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The VAN method – named after P. Varotsos, K. Alexopoulos and K. Nomicos, authors of the 1981 papers describing it^[1]^[2] – measures low frequency electric signals, termed "seismic electric signals" (SES), by which Varotsos and several colleagues claimed to have successfully predicted earthquakes in Greece.^[3]^[4] Both the method itself and the manner by which successful predictions were claimed have been severely criticized^[5]^[6]^[7] and defended.^[8]^[9] The VAN method was advanced in 2001 by improving the accuracy of the estimation of the time window of the forthcoming earthquake through a new analysis, termed "natural time", which has been independently reproduced.^[10] Research related to the VAN method is currently carried out at the Solid Earth Physics Institute, University of Athens, Greece.

Description of the VAN method

Prediction of earthquakes with this method is based on the detection, recording and evaluation of seismic electric signals or SES. These electrical signals have a fundamental frequency component of 1 Hz or less and an amplitude the logarithm of which scales with the magnitude of the earthquake.^[11] According to VAN proponents, SES are emitted by rocks under stresses caused by plate-tectonic forces. There are three types of reported electric signal:^[12]

Electric signals that occur shortly before as a major earthquake. Signals of this type were recorded 6.5 hours before the 1995 Kobe earthquake in Japan, for example.^[13]
Electric signals that occur some time before a major earthquake.
A gradual variation in the Earth's electric field some time before an earthquake.

Several hypotheses have been proposed to explain SES:

Stress-related phenomena: Seismic electric signals are perhaps attributed to the piezoelectric behaviour of some minerals, especially quartz, or to effects related to the behavior of crystallographic defects under stress or strain. Series of SES, termed SES activities (which are recorded before major earthquakes), may appear a few weeks to a few months before an earthquake, when the mechanical stress reaches a critical value.^[14]^[15] The generation of electric signals by minerals under high stress leading to fracture has been confirmed with laboratory experiments.^[16]
Thermoelectric phenomena: Alternately, Chinese researchers proposed a mechanism which relies on the thermoelectric effect in magnetite.^[17]
Groundwater phenomena: Three mechanisms have been proposed relying on the presence of groundwater in generating SES. The electrokinetic effect is associated with the motion of groundwater during a change in pore pressure.^[18] The seismic dynamo effect is associated with the motion of ions in groundwater relative to the geomagnetic field as a seismic wave creates displacement. Circular polarization would be characteristic of the seismic dynamo effect, and this has been observed both for artificial and natural seismic events.^[19] A radon ionization effect, caused by radon release and then subsequent ionization of material in groundwater, may also be active. The main isotope of radon is radioactive with a half-life of 3.9 days, and the nuclear decay of radon is known to have an ionizing effect on air. Many publications have reported increased radon concentration in the vicinity of some active tectonic faults a few weeks prior to strong seismic events.^[20] However, a strong correlation between radon anomalies and seismic events has not been demonstrated.^[21]

While the electrokinetic effect may be consistent with signal detection tens or hundreds of kilometers away, the other mechanisms require a second mechanism to account for propagation:

Signal transmission along faults: In one model, seismic electric signals propagate with relatively low attenuation along tectonic faults, due to the increased electrical conductivity caused either by the intrusion of ground water into the fault zone(s) or by the ionic characteristics of the minerals.^[22]
Rock circuit: In the defect model, the presence of charge carriers and holes can be modeled as making an extensive circuit.^[23]

Seismic electric signals are detected at stations which consist of pairs of electrodes (oriented NS and EW) inserted into the ground, with amplifiers and filters. The signals are then transmitted to the VAN scientists in Athens where they are recorded and evaluated. Currently the VAN team operates 9 stations, while in the past (1989) they could afford up to 17.^[24]

The VAN team claimed that they were able to predict earthquakes of magnitude larger than 5, with an uncertainty of 0.7 units of magnitude, within a radius of 100 km, and in time window ranging from several hours to a few weeks. Several papers confirmed this success rate, leading to statistically significant conclusion.^[25] For example, there were eight M ≥ 5.5 earthquakes in Greece from January 1, 1984 through September 10, 1995, and the VAN network forecast six of these.^[26]

