Properties of the magnetotelluric frequency-normalised impedance over a layered medium

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1 JOURNAL OF THE BALKAN GEOPHSICAL SOCIET, Vol., No 3, August 999, p , 7 fgs. Popetes of the agnetotelluc fequency-noalsed pedance ove a layeed edu Ahet T. Basoku Ankaa Unvestes, Fen Fakultes, Jeofzk Muh. B., Togan, 0600 Ankaa, Tukey. E-al: basoku@scence.ankaa.edu.t ( Receved Januay 999; accepted 9 Apl 999 ) Abstact: The fequency-noalsed pedance (FNI) functon s ntoduced to gve a physcal sgnfcance to the agnetotelluc data. The FNI functon s sepaated nto ts eal agnay pats that have the sae denonato to estate the values n the hgh- low-fequency lts. The behavou of the appaent esstvty defntons the phase s explaned theoetcally by consdeng the eal the agnay pats of the FNI functon. The oscllatons on the appaent esstvty cuves ae explaned by usng ascendng descendng types two-laye cuves of the FNI functon. The concept of the ecpocal geoelectc secton s developed by usng the popetes of the FNI functon. It has been shown that the appaent esstvty cuves of a geoelectc secton those of coespondng to the ecpocal geoelectc secton ae syetc. The axs of syety s the hozontal axs that ntesects the vetcal axs at unty. The FNI functon asssts the ntepete by gvng a clea dea about the nube of layes, the esstvty ato between consecutve layes t seves a good appoxaton of the tue esstvty values of the subsuface layes. Key Wods: Fequency-noalzed Ipedance, Magnetotellucs, Appaent Resstvty Defntons. INTRODUCTION The agnetotelluc (MT) soundng s caed out by easung the hozontal electc feld the othogonal hozontal agnetc feld vesus te. Howeve, the Foue tansfoatons of the easued feld quanttes ae estated the MT data ae ntepeted n the fequency doan. A ato of the electc feld to the agnetc feld yelds the pedance n a specfed fequency ange. The pedance s not dectly popotonal to the tue esstvty dstbuton of the subsuface. The pedance can be noalsed vesus fequency to obtan a bette epesentaton of the MT esponse (Basoku, 994a). Ths data noalsaton vesus fequency connects the feld ato to the subsuface stuctual patten. In ths pape, the ets of the suggested type of data pesentaton the use the FNI functon fo the ntepetaton of the MT data wll be dscussed. Fo splcty, the dscusson wll be lted to -D stuaton to exane the behavou of the FNI functon, but sla analyss can be extended to any type of eath stuctue. THEOR The pedance n MT ethod s gven as: Z = E / H () whee E H denote the electc the othogonal agnetc felds, espectvely. The pedance can be noalsed vesus fequency as follows: E x = Z / ωµ = = () ωµ H y whee ω s the angula fequency, µ s the agnetc 999 Balkan Geophyscal Socety (access bgs.ankaa.edu.t) 63

2 64 Fequency-noalsed Ipedance peeablty of fee space, s known as the fequency-noalsed pedance functon (Basoku 994a). The notaton fo the FNI functon s abtay selected. The FNI functon should not be confused wth the adttance that s also denoted by the sybol (). The eal agnay pats of the FNI functon can be gven n tes of the eal agnay pats of the pedance (Szaka, 994): The ecuence expesson (7) can also be wtten n the followng equvalent fos (Basoku et al., 997a): o + / P + tanh ( ut / P ) = P (0) + ( / P ) tanh( ut / P ) + = (Z + Z ) / ωµ (3) snce + + P tanh ( ut / P ) = + ( / P ) tanh( ut / P ) + () = (Z Z ) / ωµ. (4) Fo the hozontally statfed eath odel, consstng of n hoogeneous sotopc layes of esstvtes,,..., n thcknesses t, t,..., t n, can be deved by followng the conventonal way descbed n textbooks (e.g. Kaufan Kelle, 98): { = P tanh u t / P + acth ( P / P. tanh ( u t / P acth [ Pn / Pn ]))...