AVA inversion of the top Utsira Sand reflection at the Sleipner field

Geophysics ◽  
2011 ◽  
Vol 76 (3) ◽  
pp. C53-C63 ◽  
Author(s):  
Tor Erik Rabben ◽  
Bjørn Ursin
Keyword(s):  
Wave Impedance ◽  
P Wave ◽  
Damping Factor ◽  
S Wave ◽  
Elastic Parameters ◽  
Zoeppritz Equations ◽  
Gassmann’S Equation ◽  
Inversion Procedure ◽  
Global Scaling ◽  
Amplitude Variation With Angle

Amplitude variation with angle (AVA) inversion is performed on the top Utsira Sand reflector at the Sleipner field, North Sea, Norway. This interface is of particular interest because of the accumulation of [Formula: see text] injected from a point deeper in the Utsira Sand. The focus is on the postmigration processing of angle gathers together with the actual inversion procedure. The processing treats amplitude extraction, offset-to-angle mapping, and global scaling in detail. Two algorithms are used for the inversion of AVA data, one that assesses uncertainties and one fast least-squares variant. Both are very suitable for this type of problem because of their covariance matrices and built-in regularization. In addition, two three-parameter approximations of the Zoeppritz equations are used. One is linear approximation and the other is quadratic. The results show significant signals for all three elastic parameters, but the substitution of brine by [Formula: see text] using Gassmann’s equation indicates that the contrasts in S-wave impedance and density are overestimated. For the contrasts in P-wave impedance the results are in agreement with the fluid substitution. A simple sensitivity analysis shows that the offset-to-angle mapping and the damping factor in the inversion are the most plausible explanations of the discrepancy.

Approximations to the Zoeppritz equations and their use in AVO analysis

Geophysics ◽  
1999 ◽  
Vol 64 (6) ◽  
pp. 1920-1927 ◽  
Author(s):  
Yanghua Wang
Keyword(s):  
Linear Approximation ◽  
Wave Velocity ◽  
Order Approximation ◽  
Quadratic Function ◽  
P Wave ◽  
S Wave ◽  
Elastic Parameters ◽  
Amplitude Variation With Offset ◽  
Zoeppritz Equations ◽  
Avo Analysis

To efficiently invert seismic amplitudes for elastic parameters, pseudoquartic approximations to the Zoeppritz equations are derived to calculate P-P-wave reflection and transmission coefficients as a function of the ray parameter p. These explicit expressions have a compact form in which the coefficients of the p2 and p4 terms are given in terms of the vertical slownesses. The amplitude coefficients are also represented as a quadratic function of the elastic contrasts at an interface and are compared to the linear approximation used in conventional amplitude variation with offset (AVO) analysis, which can invert for only two elastic parameters. Numerical analysis with the second‐order approximation shows that the condition number of the Fréchet matrix for three elastic parameters is improved significantly from using a linear approximation. Therefore, those quadratic approximations can be used directly with amplitude information to estimate not only two but three parameters: P-wave velocity contrast, S-wave velocity contrast, and the ratio of S-wave and P-wave velocities at an interface.

Seismic simultaneous inversion using a multidamped subspace method

Geophysics ◽  
2019 ◽  
Vol 85 (1) ◽  
pp. R1-R10 ◽  
Author(s):  
Jinyue Liu ◽  
Yanghua Wang
Keyword(s):  
Fourier Coefficients ◽  
Hessian Matrix ◽  
Wave Impedance ◽  
Seismic Inversion ◽  
P Wave ◽  
Inversion Method ◽  
Subspace Method ◽  
S Wave ◽  
Elastic Parameters ◽  
Simultaneous Inversion

Seismic inversion of amplitude variation with offset (AVO) plays a key role in seismic interpretation and reservoir characterization. The AVO inversion should be a simultaneous inversion that inverts for three elastic parameters simultaneously: the P-wave impedance, S-wave impedance, and density. Using only seismic P-wave reflection data with a limited source-receiver offset range, the AVO simultaneous inversion can obtain two elastic parameters reliably, but it is difficult to invert for the third parameter, usually the density term. To address this difficulty in the AVO simultaneous inversion, we used a subspace inversion method in which we partitioned the elastic parameters into different subspaces. We parameterized each single elastic parameter with a truncated Fourier series and inverted for the Fourier coefficients. Because the Fourier coefficients of different wavenumber components have different sensitivities, we grouped the Fourier coefficients of low-, medium-, and high-wavenumber components into different subspaces. We further assigned different damping factors to the Hessian matrix corresponding to different wavenumber components within each subspace. This inversion scheme is referred to as a multidamped subspace method. Synthetic and field seismic data examples confirmed that the AVO simultaneous inversion with this multidamped subspace method is capable of producing reliable estimation of the three elastic parameters simultaneously.

