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Non-Euclidean Spatial Covariance for Bayesian Post-Stack Inversion and Ordinary Kriging with Hamiltonian Fast Marching
- Publisher: European Association of Geoscientists & Engineers
- Source: Conference Proceedings, Fifth EAGE Conference on Petroleum Geostatistics, Nov 2023, Volume 2023, p.1 - 5
Abstract
Summary
We introduce a novel workflow that integrates non-Euclidean shortest path distances (SPD) using locally varying geometric anisotropy (LVA) to define spatial covariance matrices. The resulting covariance can be used in both geophysical and geostatistical algorithms where spatial continuity is utilized. The use of LVA in proposed methodology bypasses the limitation of constant geometric anisotropy traditionally assumed in geostatistical methods; it produces a more accurate covariance and generates more geologically realistic models. The Hamiltonian Fast Marching (HFM) algorithm is more precise than other approaches to evaluate SPD, such as the Dijkstra algorithm. While robust spatial covariance estimation needs redundant measurements in any direction, in petroleum exploration only the vertical direction is sampled sufficiently. Lateral direction data scarcity is mitigated by extracting the local dips and anisotropy ratios along the major and minor continuity directions from the seismic data itself. We demonstrate the HFM method on Bayesian post-stack inversion and LVA ordinary kriging (OK) for estimating acoustic impedance. The proposed workflow is also valid for other inversion algorithms, varieties of kriging, and sequential Gaussian simulation.
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