Tunnel Geological Prediction Radar Alternating Electromagnetic Field Propagation Attenuation in Lossy Inhomogeneous Medium

Transcription

1 Tunne Geoogica Prediction Radar Aternating Eectromagnetic Fied Propagation Attenuation in Lossy Inhomogeneous Medium Si Yang Chen,a, Yan Peng Zhu,b, Zhong Li,c, Tian Yu Zhang Coage of civi engineering,lanhou University of Technoogy,anhou735,China; Lanhou miitary poitica department management office,anhou73,china; a. b c. Keywords: Tunne geoogica prediction; Radar; Dieectric reaation properties; Attenuation Abstract. Tunne geoogica prediction of ground-penetrating radar waves propagation in a ossy inhomogeneous medium, there must be a high-frequency attenuation. We must consider the eectrica energy and magnetic energy of the reaation oss, whie the tunne surrounding the quaity factor in determining the attenuation of the necessary eements. Three parameters are not independent of unreated, but from a different side to refect the attenuation. Considering the couping effect between three parameters, cuminating in the estabishment of the radar eectromagnetic waves attenuation coefficient, in inhomogeneous rock medium eists the presence of reaation phenomenon. For the geoogica radar effectivey identify the refected wave with different properties, different absorption and attenuation characteristics to anaye and study the surrounding rock structures, are we ahead of geoogica forecast guidance tunneing significance. Introduction Eectromagnetic induction method is the important branch of eectrica prospecting, using mainy the eectrica conductivity, permeabiity and dieectric properties of geomaterias appied the principe of eectromagnetic induction, observation and study of artificia or natura eectromagnetic fied frequency distribution and time characteristics [,], and then sove the various geoogica probems. GPR is by transmitting and receiving high frequency, narrow puse wide frequency eectromagnetic puses (MH-GH, use of different dieectric constant of the medium at the interface wi produce eectromagnetic wave refection and the ampitude of the received eectromagnetic waves, waveform, frequency characteristics to identify and infer the subsurface structure, stratigraphic and ithoogic characteristics of a geophysica technoogy, with high observationa accuracy of the information-rich, the very wide range of appications in the tunne geoogica prediction. Tunne geoogica prediction of ground-penetrating radar eectromagnetic wave propagation in a ossy inhomogeneous medium, so there must be a high-frequency attenuation. Eectromagnetic wave attenuation phenomenon in ossy inhomogeneous media communication process, generay considered to be caused due to eectrica conductivity, dieectric reaation nature and magnetic reaation properties of a variety of factors [3,4], the theoretica study of the eectromagnetic method in the previous discussion aternating the magnetiation of the magnetic body in the eectromagnetic fied in the quasi-steady state conditions, without considering the magnetiation state to stabiie the process, whie in the eectric fied changes simiar. Power attenuation and magnetic energy decay mechanism is simiar. Basic theory of radar waves underground aternating eectromagnetic fied propagation in the homogeneous medium The basic theory of eectromagnetic wave propagation. High frequency eectromagnetic wave propagation in the medium of obedience to the differentia form of Mawe equations: 74

2 D H = J + B E = B = D = q Where, E is the eectric fied,h is the magnetic fied strength, D is the potentia vector, B the magnetic induction, t is time, J is current density, q is the density of free charge.at the same time, there is the foowing reationship: J = σe D = εe B = μh Where σ is the conductivity, μ is permeabiity, ε for the dieectric constant. In the conductivity is not ero with media, the buk charge can not be gathered in one pace, so in the eectric prospecting in conductive medium D =.Mawe equations in five variabes eimination into three, the foowing equations: E H = σe + ε H E = μ H = E = The equations of the first type of rotation on both sides, and the type second substitution: H = H εμ σμ (4 Because of the vector identity: H = H H (5 H = E = H + εμ E E + εμ σμ (6 σμ (7 If the eectromagnetic fied frequency is high, medium high resistance ( σ Eq.7 the right end of the first can be ignored foowing epression: ( ( (3 can be seen Eq.6, E E = εμ (9 Because v = εμ, so we can get: H = εμ (8 E E = v H = v This shows that eectromagnetic fied vector E, H in free space to speed according to the form of wave speed, sie and medium concerned. Harmonic varying fied case of radar eectromagnetic waves in a homogeneous medium propagation characteristics. Pura forms of epression of the harmonic varying fied as foows: H = H e i E = E e iωρ ωρ Where: ρ resistivity. The Eq. into Eq.5, the transformation can be the pura form of the Mawe equations: 75 ( (