The VAN method has also been used in Japan,^[27] but in early attempts success comparable to that achieved in Greece was "difficult" to attain.^[28] A preliminary investigation of seismic electric signals in France led to encouraging results.^[29]

Earthquake prediction using "natural time" analysis

Since 2001 the VAN team has tried to improve the accuracy of the estimation of the time of the forthcoming earthquake. They introduced the concept of natural time, a time series analysis technique which puts weight on a process based on the ordering of events.^[30] They define a variance term κ in the time series analysis. Their current method detects SES as valid when κ = 0.070. That is the first part of their protocol. Once the SES are deemed valid, a second analysis is started. All the subsequent seismic (not electric) events are now noted, and the region is divided up as a Venn diagram with at least two seismic events per overlapping rectangle. When the distribution of κ for the rectangular regions has its maximum at κ = 0.070, the critical seismic event is imminent, i.e. it will occur in a few days to one week or so, and a prediction is issued.^[31]

Here is a brief introduction to the analysis. Two terms, χ and Q, characterize each event. χ is defined as k/N, where k is an integer (the k-th event) and N is the total number of events in the time sequence of data. Q is the energy released for each event. A related term, p, is the ratio Q/Q(total), and describes the fractional energy released. They introduce a critical term κ, defined as κ = [ Σ p(k) (k/N)^2 ] − [ Σ (k/N) p(k) ]^2, where κ is the variance in natural time, k is the event index, N is the number of events, Σ signifies summation, for k = 1 to N, and p(k) is the fractional quantity of energy for the k-th event. This variance puts extra weight on the energy term, p(k).

Results

The VAN team published to have successfully predicted twenty five of the 28 major earthquakes from 2001 through 2010 in the region of latitude N 36° to N 41° and longitude E 19° to E 27° with this new analysis.^[32] Predictions are part of papers housed in arXiv, and new predictions are currently being made and uploaded there.^[33] For example, the prediction of the strongest earthquake in Greece during the period 1983-2011, which occurred on February 14, 2008, with magnitude (Mw) 6.9, was publicized in arXiv almost two weeks before, on February 1, 2008. A description of the updated VAN method was collected in a book published by Springer in 2011, titled "Natural Time Analysis: The New View of Time."^[34]

Natural time analysis also revealed an additional fact showing the physical connection of SES activities with earthquakes as follows: Taking the view that the earthquake occurrence is a phase-change (critical phenomenon) where the new phase is the mainshock occurrence, the above mentioned variance term κ is the corresponding order parameter.^[35] The κ value calculated for a window comprising a number of seismic events comparable to the average number of earthquakes occurring within a few months, fluctuates when the window is sliding through a seismic catalogue. It was found that these κ fluctuations exhibit a minimum a few months before a mainshock occurrence and in addition this minimum occurs simultaneously with the initiation of the corresponding SES activity. Such a simultaneous appearance of two precursory phenomena in independent datasets of different geophysical observables (electrical measurements, seismicity) has been observed for the first time in the literature.^[36] Furthermore the natural time analysis of the seismic catalogue of Japan during the period from January 1, 1984 until the occurrence of the magnitude 9.0 Tohoku earthquake on March 11, 2011, revealed that such clear minima of the κ fluctuations appeared before all major earthquakes with magnitude 7.6 or larger. The deepest of these minima was found to occur on January 5, 2011, i.e., almost two months before the Tohoku earthquake occurrence.^[37] Finally, by dividing the Japanese region into small areas, it has been found that some small areas show minimum of the κ fluctuations almost simultaneously with the large area covering the whole Japan and such small areas clustered within a few hundred kilometers from the actual epicenter of the impending major earthquake.^[38]^[39]

Criticisms of VAN

Historically, the usefulness of the VAN method for prediction of earthquakes had been a matter of debate. Both positive and negative criticism on the early conception of the VAN method is summarized in the 1996 book "A Critical Review of VAN", edited by Sir James Lighthill^[40] and in the debate issue of Geophysical Research Letters in 1996^[9]. This criticism predates the time series analysis methods introduced by the VAN group in 2001. The main points of the criticism were:

