A study of VLF wave propagation characteristics in the earth-ionosphere waveguide

Transcription

1 Erth Plnets Spe, 60, , 008 A study of VLF wve propgtion hrteristis in the erth-ionosphere wveguide M. Indir Devi, I. Khn, nd D. N. Mdhusudhn Ro Deprtment of Physis, Andhr University, Viskhptnm , A. P. Indi Deprtment of Instrumenttion Tehnology, College of Engineering, Andhr University, Viskhptnm , A. P. Indi Reeived Jnury, 008; Revised April, 008; Aepted April 9, 008; Online published August 4, 008) In the light of newly found pplitions for very low frequeny VLF) 3 30 khz) mesurements in the predition of erthqukes nd the detetion of lightning dishrges nd gmm ry bursts, there hs been revivl of interest in the study of VLF propgtion in the erth-ionosphere wveguide. The propgtion hrteristis of VLF rdiowves in the erth-ionosphere wveguide ritilly depend upon the lower ionospheri ioniztion, whih determines the ondutivity profile of the upper boundry of the wveguide. In this ontext, it is potentilly worthwhile to revisit the wveguide mode nlysis to ompute propgtion prmeters of long-distne VLF trnsmissions while tking into ount different pproximtions to the ionospheri ondutivity. We hve rried out wveguide mode nlysis of 6-kHz VLF wves trveling gret distnes, ssuming three different models for ondutivity. The omputtionl results show tht t heights of less thn 70 km, the hnge in the phse of the VLF wves due to hnges in phse veloity is smller when the ionosphere is shrply bound nd ssumed to hve finite ondutivity rther thn infinite ondutivity. The effet of non-shrp or diffuse boundry t the top of the erth-ionosphere wveguide is found to use lowering of the height of refletion. Key words: VLF propgtion, erth-ionosphere wveguide.. Introdution Very low frequeny VLF) rdiowves in the frequeny rnge 3 30 khz hve long been in use for long-distne ommunition nd nvigtion. As these wves exhibit high-phse stbility, they hve found pplition in stndrd frequeny nd time informtion dissemintion. In ddition, VLF phse nd mplitude mesurements hve filitted the study of the D-region of the ionosphere, sine the height of the refletion of these wves lies entirely in the D-region both dy nd night, nd they hve lso been used for solr flre ptrolling. Although reent yers hve seen the inresed use of stellite-bsed ommunition systems nd nvigtionl GPS) ids, ground-bsed systems re still useful beuse they re seen s relible lterntives to the stellite systems, whih re vulnerble to hzrds in spe nd the vgries of spe wether. Submrine ommunition still relies on VLF trnsmitters. There hs lso been renewed interest in VLF in the light of some reent studies showing seismi tivity signtures on VLF reords. These findings suggest tht suh mesurements my filitte erthquke predition Singh et l., 005; Chkrbrti et l., 007). In ddition, there hve been reports of perturbtions indued in VLF trnsmissions by lightning dishrges, γ -ry bursts nd meteor tivity Inn et l., 996; Cummer, 000; Otsuym et l., 003; De et l., 006). In this ontext, model studies of propgtion hrteristis of VLF wves re ritilly importnt nd re being rried Copyright The Soiety of Geomgnetism nd Erth, Plnetry nd Spe Sienes SGEPSS); The Seismologil Soiety of Jpn; The Volnologil Soiety of Jpn; The Geodeti Soiety of Jpn; The Jpnese Soiety for Plnetry Sienes; TERRAPUB. out by mny workers Cummer, 000; Grubor et l., 005). The propgtion of VLF wves over long distnes is generlly treted s propgtion through wveguide onstituted by the erth onsidered perfet ondutor s one wll nd the lower ionosphere D-region) s the other. An importnt problem in VLF ommunition is the vrition in propgtion time due to hnge in the veloity of propgtion used by vrition in the width of erthionosphere wveguide. The D-region ioniztion, being solr ontrolled, undergoes regulr nd irregulr vritions. These hnges in ioniztion lter the height of refletion of the VLF signls nd thereby the width of the erthionosphere wveguide; onsequently, the veloity of propgtion is modified. This is lerly evident t night, when the height of the refletion of the VLF wves inreses by bout 5 0 km from its dytime vlue, resulting in onsiderble inrese in the