} (5) wth u = ωµ = ( + ) µπf (6) P =. The above expesson can be wtten as a ecuence foula [ ut / P + acth ( / P )] = P tanh (7) + wth = n-,...,, fo substatu n = P n. (8) Statng fo the substatu, the new functon can be found by addng a new laye at the top of the laye sequence. The ecuent applcaton of (7) gves the fnal functon: =. (9) tanh(a) + tanh(b) tanh(a + b) =. () + tanh(a) tanh(b) APPARENT RESISTIVIT AND PHASE DEFINITIONS The easued feld quanttes ae usually conveted to the appaent esstvty values n ode to gve physcal sgnfcance to the data. The appaent esstvty defned by Cagnad(953) has tadtonally been used fo the pesentaton of MT data. Ths defnton can be gven n tes of the eal agnay pats of the FNI functon as follows: ac = Z = + (3) µω whee ae the eal the agnay pats of the FNI functon, espectvely. Soe defntons poduce bette esults than the Cagnad s(953) defnton to each tue esstvtes of the subsuface layes (Spes Egges, 986). At pesent, the defnton defned by Basoku(994a) sees to be one of the ost successful, gvng appaent esstvty values close to the tue esstvtes of the layes suppessng the oscllatons of the MT cuve whch ae not elated to the featues pesented n the secton. The appaent esstvty defnton, whch can be appled to the descendng banches of the eal pat of the FNI, s gven as ( - ) (4) = the appaent esstvty defnton fo the ascendng banches of the eal pat s. (5) = ( + ) / ( + ) Snce the sgn of the agnay pat dstngushes between the descendng ascendng banches, the

3 Ahet T. Basoku 65 above defntons can be cobned nto a sngle equaton (Basoku, 994a): [( - sgn ( ). ) / ( + ) ] =. (6) The above defnton has been deved theoetcally by akng use of the popetes of the FNI functon. The econclaton of ths defnton wth the pevously publshed defntons has been shown by Szaka(994). He ewtes equatons (4) (5) n tes of the pedance as follows: = Z fo φz π / 4 (7) ωµ Z = fo φz π / 4. (8) ωµ Z whee φ Z s the agnetotelluc phase t s defned as φ actan( Z / Z ) (9) Z = whee Z Z epesent the eal agnay pats, espectvely, of the pedance. Afte the Szaka s(994) devaton, a lttle algeba leads to new equatons fo (4) (5) n tes of the phase of pedance = cos ( φ ) fo φ π / 4 (0) ac Z Z = ( sn ( φ ) ) fo φ π / 4. () ac / Z Z The above pa of equatons s equal to the defntons developed by Schucke(970). Now, t becoes clea that the equatons (4), (0) the defnton of Spes Egges(986) ae exactly equvalent. The defnton (5) s equvalent to the Schucke s(970) tansfoaton gven by (). Howeve, the copason of the appaent esstvty defntons theoetcal explanaton of the behavou can easly be done by exanng the FNI functon. The elaton between the phases of the FNI the pedance can be found fo () as φ = φ π / 4 () snce Z phase { / } = π / 4 ωµ (3) As t s clea fo (9 (), the shape of the phase cuve s anly contolled by the agnay pat of the FNI functon. Thus, the behavou of the MT phase can also be explaned usng the popetes of the FNI functon, naely by usng the ato of the agnay eal pats of the FNI functon. BEHAVIOR OF THE FNI FUNCTION As a fst step, t s convenent to nvestgate the two-laye case to explan the behavou of the eal agnay pats of the functon. Fo equaton (7), the FNI functon can be wtten as: ( ( + ) µπf (t/p ) acth(p / P )) = P tanh +. (4) If we denote a = t / P. µπf (5) b = acth( P / P ) = 0.5 ln( k ) (6) wth k = ( P + P) / ( P P ), (7) we obtan = P tanh( ( a + b) + a). (8) Knowng that snh( x ) + sn( y ) tanh(x + y) =, (9) cosh( x ) + cos( y ) we can sepaate the functon nto ts eal agnay pats that have the sae denonato as follows: [ snh( a + b ) / v sn( a ) / v] = P + (30) whee v = cosh( a + b ) + cos ( a ), (3) x = a + b, y = a. By ultplyng dvdng the ght-h sde of (30) by cosh( a + b ), we can edefne the eal agnay pats of the FNI functon as follows:

4 66 Fequency-noalsed Ipedance = P R( f ) / D( f ) (3) = P I( f ) / D( f ) (33) whee R(f) = tanh( a + b ), (34) I(f) = sn( a ) / cosh( a + b ) (35) D(f) = + cos( a )/ cosh( a + b ). (36) Fo (5) (6), we can pove that snh( a + b ) = ( c - /c ) /, (37) cosh( a + b ) = ( c + /c ) / (38) tanh( a + b ) = ( c - /c ) / ( c + /c ) (39) wth c = k exp ( a ). (40) 30 (a) FNI functon Re 0 5 I (b) Fequency (hetz) Appaent esstvty ( Ω ) C 00 F FIG.. (a) The eal (Re) the agnay (I) pats of the FNI functon vesus deceasng fequency fo the odel: = 500 oh-, = 0 oh-, t = 350. (b) a copason between Cagnad's appaent esstvty (C) the appaent esstvty defnton (F).

