Representative-Volume Sizing in Finite Cylindrical Computed Tomography by Low-Wavenumber Spectral Convergence

Choosing a representative element volume (REV) from finite cylindrical computed tomography (CT) scans becomes ambiguous when a key field variable exhibits a slow axial trend, which may reflect both genuine geological variability and CT acquisition/reconstruction artifacts, because estimated statistics can change systematically with subvolume size and position rather than converging under simple averaging. A practical workflow is presented for sizing an REV under nonstationary conditions by first suppressing axial drift/trend to obtain a residual field suitable for second-order analysis, and then selecting the smallest analysis diameter for which the low-wavenumber content stabilizes within a prescribed tolerance. The approach is demonstrated on Thalassinoides-bearing rocks, whose branching, interconnected burrow networks introduce heterogeneity at length scales comparable to typical laboratory core diameters, making imaging-based microstructural statistics and downstream digital-rock estimates highly sensitive to the chosen subvolume. From segmented data, a scalar “burrowsity” field–capturing burrow-related pore spaces and infills–is defined, and axial detrending (with optional normalization) is applied to mitigate acquisition drift and nonstationary trends, while the subsequent covariance/spectral test is evaluated on nested cylinders consistent with the core geometry. Representativeness is then posed as a diameter-convergence problem on nested inscribed cylinders: the two-point covariance and its isotropic spectral counterpart C^ are estimated, and the smallest diameter at which the low-wavenumber plateau becomes stable is selected. Applied to a segmented Thalassinoides core, the method identifies a minimum analysis cylinder of approximately DREV≈93mm and HREV≈83mm, enabling reproducible correlation-scale reporting and connectivity-sensitive property estimation.