Nonlinear two‐dimensional elastic inversion of multioffset seismic data

Geophysics ◽  
1987 ◽  
Vol 52 (9) ◽  
pp. 1211-1228 ◽  
Author(s):  
Peter Mora
Keyword(s):  
Wave Equation ◽  
Wave Velocity ◽  
A Priori ◽  
Gaussian Model ◽  
Wave Impedance ◽  
P Wave ◽  
S Wave ◽  
Elastic Wave Equation ◽  
Gradient Direction ◽  
P Wave Velocity

The treatment of multioffset seismic data as an acoustic wave field is becoming increasingly disturbing to many geophysicists who see a multitude of wave phenomena, such as amplitude‐offset variations and shearwave events, which can only be explained by using the more correct elastic wave equation. Not only are such phenomena ignored by acoustic theory, but they are also treated as undesirable noise when they should be used to provide extra information, such as S‐wave velocity, about the subsurface. The problems of using the conventional acoustic wave equation approach can be eliminated via an elastic approach. In this paper, equations have been derived to perform an inversion for P‐wave velocity, S‐wave velocity, and density as well as the P‐wave impedance, S‐wave impedance, and density. These are better resolved than the Lamé parameters. The inversion is based on nonlinear least squares and proceeds by iteratively updating the earth parameters until a good fit is achieved between the observed data and the modeled data corresponding to these earth parameters. The iterations are based on the preconditioned conjugate gradient algorithm. The fundamental requirement of such a least‐squares algorithm is the gradient direction which tells how to update the model parameters. The gradient direction can be derived directly from the wave equation and it may be computed by several wave propagations. Although in principle any scheme could be chosen to perform the wave propagations, the elastic finite‐ difference method is used because it directly simulates the elastic wave equation and can handle complex, and thus realistic, distributions of elastic parameters. This method of inversion is costly since it is similar to an iterative prestack shot‐profile migration. However, it has greater power than any migration since it solves for the P‐wave velocity, S‐wave velocity, and density and can handle very general situations including transmission problems. Three main weaknesses of this technique are that it requires fairly accurate a priori knowledge of the low‐ wavenumber velocity model, it assumes Gaussian model statistics, and it is very computer‐intensive. All these problems seem surmountable. The low‐wavenumber information can be obtained either by a prior tomographic step, by the conventional normal‐moveout method, by a priori knowledge and empirical relationships, or by adding an additional inversion step for low wavenumbers to each iteration. The Gaussian statistics can be altered by preconditioning the gradient direction, perhaps to make the solution blocky in appearance like well logs, or by using large model variances in the inversion to reduce the effect of the Gaussian model constraints. Moreover, with some improvements to the algorithm and more parallel computers, it is hoped the technique will soon become routinely feasible.

Accuracy Comparison of Elastic Impedance Formula

2012 ◽  
Vol 466-467 ◽  
pp. 400-404
Author(s):  
Jin Zhang ◽  
Huai Shan Liu ◽  
Si You Tong ◽  
Lin Fei Wang ◽  
Bing Xu
Keyword(s):  
Seismic Data ◽  
Poisson Ratio ◽  
Seismic Inversion ◽  
P Wave ◽  
S Wave ◽  
Elastic Parameters ◽  
Accuracy Comparison ◽  
Elastic Impedance ◽  
Prestack Seismic Inversion ◽  
Lamé Coefficients

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.

scholarly journals Bayesian Time-lapse Difference Inversion Based on the exact Zoeppritz Equations with Blockiness Constraint

2020 ◽  
Vol 25 (1) ◽  
pp. 89-100
Author(s):  
Lin Zhou ◽  
Jianping Liao ◽  
Jingye Li ◽  
Xiaohong Chen ◽  
Tianchun Yang ◽  
...  
Keyword(s):  
Wave Equations ◽  
Oil And Gas ◽  
Time Lapse ◽  
Seismic Inversion ◽  
Field Application ◽  
Inversion Method ◽  
S Wave ◽  
Elastic Parameters ◽  
Zoeppritz Equations ◽  
Approximate Formulas

