A Bayes tour of inversion: A tutorial

Ulrych, Tadeusz J.; Sacchi, Mauricio D.; Woodbury, Allan D.

doi:10.1190/1.1444923

Cited by 240 publications

(92 citation statements)

References 15 publications

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“…the PDF of unknown parameters x, given measured data y). Furthermore, π(y) is called the evidence and can be calculated using the law of total probabilities (Ulrych et al 2001) as follows:…”

Section: Bayes' Theoremmentioning

confidence: 99%

Bayesian inference to identify parameters in viscoelasticity

Rappel

Beex

Bordas

2017

Mech Time-Depend Mater

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This contribution discusses Bayesian inference (BI) as an approach to identify parameters in viscoelasticity. The aims are (i) to show that the prior has a substantial influence for viscoelasticity, (ii) to show that this influence decreases for an increasing number of measurements and (iii) to show how different types of experiments influence the identified parameters and their uncertainties. The standard linear solid model is the material description of interest and a relaxation test, a constant strain-rate test and a creep test are the tensile experiments focused on. The experimental data are artificially created, allowing us to make a one-to-one comparison between the input parameters and the identified parameter values. Besides dealing with the aforementioned aims, we believe that this contribution forms a comprehensible start for those interested in applying BI in viscoelasticity.

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Section: Bayes' Theoremmentioning

confidence: 99%

Bayesian inference to identify parameters in viscoelasticity

Rappel

Beex

Bordas

2017

Mech Time-Depend Mater

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“…Equation (19) is motivated by the analysis of Ulrych et al (2001), Mavko and Mukerji (1998b) and Kirkpatrick et al (1983).…”

Section: Bayesian Inversion Scheme For Water Saturation and Reservoirmentioning

confidence: 99%

Estimating gas saturation in a thin layer by using frequency‐dependent amplitude versus offset modelling

Jin

Chapman

et al. 2016

Geophysical Prospecting

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Various models have been proposed to link partial gas saturation to seismic attenuation and dispersion, suggesting that the reflection coefficient should be frequency-dependent in many cases of practical importance. Previous approaches to studying this phenomenon have typically been limited to single interface models. Here we propose a modelling technique which allows us to incorporate frequency-dependent reflectivity into convolutional modelling. With this modelling framework, seismic data can be synthesized from well logs of velocity, density, porosity and water saturation. This forward modelling could act as a basis for inversion schemes aimed at recovering gas saturation variations with depth. We present a Bayesian inversion scheme for a simple thin layer case and a particular rock physics model, and show that although the method is very sensitive to prior information and constrains, gas saturation and layer thickness can both theoretically be estimated in the case of interfering reflections.

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“…Standard references for Bayesian inference are by Box and Tiao (1973) and Smith et al (1992). Its applications in geophysics are given by Tarantola and Valette (1982b), Jackson and Matsu'ura (1985), Duijndam (1988a,b), Mosegaard and Tarantola (1995), Stoffa (1995, 1996), Malinverno (2000) and Ulrych et al (2001). The application specifically in seismic inversion is given by Gouveia and Scales (1998) and Buland and Omre (2003).…”

Section: Bayesian Inferencementioning

confidence: 99%

Seismic inversion and uncertainty analysis using a transdimensional Markov chain Monte Carlo method

Zhu

Gibson

2016

SEG Technical Program Expanded Abstracts 2016

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We use a transdimensional inversion algorithm, reversible jump MCMC (rjMCMC), in the seismic waveform inversion of post-stack and prestack data to characterize reservoir properties such as seismic wave velocity, density as well as impedance and then estimate uncertainty. Each seismic trace is inverted independently based on a layered earth model. The model dimensionality is defined as the number of the layers multiplied with the number of model parameters per layer. The rjMCMC is able to infer the number of model parameters from data itself by allowing it to vary in the iterative inversion process, converge to proper parameterization and prevent underparameterization and overparameterization. We also use rjMCMC to enhance uncertainty estimation since it can transdimensionally sample different model spaces of different dimensionalities and can prevent a biased sampling in only one space which may have a different dimensionality than that of the true model space. An ensemble of solutions from difference spaces can statistically reduce the bias for parameter estimation and uncertainty quantification. Inversion uncertainty is comprised of property uncertainty and location uncertainty. Our study revealed that the inversion uncertainty is correlated with the discontinuity of property in such a way that 1) a smaller discontinuity will induce a lower uncertainty in property at the discontinuity but also a higher uncertainty of the location of that discontinuity and 2) a larger discontinuity will induce a higher uncertainty in property at the discontinuity but also a higher ''certainty'' of the location of that discontinuity. Therefore, there is a trade-off between the property uncertainty and the location uncertainty. To our surprise, there is a lot of hidden information in the uncertainty result that we can actually take advantage of due to this trade-off effect. On the basis of our study ii using rjMCMC, we propose to use the inversion uncertainty as a novel attribute in an optimistic way to characterize the magnitude and the location of subsurface discontinuities and reflectors. important it is to estimate the uncertainty, and I used another method for two years but it turned out that method was unsuccessful for solving my research problems because it couldn't answer the question for uncertainty assessment. This is one of the biggest mistakes that I have ever made because I wasn't aware of the importance of my advisor's words and questions. Indeed, research is not always successful and smooth and I did encounter failures, but I didn't give up.

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A Bayes tour of inversion: A tutorial

Cited by 240 publications

References 15 publications

Bayesian inference to identify parameters in viscoelasticity

Bayesian inference to identify parameters in viscoelasticity

Estimating gas saturation in a thin layer by using frequency‐dependent amplitude versus offset modelling

Seismic inversion and uncertainty analysis using a transdimensional Markov chain Monte Carlo method

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