Continuous Wavelet Transformation to Quantify small-scale Cycles of Petrophysical Properties; a New Approach Applied in a Potential Disposal Repository of Nuclear Waste, SW Hungary

Continuous Wavelet Transformation (CWT) was applied to study the small-scale repetitive oscillations of porosity distribution patterns in a 5 m silty-claystone core sample of the Boda Claystone Formation. We handled the fluctuations in voxel porosity averages over unequal depth distributions as signals over uneven time intervals. The strength of wavelet analysis lies in the ability to study the fluctuation of a signal in detail, i.e., the wavelet transforms permit automatic localization of the cyclic attributes' sequences both in time (the depth domain) and according to their frequency (the frequency domain). Thereupon, three main frequency branches (cycles) were discerned: small scale (5, 6.67, and 11 cm), intermediate scale (20, 30 cm), and large scale (66.67 cm). Depending on the CWT coefficients magnitude plot, we were able to detect the developments of porosity oscillation according to the depth variable. Thus, small-scale cycles were seen throughout the core sample., the intermediate-scale cycles were strong in the upper parts of the core sample and dwindled toward greater depths, and the large cycle was predominant in the lower part of the core sample. The cross-correlation of the wavelet coefficients of porosity and rock-forming components allows a detailed study of the inter-dependence of such parameters as their relationship changes over time. The distinct peaks at zero lag indicates that the measured wavelet coefficient series were contemporaneously correlated; their strong positive correlations suggest that both examined series respond similarly and simultaneously to other exogenous factors. The results emphasize that cyclical porosity fluctuations at all scales would concern three main factors; sediment deposition, diagenetic processes, and structural deformation (i.e., convolute laminations).