Chaotic behaviour of coda waves in the eastern Pyrenees

SUMMARY 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 deterministic 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 system (i.e. the recorded ground velocity of the medium) was characterized by means of the correlation dimension. In all cases we obtained a fractal dimension that ranges between 3.43 and 3.94. The Kolmogorov entropy was estimated from the correlation function; in all cases it was positive and finite, and the computation of the divergence of nearby orbits revealed positive, finite maximum Lyapunov exponents for all events. Thus, all evidence is in favour of the hypothesis that the attractor is a strange attractor, and that the propagation is chaotic deterministic. Errors in the measurements are estimated at 8 per cent for the correlation dimension and 12 per cent for the Lyapunov exponent. Because of natural noise in the seismic records, the above determinations should be considered as lower bounds. The above results constitute strong evidence in favour of chaotic coda‐wave propagation in the zone under study, and suggest that the chaotic behaviour is generated by multiple scattering. To account for characteristics such as those found, mathematical models should be formulated in terms of non‐linear equations with a minimum of four degrees of freedom.