Modeling seismic impedance with Markov chains

Godfrey, Robert; Muir, Francis; Rocca, F.

doi:10.1190/1.1441128

Cited by 56 publications

(19 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The random process with covariance function (6) corresponds to a "random walk" in the z direction. Godfrey et al (1980) suggest use of more general Markov chains. In the x-y directions, the random process with covariance function (6) is white noise.…”

Section: Choice Of the Weighting Functionsmentioning

confidence: 99%

A strategy for nonlinear elastic inversion of seismic reflection data

1986

View full text Add to dashboard Cite

show abstract

Section: Choice Of the Weighting Functionsmentioning

confidence: 99%

A strategy for nonlinear elastic inversion of seismic reflection data

1986

View full text Add to dashboard Cite

show abstract

“…This is also the case for non-binary sediments with exponentially distributed layer thicknesses, provided the transition probabilities from one layer type to another are also independent of layer thickness (e.g. Godfrey, Muir & Rocca 1980). Non-telegraph binary sediments (i.e.…”

Section: Stratigraphic Operatormentioning

confidence: 96%

A pulse in a binary sediment

Frazer

1994

Geophysical Journal International

View full text Add to dashboard Cite

Synthetic seismograms are generated by an exact method that automatically separates stratigraphic effects from intrinsic effects. Then three different methods are used to derive rather simple expressions for the effective sound speed of a binary sediment for vertical propagation at wavelengths greater than the average layer thickness. A single-scatter theory (SST) is based on the notion that transmitted energy is reflected once less than absorbed energy. A path sum theory (PST) is used to explicitly sum the contribution of rays corresponding to multiple reflections. An averaged-multiple imbedding theory (AMI) is developed that explicitly averages multiple reflections over the distribution of layer thicknesses. Although each of these theories has a different ansatz they all agree remarkably well with numerical simulation and with each other. Unlike some earlier theories, they do not require that the impedance contrast of the layers decrease as the number of layers increases. They take account of the effect of intrinsic attenuation on multiples as well as the primary wave. They use the layer-thickness probability distributions directly rather than the autocorrelation of the reflectivity or the impedance variation. SST is shown to agree with earlier static theories of effective sound-speed in the limit as 0-0. PST gives a stratigraphic (scattering) Q that vanishes as 0-0. Both PST and AM1 permit scattering losses due to spatial irregularities of the sand-shale interfaces, and they are more accurate than SST if reflection coefficients are large.

show abstract

“…MCMC is generally cast in a Bayesian framework and is widely used in geophysical inversion (Mosegaard and Tarantola, 1995;Stoffa, 1995, 1996;Curtis and Lomax, 2001;Mosegaard and Sambridge, 2002;Sambridge and Mosegaard, 2002;Malinverno and Briggs, 2004;Malinverno and Leaney, 2005) and particularly in seismic inversion (Godfrey et al, 1980;Mosegaard et al, 1997;Eidsvik et al, 2004;Hong and Sen, 2009;van der Burg et al, 2009;Martin et al, 2012;Chen and Glinsky, 2014).…”

Section: Brief Overview Of Conventional Algorithmsmentioning

confidence: 99%

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

Zhu

Gibson

2016

SEG Technical Program Expanded Abstracts 2016

View full text Add to dashboard Cite

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.

show abstract

Modeling seismic impedance with Markov chains

Cited by 56 publications

References 5 publications

A strategy for nonlinear elastic inversion of seismic reflection data

A strategy for nonlinear elastic inversion of seismic reflection data

A pulse in a binary sediment

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

Contact Info

Product

Resources

About