Accurately inverting changes in the reservoir elastic parameters that are caused by oil and gas exploitation is of great importance in accurately describing reservoir dynamics and enhancing recovery. Previously numerous time-lapse seismic inversion methods based on the approximate formulas of exact Zoeppritz equations or wave equations have been used to estimate these changes. However the low accuracy of calculations using approximate formulas and the significant calculation effort for the wave equations seriously limits the field application of these methods. However, these limitations can be overcome by using exact Zoeppritz equations. Therefore, we study the time-lapse seismic difference inversion method using the exact Zoeppritz equations. Firstly, the forward equation of time-lapse seismic difference data is derived based on the exact Zoeppritz equations. Secondly, the objective function based on Bayesian inversion theory is constructed using this equation, with the changes in elastic parameters assumed to obey a Gaussian distribution. In order to capture the sharp time-lapse changes of elastic parameters and further enhance the resolution of the inversion results, the blockiness constraint, which follows the differentiable Laplace distribution, is added to the prior Gaussian background model. All examples of its application show that the proposed method can obtain stable and reasonable P- and S-wave velocities and density changes from the difference data. The accuracy of estimation is higher than for existing methods, which verifies the effectiveness and feasibility of the new method. It can provide high-quality seismic inversion results for dynamic detailed reservoir description and well location during development.

Inversion and interpretation of a 3D seismic data set from the Ouachita Mountains, Oklahoma

Geophysics ◽  
2009 ◽  
Vol 74 (2) ◽  
pp. B37-B45 ◽  
Author(s):  
Abuduwali Aibaidula ◽  
George McMechan
Keyword(s):  
Seismic Data ◽  
Acoustic Impedance ◽  
3D Visualization ◽  
Wave Impedance ◽  
P Wave ◽  
3D Seismic ◽  
S Wave ◽  
Ouachita Mountains ◽  
Data Set ◽  
3D Seismic Data

Acoustic impedance inversion (AI) and simultaneous angle-dependent inversion (SADI) of a 3D seismic data set characterize reservoirs of Mississippian Morrowan age in the triangle zone of the frontal Ouachita Mountains, Oklahoma. Acoustic impedance of the near-angle seismic data images the 3D spatial distributions of Wapanucka limestone and Cromwell sandstone. Lamé [Formula: see text] ([Formula: see text] and [Formula: see text]) and [Formula: see text] sections are derived from the P-wave and S-wave impedance ([Formula: see text] and [Formula: see text]) sections produced by the SADI. Lithology is identified from the gamma logs and [Formula: see text]. The [Formula: see text], [Formula: see text], and [Formula: see text] are interpreted in terms of a hydrocarbon distribution pattern. The [Formula: see text] is used to identify high [Formula: see text] regions that are consistent with high sand/shale ratio. The estimated impedances and derived Lamé parameter sections are consistent with the interpretation that parts of the Wapanucka limestone and Cromwell sandstone contain potential gas reservoirs in fault-bounded compartments. The Cromwell sandstone contains the main inferred reservoirs; the two largest of these are each [Formula: see text] in pore volume. The inversion results also explain the observed low production in previous wells because those did not sample the best compartments. We propose a single new well location that would penetrate both reservoirs; 3D visualization facilitates this recommendation.

S-wave velocity prediction of marine-continental transitional coal measure rocks using multipole array sonic logs and the rock-matrix modulus extraction method

2019 ◽  
Vol 7 (1) ◽  
pp. T241-T253
Author(s):  
Siqi Wang ◽  
Jianguo Zhang ◽  
Shuai Yin ◽  
Chao Han
Keyword(s):  
Wave Velocity ◽  
Wave Impedance ◽  
Empirical Method ◽  
Computational Method ◽  
P Wave ◽  
Coal Measure ◽  
Rock Matrix ◽  
S Wave ◽  
Matrix Modulus ◽  
Sonic Logs

