A Monte Carlo method to quantify uncertainty in the inversion of zero‐offset VSP data

Malinverno, Alberto; Leaney, Scott

doi:10.1190/1.1815943

Cited by 41 publications

(36 citation statements)

References 4 publications

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“…The Gaussian random fields are suitable for modelling spatial continuity, and are routinely used for this purpose see, for example, Tarantola (1987), Cressie (1991), Christakos (1992), and Stein Downloaded by [University of Stellenbosch] at 03:43 09 October 2014 (1999). Discrete phenomena and phenomena with sparse representations require other types of models; see, for example, Salomão and Remacre (2001) and Malinverno and Leaney (2000). These models are not covered by the results in this article.…”

Section: Discussionmentioning

confidence: 89%

“…Problems in earth sciences have inspired the study reported here, and all these methods have merits in solving earth science-related inverse problems. There are numerous variants of their implementations, for example, Mosegaard and Tarantola (1995); Malinverno and Leaney (2000); Khan, Mosegaard, and Rasmussen (2000); and Hegstad and Omre (2001). The Markov chain-based methods appear as the most general ones and are extensively used.…”

Section: Introductionmentioning

confidence: 99%

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Bayesian Inversion of Piecewise Affine Operators in a Gaussian Framework

Kolbjørnsen

Omre

2005

Journal of Computational and Graphical Statistics

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Piecewise affine inverse problems form a general class of nonlinear inverse problems.In particular inverse problems obeying certain variational structures, such as Fermat's principle in travel time tomography, are of this type. In a piecewise affine inverse problem a parameter is to be reconstructed when its mapping through a piecewise affine operator is observed, possibly with errors. A piecewise affine operator is defined by partitioning the parameter space and assigning a specific affine operator to each part. A Bayesian approach with a Gaussian random field prior on the parameter space is used. Both problems with a discrete finite partition and a continuous partition of the parameter space are considered.The main result is that the posterior distribution is decomposed into a mixture of truncated Gaussian distributions, and the expression for the mixing distribution is partially analytically tractable. The general framework has, to the authors' knowledge, not previously been published, although the result for the finite partition is generally known.Inverse problems are currently of large interest in many fields. The Bayesian approach is popular and most often highly computer intensive. The posterior distribution is frequently concentrated close to high-dimensional nonlinear spaces, resulting in slow mixing for generic sampling algorithms. Inverse problems are, however, often highly structured. In order to develop efficient sampling algorithms for a problem at hand, the problem structure must be exploited.The decomposition of the posterior distribution that is derived in the current work can be used to develop specialized sampling algorithms. The article contains examples of such sampling algorithms. The proposed algorithms are applicable also for problems with exact observations. This is a case for which generic sampling algorithms tend to fail.

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Section: Discussionmentioning

confidence: 89%

Section: Introductionmentioning

confidence: 99%

Bayesian Inversion of Piecewise Affine Operators in a Gaussian Framework

Kolbjørnsen

Omre

2005

Journal of Computational and Graphical Statistics

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“…In the two case histories presented in this paper, the missing low-frequency component was handled with a basement velocity constraint at far below TD, obtained from surface seismic and field study. These look-ahead predictions have an inherent depth uncertainty, which is proportional to the distance between the deepest receiver and the target horizon (Malinverno and Leaney 2000).…”

Section: Depth and Timementioning

confidence: 99%

Drilling on Target With VSP Look-Ahead Technique in a Deepwater India Exploratory Environment