Predictive success: The first article in 1981 by VAN reporting the observation of the correlation between SESs and earthquakes was later criticized by claiming that the list of earthquakes used for the correlation was inaccurate.^[41] VAN refuted this criticism by explaining that the data came from the preliminary bulletin of the National Observatory of Athens (NOA), which is expected to differ somewhat from the final NOA bulletin and does not affect the observed correlation between SES and earthquakes.^[42] An additional criticism was raised when examining the probability of chance correlation of 22 claims of successful predictions by VAN from January 1, 1987 through November 30, 1989.^[43] This criticism was also refuted by VAN showing that the methodology on which the criticism was based cannot be correct since it rejects even an ideal prediction method (i.e., all earthquakes above a threshold are successfully predicted, no false alarm).^[44]
Proposed SES propagation mechanism: An analysis of the propagation properties of SES was published by applying a simplified model of homogeneous or a horizontally layered Earth and concluded that it is impossible that signals with the amplitude reported by VAN could be recorded at distances several hundred kilometers away from the epicenter.^[45] This model however is far from the reality since it does not consider that Earth's crust contains heterogeneities as for example the case of the faults along which the electrical conductivity exceeds by a factor around 10²-10³ the conductivity of the surrounding medium.^[46] When an SES is emitted from the focal area, most of the current density follows the neighboring fault and when it reaches the measuring site at the Earth's surface, the electric field is amplified there by a factor ~10²-10³ (according to the well known edge effect) leading to values that are comparable to those reported by the VAN group.^[47]
Electromagnetic compatibility issues: It has been claimed that VAN early publications have failed to address the problem of eliminating the many and strong sources of change in the magneto-electric field measured by them, such as telluric currents from weather, and electromagnetic interference (EMI) from man-made signals, e.g. those arising from digital radio transmissions made from a military base.^[48] This problem has been addressed by the VAN group by suggesting precise criteria that distinguish true precursory SES from non-precursory signals.^[49] The application of these criteria successfully separates SES from electric signals due to digital radio transmissions.^[50]
Scientific reporting: The method is criticized for lack of statistical testing of the validity of the VAN hypothesis because the researchers keep changing the parameters of the hypothesis.^[51] This criticism has been shown to be invalid by independent workers who demonstrated that the results are statistically significant^[52] as well as by the VAN group who refuted the claims of the VAN critics in a debate issue^[9].

Public policy: Finally, one requirement for any earthquake prediction method is that, in order for any prediction to be useful, it must predict a forthcoming earthquake within a reasonable time-frame, epicenter and magnitude. If the prediction is too vague, no feasible decision (such as to evacuate the population of a certain area for a given period of time) can be made. VAN predictions have been criticized as being too vague^[53]. In practice, the VAN group in the 1980s issued predictions in the form of telegrams that have been evaluated by several workers^[54]^[55]^[56]^[57]. From twelve such predictions issued for earthquakes with expected magnitude larger than 5.3, ten were successful and two were not.^[58] After 2006 all VAN predictions are being uploaded in www.arxiv.org, in the library of Cornell University, which is publicly available.

