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Geophys. J. R. astr. SOC.(1982) 70, 323-337 Magnetotelluric studies in the Market Weighton area of eastern England D. Kao and D. Orr Depnrtment ofphysics, University of York, Heslington, York YO1 5DD Received 1981 September 23; in original form 1981 May 22 Summary. Magnetotelluric measurements at periods from 30 to 1000s were made at eight locations in the Market Weighton (MW) area, along an east-west profile across gravity and magnetic anomalies. Dimensional parameters were developed for assessing the structural dimensionality of the electrical conductivity of the Earth from the data. One-dimensional inversion modelling techniques were employed to interpret the data at each site, and four-layer models were obtained to explain the main structure of the crust in the area studied. If it is assumed that all strata are unmagnetized then the results show that there is a highly resistive layer in the crust, the thickness of the highly resistive layer ranges from 12km in the east to 44 km in the west with a large change in the middle near the MW site. A structural boundary lying northsouth near MW was also indicated by the principal directions of rotated apparent resistivities and transfer functions. Both electrical conductivity and magnetic permeability contrast in the ground were considered in an attempt to interpret the observed variations in apparent resistivity at different periods. 1 Introduction The Market Weighton region in East Yorkshire as shown in Fig. 1 has long been of interest to geologists because of its distinctive geological situation. Various geological and geophysical investigations have been undertaken in the past, and many of the results can be found in the reports of Jeans (1973), Kent (1974) and Bott, Robinson & Kohnstamm (1978). Thermal investigations (Richardson & Oxburgh 1979) have shown that there is a relatively high heat flow region in the south-west of East Yorkshire. Bott et al. (1978) have analysed the gravity and magnetic anomalies, and their interpretation was of a moderately magnetized granite emplaced within a more highly magnetic basement, the basement rocks being at least 2km below the ground surface. To complement these studies, we have made magnetotelluric (MT) measurements to determine the electrical conductivity structure of the deep crust. 2 The MT project The eight locations at which the MT soundings were made are shown in Fig. 1. They were chosen such that the main traverse from sites 1 to 6 crossed the magnetic and the gravity 324 D.Kao and D.Orr Figure 1. Map showing the locations of the MT sites from (1) to (8). - G indicates the centre of the gravity low, and + M is a positive magnetic anomaly. anomalies and was approximately perpendicular to the coast line. The two horizontal components of the electric field, Ex and E,,, and the three components of the magnetic field, H,, H,, and H,, were measured at each site. A fluxgate magnetometer was used to measure the time variations of the magnetic field. The variations were amplified and frequency modulated, and the modulated signals were recorded on analogue magnetic tape. The electric fields were measured by using lead electrodes in an ‘L’ array buried in the ground about lOOm apart. The electric field recording system was identical to that of the magnetic field system, except that a high gain preamplifier was employed. The overall frequency response of the system was flat in the range 10-1000s. Total time of data collection at each site varied from three days to two weeks, depending on the weather conditions, the level of magnetic activity and local noise. Basically, we required 20 to 30 sections of useful data to be collected from each site. A ‘useful’ data section here means continuous signals with high signal to noise ratio (s/n) and good coherences lasting more than 1hr. Data recorded on magnetic tapes were replayed on a chart recorder and were then evaluated visually in the preliminary selection procedure. 3 Data analysis Data processing mainly followed the procedure given by Vozoff (1972). After Fourier transformation of each data section into the frequency domain, smoothed auto- and cross-power densities, by frequency-band averaging, were computed. The following parameters were calculated for each data section: (a) ordinary coherences of Ex H, and E, Hx , (b) magnetic and electric field polarization parameters, (c) magnetic field transfer functions, (d) unrotated and rotated tensor impedance and apparent resistivity, (e) predicted coherence (7’)’and (f) dimensional parameters. 