Rapid spatially coupled AVO inversion in the Fourier domain

Buland, A.; Kolbjørnsen, Odd; Omre, Henning

doi:10.1190/1.1581035

Cited by 75 publications

(26 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Sampling of multivariate Gaussian variables and evaluating the prior and likelihood can be done efficiently in the Fourier domain (Chan and Wood 1997), since we have specified the matrices V l and V 0 in (23) and (24) as circular, wrapping the data on a circle, see also Buland, Kolbjørnsen and Omre (2003).…”

Section: Seismic Inversionmentioning

confidence: 99%

See 1 more Smart Citation

On directional Metropolis–Hastings algorithms

Eidsvik¹,

Tjelmeland²

2006

Stat Comput

View full text Add to dashboard Cite

New Metropolis-Hastings algorithms using directional updates are introduced in this paper. Each iteration of a directional Metropolis-Hastings algorithm consists of three steps (i) generate a line by sampling an auxiliary variable, (ii) propose a new state along the line, and (iii) accept/reject according to the Metropolis-Hastings acceptance probability. We consider two classes of directional updates. The first uses a point in R n as auxiliary variable, the second an auxiliary direction vector. The proposed algorithms generalize previous directional updating schemes since we allow the distribution of the auxiliary variable to depend on properties of the target at the current state. By letting the proposal distribution along the line depend on the density of the auxiliary variable, we identify proposal mechanisms that give unit acceptance rate. When we use direction vector as auxiliary variable, we get the advantageous effect of large moves in the Markov chain and hence the autocorrelation length of the samples is small. We apply the directional Metropolis-Hastings algorithms to a Gaussian example, a mixture of Gaussian densities, and a Bayesian model for seismic data.

show abstract

Section: Seismic Inversionmentioning

confidence: 99%

“…These covariance parameters are treated as fixed here, see . We follow the Bayesian method used in and Buland, Kolbjørnsen and Omre (2003), assigning a Gaussian prior for the reservoir properties:…”

Section: Seismic Inversionmentioning

confidence: 99%

On directional Metropolis–Hastings algorithms

Eidsvik¹,

Tjelmeland²

2006

Stat Comput

View full text Add to dashboard Cite

show abstract

“…But note that in general this becomes computationally expensive in high dimensions. With our torus assumption discussed above, the covariance matrices involved become circular and the linearized posterior can then be evaluated and sampled from effectively in the Fourier domain (Cressie (1991), Buland, Kolbjørnsen, and Omre (2003)). The actual nonlinear posterior can also be evaluated, up to a normalizing constant, in the Fourier domain, by treating the prior and likelihood terms in equation (1) separately.…”

Section: Prior and Likelihood Assumptionsmentioning

confidence: 99%

Directional Metropolis : Hastings Updates for Posteriors with Nonlinear Likelihoods

Tjelmeland¹,

Eidsvik

2005

Geostatistics Banff 2004

View full text Add to dashboard Cite

In this paper we consider spatial problems modeled by a Gaussian random field prior and a nonlinear likelihood linking the hidden variables to the data. We define a directional block Metropolis-Hastings algorithm to explore the posterior. The method is applied to seismic data from the North Sea. Based on our results we believe it is important to assess the actual posterior in order to understand possible shortcomings of linear approximations. POSTERIORS 95 2004, 95-104. © 2005 Springer. Printed in the Netherlands. tics O. Leuangthong and C. V. Deutsch (eds.), Geostatis Banff : DIRECTIONAL METROPOLIS HASTINGS UPDATES FOR

show abstract

“…The methodology of Bayesian inversion described in Buland et al (2003) is used. The Bayesian approach defines the prior distribution and constrains this by data to form the posterior distribution.…”

Section: Elastic Seismic Inversionmentioning

confidence: 99%

Information Content in Forward 4D-Seismic Modelling and Elastic Inversion

et al. 2005

View full text Add to dashboard Cite

TX 75083-3836, U.S.A., fax 01-972-952-9435. AbstractElastic seismic inversion is a tool frequently used in analysis of seismic data. Elastic inversion relies on a simplified seismic model, and generally produces 3D cubes for Vp, Vs and density. By applying rock physics theory such volumes may be interpreted in terms of lithology and fluid properties. Understanding the robustness of forward and inverse techniques is important when deciding how much information seismic data really carry.This paper discusses the observed deviation between a reference and simulated reservoir, and its dependency on the seismic parameters and the reservoir characterization parameters. The ability to utilize the results from a 4D seismic survey in reservoir characterization will depend on several aspects. To investigate this, a loop that performs independent forward seismic modeling and elastic inversion at two time stages has been established.The multi-disciplinary workflow has several independent steps:1. Generation of a synthetic reference reservoir, by realistic geostatistical modeling. 2. Flow simulation of the reference reservoir to predict reservoir conditions at survey acquisition times. 3. Establishing a relationship between petrophysical and fluid properties and seismic parameters by a rock physics model. 4. Generation of seismic AVA responses corresponding to reservoir conditions at base and monitor survey times. 5. Elastic seismic inversion of both AVA response sets. 6. Simulation of lithology and fluid parameters conditioned on seismic inversion. 7. Comparison of static reservoir parameters of reference and simulated realization.8. Comparison of seismic responses at initial and monitor survey times. By working on a realistic synthetic reservoir, full knowledge of the reservoir characteristics is achieved. This makes the evaluation of the questions regarding the fundamental dependency between the seismic and petrophysical domains stronger. The theoretical limitations of the information content of the seismic data, including 4D, are investigated since the synthetic reservoir is an ideal case with accuracy never achieved in the applied situation.The production deviation between the reference and predicted reservoir was significantly decreased by using 4D seismic data in addition to the 3D inverted elastic parameters.

show abstract

Rapid spatially coupled AVO inversion in the Fourier domain

Cited by 75 publications

References 14 publications

On directional Metropolis–Hastings algorithms

On directional Metropolis–Hastings algorithms

Directional Metropolis : Hastings Updates for Posteriors with Nonlinear Likelihoods

Information Content in Forward 4D-Seismic Modelling and Elastic Inversion

Contact Info

Product

Resources

About