seprtion between the wlls of the wveguide. As onsequene of this seprtion, the phse veloity of the wves dereses nd the signls will be delyed t the reeiver. The phse veloity, however, is determined by the nture of the ondutivity profile of the ionosphere. Therefore, it is importnt to hve n understnding of the propgtion hrteristis in the wveguide to be ble to interpret the experimentl results s well s to use these wves for erthquke preditions. We report here our study of the propgtion of 6-kHz VLF wves to gret distnes through the erth-ionosphere wveguide. This frequeny is hosen sine phse vrition mesurements of 6-kHz trnsmissions originting from Rugby 5.3 N,. W), UK, nd mde t Viskhptnm 7.7 N, 83.3 E), Indi, re vilble. 737

2 738 M. INDIRA DEVI et l.: VLF WAVE PROPAGATION CHARACTERISTICS Tble. Chnge in phse of the 6-kHz signl for trnsition from the ll-dy to ll-night pth for different dytime refletion heights, ssuming n infinitely onduting ionosphere. S. no. h km) v d ϕ h deg/km Shrply bounded ionosphere with infinite nd finite ondutivity Wit 959) hs shown tht the phse veloity of the nth order mode of rdiowves pssing through the erth nd shrply bounded ionosphere, ssuming the erth nd the ionosphere to possess infinite ondutivity, is pproximtely given by v n = Cn ) h ) ) Fig.. Vrition in diurnl hnge of trnsmission time with distne fter Chilton et l., 964).. Model Computtions Model lultions of wve propgtion in the erthionsophere wveguide generlly employ the wveguide mode theory Wit, 970). Other methods, suh s diret finite-differene time-domin FDTD) modeling, re lso being used for suh lultions Cummer, 000 nd referenes therein). However, in ny of these methods the upper boundry of the wveguide, nmely the ionosphere, is treted with different pproximtions in terms of its ondutivity. In omprtive study of mode theory nd FDTD method, Cummer 000) observed tht, in generl, there is n exellent greement between the omputtionl results obtined using these two methods. Here, in the present study, the omputtions re bsed on the mode theory. Conventionl model omputtions onsider wveguide whose lower boundry is perfetly onduting erth nd whose upper boundry is shrply bounded ionosphere with either finite ondutivity or infinite ondutivity or non-shrp diffuse) ionosphere Kikuhi, 986; Reznikov et l., 993). Here, we lso the propgtion hrteristis of 6-kHz trnsmissions through the Rugby-Viskhptnm pth tht hve been omputed using the wveguide mode equtions for the three pproximtions to the ondutivity profile. where is the veloity of light in free spe m/s), C n = ) n λ, h is the height of refletion of the VLF h wve mode from the ionosphere nd nd λ re the erth s rdius nd wvelength of the wve orresponding to 6- khz Rugby trnsmissions in the present se), respetively. At gret distnes greter thn 5000 km) from the trnsmitter, suh s in the se reported here, where the gret irle distne between Rugby nd Viskhptnm is 803 km, the ttenution of higher order modes will be very high. Hene, only the first order n = ) mode needs to be onsidered. As suh, Eq. ) beomes ) v = λ h ). ) 6h If v d nd v n re the phse veloities of the 6-kHz trnsmissions for the ll-dy nd ll-night pths, respetively, the hnge in phse veloity will be v = v n v d = { h ) } ) λ, 6h 3) whih n be pproximted to { v = h )} ) + λ 3h + h = + λ 6h ) h h. 4) It n be esily shown from Eqs. 3) nd 4) tht the differene in time of trvel from the ll-dy pth to the ll-night pth, t, beomes t d = v n v d ) µs/mm 5)

3 M. INDIRA DEVI et l.: VLF WAVE PROPAGATION CHARACTERISTICS 739 Tble. Chnge in phse of the 6-kHz signl for trnsition from the ll-dy to ll-night pth for different dytime refletion heights, ssuming finitely onduting ionosphere. S. no. h km0 3 Cd v d ϕ h deg/km i i.380) i.333) i.95) i.6) i.34) i.0) i.89) i.70) where d is the distne of trvel. Bsed on the phse vrition mesurements of the 6-kHz trnsmissions from Rugby mde t Viskhptnm over period of nerly yers, the verge diurnl hnge in trnsmission time t) is 8.5 µs/mm Khn et l., 00). This vlue ompres very well with erlier mesurements, s n be seen from Fig., in whih this vlue of t is indited on the plot of t versus distne given by Chilton et