Cross-mode modulation eect in Schumann resonances Y.M. Yampolski*, V.S. Beley, S.B. Kascheev, B.V. Lazebny, V.E. Paznukhov, A.G. Rokhman Institute of Radio Astronomy, National Academy of Sciences of Ukraine, 4 Krasnoznamennaya St, Kharkov, 310002, Ukraine Received 1 October 1998; received in revised form 29 March 1999; accepted 27 April 1999 Abstract Nonlinear interactions of the ELF (4±40 Hz) signals excited by worldwide lightning activity in the Earth- ionosphere cavity are investigated. A special algorithm for detecting weak nonlinearities, based on the calculation of a coherence function between the received signal and the multiplicative response of a digital analyzer, has been developed. Using long-term observations of the ELF signals, combination lines at double, sum and dierence frequencies of the ®rst three Schumann modes were detected. Possible mechanisms for the cross-modulation due to natural nonlinear eects in the atmosphere and lower ionosphere are discussed. # 1999 Elsevier Science Ltd. All rights reserved. 1. Introduction The propagation of radio waves through the iono- sphere generally results in nonlinear interactions of the electromagnetic ®eld with the plasma, modifying the electrodynamical characteristics of the latter. The ques- tion of principal importance for the observation of such eects is the sensitivity of the methods and devices applied for the registrations. There are two basic approaches underlying the diagnostics of non- linear interactions. The ®rst is based on investigating the characteristics of the ®eld passing through and act- ing upon the medium, while the second suggests diag- nostics of the medium itself with the use of `independent sensors', like probe signals from external sources, stimulated radiation of the ionosphere, etc. It should be noted that the threshold levels of the exter- nal ®elds for stimulating nonlinear eects in the iono- spheric plasma are quite low, varying between 10 5 and 10 2 V/m for dierent types of the eects at dier- ent heights (Gurevich and Shwarzburg, 1973). Such estimates made in the late sixties and early seventies stimulated the construction of special powerful ground-based transmitting systems to modify the iono- sphere. Active experiments with the `heating' facilities in the USA, the USSR (and later in Russia and Ukraine), and Norway allowed the investigation of a series of new phenomena in the ionosphere (Stubbe, 1996). Obviously, the implementation of such exper- iments is very complicated, both from technical and ®nancial points of view. Besides, the arti®cial modi®- cation of the terrestrial plasma encounters protests from green movements. Meanwhile, other possibilities exist to investigate nonlinear interactions between natural wave ®elds and the ionosphere, involving no active (i.e. dedicated transmitters) experiments. Such an approach was realized by Yampolski et al. (1997), where a cross-modulation eect between the Schumann resonances (SR) and round-the-world HF signals was detected and interpreted. The role of the Journal of Atmospheric and Solar-Terrestrial Physics 61 (1999) 693±699 1364-6826/99/$ - see front matter # 1999 Elsevier Science Ltd. All rights reserved. PII: S1364-6826(99)00024-3 * Corresponding author Tel.: +7-572-448-579; fax: +7-572- 476-506. E-mail address: yampol@rian.ira.kharkov.ua (Y.M. Yampolski)