5 Coponents of the FNI functon Ahet T. Basoku 67.5 D(f) R(f) I(f) Fequency (hetz) FIG.. Plots of the eal R(f) the agnay I(f) pats of the FNI functon vesus deceasng fequency. D(f) s the denonato of the FNI functon. The odel s the sae wth Fgue, but the saple values ae noalsed by the esstvty of the fst laye. These expessons lead to the analyss of the behavou of the FNI functon fo descendng ascendng types two-laye cuves. Descendng Type Two-laye Cuves Fgue a shows the eal agnay pats of the FNI functon coputed fo the case whee the laye esstvtes ae oh-etes the thckness of the top laye s 350. The behavous of the eal agnay pats can be analysed by the help of the pevously defned R(f), I(f) D(f) functons. R(f) s equal to unty n the hgh fequency lt snce tanh ( )=. The te cos(a) n D(f) has postve nuecal values except a few saple values at hgh fequences whee t becoes negatve consequently causes an oscllatons n D(f) wth salle values than unty (Fg. ). appoaches the squae oot of the esstvty of the fst laye snce both R(f) D(f) appoach unty n the hgh fequency lt. Accodng to (7), k s postve R(f) onotonously deceases wth loweng fequency (Fg. ). To fnd the nuecal value of R(f) n the low fequency lt, we put f=0 nto (40). By the help of (37) (38) one fnds: R (f ) = P P / ( P P ). (4) + In contast to the behavo of R(f), the saple values of D(f) tend to ncease wth deceasng fequency snce cosh(a + b) has postve nuecal values t deceases wth deceasng fequency (expesson 36). If we put f=0 nto (36) then we can fnd the followng asyptotc value of D(f) by the help of (38) (40) fo the low fequency lt: D( f ) = P / ( P P ). (4) + Substtutng (4) (4) nto (3), we fnd that the eal pat of the FNI functon equals to the squae oot of the esstvty of the second laye n the low fequency lt. The eal pat of the FNI functon conssts of the dvson of a deceasng functon (R(f)) by an nceasng functon (D(f)). As a esult of ths dvson, apdly deceases n copason wth R(f). The oscllaton on the D(f) s tansfeed to n evese decton has nuecal values geate than the squae oot of the esstvty of the fst laye at the abscssa ange close to hgh fequency lt (Fg. a Fg. ). The agnay pat of the FNI functon becoes zeo at hgh low fequency lts (Fg. a). Because, the te cosh(a + b) n I(f) has exteely hgh nuecal values fo hgh fequences consequently I(f) becoes zeo. In the low fequency lt, the te sn(a) n I(f) appoaches zeo (Fg. ). At nteedate fequences, the dvson sn(a) / cosh(a + b) s postve except the fequency ange nea hgh fequency lt whee sn(a) becoes negatve. As entoned befoe, D(f) also shows oscllatoy behavou n ths fequency ange. Snce

6 68 Fequency-noalsed Ipedance I(f) has elatvely sall nuecal values n ths fequency ange, the oscllaton of the agnay pat of the FNI functon s uch salle than that of the eal pat. Afte ths oscllaton nea the hgh fequency lt, nceases wth deceasng fequency, passng though a axu value t stats to decease contnuously appoaches zeo at low fequency lt. It s nteestng to note that R(f) I(f) ae paallel to each othe fo elatvely low fequency values (Fg. ). Ths suggests that the dffeence between R(f) I(f) s constant fo sall values of fequency. The followng appoxaton s vald fo (6) because P P fo ths case: b = acth ( P. (43) / P ) P / P We can also ake the followng appoxatons fo sall values of fequency: R(f) = tanh( a + b ) a + b (44) D(f) = + cos( a ) / cosh( a + b) (45) snce cos( a ) (46) cosh( a + b ) (47) I(f) = sn( a ) / cosh( a + b ) a. (48) If we subtact (48) fo (44), we obtan R(f) - I(f) b P / P. (49) Ths esult explans why R(f) I(f) ean paallel fo the elatvely sall values of fequency ( Fg. ). Consequently, the sae paallels s also obseved n the eal agnay pats of the FNI functon as can be seen on Fg. a. Fo (3) (33) one fnds that P ( R ( f ) I ( f ) ) / D( f ). (50) If (45) (49) ae substtuted nto (50), then the dffeences of the eal agnay pats of the FNI