Combining and Forward-Carrying Overlapping Wellbore Surveys: An Open Implementation Demonstrated on Public Volve Data

Version 2.1. An open, reproducible implementation (welleng) for combining and forward-carrying overlapping wellbore surveys, demonstrated end-to-end on the public Volve dataset. Combination uses the best linear unbiased estimator on the analytical arc-faithful interior covariance so the result is continuous in measured depth; forward-carry conditions an MWD run's systematic (magnetic) error on an overlapping gyro and carries the reduced systematic into the gyro-free section below. v2.0 added the covariance EOU (formerly the 'covariated' ellipse of uncertainty): the whole well as one block covariance with off-diagonal cross-station correlation, so conditioning on a single gyro station propagates through the correlation to tighten the entire run (on F-4, about a third at total depth from one station, about a half from the whole overlap), with the forward-carry recovered as its forward-only slice; plus an arc-faithful off-station covariance-EOU surface. The covariance-EOU framework is the method of K. Bulychenkov (2026, concept doi:10.5281/zenodo.22148755, v1 doi:10.5281/zenodo.22148756); this paper is its open, validated implementation and a quantified demonstration on public field data. v2.1 adds an overlap-innovation QC gate before conditioning, the smooth separation-factor-constraint application for gradient-based planning, and an open-benchmark framing, following peer review by K. Bulychenkov. Estimation theory (BLUE fusion, Gaussian conditioning) is standard and cited; validated against an independent stacked-GLS oracle (1e-8), a Monte-Carlo oracle, and reproduces the ~29% equal-accuracy reduction of Bang (2019, SPE-195621). Volve data (c) Equinor and the Volve licence partners, CC BY 4.0. Use requires citation of this work and welleng.