Stochastic Inversion of Geophysical Data for Earth Model Parameters
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Solution Overview
Problem
Current methods for estimating model parameters from geophysical data, such as seismic and electromagnetic data, face challenges in accurately discriminating fluid saturation and porosity due to limited spatial resolution and reliance on gradient-based techniques that may not converge to the global model, resulting in insufficient model parameter error estimates.
Innovation Solution
A sampling-based stochastic method, specifically using Markov Chain Monte Carlo (MCMC) techniques for importance sampling, is employed to generate boundary-based multi-dimensional models, allowing for joint inversion of multiple geophysical data sets and providing accurate probability density functions (PDFs) of model parameters, which quantify variance and improve estimation of fluid saturation and porosity.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If gradient-based inversion techniques are used to minimize object functions, then computational efficiency is improved, but model parameter error estimates become inaccurate and insufficient
Solution Approach 1:
The patent replaces gradient-based deterministic inversion methods with a stochastic sampling-based approach (Markov Chain Monte Carlo). This substitution transitions from a mechanical optimization process to a probabilistic sampling process that explores the model parameter space more thoroughly, providing accurate error estimates while maintaining computational feasibility through efficient sampling algorithms.
Solution Approach 2:
The patent changes the fundamental approach from minimizing an object function to sampling from probability density functions. By transforming the inversion problem from a deterministic optimization task to a stochastic sampling task, the method achieves both computational efficiency and accurate error characterization through proper sampling techniques.
2Measurement precision
If joint inversion of multiple geophysical data sets is performed, then estimation accuracy of earth model parameters is improved, but computational burden increases
Solution Approach 1:
The patent segments the joint inversion problem into separate probability density function estimations for different data types (seismic and EM). By treating each data set's contribution separately and combining them through Bayesian inference, the method reduces computational complexity while maintaining the benefits of joint inversion for improved parameter estimation accuracy.
3Measurement precision
If sampling-based stochastic methods are used for joint inversion, then accurate probability density functions of model parameters are obtained, but computational time increases
Solution Approach 1:
The patent performs preliminary sampling and importance weighting to identify the most significant regions of the model parameter space before conducting the full inversion. This preliminary action allows the stochastic method to focus computational resources on high-probability areas, reducing overall computational time while maintaining accurate PDF estimation.
Data Source
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AI summary
A computer implemented stochastic inversion method for estimating model parameters of an earth model. In an embodiment, the method utilizes a sampling-based stochastic technique to determine the probability density functions (PDF) of the model parameters that define a boundary-based multi-dimensional model of the subsurface. In some embodiments a sampling technique known as Markov Chain Monte Carlo (MCMC) is utilized. MCMC techniques fall into the class of "importance sampling" techniques, in which the posterior probability distribution is sampled in proportion to the model's ability to fit or match the specified acquisition geometry. In another embodiment, the inversion includes the joint inversion of multiple geophysical data sets. Embodiments of the invention also relate to a computer system configured to perform a method for estimating model parameters for accurate interpretation of the earth's subsurface.