sankar Muhuri, William L. Abriel, William Haworth, Mark Chapin, Peter Swinburn, Raphic van der Weiden, Dieter Skaloud, Sola Adesanya, David Stevens, Chris Varley, Jacob Wilkie, Eric Brentjens, Martijn Blaauw, Liz Ross, Kevin King, Gerard Bodewitz, Hajo van Hasselt, Greg Stone, Wim Twigt, Wim Swinkels, Andrew James, Tony Addis, Chris Parsons, Robert Meij, Sarah Bell, Alexei Trofimov, Patrick Jackson, Valery Cholovsky, Edwin Lamers, Syrie Crouch, Rusty (John) Gilbert, Yuhong Liu, William Abriel, Rachel Preece, Dongjun (Taller) Fu, E. Charlotte Sullivan, Kurt J. Marfurt, Jose Luis Masaferro, Ruth Bourne, Jean-Claude Jauffred, P. Avseth, T. Mukerji, A. Jørstad, G. Mavko, T. Veggeland, M. K. MacLeod, R. A. Hanson, C. R. Bell, S. McHugo, Jan H. Kommedal, Susan Fowler, John McGarrity, C. R. Bates, D. R. Phillips, R. Grimm, H. Lynn, B. Blonk, R. W. Calvert, J. K. Koster, and G. van der Zee21 March 2012Quantitative Seismic Interpretation27 January 2010 | , Vol. 80Tuning effect on fluid properties estimated from AVO inversionMaria Rojas and De‐hua Han7 December 2005Analysis and interpretation of seismic data from thin reservoirs: Northwest Java Basin, IndonesiaA. Adriansyah and George A. McMechan7 February 2012 | GEOPHYSICS, Vol. 67, No. 1Seismic reservoir mapping from 3‐D AVO in a North Sea turbidite systemP. Avseth, T. Mukerji, A. Jørstad, G. Mavko, and T. Veggeland7 February 2012 | GEOPHYSICS, Vol. 66, No. 4 SEG Technical Program Expanded Abstracts 1998ISSN (print):1052-3812 ISSN (online):1949-4645Copyright: 1998 Pages: 2092 publication data© 1998 Copyright © 1998 Society of Exploration GeophysicistsPublisher:Society of Exploration Geophysicists HistoryPublished: 06 Jan 2005 CITATION INFORMATION Wenjie Dong, (1998), "AVO detectability against tuning and stretching artifacts," SEG Technical Program Expanded Abstracts : 236-239. https://doi.org/10.1190/1.1820387 Plain-Language Summary PDF DownloadLoading ...

This paper uses a Bayesian approach for inverting seismic amplitude versus offset (AVO) data to provide estimates and uncertainties of the viscoelastic physical parameters at an interface. The inversion is based on Gibbs' sampling approach to determine properties of the posterior probability distribution (PPD), such as the posterior mean, maximum a posteriori (MAP) estimate, marginal probability distributions, and covariances. The Bayesian formulation represents a fully nonlinear inversion; the results are compared to those of standard linearized inversion. The nonlinear and linearized approaches are applied to synthetic test cases which consider AVO inversion for shallow marine environments with both unconsolidated and consolidated seabeds. The result of neglecting attenuation in the seabed is investigated, and the effects of data factors such as independent and systematic errors and the range of incident angles are considered. The Bayesian approach is also applied to estimate the physical parameters and uncertainties from AVO data collected at two sites along a seismic line in the Baltic Sea with differing sediment types; it clearly identifies the distinct seabed compositions. Data uncertainties (independent and systematic) required for this analysis are estimated using a maximum‐likelihood approach.

Velocity anisotropy should be taken into account when analyzing the amplitude variation with offset (AVO) response of gas sands encased in shales. The anisotropic effects on the AVO of gas sands in transversely isotropic (TI) media are reviewed. Reflection coefficients in TI media are computed using a planewave formula based on ray theory. We present results of modeling special cases of exploration interest having positive reflectivity, near‐zero reflectivity, and negative reflectivity. The AVO reflectivity in anisotropic media can be decomposed into two parts; one for isotropy and the other for anisotropy. Zero‐offset reflectivity and Poisson’s ratio contrast are the most significant parameters for the isotropic component while the δ difference (Δδ) between shale and gas sand is the most important factor for the anisotropic component. For typical values of Tl anisotropy in shale (positive δ and ε), both δ difference (Δδ) and ε difference (Δε) amplify AVO effects. For small angles of incidence, Δδ plays an important role in AVO while Δε dominates for large angles of incidence. For typical values of δ and ε, the effects of anisotropy in shale are: (1) a more rapid increase in AVO for Class 3 and Class 2 gas sands, (2) a more rapid decrease in AVO for Class 1 gas sands, and (3) a shift in the offset of polarity reversal for some Class 1 and Class 2 gas sands.


 
 
 Porosity and water saturation are among the important reservoir parameters in terms of reservoir monitoring which in turn are necessary for placement of future production wells. Amplitude versus offset (AVO) modelling and analysis technique have been utilized for quantitative interpretation of porosity and water saturation. For AVO modeling, Gassmann fluid substitution model in connection with 2D seismic angle gathers were used for reservoir monitoring over Sawan-4 and Sawan-7 wells. AVO modellingresults showed significant increase of density log by substituting gas by water, moderate increase of P-wave velocity and no change in S-wave velocity. Moreover, AVO modelling proved a strong relationship between porosity and reflection amplitude for all offset ranges. The class IV anomaly was evident for all porosities down to 5%. From fluid substitution modelling it is evidentthat changes in water saturation do not change the AVO effect significantly which further substantiate by investigation of pre-stack time migration (PSTM) gathers verifying the modelling results. The amplitude relationship between Sawan-4 and Sawan-7 is close to the modelled result. The amplitude and the AVO behaviour indicate lower porosity or significantly reduced sand thickness in the vicinity of Sawan-4 and Sawan-7 wells.