CHAOTIC BEHAVIOR OF CODA WAVES IN THE EASTERN PYRENEES

S-coda waves of 10 local events that occurred in the eastern Pyrenees and were recorded at La Cerdanya seismic station have been analysed to determine whether the complexity they present is chaotic deterministi c or random. The data were first subjected to a qualitative analysis, the construction of a phase portrait by the delay method. This clearly displays the possibility of deterministic chaos. Under the assumption that part of the coda can be considered stationary, in the sense that transients are no longer present, we performed a non-linear analysis of coda waves. The geometry of the attractor of the motion of the syst em (i.e. the recorded ground velocity of the medium) was characterized by means of the correlation dimension. In all cases we obtained a fra ctal dimension that ranges between 3.43 and 3.94. The Kolmogorov entro py was estimated from the correlation function; in all cases it was po sitive and finite, and the computation of the divergence of nearby orb its revealed positive, finite maximum Lyapunov exponents for all event s. Thus, all evidence is in favour of the hypothesis that the attracto r is a strange attractor, and that the propagation is chaotic determin istic. Errors in the measurements are estimated at 8 per cent for the correlation dimension and 12 per cent for the Lyapunov exponent. Becau se of natural noise in the seismic records, the above determinations s hould be considered as lower bounds. The above results constitute stro ng evidence in favour of chaotic coda-wave propagation in the zone und er study, and suggest that the chaotic behaviour is generated by multi ple scattering. To account for characteristics such as those found, ma thematical models should be formulated in terms of non-linear equation s with a minimum of four degrees of freedom.