325 Magneto telluric studies in eastern England The results from the 20-30 sets from each site were not used for interpretation, but were further evaluated. In addition to high coherence and favourable polarizations, the main criteria for data selection at this stage was the smoothness of the rotated apparent resistivity and phase curves and the consistency of the results over all sections. Those sections having apparent resistivity and phase curves consistently smooth were selected, otherwise they were rejected. In general, 15-20 sections were selected out of the 20-30 original ones, i.e. about one-third were rejected. For the selected data, power densities were summed and averaged to give the final power estimates, which were then used to compute the parameters from (a) to (f) given above to yield the final results. Further selection was undertaken by using data with predicted coherence greater than 0.9. Those data, whose predicted coherence were less than 0.9 or where the results were very scattered, were rejected. As an example, the results for site 8 are shown in some detail in Fig. 2; the rotated MT responses are given in the period range from 30 to 1000s. The top graph indicates that the apparent resistivity anisotropy is small at the shortest period but increases for longer periods. Both phases, d,, and $,in, increase with period reasonably smoothly from low values close to zero degrees to approximately 45". The skew, cy, in the third graph from the top in Fig. 2, is less than 0.1 at all periods. Finally, the transfer function IA I is depicted, it has a maximum at the longer periods. The final results from all the sites are given in summary form in Figs 3 and 4. These figures contain additional information in the form of arrows; the upper set indicate the direction of pmaxand the lower set refer to the direction deduced from the transfer function analysis pointing in the direction in which IA I is a maximum. The positive directions of the ordinate and abscissa axes are north and east respectively. E c o + t + + + + t t t * o + + !i f $ +?4 ' 4 4 pma" t+++t++++t+ P- 1440- 1L a A A A A A A A ~ A A A A A A A A A A LOG T Figure 2. The rotated MT responses for site 8 in detail. The four graphs show the variation with period of: (1) the maximum and minimum apparent resistivity, (2) the maximum and minimum phase, (3) the dimensional indicator, skew (Y (4) the transfer function iA I. 326 D. Kao and D. Orr .2 A A A A A n .2 A A A \\ t t \ \ / / / / / , / / - . 11 .so 0 lo'. . .. b, l A Figure 3. The MT response at sites 1, 2 , 3 , and 4 in a similar format to Fig. 2. The two sets of arrows give additional information on the directions of the maximum apparent resistivity, omax (upper set) and the transfer function (lower set). The directions are given by up is north and to the right is east. 4 Dimensionality analysis In this section we will develop dimensional parameters to assess the dimensionality of the structure of the Earth revealed from the measured data. Traditionally skew, a!,introduced by Swift (1967), is used as a dimensional indicator. In the theory, a! = O where the electrical conductivity structure of the Earth is one- or two-dimensional (1-Dor 2-D),and a! > 0 for three-dimensional (3-D)structures. However, the upper limit of the value of a! for a 3-D structure has not been clearly defined. In the 3-Dmodelling study by Reddy, Rankin & Phillips (1977), the largest value of a! found was 0.4,and a! 0.2 was considered to be significant evidence for 3-Dconductivity variation. Ting & Hohmann (1981)calculated a! 7 0.12in1 their 3-Dmodelling results. However, results from field data analysis often show that a! 0.4 is rather moderate, and on many occasions a! is much larger than 0.4 even when other factors such as apparent resistivity and phase anisotropies indicate 1-Dor 2-Ddomination. Skew a! appears to be easily contaminated by noise contributions, and as noise is inevitably present 9 Magnetotelluric studies in eastern England I \ \ \ f \ \\ / / 321 / .2 [oA A A A 1 .z\ \ naA A A A A A A A A A a \ t \ \ \ I t .. .. ... '. Pmap.. LOG T Figure 4. The MT responses at sites 5,6,7,and 8; the format is the same as Fig. 3. in the field data it makes an uncertain parameter with which to estimate the dimensionality of the Earth. For this reason we introduce new dimensional factors to assess the structural dimensionality from the field data. Impedance tensor elements related to the electric and magnetic fields in the original (or sounding) coordinates are The rotated impedance Z(e) was derived from the matrix equation z(e)= R Z R ~ where I cose sine -sin0 C O S ~ 328 D.Kao and D. On and 8 is the rotation angle measured in a clockwise sense from the measurement coordinates looking down on the Earth from above the site. We define Zil{8) as the rotated impedance elements which are a function of the rotation angle 8. The elements ZY are the impedances in the original coordinate system. The following relations hold: zx,(e) - Z,,@) =z x , Z,,(8) +Z,,@) = z x , z,(e) = - zx,(e t z(,e) = z,,(e - z y x (= 2 2 1 ) (44 (= (4b) +zyy 223) 90") (4c) + 90"). (4d) Following Sims (1969), the loci of the Zi,(0) in the complex plane as a function of rotation angle 8 are elliptical in the general cases (3-D earth) as shown in Fig. 5. These ellipses are centred at +Zl and Z 3 ,and have the principal axes as follows: Major axis = Zx,(80) + z,,(eo) minor axis = Zxx(80)- Z y y ( b ) . In equations ( 5 ) O0 is the angle between the original direction (usually north) and the direction where \Zxy(80)tZ,,(8,)l is a maximum. This is also the direction which is termed the 'principal direction' where pmax is presented. These graphical representations in Fig. 5 show the impedance behaviour with rotation and are helpful in the determination of structural dimensionality. The skew equals the ratio of the two centres as follows a = I( z x x zyy)/(zxy - Zyx) I = Iz3/z1 I (6) which is invariant with rotation and is greater than zero in 3-D cases. In 2-D or 2-D equivalent cases (Ward, Smith & Bostick 1971),Zxx(80)= Z,,(80) = 0 and Z,, t Z,,, = 0 for all 8. The loci become straight line ellipses as shown in Fig. 5 , centred at the origin for Zxx( 8)and at Z1for Zx,(8). 