Notes

^ Varotsos, Alexopoulos & Nomicos 1981a, 1981b
^ Varotsos & Alexopoulos 1984
^ Varotsos & Kuhlanek 1993 (preface to a special edition about VAN)
^ Varotsos, Alexopoulos & Lazaridou 1993
^ Mulargia & Gasperini 1992
^ Geller 1997, §4.5
^ ICEF 2011, p. 335
^ Lighthill 1996 (proceedings of a conference that reviewed VAN)
^ ^a ^b ^c twenty articles in a special issue of Geophysical Research Letters (table of contents)
^ Uyeda, Kamogawa & Tanaka 2009
^ Varotsos, Alexopoulos & Nomicos 1981a; Varotsos et al. 1981; Varotsos, Alexopoulos & Nomicos 1982.
^ Varotsos, Alexopoulos & Lazaridou 1993
^ Matsumoto, Ikeya & Yamanaka 1998.
^ Varotsos et al. 1986, p. 120.
^ Varotsos & Alexopoulos 1984
^ Hadjicontis et al. 2007
^ Shen et al. 2011.
^ Gershenzon, Gokhberg & Yunga 1993.
^ Honkura et al. 2009.
^ Pulinets 2007.
^ ICEF 2011, p. 334.
^ Varotsos et al. 1998.
^ Freund 1998.
^ Varotsos & Lazaridou 1991
^ Hamada 1993
^ Uyeda 1996
^ Uyeda, Kamogawa & Tanaka 2009
^ Utada 1993, p. 153
^ Maron et al. 1993
^ Varotsos, Sarlis & Skordas 2002; Varotsos 2006.
^ Varotsos, Sarlis & Skordas 2011, Chapter 7.
^ Varotsos, Sarlis & Skordas 2011, p. 326
^ http://arxiv.org/, search for "Varotsos"
^ Varotsos, Sarlis & Skordas 2011
^ Varotsos, Sarlis & Skordas 2011
^ Varotsos et al. 2013
^ Sarlis et al. 2013
^ Sarlis et al. 2015
^ Huang 2015
^ Lighthill 1996.
^ Wyss 1996a
^ Varotsos et al. 1996a
^ Wyss & Allmann 1996 harvnb error: multiple targets (2×): CITEREFWyssAllmann1996 (help)
^ Varotsos et al. 1996b
^ Bernard 1992; Bernard & LeMouel 1996.
^ Varotsos et al. 1998
^ Varotsos et al. 1998
^ Pham et al. 1998.
^ Varotsos & Lazaridou 1991
^ Sarlis et al. 1999
^ Mulargia & Gasperini 1992; Mulargia & Gasperini 1996; Wyss 1996b.
^ Hamada 1993
^ Mulargia & Geller 2003, p. 318.
^ Varotsos, Alexopoulos & Lazaridou 1993
^ Mulargia & Gasperini 1992
^ Geller 1997, §4.5
^ Hamada 1993
^ Hamada 1993

