Scaling and extended scaling in sediment registers of a paleolake perturbed by volcanic activity

We analyze a sequence of density variations of sedimentary material from an extinct paleolake of the state of Tlaxcala, Mexico, which we previously obtained by means of computer-aided tomography [J. Miranda, A. Oliver, G. Vilaclara, R. Rico-Montiel, V.M. Macias, J.L. Ruvalcava, M.A. Zenteno, Nucl. Instrum. Methods Phys. Res. B 85 (1994) 886]. In the stratified blocks chiselled out of mines at the lake bed, low-density sediments have a high concentration of diatomite, while high-density strata show a considerable amount of material external to the lake, mostly of volcanic origin. Two regions can be distinguished by visual inspection: a darker and older one which we attribute to a strongly externally perturbed regime, and a whiter more recent one which appears to have been subjected to less frequent volcanic perturbations. By means of a scaling analysis of the distribution function of density fluctuations, we show that for the most recent region there is a range of scales where these fluctuations present a self-similar behavior. We attribute this observation to a rare event response, namely, the onset of correlations in the lake relaxation processes to steady-state conditions following intense volcanic disturbances. Based on scaling properties of the structure function, we also show that the complete data series presents extended self-similarity as encountered in turbulence studies [R. Benzi, S. Ciliberto, R. Tripiccione, C. Baudet, F. Massoli, S. Succi, Phys. Rev. E 48 (1993) R29]. Our characterization of the statistical behavior of the density fluctuations contributes to our knowledge of the volcanic activity over a period of thousands of years, as well as aspects of ecological interest of the lake's response to these disturbances [G. Vilaclara, E. Ugalde, E. Cuna, G. Martinez-Mekler, Complex dynamics of the evolution of a Paleolake subjected to volcanic activity: geology meets ecology, submitted for publication]. Our approach can be implemented in general to other situations where a scaling characterization may be of interest.