functon becoes alost equal to the squae oot of the esstvty of the botto laye: P. (5) Ths esult explans the eason why the defnton (4) s successful n eachng the tue esstvty of the second laye at elatvely hgh fequences. Because of the stuctue of the defnton (3), the Cagnad s(953) defnton could only each the tue esstvty of the substatu n low fequency lt whee the agnay eal pats of the FNI becoe equal to zeo the squae oot of the esstvty of the fst laye. Snce we have noally oe than two layes, the contbuton of deepe layes stats at nteedate fequences thus the Cagnad s(953) defnton neve eaches the ntnsc esstvty of a laye. But, the defnton (4) can attan the tue esstvty of a laye befoe the contbuton of the botto laye stats. Fgue b copaes the behavous of the appaent esstvty defntons. Ascendng Type Two-laye Cuves Fgue 3a shows the eal agnay pats of the FNI functon coputed fo the case whee the laye esstvtes ae 0 00 oh-etes the thckness of the top laye s 00. Snce the esstvty of the second laye s geate than that of the fst laye, k s negatve. R(f) s equal to unty fo hgh fequency values. The denonato D(f) s also equal to unty n the hgh fequency lt snce cosh( a + b ) equals to nfnty ( Fg. 4 ). And the eal pat of the FNI functon becoes equal to the squae oot of the esstvty of the fst laye (Fg. 3a). (37) (38) have always negatve nuecal values consequently R(f) becoes deceasng functon of loweng fequency. The te cosh(a + b) n the denonato D(f) has always negatve values ts absolute values decease wth loweng fequency. The te cos(a) geneally has postve values except fo the fequency values close to the hgh fequency lt. Then the dvson cos / cosh gves negatve values wth less than -. Then D(f) becoes a deceasng functon of loweng fequency. But, cos(a) causes an oscllaton on D(f) when t has negatve values nea hgh fequency lt whee D(f) becoes geate than unty fo a few saple values (Fg. 4). The eal pat of the FNI functon s obtaned by dvdng R(f) to D(f) whch both of the ae deceasng functons of loweng fequency. Howeve, D(f) deceases apdly than R(f) the fnal dvson gves an nceasng functon of deceasng fequency. The oscllaton of D(f) due to the te cos(a) also causes an oscllaton on the eal pat of the FNI functon n the evese decton whee the saple values of the FNI functon becoe less than P (Fg. 3a). Cagnad appaent esstvty also shows oscllatng behavou at the sae saple ponts as slghtly salle appaent esstvty values than the tue esstvty of the fst

7 Appaent esstvty ( Ω ) Ahet T. Basoku 69 0 (a) FNI functon Re I Fequency (hetz) 000 (b) 00 F C FIG. 3. (a) The eal (Re) the agnay (I) pats of the FNI functon vesus deceasng fequency fo the odel: = 0 oh-, = 00 oh-, t = 00. (b) a copason between Cagnad's appaent esstvty (C) the appaent esstvty defnton a F (F). laye because of the sae eason. As n the case of descendng type cuves, the eal pat of the FNI functon appoaches the squae oot of the esstvty of the substatu n the low fequency lt. Expessons (4) (4) ae also vald fo ths case. The nueato of the agnay pat of the FNI functon I(f) becoes zeo n hgh low fequency lts (Fg. 4). Because, cosh(a + b) has exteely hgh nuecal values fo hgh fequences consequently I(f) becoes zeo. In low fequency lt, I(f) s zeo snce sn(a) becoes zeo fo vey sall fequency values. At nteedate fequences, the dvson sn(a) / cosh(a + b) becoes negatve because sn(a) s postve except the fequency ange close to hgh fequency lt whee D(f) also shows oscllatoy behavou. Snce the agntude of D(f) s geate than I(f), the fnal dvson (35) esults that the absolute values of the agnay pat of the FNI functon s always less than that of the eal pat except pefectly nsulatng conductng substatu cases. And also the agntude of the oscllaton on the agnay pat s salle than that of eal pat. Due to the sae eason, the agntude of oscllaton of the phase becoes elatvely salle than that of the Cagnad appaent esstvty.

