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.

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.

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.

scholarly journals Seismic pre-stack AVA inversion scheme based on lithology constraints

2020 ◽  
Vol 17 (3) ◽  
pp. 411-428
Author(s):  
Shuang Xiao ◽  
Jing Ba ◽  
Qiang Guo ◽  
J M Carcione ◽  
Lin Zhang ◽  
...  
Keyword(s):  
Model Updating ◽  
Optimal Solution ◽  
Seismic Inversion ◽  
Inversion Method ◽  
Good Resolution ◽  
S Wave ◽  
Elastic Parameters ◽  
Multivariate Gaussian Distribution ◽  
Stability Performance ◽  
The Stability

Abstract Seismic pre-stack AVA inversion using the Zoeppritz equation and its approximations as a forward engine yields P- and S-wave velocities and density. Due to the presence of seismic noise and other factors, the solution to seismic inversion is generally ill-posed and it is necessary to add constraints to regularize the algorithm. Moreover, since pre-stack inversion is a nonlinear problem, linearized optimization algorithms may fall into false local minima. The simulated annealing (SA) algorithm, on the other hand, is capable of finding the global optimal solution regardless of the initial model. However, when applied to multi-parameter pre-stack inversion, standard SA suffers from instability. Thus, a nonlinear pre-stack inversion method is proposed based on lithology constraints. Specifically, correlations among the elastic parameters are introduced to establish constraints based on a Bayesian framework, with special intention of mitigating the ill-posedness of the inversion problem as well as addressing the lithological characteristics of the formations. In particular, to improve the stability, a multivariate Gaussian distribution of elastic parameters is incorporated into the model updating the SA algorithm. We apply the algorithm to synthetic and field seismic data, indicating that the proposed method has a good resolution and stability performance.

Simultaneous inversion of PP and PS seismic data

Geophysics ◽  
2006 ◽  
Vol 71 (3) ◽  
pp. R1-R10 ◽  
Author(s):  
Helene Hafslund Veire ◽  
Martin Landrø
Keyword(s):  
Seismic Data ◽  
Reservoir Characterization ◽  
Model Building ◽  
Joint Inversion ◽  
P Wave ◽  
Inversion Method ◽  
System Of Equations ◽  
S Wave ◽  
Data Set ◽  
Simultaneous Inversion

Elastic parameters derived from seismic data are valuable input for reservoir characterization because they can be related to lithology and fluid content of the reservoir through empirical relationships. The relationship between physical properties of rocks and fluids and P-wave seismic data is nonunique. This leads to large uncertainties in reservoir models derived from P-wave seismic data. Because S- waves do not propagate through fluids, the combined use of P-and S-wave seismic data might increase our ability to derive fluid and lithology effects from seismic data, reducing the uncertainty in reservoir characterization and thereby improving 3D reservoir model-building. We present a joint inversion method for PP and PS seismic data by solving approximated linear expressions of PP and PS reflection coefficients simultaneously using a least-squares estimation algorithm. The resulting system of equations is solved by singular-value decomposition (SVD). By combining the two independent measurements (PP and PS seismic data), we stabilize the system of equations for PP and PS seismic data separately, leading to more robust parameter estimation. The method does not require any knowledge of PP and PS wavelets. We tested the stability of this joint inversion method on a 1D synthetic data set. We also applied the methodology to North Sea multicomponent field data to identify sand layers in a shallow formation. The identified sand layers from our inverted sections are consistent with observations from nearby well logs.

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.

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.

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.

scholarly journals Variational Bayesian inversion of seismic attributes jointly for geologic facies and petrophysical rock properties

Geophysics ◽  
2020 ◽  
Vol 85 (4) ◽  
pp. MR213-MR233 ◽  
Author(s):  
Muhammad Atif Nawaz ◽  
Andrew Curtis ◽  
Mohammad Sadegh Shahraeeni ◽  
Constantin Gerea
Keyword(s):  
Gaussian Mixture ◽  
Seismic Attributes ◽  
Joint Estimation ◽  
Training Data ◽  
P Wave ◽  
Rock Properties ◽  
Inversion Method ◽  
Computationally Efficient ◽  
S Wave ◽  
Well Data

Seismic attributes (derived quantities) such as P-wave and S-wave impedances and P-wave to S-wave velocity ratios may be used to classify subsurface volume of rock into geologic facies (distinct lithology-fluid classes) using pattern recognition methods. Seismic attributes may also be used to estimate subsurface petrophysical rock properties such as porosity, mineral composition, and pore-fluid saturations. Both of these estimation processes are conventionally carried out independent of each other and involve considerable uncertainties, which may be reduced significantly by a joint estimation process. We have developed an efficient probabilistic inversion method for joint estimation of geologic facies and petrophysical rock properties. Seismic attributes and petrophysical properties are jointly modeled using a Gaussian mixture distribution whose parameters are initialized by unsupervised learning using well-log data. Rock-physics models may be used in our method to augment the training data if the existing well data are limited; however, this is not required if sufficient well data are available. The inverse problem is solved using the Bayesian paradigm that models uncertainties in the form of probability distributions. Probabilistic inference is performed using variational optimization, which is a computationally efficient deterministic alternative to the commonly used sampling-based stochastic inference methods. With the help of a real data application from the North Sea, we find that our method is computationally efficient, honors expected spatial correlations of geologic facies, allows reliable detection of convergence, and provides full probabilistic results without stochastic sampling of the posterior distribution.

Three-parameter prestack seismic inversion based on L1-2 minimization

Geophysics ◽  
2019 ◽  
Vol 84 (5) ◽  
pp. R753-R766 ◽  
Author(s):  
Lingqian Wang ◽  
Hui Zhou ◽  
Yufeng Wang ◽  
Bo Yu ◽  
Yuanpeng Zhang ◽  
...  
Keyword(s):  
Wave Velocity ◽  
Seismic Inversion ◽  
Thin Layers ◽  
P Wave ◽  
S Wave ◽  
Reservoir Prediction ◽  
Linear Inversion ◽  
Prestack Inversion ◽  
The Difference ◽  
Predictive Filtering

Prestack inversion has become a common approach in reservoir prediction. At present, the critical issue in the application of seismic inversion is the estimation of elastic parameters in the thin layers and weak reflectors. To improve the resolution and the accuracy of the inversion results, we introduced the difference of [Formula: see text] and [Formula: see text] norms as a nearly unbiased approximation of the sparsity of a vector, denoted as the [Formula: see text] norm, to the prestack inversion. The nonconvex penalty function of the [Formula: see text] norm can be decomposed into two convex subproblems via the difference of convex algorithm, and each subproblem can be solved efficiently by the alternating direction method of multipliers. Compared with the [Formula: see text] norm regularization, the [Formula: see text] minimization can reconstruct reflectivities more accurately. In addition, the [Formula: see text]-[Formula: see text] predictive filtering was introduced to guarantee the lateral continuity of the location and the amplitude of the reflectivity series. The generalized linear inversion and [Formula: see text]-[Formula: see text] predictive filtering are combined for stable elastic impedance inversion results, and three parameters of P-wave velocity, S-wave velocity, and density can be inverted with the Bayesian linearized amplitude variation with offset inversion. The inversion results of synthetic and real seismic data demonstrate that the proposed method can effectively improve the resolution and accuracy of the inversion results.

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