References

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Lazaridou-Varotsos, M. (2013), Earthquake Prediction by Seismic Electric Signals: The Success of the VAN method over thirty years, Springer-Praxis, doi:10.1007/978-3-642-24406-3, ISBN 978-3-642-24405-6
Lighthill, Sir James, ed. (1996), A Critical Review of VAN – Earthquake Prediction from Seismic Electrical Signals, London, UK: World Scientific Publishing Co Pte Ltd, ISBN 978-981-02-2670-1
Maron, C.; Baubron, G.; Herbreteau, L.; Massinon, B. (August 1993), "Experimental study of a VAN network in the French Alps", Tectonophysics, 224 (1–3): 51–81, Bibcode:1993Tectp.224...51M, doi:10.1016/0040-1951(93)90058-R
Matsumoto, H.; Ikeya, M.; Yamanaka, C. (1998), "Analysis of barber-pole color and speckle noises recorded 6 and a half hours before the Kobe earthquake", Japanese Journal of Applied Physics, 37 (1): L1409–L1411, Bibcode:1998JaJAP..37L1409M, doi:10.1143/JJAP.37.L1409
Mulargia, F.; Gasperini, P. (July 1992), "Analyzing the statistical validity of earthquake precursors. An application to the "VAN" method", Geophysical Journal International, 111 (1): 32–44, doi:10.1111/j.1365-246x.1992.tb00552.x
Mulargia, F.; Gasperini, P. (1996), "Behind VAN: Tectonic stress changes or earthquake induced alertness?", in Sir James Lighthill (ed.), A Critical Review of VAN – Earthquake Prediction from Seismic Electrical Signals, London, UK: World Scientific Publishing Co Pte Ltd, pp. 244–249, ISBN 978-981-02-2670-1
Mulargia, F.; Geller, R. (2003), Earthquake Science and Seismic Risk Reduction, Springer, ISBN 978-1402017773
Pham, V.; Boyer, D.; Chouliaras, G.; Le Mouël, J.; Rossignol, J.; Stavrakakis, G. (June 1998), "Characteristics of electromagnetic noise in the Ioannina region (Greece); a possible origin for so called 'Seismic Electric Signal' (SES)", Geophysical Research Letters, 25 (12): 2229–2232, Bibcode:1998GeoRL..25.2229P, doi:10.1029/98GL01593
Pulinets, S. (May 2007), "Natural radioactivity, earthquakes, and the ionosphere", Eos, Transactions, American Geophysical Union, 88 (20): 217–218, Bibcode:2007EOSTr..88..217P, doi:10.1029/2007EO200001
Shen, X.; Zhang, X.; Wang, L.; Chen, H.; Wu, Y.; Yuan, S.; Shen, J.; Zhao, S. (2011), "The earthquake-related disturbances in ionosphere and project of the first China seismo-electromagnetic satellite", Earthquake Science, 24 (6): 639–650, Bibcode:2011EaSci..24..639S, doi:10.1007/s11589-011-0824-0 {{citation}}: Unknown parameter |coauthors= ignored (|author= suggested) (help)
Sarlis, Nicholas V.; Skordas, Efthimios S.; Varotsos, Panayiotis A.; Nagao, Toshiyasu; Kamogawa, Masashi; Tanaka, Haruo; Uyeda, Seiya (2013-08-20). "Minimum of the order parameter fluctuations of seismicity before major earthquakes in Japan". Proceedings of the National Academy of Sciences. 110 (34): 13734–13738. doi:10.1073/pnas.1312740110. ISSN 0027-8424. PMC 3752201. PMID 23918353. {{cite journal}}: Invalid |ref=harv (help)
Sarlis, Nicholas V.; Skordas, Efthimios S.; Varotsos, Panayiotis A.; Nagao, Toshiyasu; Kamogawa, Masashi; Uyeda, Seiya (2015-01-27). "Spatiotemporal variations of seismicity before major earthquakes in the Japanese area and their relation with the epicentral locations". Proceedings of the National Academy of Sciences. 112 (4): 986–989. doi:10.1073/pnas.1422893112. ISSN 0027-8424. PMC 4313817. PMID 25548194.
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Sarlis, N.; Lazaridou, M.; Kapiris, P.; Varotsos, P. (1999-11-01). "Numerical model of the selectivity effect and the ΔV/L criterion". Geophysical Research Letters. 26 (21): 3245–3248. doi:10.1029/1998GL005265. ISSN 1944-8007.
Uyeda, S. (1996), "Introduction to the VAN method of earthquake prediction", in Sir James Lighthill (ed.), A Critical Review of VAN – Earthquake Prediction from Seismic Electrical Signals, London, UK: World Scientific Publishing Co Pte Ltd, ISBN 978-981-02-2670-1
Uyeda, S.; Kamogawa, M.; Tanaka, H. (February 2009), "Analysis of electrical activity and seismicity in the natural time domain for the volcanic-seismic swarm activity in 2000 in the Izu Island region, Japan", Journal Geophysical Research, 114 (B2): B02310, Bibcode:2009JGRB..11402310U, doi:10.1029/2007JB005332
P. Varotsos and K. Alexopoulos, Physical properties of the variations of the electric field of the earth preceding earthquakes, I. Tectonophysics 110, 73-98, 1984. DOI: 10.1016/0040-1951(84)90059-3