l. 964) for severl propgtion pth lengths. It n lso be inferred from this figure tht modl interferene is importnt up to bout 5.5 Mm nd tht beyond this distne, only the first order mode beomes signifint nd t vries linerly with distne with slope of 7.75 µs/mm. Sine the hnges in time nd phse ϕ) re relted through ϕ = t 360 f degrees 6) with f being the frequeny, the hnge in phse for - km hnge in the dy-to-night height of refletion n be shown, using Eqs. 4), 5) nd 6), s ) ϕ = h + λ 6h 3 ) d degrees/km. 7) v d The rtio of the dytime phse veloity of the first order mode to free spe veloity v d /) nd ϕ/ h hve been lulted using Eqs. ) nd 7), with λ = 8.75 km, whih orresponds to the 6-kHz Rugby trnsmission frequeny, nd d = 803 km for the Rugby-Viskhptnm pth, for different heights of refletion. The results re presented in Tble. Wit 963) hs studied the hrteristis of VLF wves propgting to gret distnes through wveguide onstituted by the onduting erth nd shrply bounded ionosphere with finite ondutivity nd showed tht the first order mode phse veloity is given by v C ) = + Re 8) in whih C is given by C = 7π 6 k 3 h k h ) 3 + iα h iα ) h. 9) In Eq. 9), prt from the symbols lredy defined, k = π/λ, the propgtion onstnt, nd α = i / ω/ω r / iω r /ω), where ω is the ngulr frequeny of the VLF wve nd ω r is the ionospheri ondutivity prmeter given by ω r = ωo /υ, ω o, with υ being the ngulr plsm frequeny nd the effetive ollision frequeny, respetively. α is prmeter tht defines the ionospheri refletion oeffiient R through R = expαc ), 0) where C is the osine of the ngle of inidene given by C = C + h α ) for the first order mode. The hnge in phse for -km hnge in refletion height, ϕ/ h, nd the rtio of dytime phse veloity to free spe veloity v d /) for different ll-dy pth refletion heights rnging from 60 to 00 km in steps of 5 km hve been lulted using Eqs. 7) nd 8) with finite vlue for ondutivity, ω r = 0 5. The results re presented in Tble. A omprison of results presented in Tbles nd shows tht v d / is lrger for the se of shrply bounded ionosphere with finite ondutivity thn for the se of infinite ondutivity i.e. phse veloities re lrger for the finite ondutivity se. Further, it n be seen tht for refletion heights 60 nd 65 km, ϕ/ h is smller in the se of the finitely onduting thn infinitely onduting shrply bounded ionosphere, wheres it is lrger t nd bove 70 km. Also, the spred in ϕ/ h is only 4. /km s h inreses from 60 to 00 km for the finite ondutivity model, wheres in the se of the infinite ondutivity model, it is s muh s.5 /km.. Diffuse ionosphere with exponentilly vrying ondutivity A non-shrp or diffuse ionosphere is onsidered here, in whih the ondutivity of the D-region hnges exponentilly Wit, 963) s ω r = ω ro exp [βz h)] ) where ω ro is the vlue of ω r t the referene height, z = h, tken s following Wit 963) nd β is the height grdient. The refletion oeffiient for suh n exponentil

4 740 M. INDIRA DEVI et l.: VLF WAVE PROPAGATION CHARACTERISTICS Tble 3. Cosine of the omplex ngle of inidene, C s funtion of ltitude for the first order mode. C r Ci ) 0 3 C i C r 0 3 4C i Cr ) 0 3 p r pi ) p r + pi ) # p r p i S. no. h km) h pr p i C = r C i + h ) [ 0 3. # pr + p i = Cr C i + h ) + 4Ci r] C 0 3. Tble 4. α r + iα i ) for diffuse ionosphere for different vlues of β. S. no. Height km) β = 0.5 per km α β = 0.3 per km h referene height) i i.333 h i i h.89 i i h 3.95 i i h i i0.4 6 h i i0.846 In Eq. 3), expp r α r p i α i ) is the mplitude of the refletion oeffiient nd π + p r α i + p i α r ) is its phse; p r nd p i re given by p r + ip i = C = C + h + Cr C i + h + ic rc i 4) Fig.. Chnge in height of refletion for the diffusive prmeters for β = 0.5 nd 0.3 km. lyer my lso be expressed in the form expαc ),sin Eq. 0), ssuming α to be nerly onstnt for wide rnge of ngles of inidene. Writing α = α r + iα i, the refletion oeffiient of the first order mode of the 6-kHz VLF signl my be written s R = expαc ) = exp π)expαc ) = expp r α r p i α i ) exp{ iπ + p r α i + p i α r )}. 