Daniel Barker

We describe different approaches that were used to test and investigate potential improvements in various aspects of the posterior Markov chain. This includes different ways of combining Up and Down chains, and inclusion of all available transitions within a window. Additionally, an alternative algorithm for computing the posterior Markov chain was tested, relying on forward-backward algorithm, using a higher order chain to obtain the posterior Lfcs. Proposed approaches were tested on both PCube paper example and Volund dataset, and results from the latter are presented. First approaches yielded some changes, but not significant improvements implying that current approach is a robust and reasonable choice. On the other hand, the proposed alternative algorithm produced different results. However, it is not straightforward to conclude, whether the results are to be preferred over the ones produced by the existing approach.

We describe the work done to estimate residual time-shifts (after initial correction) using PCube+ likelihood calculations. The method shows some promise, but low-frequency variations of likelihoods currently cause too much alignment discrepancy to give a satisfactory solution.

The GIG, Geophysical Inversion to Geology, consortium is a research consortium run by Norwegian Computing Center, with the aim of developing new understanding, new methods and software for obtaining reservoir properties from geophysical measurements This note gives a summary of the work in 2021 and the suggested work plan for 2022. The final work plan for 2022 will be decided on the annual meeting in Jan 2022.

The GIG, Geophysical Inversion to Geology, consortium is a research consortium run by Norwegian Computing Center, with the aim of developing new understanding, new methods and software for obtaining reservoir properties from geophysical measurements This note gives a status of the GIG consortium after its fourth year of operation, and also gives the suggested work plan for 2021.

We generate independent Gaussian random variables on a regular grid and use a spatial filter to smooth the independent random variables to obtain a spatially correlated Gaussian random field. The FFT is used to speed up the smoothing since convolution is a simple cell by-cell multiplication in the Fourier domain. A representation of the spatial convolution filter in the Fourier domain is efficiently obtained from the FFT of any stationary correlation function. Since FFT is cyclic, the grid must be padded to ensure that opposite sides are uncorrelated. The size of the padding is discussed in detail. Most standard covariance functions fail to be positive definite on finite cyclic domains. This causes striping artifacts in the final simulated realizations and failure to meet statistical properties such as variogram reproduction in the simulated realizations. These problems are addressed and solutions are provided to ensure near perfect statistical properties of the generated realizations. The method is fast and can generate a hundred million grid cell realization in approximately 1.5 minutes on a standard laptop PC. The method scales approximately linearly in the number of grid cells.