8 Coponents of the FNI functon 70 Fequency-noalsed Ipedance R(f) D(f) I(f) Fequency (hetz) FIG. 4. Plots of the eal R(f) the agnay I(f) pats of the FNI functon vesus deceasng fequency. D(f) s the denonato of the FNI functon. The agnay pat s ultpled by -. The odel s the sae wth Fgue 3, but the saple values ae noalsed by the esstvty of the fst laye. Fnally, we see that f the esstvty of the second laye s geate than that of the fst laye, the agnay pat of the FNI functon s zeo at hgh low fequency lts. At nteedate fequences, t s negatve t deceases wth loweng fequency, passng though a nu value then eaches zeo n low fequency lt except the elatvely sall oscllaton at hgh fequences. Sla to descendng type two-laye cuves, we can ty to estate the esstvty of substatu by usng the saple values of the eal the agnay pat of the FNI functon. Howeve, the appoxatons fo (43) to (5) ae not vald fo ths case snce P P. To detene the esstvty of the second laye, the concept of the ecpocal geoelectc secton can be used (Basoku, 994b). Ths secton s obtaned when = / (5) \ \ = / (53) t \ = t / (54) eplace the ognal paaetes. Takng nto account the followng popety tanh[ z + acth(w)] = / tanh[ z + acth(/w)] (55) n vew of (8), one fnds \ \ + = /( ). (56) + Multplyng dvdng the ght-h sde of the above equaton by the conjugate of the denonato, we can obtan the eal agnay pats of the FNI functon fo the ecpocal geoelectc secton as follows: \ = / ( ) (57) + \ = / ( ). (58) + Now, we can apply the appoxatons fo (43) to (5) to the ecpocal geoelectc secton. Accodng to (5), we wte P \ \ \. (59) We can tun back to ognal geoelectc secton by consdeng the ecpocal secton of the equaton (59). Substtutng (53), (57) (58) nto (59), one fnds P ( + ) / ( + ). (60) Ths equaton seves to estaton of the esstvty of the second laye by usng the saple values of the FNI functon at nteedate fequences. Howeve, n the hgh fequency lt, s zeo (60) becoes equal to the squae oot of the esstvty of the fst laye. Snce the appaent esstvty defnton (5) the equaton (60) equal to each othe, one can expect that the defnton (5) would gve appaent esstvty

9 Ahet T. Basoku 7 30 (a) FNI functon Re I (b) Fequency (hetz) Appaent esstvty ( Ω ) C 00 F FIG. 5. a) The FNI functon vesus deceasng fequency fo the pefectly conductng substatu case whee the odel: = 500 oh-, = 0 oh-, t = 350. (b) a copason between Cagnad's appaent esstvty (C) the appaent esstvty defnton a F ( F). values vey close to the tue esstvtes of the subsuface layes n case of ascendng banches. Pefectly Conductng Insulatng Substatu In the case of pefectly conductng substatu ( = 0, P = 0 ), one can pove that the coeffcent k s equal to unty by substtutng P = 0 nto (7). In vew of (37), (38) (40), the nueato the denonato of the eal pat becoe R(f) = snh( a ) / cosh( a ) (6) D(f) = + cos( a ) / cosh( a ). (6) Fo (35) the nueato of the agnay pat can be wtten as follow: I(f) = sn( a ) / cosh( a ). (63) It can be poved that the eal the agnay pats of the FNI functon ae equal to each othe fo suffcently low fequency values: = (64) snce