3 H = iωε E E = iωμh H = E = ε ε + i ωμ Where: coefficient is ( εμω iωσμ = the compe permittivity.assume that the eectromagnetic wave propagation ω k = = ω εμ.if ε wi change for the pura form of the ε propagation coefficient v k =, by inference harmonic eectromagnetic fied differentia equations - Hemhot homogeneous equation: H = k H E = k E In a uniform medium of resistivity A, make the foowing assumptions: X, Y ais in the wave poariation pane; Z-ais direction of wave propagation; 3 The ampitude of the eectromagnetic fied in the XOY pane. Then caused by the current source vector potentia A, the formua A desirabe A, A y, A, the eistence: A = k A Soving Eq.4, can be obtained: k k A = C e + Ce (5 The first positive wave, graduay reduced from the eectromagnetic radiation source, the second negative wave, the medium is homogeneous medium negative wave C =, the fina soution: k A, y, = C, y, e (6 The component of the eectromagnetic fied soution: k H = C yke E = C iωμe, Hy = C k e k k, Ey = C iωμe y, H k =, E = The above kinds of pura forms, and attenuation aong the Z-ais direction, if the propagation coefficient k is divided into rea and imaginary part, assume that: k = b + ai (8 Combination of wave propagation coefficient Eq.4, the square after the soution: b = ω εμ ( + m (9 a = ω εμ ( + m + σ Where m = is the eectromagnetic coefficient of the medium, Eq.9 into Eq.8,avaiabe to the ωε E component: π i( ωt+ a iωt b E = E e = ωμc e e ( Ampitude and phase can be drawn from the above equation: b E = ωμ C e ( π ϕ( = ωt + a t ( Can be caed a phase coefficient, attenuation coefficient for the b.the above-mentioned reguarity in physics can be interpreted as: when the propagation of the eectromagnetic fied in a conductor, the induced current, resuting in heat oss, the better the conductivity of the conductor, the free charge in the medium is more energy consumption. ( (3 (4 (7 76

4 Radar eectromagnetic wave propagation in inhomogeneous media oss mechanism Dieectric reaation and magnetic reaation of dissipative effects in some sense, but so far, for this type of dissipation effect is sti weak inks [5].Due to the non-uniform medium of dieectric reaation and magnetic reaation is the major factor in the attenuation of the rock in the media is a non-homogeneous medium, the propagation of the geoogica radar in the wa rock. Radar eectromagnetic waves in inhomogeneous medium the oss of eectric energy.the introduction of the compe dieectric constant, the non uniform medium become reaation poariation medium: ε ε ε = ε + (3 + iωτ ε = ε ' ε '' i ε '' tgθ = ε ' Where: ε ' for the compe permittivity of the rea part of the dieectric constant, that is the usua dieectric constant; ε '' is the imaginary part, aso caed the oss factor, i =, ε and ε were measured ρ in conditions of high and ow frequency reative permittivity. can ignore the case of high ωε frequency eectromagnetic wave, τ is reaation time. ε ' and ε '' and the frequency of the reaation poariation medium can be epressed as: ε ε ε ' = ε + + ( ωτ (5 ( ε ε ωτ ε '' = + ( ωτ In the case of a singe reaation, from Eq.5 to eiminateω t, coe-coe mode can be a form of epression: ( ε ' ε ' + ( ε" = R (6 In the case of a group of reaation time,ks Car and RH Carr 's study pointed out that the reationship between ε ' and ε '' is sti a circe. ε frequency reations from Eq.3 becomes: ε ε ε = ε + (7 α + ( iωτ Where < α < represents the dispersion of the reaation time. Eq.6 be epressed as a negative form: α + ( ωτ sin ε ' = ε + ( ε ε α ( α + ( ωτ sin + ( ωτ α ( ωτ cos " = ( (7 ε ε ε α ( α + ( ωτ sin + ( ωτ At this time of eectromagnetic waves in an inhomogeneous medium energy oss factor ε '' can be soved. Radar eectromagnetic wave in inhomogeneous medium the oss of magnetic energy. Simiary, Eectromagnetic wave eectrica equations can be transformed to the magnetic equation, when assuming that the permeabiity of the magnetic body to use the pura to describe: μ μ μ = μ + (8 α + ( iωτ After a compe operation, the rea and imaginary components: (4 77

