Gaussian mixture Markov chain Monte Carlo method for linear seismic inversion

Abstract

We have developed a Markov chain Monte Carlo (MCMC) method for joint inversion of seismic data for the prediction of facies and elastic properties. The solution of the inverse problem is defined by the Bayesian posterior distribution of the properties of interest. The prior distribution is a Gaussian mixture model, and each component is associated to a potential configuration of the facies sequence along the seismic trace. The low frequency is incorporated by using facies-dependent depositional trend models for the prior means of the elastic properties in each facies. The posterior distribution is also a Gaussian mixture, for which the Gaussian component can be analytically computed. However, due to the high number of components of the mixture, i.e., the large number of facies configurations, the computation of the full posterior distribution is impractical. Our Gaussian mixture MCMC method allows for the calculation of the full posterior distribution by sampling the facies configurations according to the acceptance/rejection probability. The novelty of the method is the use of an MCMC framework with multimodal distributions for the description of the model properties and the facies along the entire seismic trace. Our method is tested on synthetic seismic data, applied to real seismic data, and validated using a well test.

Deep Learning for Geophysics: Current and Future Trends

“…One of the remaining questions associated with applying DL in geophysics is related to whether the results of DL-based methods without a solid theoretical foundation can be trusted. DL-based uncertainty analysis methods include Monte Carlo dropout (Gal & Ghahramani, 2016), Markov chain Monte Carlo (MCMC) (de Figueiredo et al, 2019), variational inference (Subedar et al, 2019), etc. For example, in Monte Carlo dropout, dropout layers are added to each original layer to simulate a Bernoulli distribution.…”

Choosing between Gaussian and MPS simulation: the role of data information content—a case study using uncertain interpretation data points

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Direct Geostatistical Seismic Amplitude Versus Angle Inversion for Shale Rock Properties

“…In a statistical seismic inversion, the inverse solution is expressed as a probability density function in the model parameters space. There are two main statistical-based seismic inversion approaches: Bayesian linearized methods (see [5], [8], [10], and [11]) and those based on geostatistical simulation as model perturbation technique (see [12]- [15]). These methods have been described in numerous works, summarized in [1], [4], and [15], which include the following list of most-cited works: [2], [3], [6]- [8], [12], [13], and [16]- [25].…”

“…Geostatistical-based inversion methods are iterative procedures that use a global optimizer based on different stochastic optimization algorithms, such as simulated annealing, genetic algorithms, probability perturbation method, This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ gradual deformation, and neighborhood algorithm (see [11]- [13], [15], [27]- [32]), to ensure convergence from iteration to iteration. These methods do not imply any assumptions about the prior distribution of the property of interest or the errors present in the data, and consequently, and contrary to Bayesian linearized inversion methods, analytical solutions are not available.…”