Representative-volume sizing in finite cylindrical computed tomography by low-wavenumber spectral convergence

Abstract

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, reflecting either geological variability or CT acquisition/reconstruction artifacts. In such cases, estimated statistics may vary systematically with subvolume size and position rather than converging by simple averaging. We present a practical workflow 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 spectral content stabilizes within a prescribed tolerance. The method is demonstrated on \textit{Thalassinoides}-bearing rocks, where branching burrow networks introduce heterogeneity at length scales comparable to laboratory core diameters, making imaging-based microstructural statistics and digital-rock estimates sensitive to subvolume choice. From segmented data, we define a scalar ``burrowsity'' field capturing burrow-related pore spaces and infills. Axial detrending, with optional normalization, mitigates acquisition drift and nonstationary trends, while covariance/spectral convergence is evaluated on nested cylinders consistent with the core geometry. Representativeness is posed as diameter convergence on nested inscribed cylinders: the two-point covariance and isotropic spectrum $\widehat{C}$ are estimated, and the smallest diameter at which the low-wavenumber plateau becomes stable is selected. Applied to a segmented \textit{Thalassinoides} core, the method gives $D_{\mathrm{REV}}\simeq 93~\mathrm{mm}$ and $H_{\mathrm{REV}}\simeq 83~\mathrm{mm}$, enabling reproducible correlation-scale reporting and connectivity-sensitive property estimation.