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Varotsos, P. (2006), "What happened before the last five strong earthquakes in Greece", Proc. Jpn. Acad. Ser. B, 82 (2): 86–91, Bibcode:2006PJAB...82...86V, doi:10.2183/pjab.82.86
Varotsos, P.; Alexopoulos, K.; Lazaridou, M. (1993), "Latest aspects of earthquake prediction in Greece based on seismic electric signals, II", Tectonophysics, 224: 1–37, Bibcode:1993Tectp.224....1V, doi:10.1016/0040-1951(93)90055-O
Varotsos, P.; Alexopoulos, K.; Nomicos, K. (1981a), "Seismic electric currents", Proceedings of the Academy of Athens, 56: 277–286
Varotsos, P.; Alexopoulos, K.; Nomicos, K. (1981b), "Seven-hour precursors to earthquakes determined from telluric currents", Praktika of the Academy of Athens, 56: 417–433
Varotsos, P.; Alexopoulos, K.; Nomicos, K. (1982), "Electrotelluric precursors to earthquakes", Proceedings of the Academy of Athens, 57: 341–363
Varotsos, P.; Alexopoulos, K.; Nomicos, K.; Lazaridou, M. (1986), "Earthquake prediction and electric signals", Nature, 322 (6075): 120, Bibcode:1986Natur.322..120V, doi:10.1038/322120a0
Varotsos, P.; Alexopoulos, K.; Nomicos, K.; Papaioannou, G.; Varotsos, M.; Revelioti-Dologlou, E. (1981), "Determination of the epicenter of impending earthquakes from precursor changes of the telluric current", Proceedings of the Academy of Athens, 56: 434–446
Varotsos, P.; Kuhlanek, P. (August 1993), "Preface [to special issue: "Measurements and Theoretical Models of the Earth's Electric Field Variations Related to Earthquakes"]", Tectonophysics, 224 (1–3): vii–viii, doi:10.1016/0040-1951(93)90054-n
Varotsos, P.; Lazaridou, M. (March 1991), "Latest aspects of earthquake prediction in Greece based on seismic electric signals" (PDF), Tectonophysics, 188 (3–4): 321–347, Bibcode:1991Tectp.188..321V, doi:10.1016/0040-1951(91)90462-2
Varotsos, P.; Eftaxias, K.; Lazaridou, M.; Dologlou, E.; Hadjicontis, V. (1996-05-27). "Reply to "Inaccuracies in seismicity and magnitude data used by Varotsos and Co-workers," by M. Wyss". Geophysical Research Letters. 23 (11): 1303–1306. doi:10.1029/96GL01415. ISSN 1944-8007. {{cite journal}}: Invalid |ref=harv (help)
Varotsos, P.; Eftaxias, K.; Lazaridou, M.; Dologlou, E.; Hadjicontis, V. (1996-05-27). "Reply to "Probability of chance correlations of earthquakes with predictions in areas of heterogeneous seismicity rate: The VAN Case," by M. Wyss and A. Allmann". Geophysical Research Letters. 23 (11): 1311–1314. doi:10.1029/96GL00908. ISSN 1944-8007. {{cite journal}}: Invalid |ref=harv (help)
Varotsos, P.; Sarlis, N.; Lazaridou, M.; Kapiris, P. (1998), "Transmission of stress induced electric signals", Journal of Applied Physics, 83: 60–70, Bibcode:1998JAP....83...60V, doi:10.1063/1.366702
Varotsos, P.; Sarlis, N.; Skordas, E. (2002), "Long-range correlations in the electric signals that precede rupture" (PDF), Physical Review E, 66: 011902, doi:10.1103/physreve.66.011902
Varotsos, P.; Sarlis, N.; Skordas, E. (2011), Natural time analysis : the new view of time ; Precursory seismic electric signals, earthquakes and other complex time series, Springer Praxis, ISBN 364216448-X
Varotsos, P. A.; Sarlis, N. V.; Skordas, E. S.; Lazaridou, M. S. (2013-03-18). "Seismic Electric Signals: An additional fact showing their physical interconnection with seismicity". Tectonophysics. 589: 116–125. doi:10.1016/j.tecto.2012.12.020. {{cite journal}}: Invalid |ref=harv (help)
Wyss, M. (May 1996a), "Inaccuracies in seismicity and magnitude data used by Varotsos and coworkers", Geophysical Research Letters, 23 (11): 1299–1302, Bibcode:1996GeoRL..23.1299W, doi:10.1029/95GL03545{{citation}}: CS1 maint: ref duplicates default (link)
Wyss, M. (1996b), "Brief summary of some reasons why the VAN hypothesis for predicting earthquakes has to be rejected", in Sir James Lighthill (ed.), A Critical Review of VAN – Earthquake Prediction from Seismic Electrical Signals, London, UK: World Scientific Publishing Co Pte Ltd, pp. 250–266, ISBN 978-981-02-2670-1
Wyss, M.; Allmann, A. (May 1996), "Probability of chance correlations of earthquakes with predictions in areas of heterogeneous seismicity rate: the VAN case", Geophysical Research Letters, 23 (11): 1307–1310, Bibcode:1996GeoRL..23.1307W, doi:10.1029/95GL03548
Wyss, M.; Allmann, A. (1996-05-27). "Probability of chance correlations of earthquakes with predictions in areas of heterogeneous seismicity rate: The VAN Case". Geophysical Research Letters. 23 (11): 1307–1310. doi:10.1029/95GL03548. ISSN 1944-8007. {{cite journal}}: Invalid |ref=harv (help)