10 Appaent esstvty ( Ω ) 7 Fequency-noalsed Ipedance 5 (a) 0 FNI functon 5 0 Re -5-0 I Fequency (hetz) 000 (b) 00 F C FIG. 6. (a) The FNI functon vesus deceasng fequency fo the pefectly nsulatng substatu case whee the odel: = 500 oh-, = oh-, t = 350. The stas show the absolute values of the agnay pat appoachng to the eal pat fo hgh fequency values. (b) a copason between Cagnad's appaent esstvty (C) the appaent esstvty defnton (F). a F sn( a ) a snh( a ) a, fo sall values of a (Fg. 5a). The dffeence between the eal the agnay pats becoes zeo equals to the esstvty of the second laye as defned by (5) o (4). In the case of nsulatng baseent ( P = ), (7) can be wtten n the followng fo by dvdng both nueato denonato by P : = ( P / P + ) / ( P / P ) (65) k Snce P = then k becoes equal to -. Puttng k= - nto (40) (4), we obtan -snh( a ) = - ( exp( a ) - / exp( a ) ) (66) -cosh( a ) = - ( exp( a ) + / exp( a ) ) (67) the nueato the denonato of the eal pat becoe

11 Appaent esstvty ( Ω ) Ahet T. Basoku 73 0 F C F C Fequency (hetz) FIG. 7. (a) Syety of appaent esstvty cuves wth espect to the hozontal axs Cagnad's appaent esstvty the appaent esstvty defnton a =. C F ndcate, espectvely. The uppe cuves ae coputed fo the odel: = 3 oh-, = 0 oh-, 3 = oh-, t = 0, t = 50. The lowe cuves of the coespondng ecpocal geoelectc secton ae coputed fo the odel: = /3 oh-, = 0. oh-, 3 = oh-, t = 0/3, t = 5. a F R(f) = snh( a ) /cosh( a ), (68) D(f) = - cos( a ) / cosh( a ). (69) The nueato of the agnay pat can be wtten n sla way as I(f) = - sn( a ) / cosh( a ). (70) Fo sall values of fequency, the agnay pat s negatve ts absolute values ae appoxately equal to the eal pat (Fg 6a): R(f) - I(f) (7) o snce - (7) -sn( a ) - a, snh( a ) a. (7) can also be poved by usng the concept of ecpocal geoelectc secton. The pefectly nsulatng substatu case s the ecpocal secton of pefectly nsulatng case vce-vesa. By the help of (57), (58) (64) by usng the popetes of the ecpocal secton, (7) can also be obtaned. The stuaton can easly be seen n Fg. 6a. The absolute values of the agnay pat ae plotted as contnuous cuve to show how the agnay pat eaches to the eal pat. In that way, we pove the obustness of (5). Due to (7), the denonato of (5) becoes zeo fo ths case consequently the appaent esstvty defnton (5) tends to appoach nfnty. These esults show that the agntude of the agnay pat of the FNI functon vaes between zeo the agntude of the eal pat dependng on the esstvty ato of layes. It s zeo f thee s no contast. Ths coesponds to hoogenous eath case. The eath also behaves lke hoogeneous eath n hgh fequency lt whee the second laye has no contbuton on the FNI functon. Afte eachng a axu o a nu value the agnay pat becoes zeo at low fequency lt. RECIPROCAL PROPERT OF APPARENT RESISTIVIT As defned befoe, the ecpocal geoelectc secton s obtaned when the esstvty values of the subsuface layes ae eplaced by the ecpocals.

