Journal ArticleDOI
Modeling seismic impedance with Markov chains
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TLDR
In this article, a special type of Markov chain is used to model acoustic impedance, which is constrained to have a purely exponential correlation function, and the stochastic model is parsimoniously described by M parameters, where M is the number of states or rocks composing an impedance well log.Abstract:
Acoustic impedance is modeled as a special type of Markov chain, one which is constrained to have a purely exponential correlation function. The stochastic model is parsimoniously described by M parameters, where M is the number of states or rocks composing an impedance well log. The probability mass function of the states provides M-1 parameters, and the “blockiness” of the log determines the remaining degree of freedom. Synthetic impedance and reflectivity logs constructed using the Markov model mimic the blockiness of the original logs. Both synthetic impedance and reflectivity are shown to be Bussgang, i.e., if the sequence is input into an instantaneous nonlinear device, then the correlation of input and output is proportional to the autocorrelation of the input. The final part of the paper uses the stochastic model in formulating an algorithm that transforms a deconvolved seismogram into acoustic impedance. The resulting function is blocky and free of random walks or sags. Low‐frequency information,...read more
Citations
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Journal ArticleDOI
A strategy for nonlinear elastic inversion of seismic reflection data
TL;DR: In this article, the inverse problem of interpreting seismic reflection data can be posed with sufficient generality using the concepts of inverse theory, which consists of obtaining the Earth model for which the predicted data best fit the observed data.
Book
Quantitative Seismic Interpretation: Applying Rock Physics Tools to Reduce Interpretation Risk
TL;DR: In this paper, the authors present a statistical rock physics approach combining rock physics, information theory, and statistics to reduce uncertainty in seismic data. But they do not discuss the use of statistical methods for quantitative seismic interpretation.
Journal ArticleDOI
An investigation of the spectral properties of primary reflection coefficients
Andrew T. Walden,J. W. J. Hosken +1 more
TL;DR: In this article, the authors investigated the form of the nonwhiteness found in the reflection coefficients from a wide variety of rock sequences around the world, and the observed power spectra were shown to be consistent with a simple model for the logarithm of acoustic impedance consisting of a mixture of processes where the distribution of (time) scale parameters is reciprocal.
Journal ArticleDOI
Multichannel blind deconvolution of seismic signals
Kjetil F. Kaaresen,Tofinn Taxt +1 more
TL;DR: In this paper, a new algorithm for simultaneous wavelet estimation and deconvolution of seismic reflection signals is given, which combines a priori knowledge and data to derive a maximum a posteriori estimate.
Journal ArticleDOI
2-D random media with ellipsoidal autocorrelation functions
L. T. Ikelle,S. K. Yung,F. Daube +2 more
TL;DR: In this article, the authors consider a two-dimensional (2-D) model where the large scale inhomogeneities are represented by a homogeneous medium and small scale inhomalogeneities were randomly distributed inside the homogenous medium, characterized by an ellipsoidal autocorrelation function in the medium properties.
References
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Journal ArticleDOI
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TL;DR: In this paper, the authors provide an explicit treatment of the mathematical foundations on which applications of Markov processes in geology depend, and provide a mathematical comparison between the two approaches.
Journal ArticleDOI
Inversion of seismograms and pseudo velocity logs
M. Lavergne,C. Willm +1 more
TL;DR: Pseudo velocity logs can be obtained by seismogram inversion, using true amplitude processing and detailed investigation of move-out velocities as mentioned in this paper, but the precision of the results depends on the quality of the seismic data and on the possibility of deconvolving without increasing the noise.
Book
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TL;DR: In this article, a random walk simulation model of alluvial-fan deposition is presented, which is based on Markov Models of Repose-Period Patterns of Volcanoes.