Novel doorways and resonances in large-scale classical systems

¹ Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México - P.O. Box 48-3, 62251 Cuernavaca, Mor., Mexico
² Instituto de Física, Universidad Nacional Autónoma de México - P.O. Box 20-364, 01000 México, D. F., Mexico
³ Centro Internacional de Ciencias, A. C. - P.O. Box 6-101, C.P. 62131 Cuernavaca, Mor., Mexico

^a mendez@fis.unam.mx

Received: 1 December 2010
Accepted: 29 March 2011

Abstract

We show how the concept of doorway states carries beyond its typical applications and usual concepts. The scale on which it may occur is increased to large classical wave systems. Specifically we analyze the seismic response of sedimentary basins covered by water-logged clays, a rather common situation for urban sites. A model is introduced in which the doorway state is a plane wave propagating in the interface between the sediments and the clay. This wave is produced by the coupling of a Rayleigh and an evanescent SP-wave. This in turn leads to a strong resonant response in the soft clays near the surface of the basin. Our model calculations are compared with measurements during Mexico City earthquakes, showing quite good agreement. This not only provides a transparent explanation of catastrophic resonant seismic response in certain basins but at the same time constitutes up to this date the largest-scale example of the doorway state mechanism in wave scattering. Furthermore the doorway state itself has interesting and rather unusual characteristics.