Modeling of nonlinear passage of acoustic waves caused by underground fracturing through the lithosphere S. Koshevaya a, * , M. Hayakawa b , V. Grimalsky c , J. Siqueiros-A a , R. Perez-E d , A. Kotsarenko d a Autonomous University of State Morelos, Research Center of Applied Sciences and Engineering, CIICAp, FCQeI Av. Universidad 1001, Z.P. 62210, Cuernavaca, Mor., Mexico b The University of Electro-Communication, Chofu, Tokyo 182, Japan c National Institute of Astrophysics, Optics and Electronics (INAOE), P.O. 51 and 216, Z.P. 72000, Puebla, Mexico d UNAM, Centro de Geociencias, Campus Juriquilla, Apartado Postal 1-742, Queretaro, 76230, Qro, Mexico Received 30 May 2003; received in revised form 9 September 2003; accepted 20 September 2003 Abstract The nonlinear passage of the acoustic waves through the lithosphere to the surface of the Earth during earthquakes and strong underground explosions is analyzed in this report. The underlying mechanism for this is the nonlinear elastic modulus. The waves are excited at the underground source of the earthquakes. The passage of the acoustic waves propagating almost vertically upward leads to a change of the spectrum. The wide spectrum of the acoustic waves up to the radio wave range is assumed to be produced by the fracturing of the rock at the surface. This has been observed by means of satellite measurements and radio telescope investi- gation of meteor bombing of the Moon. If the fracture occurs at depth corresponding to high frequencies, the waves transform, through nonlinear interactions, into low and super low frequency waves. Low and super low elastic displacement waves reach the surface and produce a seismograph response. In the report the nonlinear excitation of ultra-low frequency (ULF) acoustic waves caused by low frequency (LF) seismic acoustic burst is also discussed. An analysis of the nonlinear transformation of LF acoustic waves (f  100 Hz) into ULF (f 6 1 Hz) waves is presented. The LF wave is excited as the burst-like envelope of a finite transverse scale by the underground seismic motion caused seismic activity of the Earth. Then, it propagates upwards and is subject to both a nonlinear process and dissipation. The nonlinearity leads to the generation of higher harmonics and, thus, to a saw-like wave structure, and also to an increase of the ULF part of the wave spectrum. This process takes place underground at a depth of about 50–30 km. Ó 2004 Elsevier Ltd. All rights reserved. 1. Introduction It is very important to investigate the mechanisms of energy flow from the lithosphere into the atmosphere and the ionosphere caused by natural hazards (seismic and volcano activity, for example experiment MASSA (Galperin, 1985)). All mechanisms have different pre- cursors (Warwick, 1963) due to three basic channels of the lithosphere-ionosphere connection, namely, electro- magnetic, geochemical, and acoustic channels (Gokh- berg et al., 1995). The electromagnetic, optic, acoustic and geochemical precursors are the most common, but there are also perturbations of the density of plasma in F and E-layers; anomaly in the absorption of cosmic radio emission; strong changes of the ionosphere parameters and moving of E and F-layers; variations of electric E and magnetic H fields and its perturbations; perturba- tions of the electromagnetic waves, first of all, ELF (extremely low frequency) and VLF (very low fre- quency); perturbation (increasing) of the intensity of the luminescence of the ionosphere in the main emission of the atomic oxygen at k ¼ 5577 and 6300 A. Finally, other phenomena were observed such as anomalies by the propagation of radio waves above volcanoes and epicenters of strong seismic active sites; perturbation of the sporadic Es-layer emission in the ionosphere; geo- chemical and biological processes in seas and ocean, and so on. The same appears before the volcanic activity * Corresponding author. Tel.: +52-17-39-7084; fax: +52-17-329- 7084. E-mail address: svetlana@uaem.mx (S. Koshevaya). 1474-7065/$ - see front matter Ó 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.pce.2003.09.021 Physics and Chemistry of the Earth 29 (2004) 599–605 www.elsevier.com/locate/pce