3-D 2-D I-D YX -P T- t zxx=o , in the complex plane, for 1-D, 2-D or 2-D equivalent and 3-D strucFigure 5. Loci of Z x y ,Z and, Z yx. tures. Zyx is symmetncal with Zxy about the origin and is omitted in the 1-D and 2-D cases. Magnetotelluric studies in eastern England 3 29 In 1-D cases, Z,, = ,Z , = 0 and Z,, = -Z, = Z for all 8. Impedance elements become isotropic functions of 8 and rotated loci become point ellipses centred at the origin and Z1 as shown in Fig. 5. Summarizing the above analysis, it concludes that the structure of the earth generally may be represented by three components, i.e. 1-D, 2-D and 3-D components. Their analot Z,,(6JO) and Zx,(0o) T Z,,(80) gous response components of impedance are Z1,Z,(80) corresponding to equations (4a), (Sa) and (4b, 5b) respectively. The amplitudes of these response components can be used to represent the relative weights of the structural components. When the dimensions of the impedance ellipses in Fig. 5 are very small compared with Z1, interpretation in terms of a one-dimensional earth is a good approximation. Therefore we use the impedance response components to define the dimensional factors (74 Dl = 12, I/S 0 2 = I [zxy(00) +zyx(80)!/2 I/s (7b) 0 3 = IZJI/S (7c) 0 3 ' = I [zxx(eo) - ~ , y ( e o ) i / 2ID (74 where D1,02, and 0 3 and 0 3 ' represent the weights of 1-D,2-D and 3-D structural components of the Earth, and S is given by The skew a,defined in equation (6) is related to these dimensional factors in a simple way as a = 03/01, and the ellipticity, Po, introduced by Sims (1969), is also a simple ratio of the dimensional factors given in equation (7) above; Po = D3'/02. The reason for defining these new dimensional factors is to give dimensional weights quantitatively, so that it becomes + ' zxy < 1x1 s e a 0 . 0 . 0 . 1. 0 *... A A A 1 a D1 . a . 0 . . 3 * * * * * * * * * * * ***:yD' A . a A 1. A 2," z+,,,,, a ZXY (100 .OF1 A D 1 A A 3 2 LOG T Figure 6. The variation of the rotated impedance, CY and the dimensional parameters with period for site 8. Two examples are shown of the complex impedances at 100 and 320s. 330 D.Kao and D.Orr F 110 ..'.. . .. .* D1 *... ... . 02 .-... 2 D1 , 0 3, LOG T Figure 7. The variation with period of average apparent resistivity and phase, defined in equations (9)and (10) and dimensional factors defied in equation (7) for sites 1, 2, 3, and 4. possible to directly measure the importance of the different structural components of the Earth. Fig. 6 shows the variation with period of these dimensional factors and a values together with the rotated impedance at site 8. Dimensional factors for all the sites are shown in Figs 7 and 8, where 0 3 corresponds to (03 t 0 3 ')/2 (equations 7c and 7d). Figs 7 and 8 show that the D2 component is typically about 0.2 and D3 contributes less than 0.1 for the majority of estimates, except those at site 1 where D2 and D3 are relatively large and the data are also relatively scattered. The best estimate of the noise-to-signal ratio of the measured data is about 10 per cent (predicted coherence 0.9),which is greater than the D3 weight. Therefore, a value for D3 of less than 0.1 suggests that the contribution to the impedance of the Earth as measured at the Earth's surface in the period range 30-1000s does not contain a significant part arising from the presence of a 3-D conductivity structure in this area. The presence of 2-D structure is also not pronounced. Thus, a I-Dmodel would be expected to satisfy the main features of the structure under each individual site. In this first attempt to obtain an electrical conductivity 33 1 Magneto telluric studies in eastern England 1- I Figure 8. The variation with period of average apparent resistivity and phase, defined in equations (9) and (10) and dimensional factors defined in equation (7) for sites 5,6,7,and 8. profile across the region we use average values of pa and @ which are given by the following equations. P = I (ZXY- Z,,)/2 6 = tan-' (94 12/~Po = 1211 2 / w o (Im Z1/Re 2,) 8' = 0.5 (@,ax (9b) (lob) + Gmin) 4' in general, and P = P' and 6 = 4' for a 1-D earth. When 6 = fi' and 6 = for all the observed frequencies, it will further indicate the validity of a I-D approximation. Figs 7 and 8 also show these average values which are almost equal. The 6 and (p in equations (9a) and (9b) will be used for 1-D modelling. P < P' 332 D.Kao and D.On 5 Results and discussion 5.1 O N E-DIM E N S I O N A L M O D E L L I N G 1-D inversion methods (Fischer e l al. 1981; Fischer & Le Quang 1981) were used to estimate the electrical conductivity structure at each site. The inversion scheme starts with the shortest periods of the available data set and seeks to explain the apparent resistivity and phase in terms of a two-layer structure. The procedure is then to shift successively to longer periods, introducing discrete new layers at progressively greater depth and seeking to minimize the standard deviation between the measured and calculated impedances. Fig. 9 shows an example of the inversion results, a four-layer model, model (a) in the figure, is found to be a good fit to the observed data at site 3. The top layer of this model has resistivity p1 = 100Rm and thickness h l = 500m, these parameters have been estimated with the help of DC resistivity soundings. The second layer is conductive and has resistivity 5.1 Rm and thickness 1.5 km. The third layer is rather prominently resistive and thick and has resistivity 10 000 Rm and thickness 32 km. The bottom half-space is relatively conductive with resistivity of about 130Rm. The regional geological structure within 1 km or so of the surface is mainly layered with a gentle dip eastward, and very likely has water-filled layers within this depth limit. It is also reported (Kent 1974; Bott et af. 1978) that moderately magnetized granite is emplaced in the more highly magnetized basement in the Market Weighton area, with the basement rocks being at least 2 km below the ground surface. b a C h h hrhml P 100 .5 100 .5 100 .5 5.1 1.5 5 .I 1.5 5.I 1.5 Plnml P p, = 1.5 p,=1.1 p,= 1 10' I o4 10. 32 4 s 29 21 4 1 130 130 130 ! ) I 1 2 # LOG 3 ,4 T Figure 9. 1-Dinversion of data from site 3. Curves (a), (b), and (c) corresponding to models a, b and c respectively where the third layer in models b and c is magnetized. 333 Magnetotelluric studies in eastern England Kao & Orr (1982) studied the effect of a magnetized layer on the MT response of a uniformly stratified earth. They showed that a magnetized layer defined in terms of permeability resistivity and thickness by ( p , po, p , h) and an unmagnetized layer ( po, p, p , prh) give equivalent MT responses, where p, is the relative magnetic permeability of the layer. In other words, the effect of a magnetized layer is to make its thickness appear pr times greater than an unmagnetized equivalent one. Models (b) and (c) in Fig. 9 show this effect; if the resistive layer has pr = 1 . 1 the thickness will reduce to h3 = 32/1.1= 29 km, and if pr = 1.5 then h3 = 21 km. We applied the above procedure to each of the sites (except site 1 where the data are relatively scattered and D1 is not so dominant, hence it may not be suitable to use a 1-D approximation). We then assembled the 1-D structures sequentially for the five sites in the west-east traverse. Thus, a 2-D model along the sounding profile was obtained, see Fig. 10, which presents a possible electrical structure of the Earth in the area studied. Also included in the figure are the results from sites 7 and 8 which are to the north of the profile. The data indicate that the general character of all the sites have similarities in both apparent resistivity and phase. As the period increases the apparent resistivity tends to increase and the phase changes from approximately zero to 45°C. In the four-layer model presented here, we have used D C resistivity measurements taken from six locations in the area to define the resistivity and thickness of the top layer; typically the depth of penetration of the current was 500m and resistivity values in the range 55-450lrtm were obtained. On the basis of these results we chose 100SZm and 500 m as the parameters which define the first layer at each site. The MT apparent resistivity measurements, at the shortest period at all sites, give values of less than 50lrtm. This, in conjunction with the assumption about the resistivity of the first layer, implies that there is a more highly conducting layer below the top one. Resistivities from 1 to 6 SZm and thicknesses from 0.5 to 1.7 km are indicated, this may correspond 7 8 2 3 My 4 5 6 V V V V I V V V - - i.3 k m l 1 0 0 Om I1 21 -lo4 n m 30 1341 .: 130 10 k m I c I V SITES or,; 330 Fmre 10. Models of possible geoelectric structure in the Market Weighton area showing the effect of on the thicknesses at site 2 and 3. The number in brackets is the thickness in km. The number without brackets is the resistivity in a m . The thicknesses of the fiist two layers are not to scale. fi>fio 334 D.Kao and D.Orr to water-filled zones. The small variations of these parameters in the second layer between different sites may not be significant, because the periods used are greater than 30 s, corresponding to a skin depth of more than 5 km which is larger than the total thickness of the first two layers. Further D C resistivity work and higher