DETRENDED FLUCTUATION ANALYSIS OF THREE-DIMENSIONAL DATA: APPLICATION TO SOIL X-RAY CT SCANS

Abstract

In this work, we compare three distinct schemes for detrended fluctuation analysis (DFA) of three-dimensional (3D) [Formula: see text] data sets: (i) an [Formula: see text] set of one-dimensional (1D) DFA runs for each vertical line of length [Formula: see text], (ii) a set of [Formula: see text] two-dimensional (2D) DFA runs for each of the [Formula: see text] planes along the vertical direction, and (iii) a single 3D DFA run. The objective of this work is two-fold: (i) to compare the performance of 1D, 2D, and 3D DFA methods in terms of compatibility as well as the richness of obtained results, and (ii) to demonstrate how these three complementary approaches shed new light on the complexity of the structure of the two real soil samples, through the analysis of grayscale high-resolution X-ray computed tomography scan images.