External links

Nature debates. Is the reliable prediction of individual earthquakes a realistic scientific goal?
VAN earthquake prediction method.
P. Varotsos' bibliography (the principal source of "VAN" papers).

[1] Varotsos, Alexopoulos & Nomicos 1981a, 1981b

[2] Varotsos & Alexopoulos 1984

[3] Varotsos & Kuhlanek 1993 (preface to a special edition about VAN)

[4] Varotsos, Alexopoulos & Lazaridou 1993

[5] Mulargia & Gasperini 1992

[6] Geller 1997, §4.5

[7] ICEF 2011, p. 335

[8] Lighthill 1996 (proceedings of a conference that reviewed VAN)

[20_GRL-9] twenty articles in a special issue of Geophysical Research Letters (table of contents)

[10] Uyeda, Kamogawa & Tanaka 2009

[11] Varotsos, Alexopoulos & Nomicos 1981a; Varotsos et al. 1981; Varotsos, Alexopoulos & Nomicos 1982.

[12] Varotsos, Alexopoulos & Lazaridou 1993

[13] Matsumoto, Ikeya & Yamanaka 1998.

[14] Varotsos et al. 1986, p. 120.

[15] Varotsos & Alexopoulos 1984

[16] Hadjicontis et al. 2007

[17] Shen et al. 2011.

[18] Gershenzon, Gokhberg & Yunga 1993.

[19] Honkura et al. 2009.

[20] Pulinets 2007.

[21] ICEF 2011, p. 334.

[22] Varotsos et al. 1998.

[23] Freund 1998.

[24] Varotsos & Lazaridou 1991

[25] Hamada 1993

[26] Uyeda 1996

[27] Uyeda, Kamogawa & Tanaka 2009

[28] Utada 1993, p. 153

[29] Maron et al. 1993

[30] Varotsos, Sarlis & Skordas 2002; Varotsos 2006.

[31] Varotsos, Sarlis & Skordas 2011, Chapter 7.

[32] Varotsos, Sarlis & Skordas 2011, p. 326

[33] ttp://arxiv.org/, search for "Varotsos"

[34] Varotsos, Sarlis & Skordas 2011

[35] Varotsos, Sarlis & Skordas 2011

[36] Varotsos et al. 2013

[37] Sarlis et al. 2013

[38] Sarlis et al. 2015

[39] Huang 2015

[40] Lighthill 1996.

[41] Wyss 1996a

[42] Varotsos et al. 1996a

[43] Wyss & Allmann 1996 harvnb error: multiple targets (2×): CITEREFWyssAllmann1996 (help)

[44] Varotsos et al. 1996b

[45] Bernard 1992; Bernard & LeMouel 1996.

[46] Varotsos et al. 1998

[47] Varotsos et al. 1998

[48] Pham et al. 1998.

[49] Varotsos & Lazaridou 1991

[50] Sarlis et al. 1999

[51] Mulargia & Gasperini 1992; Mulargia & Gasperini 1996; Wyss 1996b.

[52] Hamada 1993

[53] Mulargia & Geller 2003, p. 318.

[54] Varotsos, Alexopoulos & Lazaridou 1993

[55] Mulargia & Gasperini 1992

[56] Geller 1997, §4.5

[57] Hamada 1993

[58] Hamada 1993

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