12 74 Fequency-noalsed Ipedance The thcknesses of the coespondng ecpocal geoelectc secton ae equal to the thcknesses dvded by the esstvtes of those layes. The equatons (57) (58) gve the elaton between the eal agnay pats of the FNI functon the FNI functon of the coespondng ecpocal secton. The saple values of the coespondng ecpocal appaent esstvty defntons can easly be found fo (57) (58). The esults ae: ' ac = / ac (73) ' = / (74) These equatons show that the blogathc plot of the appaent esstvty cuves wll be syetc wth the appaent esstvty cuves of the coespondng ecpocal secton. The axs of syety s the hozontal axs that ntesects the vetcal axs at unty. Fgue 7 shows the syetes of the appaent esstvty cuves the ecpocals wth espect to the hozontal axs of appaent esstvty equals to unty. CONCLUSIONS The exanaton of the FNI cuves gves useful nfoaton about the esstvty dstbuton of the subsuface layes. The saple values of the eal pat of the FNI functon vay wthn the ange of the squae oot of the tue esstvty values. The ascendng descendng banches of the eal pat ndcate the tanston fo one laye to the next. A se-ccula shaped ac on the agnay pat epesents a bounday between two consecutve layes. In ost cases, the agntude of the eal pat s hghe than that of the agnay pat. Consequently, the contbuton fo the eal pat s donant when calculatng the appaent esstvty usng Cagnad s(953) defnton. Then, a sgnfcant pat of the nfoaton contaned n the agnay pat s lost. Fo ths eason, the effects of the elatvely thn layes on the Cagnad s(953) appaent esstvty cuves becoe nvsble. Moeove, the oscllatons of the eal pat ae tansfeed to the appaent esstvty cuve. But, these oscllatons ae suppessed n the defnton, the effect of the tue esstvty a F values of the layes s agnfed. Because, the agnay pat copensates the oscllatons caused by the eal pat. The appaent esstvty defntons ae useful fo the qualtatve ntepetaton of the MT data. A pactcal applcaton has been descbed by Basoku et al. (997b) fo a assve sulphde exploaton poble. The exanaton of the eal agnay pats of the FNI functon also gve useful nfoaton sees to be oe feasble than the appaent esstvty data fo the quanttatve ntepetaton. Usng the FNI foulaton nstead of the appaent esstvty the phase values ay cay the nveson of the MT data oe effcently n copason wth the conventonal pocedues (Ulugegel Basoku, 994). ACKNOWLEDGMENTS Ths wok suppoted by the Scentfc Techncal Reseach Councl of Tukey (TUBITAK) unde gant no. BAG-0. REFERENCES Basoku, A. T., 994a, Defntons of appaent esstvty fo the pesentaton of agnetotelluc soundng data: Geophyscal Pospectng, 4, Basoku, A. T., 994b, Reply to Coent on Defntons of appaent esstvty fo the pesentaton of agnetotelluc soundng data by L. Szaka: Geophyscal Pospectng, 4, Basoku, A. T., Kaya, C. Ulugegel, E. U., 997a, Dect ntepetaton of agnetotelluc soundng data based on the fequency-noalzed pedance, Geophyscal Pospectng, 43, 7-34 Basoku, A. T., Rasussen, T. M., Kaya, C., Altun,., Aktas, K., 997b, Copason of Induced Polazaton Contolled Souce Audo-Magnetotellucs ethods fo the assve chalcopyte exploaton n volcanc aea, Geophyscs 6, Cagnad, L., 953, Basc theoy of the agnetotelluc ethod of geophyscal pospectng: Geophyscs, 8, Kaufan, A. A., Kelle, G.V., 98, The agnetotelluc soundng ethod: Elseve. Schucke, U., 970, Anoales of geoagnetc vaatons n the southwesten Unted States: Scpps Insttuton of Oceanogaphy Bulletn, 3, Unv. of Calfona Pess, 65 pp. Spes, B.R., Egges, D.E., 986, The use suse of appaent esstvty n electoagnetc ethods: Geophyscs, 5, Szaka, L., 994, Coent on Defntons of appaent esstvty fo the pesentaton of agnetotelluc soundng data by A. T. Basoku : Geophyscal Pospectng, 4, Ulugegel, E. U. Basoku, A.T., 994, Effect of the type of data on the soluton of laye paaetes n agnetotelluc nveson (n Tuksh), Jeofzk, 8, 3-46.