3) with Cr i) C nd Cr C i s the rel nd imginry prts of C, respetively. The rel nd imginry quntities p r nd p i hve been omputed for different ltitudes nd re given in Tble 3. It my be noted from this tble tht the rel prt of C hnges from to s the height hnges from 60 to 00 km nd tht the imginry prt hnges from to in the sme height intervl. The rel nd imginry prts of the prmeter defining the refletion oeffiient, nmely α r nd α i, hve lso been omputed with ω r = nd β = 0.5 nd 0.3 km, tking the referene height s 70 km nd z vrying from 65 to 70 km in steps of km. The results re presented in Tble 4. In order tht the phse of the refletion oeffiient of the first order mode be π for the nonisotropi or diffuse ionosphere with exponentilly vrying ondutivity, the quntity p r α i + p i α r ) must vnish. In Fig., the vlue of this quntity is plotted s funtion of h h), with h in steps of km. An exmintion of this figure shows tht in the se of the diffuse ionosphere, the height of refletion is redued by bout.65 km for β = 0.5 km nd by bout.8 km for β = 0.3 km, from the referene level h. The result obtined here tht the effet of the non-shrp boundry t the top of the on-

5 M. INDIRA DEVI et l.: VLF WAVE PROPAGATION CHARACTERISTICS 74 entri erth-ionosphere wveguide uses depression in the height of refletion, is onsistent with wht hs been reported by Wit 963). 3. Conlusion Wveguide mode nlysis of VLF wves of 6-kHz frequeny trveling distne of more thn 8 Mm hs been rried out to study their propgtion prmeters while tking into ount three different ondutivity models for the ionosphere, the upper boundry of the wveguide, with the onduting erth s the lower wll. The omputtionl results show tht below 70 km the hnge in phse due to hnges in phse veloity is smller when the ionosphere is ssumed to hve finite ondutivity thn when it is infinitely onduting. We hve lso found tht the effet of nonshrp or diffuse boundry t the top of the erth-ionosphere wveguide is to lower the height of refletion. Aknowledgments. The uthors wish to express their grtitude to Prof. K. V. V. Rmn for his interest nd vluble suggestions while rrying out this work. Referenes Chkrbrti, S., S. Ssml, M. Sh, R. Khn, D. Bhoumik, nd S. K. Chkrbrti, Unusul behvior of D-region ioniztion time t 8. khz during seismilly tive dys, Indin J. Phys., 8, , 007. Chilton, C. J., D. D. Crobie, nd A. G. Jen, Phse vritions in VLF propgtion, in Propgtion of rdiowves t frequenies 300 k/s, edited by Blkbnd, 57 90, Pergmon Press, London, 964. Cummer, S. A., Modeling eletromgneti propgtion in the erthionosphere wveguide, IEEE Trns. Antenns Propgt., 48, 40 49, 000. De, S. S., D. K. De, A. Guh, nd P. K. Mndl, Detetion of 004 Leonid meteor shower by observing its effets on VLF trnsmission, Indin Rdio Spe Phys., 35, , 006. Grubor, D., D. Suli, nd V. Zigmn, Influene of solr X-ry flres on the erth-ionosphere wveguide, Serb. Astron. J., 7, 9 35, 005. Inn, U. S., A. Slingelnd, V. P. Psko, nd J. V. Rodriguez, VLF nd LF signtures of mesospheri nd ionospheri response to lightning dishrges, J. Geophys. Res., 0, 59 59, 996. Khn, I., Y. V. P. K. Rghv, nd D. N. Mdhusudhn Ro, Sesonl vrition of diurnl shift in the height of refletion of 6 khz VLF signls reorded t Viskhptnm, Pro. A. P. Akd. Si., 5, 5 9, 00. Kikuhi, T., Wveguide model nlyses of Omeg VLF wve propgtion t 3.6 khz, J. Atmos. Terr. Phys., 48, 5 3, 986. Otsuym, T., T. Kriy, nd M. Hykw, VLF signtures of ionospheri perturbtions ssoited with winter lightning in the Hokuriku re of Jpn, Adv. Polr Upper Atmos. Res., 7, 09 9, 003. Reznikov, A. E., A. I. Sukhorukov, D. E. Edemskii, V. V. Kopeikin, P. A. Morozov, B. S. Rybov, A. Yu. Shhekotov, nd V. V. Solov ev, Investigtions of the lower ionosphere over Antrti vi ELF-VLF rdiowves, Antrti Si., 5, 07 3, 993. Singh, B., V. Kushwh, V. Singh, nd M. Tomr, Simultneous ULF/VLF mplitude nomlies observed during moderte erthqukes in Indin region, Indin Rdio Spe Phys., 34, 3, 005. Wit, J. R., Diurnl hnge of ionospheri heights dedued from phse veloity mesurements t VLF, Pro. IRE, 47, 998, 959. Wit, J. R., Influene of lower ionosphere on propgtion of VLF wves to gret distnes, J. Res. NBS, 67D, , 963. Wit, J. R., Eletromgneti wves in strtified medi nd Edition), Pergmon Press, Oxford, 970. M. Indir Devi e-mil: indirmlldi@yhoo.om), I. Khn, nd D. N. Mdhusudhn Ro