**1. Introduction**

The study of the physical process connected to the preparation and onset of an earthquake is a topic of increasing interest among the scientific community, also in view of the societal impact of these phenomena. One of the challenges of these studies is to identify physical phenomena which can be directly connected, without ambiguity, with the earthquake geographical location and time window. Most of the evidence in the literature is, indeed, of a statistical nature, while event based, causal observations of the connection among ground, ionosphere and magnetosphere are much more difficult to be convincingly demonstrated. Regarding the statistical evidence, one of the the most interesting and promising result is related to electromagnetic and ionospheric disturbances occurring before and during seismic activities. Examples of these results are the experimental investigation of the lithosphere-ionosphere-magnetosphere coupling [1–3] with the observation of "anomalous" pulses of electromagnetic (EM) emissions in the frequency interval between a few Hz and up to few tens of kHz, as well as the more recent observations of changes of the density of the charged trapped particles registered by satellites [4,5]. More recently, investigations of earthquake preparation phenomena using data registered by the DEMETER satellite provided statistical evidence for spectral damping of VLF (very low frequency) radio signals at F-region altitudes and within a radius of 1000–5000 km from the earthquake epicenter, about 0–3 weeks before the event [6]. In addition, using DEMETER electric and

**Citation:** Piersanti, M.; Burger, W.J.; Carbone, V.; Battiston, R.; Iuppa, R.; Ubertini, P. On the Geomagnetic Field Line Resonance Eigenfrequency Variations during Seismic Event. *Remote Sens.* **2021**, *13*, 2839. https:// doi.org/10.3390/rs13142839

Academic Editors: Paolo Mazzanti and Saverio Romeo

Received: 8 June 2021 Accepted: 15 July 2021 Published: 19 July 2021

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magnetic field data, Bertello et al. [7] found an EM wave at ∼300 Hz propagating 2 days before the L'Aquila 2009 earthquake event. In order to better understand the physical processes present in the lithosphere-atmosphere-magnetosphere interactions, many studies focused on the disturbances induced on the atmospheric electric field [8], on the anomalous geomagnetic pulsations [9,10], as well as on other anomalous disturbances in the ionosphere [11] and magnetosphere [12,13]. Searches for possible seismo-ionospheric effects were also performed before the earthquake by the satellite Interkosmos-19 operating at F-region altitudes, providing for the first time evidence for an increase of both the intensity of VLF noise, in the frequency range between 140 Hz to 15 kHz, and for disturbances of the electron density at a distance from the epicentres up to a few 1000 km [3,14]. More recently, Carbone et al. [15], Piersanti et al. [16] started the development of an analytical model of the coupling between lithosphere-atmosphere-ionosphere-magnetosphere to be submitted to detailed experimental verification (M.I.L.C.). In the M.I.L.C. model the coupling during active seismic conditions is described by the onset of atmospheric and ionospheric EM and particle anomalies: a first successful test of the model was the analysis of the 2018 Bayan EQ, when a series of correlated phenomena were detected both by ground sensors and by low earth orbiting satellites (∼500 km) around the time of EQ occurrence. The authors explained and modelled the experimental observations as due to the generation of an acoustic gravity wave (AGW) induced by the EQ which mechanically perturbed the ionospheric medium causing both an EM emissions and plasma waves. Interestingly, the model predicts a clear decrease of the magnetospheric FLR *f* ∗ in concomitance of the EQ occurrence, which has also been observed. This phenomenon was never reported before in the literature and it is particularly interesting, since it represents a direct, unambiguous evidence of the connection between the lithosphere and the magnetosphere, which can be used both for the analysis of coseismic as well as of precursor phenomena. Following the result on the 2018 Bayan EQ, we started a systematic study of this phenomena using 42 EQ in the time span from 2001-07-17 and 2020-08-31. This paper presents the result of this study, in which we analyze the *f* ∗ variations using ground magnetometers observations, and we explain the results of these experimental observations with an analytical model describing the *f* ∗ behaviour during active seismic conditions.
