Search for strange attractors in magnetic field data: An example from a tertiary volcanic area near Bonn, Germany

Abstract

Spatial variations of the magnetic field, measured at the Earth's surface, are mainly due to geological inhomogeneities within the crust. The present state of the crust, in turn, reflects its past dynamical processes and evolution. We analyzed the magnetic field intensity along a few but densely sampled profiles in a Tertiary volcanic province near Bonn, Germany. The aim was to find out whether the variation of the magnetic intensity can be related to a deterministic, although chaotic, generating system or to a stochastic one. In the former case, the geodynamical history would depend on a few degrees of freedom, whereas in the latter case, the parameters to take into account were so many that a statistic approach appears to be more suitable. Since strange attractors do not emerge from the analyzed data, we exclude the presence of a chaos generating system. Autocorrelation functions and a rescaled-range analysis, on the other hand, reveal and quantify a certain degree of correlation among successive data points and allow calculation of a range of spectral exponents in log-log diagrams, which are clearly distinct from those of white noise and Brownian motion. Only one of the profiles exhibits similarity to uncorrelated or white noise. In this case, the signal variations do not result from the local geology but from a buried gas pipe-line, aligned subparallel to that profile. If self-organized crustal evolution generally produces signatures that can be described as correlated noise, within a limited bandwidth of spectral exponents, erraneous or disturbed data could eventually be discriminated from records containing purely natural data by applying analysis tools of the dynamic system theory together with autocorrelation tests.