Accurate prediction of the S-wave velocity of highly heterogeneous coal measure strata using high-resolution logging can effectively identify high-quality reservoirs. We have used multipole array sonic logs to predict the S-wave velocity of coal measure strata based on the conventional empirical method (CEM), multiple regression method (MRM), and rock-matrix modulus extraction (MME) method. Moreover, we used a complex multiple parameter iterative computational method of forward calculation and inversion in the MME method. Our results indicate that the MME method can effectively extract several rock modulus parameters. There are good binomial relationships between the extracted rock modulus parameters ([Formula: see text]) and between the extracted modulus parameters and the P-wave impedance ([Formula: see text]). The average relative errors of the S-wave velocities predicted by the CEM, MRM, and MME methods are 7.58%, 5.64%, and 2.31%, respectively. The MME method can effectively extract and couple effective information from different types of conventional well logs and perform high-precision S-wave time difference prediction.

Simultaneous inversion for model geometry and elastic parameters

Geophysics ◽  
1999 ◽  
Vol 64 (1) ◽  
pp. 182-190 ◽  
Author(s):  
Yanghua Wang
Keyword(s):  
Joint Inversion ◽  
Real Data ◽  
Structural Effect ◽  
P Wave ◽  
Inversion Method ◽  
S Wave ◽  
Elastic Parameters ◽  
Simultaneous Inversion ◽  
Avo Analysis ◽  
The North

Both traveltimes and amplitudes in reflection seismology are used jointly in an inversion to simultaneously invert for the interface geometry and the elastic parameters at the reflectors. The inverse problem has different physical dimensions in both data and model spaces. Practical approaches are proposed to tackle the dimensional difficulties. In using the joint inversion, which may properly take care of the structural effect, one potentially improves the estimates of the subsurface elastic parameters in the traditional analysis of amplitude variation with offset (AVO). Analysis of the elastic parameters estimated, using the ratio of s-wave to P-wave velocity contrasts and the deviation of this parameter from a normal background trend, promises to have application in AVO analysis. The inversion method is demonstrated by application to real data from the North Sea.

scholarly journals Quadri-joint inversion: Method and application to the Big Sky 9C 3D data set in northern Montana

2018 ◽  
Vol 6 (4) ◽  
pp. SN101-SN118 ◽  
Author(s):  
Vincent Clochard ◽  
Bryan C. DeVault ◽  
David Bowen ◽  
Nicolas Delépine ◽  
Kanokkarn Wangkawong
Keyword(s):  
Reservoir Characterization ◽  
Joint Inversion ◽  
Wave Impedance ◽  
P Wave ◽  
Seismic Survey ◽  
Time Shift ◽  
Inversion Method ◽  
S Wave ◽  
Data Set ◽  
Long Term Storage

The Kevin Dome [Formula: see text] storage project, located in northern Montana, attempted to characterize the Duperow Formation as a potential long-term storage zone for injected [Formula: see text]. A multicomponent (9C) seismic survey was acquired for the Big Sky Carbon Sequestration Partnership over a portion of the Kevin Dome using P- and S-wave sources. Prestack migrated PP, PS, SH, and SV data sets were generated. We then applied several stratigraphic inversion workflows using one or several kinds of seismic wavefield at the same time resulting in joint inversions of each data set. The aim of our study is to demonstrate the benefits of doing quadri-joint inversion of PP-, PS-, SH-, and SV-wavefields for the recovery of the elastic earth parameters, especially the S-wave impedance and density. These are crucial parameters because they can help determine lithology and porefill in the reservoir characterization workflow. Because the inversion workflow always uses the original seismic data recorded in its own time domain, it is necessary to compute registration laws between PP-PS-, PP-SH-, and PP-SV-wavefields using a time shift computation procedure (warping) based on inverted S-wave impedances from inversion of a single wavefield. This generated a significant improvement over methods that rely on attempting to match trace waveforms that may have a different phase, frequency content, and polarity. Finally, we wanted to investigate the reliability of the quadri-joint inversion results in the Bakken/Banff Formations, which have less lateral geologic variation than the underlying Duperow target. This interval shares many of the geophysical characterization challenges common to shale reservoirs in other North American basins. We computed geomechanical parameters, such as Poisson’s ratio and Young’s modulus, which are a proxy for brittleness. Comparison of these results with independent laboratory measurements in the Bakken interval demonstrates the superiority of the quadri-joint inversion method to the traditional inversion using P-wave data only.

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