Monte Carlo Uncertainty Estimation for Logging Parameter Correlation
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Solution Overview
Problem
Current methods for determining formation representation using logging parameters and seismic volume parameters are inadequate due to incorrect assumptions about measurement errors and lack of uncertainty representation in three-dimensional volumes.
Innovation Solution
A computer-implemented method that maps one-dimensional logging parameters to three-dimensional volumes by correlating them with seismic interval velocities, using binning and Monte Carlo simulations to establish uncertainties and regression curves, thereby providing a more accurate representation of formation characteristics.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If least-square regression is used to correlate logging parameters to seismic interval velocity, then a correlation can be established, but the measurement errors and non-systematic errors are not properly represented leading to incomplete formation characterization
Solution Approach 1:
The patent transforms the single-point least-square regression into a probabilistic framework by introducing random variables for both logging parameters and seismic interval velocity. Multiple regression curves are generated through Monte Carlo simulations, changing the parameter representation from deterministic to stochastic, which properly captures measurement errors and uncertainties in the correlation.
2Device complexity
If measurement errors are assumed to occur only in logging parameter measurements, then the least-square regression can be simplified, but this assumption is incorrect and does not provide full representation of formation characteristics
Solution Approach 1:
The patent segments the error sources into distinct components: measurement errors in logging parameters, errors in seismic interval velocity, and non-systematic errors. By separating and independently modeling each error source with appropriate probability distributions, the complex uncertainty propagation becomes manageable while maintaining high precision in formation characterization.
3Ease of operation
If non-systematic errors are assumed to be normally distributed, then the regression analysis becomes tractable, but this assumption is typically incorrect and limits the accuracy of uncertainty representation
Solution Approach 1:
The patent implements a dynamic, adaptive approach where the distribution of non-systematic errors is not fixed but determined empirically from the data itself. The Monte Carlo simulations allow the error distributions to be flexibly modeled based on actual observations, making the regression analysis both tractable and accurately reflective of real-world uncertainty patterns.
Data Source
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AI summary
A method and computer-readable medium for establishing an uncertainty for obtained values of a one-dimensional logging parameter mapped to a three-dimensional volume is disclosed. A relation is formed between the obtained values of the logging parameter and a volumetric parameter of the three-dimensional volume. A set of representative data points is obtained that relates the obtained values of the logging parameter to the volumetric parameter by binning the obtained values. A plurality of regression curves are then determined, wherein each regression curve is obtained by adding a random error to the set of representative data points to obtain a set of randomized data points and performing a regression analysis using the set of randomized data points. The plurality of regression curves are used to establish the uncertainty for the values of the logging parameter in the three-dimensional volume.