Lim

Rana

Dutta

et al. 2012

SPE Reservoir Evaluation &Amp; Engineering

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Frontier drilling in deepwater environments is challenging, with a wide range of risks that oil operators need to evaluate carefully because of high investment costs. The formation targets selected are typically depth-transformed using a velocity function obtained from conventional 3D surface-seismic data. The data are usually low resolution and may not have been processed with the best prestack-depth-migration (PSDM) techniques. This pitfall often leads to uncertainties in reaching drilling targets and completing the well on time. Common uncertainties faced by drillers include target confirmation ahead of an intermediate-depth section and the distance to these targets. One approach to reducing these uncertainties is to use borehole-seismic techniques to record a vertical seismic profile (VSP) at intermediate total depth (TD) to look ahead and estimate the target depths below the bit.Oil and Natural Gas Corporation Limited (ONGC), India's largest oil operator, has been using this simple, effective technique in drilling deepwater wells. In one case, the look-ahead prediction resulted in stopping of drilling operations because ONGC needed to ascertain if there was reservoir rock below the volcanics. The unambiguous VSP result did not show any possible reservoir below 3987-m measured depth (MD), which saved 3.5 weeks of drilling to reach the predrilling planned TD of 4415-m MD. In another example, ONGC needed to complete a vertical well that extended to a basaltic basement with TD planned at 4324 m at a subsea water depth of 2135 m. Three look-ahead VSP runs were performed at various sections for guidance throughout the drilling process, setting the casing, and reaching the deeper final target. Final TD was 6205-m MD as opposed to the planned TD of 4324-m MD.While VSP techniques have been widely used by the exploration communities, particularly geologists and geophysicists, they are also a look-ahead tool applicable for drilling-operations planning and ahead-of-bit drilling-risk mitigation.

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“…In the two case histories presented in this paper, the missing low frequency component was handled with basement velocity constraint at far below TD, obtained from surface seismic and field study. These look-ahead predictions have an inherent depth uncertainty, which is proportional to the distance between the deepest receiver and the target horizon (Malinverno and Leaney 2000).…”

Section: Vsp Processingmentioning

confidence: 99%

Drilling on Target with VSP Look-Ahead Technique in Deepwater India Exploratory Environment

et al. 2010

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Frontier drilling in deepwater environments is challenging with a wide range of risks that oil operators need to evaluate carefully because of high-investment costs. The formation targets selected are typically depth transformed using a velocity function obtained from conventional 3D surface seismic data. The data are usually low resolution and may not have been processed with the best prestack depth migration (PSDM) techniques. This pitfall often leads to uncertainties in reaching drilling targets and completing the well on time. Common uncertainties faced by drillers are target confirmation ahead of an intermediate depth section and the distance to these targets. One approach to reduce this uncertainty is to use borehole seismic techniques to record a vertical seismic profile (VSP) at intermediate total depth (TD) to look ahead and estimate the target depths below the bit.Oil and Natural Gas Corporation Limited (ONGC), India's largest oil operator, has been using this simple, effective technique in drilling deepwater wells. In one case the look-ahead prediction resulted in stopping of drilling operations because ONGC needed to ascertain if there was reservoir rock below the volcanics. The unambiguous VSP result did not show any possible reservoir below 3987 m measured depth (MD), which saved 3.5 weeks of drilling to reach the predrilling planned TD of 4415 m MD. In another example, ONGC needed to complete a vertical well that extended to basaltic basement with TD planned at 4324 m at a subsea water depth of 2135 m. Three look-ahead VSP runs were performed at various sections for guidance throughout the drilling process, setting the casing, and reaching the deeper final target. Final TD was 6205 m MD as opposed to the planned TD of 4324 m MD.While VSP techniques have been widely used by the exploration communities particularly the geologists and geophysicists, they are also a look-ahead tool applicable for drilling operations planning and ahead-of-bit drilling risk mitigation.

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A Monte Carlo method to quantify uncertainty in the inversion of zero‐offset VSP data

Cited by 41 publications

References 4 publications

Bayesian Inversion of Piecewise Affine Operators in a Gaussian Framework

Bayesian Inversion of Piecewise Affine Operators in a Gaussian Framework

Drilling on Target With VSP Look-Ahead Technique in a Deepwater India Exploratory Environment

Drilling on Target with VSP Look-Ahead Technique in Deepwater India Exploratory Environment

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