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

TL;DR

This paper introduces a workflow for accurately sizing representative volume elements in cylindrical CT scans with nonstationary features by analyzing spectral convergence after trend removal.

Contribution

It presents a practical method for determining REV size under nonstationary conditions using spectral analysis and axial detrending, demonstrated on complex geological samples.

Findings

Method yields REV sizes of approximately 93mm diameter and 83mm height for the studied core.

Spectral convergence stabilizes at specific sizes, ensuring representative microstructural statistics.

Axial detrending improves the robustness of covariance and spectral estimates in nonstationary data.

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.