5 α + ( ωτ sin μ' = μ + ( μ μ α + ( ωτ sin + ( ωτ α ( ωτ cos μ" = ( μ μ α ( α + ( ωτ sin + ( ωτ ( α This is the eectromagnetic waves in inhomogeneous media, the magnetic energy oss factor μ" can be soved. (9 Inhomogeneous medium quaity factor Tunne surrounding rock medium quaity factor Q can be defined as the resonance frequency of the system, when the signa ampitude does not change over time, the system stored energy per cyce outside the energy ratio, that is deviation from the equiibrium point of the steady-state output eponentia decay of the way, the incrementa return to the steady-state output [6,7]. EnergyStored Q = π (3 EnergyDissipatedPerCyce Fig. is coe-coe mode equivaent circuit diagram, its microscopic simuation of rock conductivity, coe-coe mode can cacuate the ampitude and phase of the rock sampes in the test band. Fig. Sketch of equivaent circuit of Coe-Coe mode Z( iω = ({ m[ ]} (3 c + ( iωτ Where: ( is the frequency of when the impedance; m as the charging rate; τ for description of ecitation poariation process of sow time constant, c is the frequency correation coefficient.ω is anguar frequency of the aternating current fied. The rea and imaginary parts of decomposabe: c c cπ ( m( ωτ + ( m( ωτ cos Re Z( iω = c c cπ + ( ωτ + ( ωτ cos c cπ m( ωτ sin LmZ( iω = (3 c c cπ + ( ωτ + ( ωτ cos The ampitude and phase of the rock sampes in the test band: Z = [Re Z( iω] + [ LmZ( iω] (33 Lm θ = tan (34 Re The attenuation coefficient of radar eectromagnetic wave propagation in inhomogeneous media According to the anaysis of eectromagnetic wave propagation in uniform media, the attenuation coefficient (9, the reaation phenomena of eectromagnetic waves in an inhomogeneous medium 78

6 of eectric energy and magnetic energy oss, as we as the non-uniform medium of tunne surrounding rock quaity factor of eectrica energy and magnetic energy, compared various variabes in the anaysis (9 can be obtained for the attenuation coefficient of eectromagnetic waves in the medium reaation phenomena in inhomogeneous media: ω μ ( ω b( ω = { Re[ ε ( ω] + Q ( ω } (35 ε C Concusion Anaysis of eectromagnetic wave propagation in inhomogeneous media must consider the reaation oss of the eectrica and magnetic energy, whie the tunne surrounding the quaity factor in determining the attenuation of the necessary [8]. These three parameters are not independent of unreated, but from a different side to refect the eectromagnetic wave attenuation. Consider couping between the three, Competed the soution of the attenuation coefficient of eectromagnetic waves of radar waves in the non-uniform tunne surrounding medium. Acknowedgements This work was financiay supported by The Nationa Natura Science Foundation of China (No References [] Annan,A P. and Davis,J L.Impuse radar sounding in permafrost.radio science II,976,383~394 [] Tong Xu,McMechen Geodge A.GPR attention and its numerica simuation in.5 dimensions. Geophysics[J],997,6(:43~44 [3] Von Hippe A R.Dieectrics and Waves[M].New York:John Wiey Sons,96 [4] Tong M S,Ding Z.The Frequence Dispersion Modes of Rock Compe Resistivity and Their Parameters Inversion[J].We Logging Technoogy,6,3(4,33~35 [5] Xiao Z S, Zeng Z G,Zhu S H,et a.an Eperimenta Study of Wettabiity Evauation Based on Frequency Dispersion Property of Rock Eectric Parameters[J],9,5(5:36~33 [6] Igor Sevostianov,Mark Kachanov.Epicit easticity-conductivity connections for composites with anisotropic inhomogeneities[j].mechanics and Physics of soids.7,55:8~5 [7] Torqutao S.Modeing of physica properties of composite materias[j].soids and Structures., 37:4~4 [8] Peton W H.Interpretation of induced poariation and resistivity data[d].sat Lake City: University of Utah