frequency MT measurements will be undertaken close to the MT sites in order to define the first 2 km more accurately. The third layer (unmagnetized model a) is highly resistive and thick at all sites, having resistivity in the range 7000-20 000 a m ; in this model we fixed the resistivity at 10 000 a m , the thicknesses were found to vary from 12 km at site 6 increasing westward to 44 km at site 2. There are several possible explanations for this systemative change in thickness of the resistive third layer, we draw particular attention to two of them: (a) The transition to the more highly conducting lower half-space at shallower depths for the eastern part of the traverse may correspond to a change from a poor conductor to a hydrated granite which is sufficiently hot to become a relatively good conductor. Wyllie (1971) has studied the beginning of melting of various rock types in the presence of water; he concludes that partial melting of granite can occur ar relatively low temperatures, for example, partial melting of hydrated granite occurs at about 600°C for pressures in the range 3-20 kbar (corresponding to depths of 10-60km). If we assume a thermal gradient of 30-40°C km-' in this area, then partial melting of hydrated granite would occur at depths in the range 20-15 km. Further work on the electrical properties of granite (Olhoeft 1981) has emphasized the possibility of low resistivity when free water is available and the temperature is above 500°C. Similar conclusions concerning a conducting layer in the lower crust and, or, upper mantle have been deduced by Jones & Hutton (1979). (b) Magnetization effect, as mentioned previously, the effect of a magnetized layer of relative permeability p, > 1 , is to make it appear pr times thicker than the equivalent layer which is assumed to have = 1 . Fig. 10 shows the models with the effect on the thickness of the third layer of different relative permeabilities. 5.2 DIRECTIONAL PROPERTIES OF THE IMPEDANCE AND TRANSFER FUNCTIONS Two perpendicular principal directions of the impedance tensors are determined by maximizing I Zx y ( 0 )+ Z,,,(O) I. The direction in which the apparent resistivity is a maximum, pmax,is used as the 'major principal directions' (actually two opposite directions) which is illustrated by arrows at the top of each diagram in Figs 3 and 4. For a 2-D or 2-D equivalent structure of the Earth, the major principal direction is parallel to the strike on the conductive side, and perpendicular to the strike on the resistive side. The transfer function and its principal direction, which are termed tipper and tipper direction (Vozoff 1972;Jupp & Vozoff 1976) are obtained from maximizing the modulus of A by rotating the following relationship H, = A Hx + B H y . There are two directions (opposite to each other) between 0 and 360" which give maximum values of I A I. The one where I A 1 maximum tends to give the rotated Hx and H, in phase is used as the 'major principal direction' and is illustrated by the lower set of arrows in Figs 3 and 4, associated with the amplitude IA I. In a 2-D or 2-D equivalent structure of the Earth, the principal directions of the transfer function are always perpendicular to the strike; the major principal direction will change by 180" close to a structural boundary. Fig. 1 1 shows the major principal directions at each site for data averaged in the period range 100-500s. The amplitude of the solid arrow represents the relative amplitude of IA I maximum. For the case of apparent resistivity, the length of the dashed segment is 0 2 Magnetotelluric studies in eastern England 335 I 10 KM _____( (iJ sites Figure 11. Major principal directions of the transfer function (solid arrow) and of 0 2 or anisotropy of the rotated apparent resistivities (dashed segment). The data have been averaged for the period range from 100 to 500 s. A structural boundary between sites 3 and 4 is indicated. The dotted line maps the approximate location of a geological boundary. given in equation (7b), which is equivalent to the anisotropy between the two rotated apparent resistivities. The major principal directions indicate that a structural boundary lies approximately north-south in the region of sites 3 and 4. This boundary indication could be the response from: (a) the boundary between the base of the chalk and the Permian rocks as shown in Fig. 11 (Kent 1974); (b) the boundary between the magnetized basement and the emplaced granite as mapped by Bott et al. (1978), i.e. the magnetization contrast in the basement rocks as shown in Fig. 10; or (c) The change of thickness of the highly resistive layer between sites 3 and 4 as is also shown in Fig. 10. 6 Conclusions MT measurements in the period range 30-1000s were made at eight locations in the MW region. Dimensional factors were developed for estimating the structural dimensionality of the Earth from the measured data. A 1-D inversion method was used to model the data at each site, and four-layer models were obtained to explain the main structure of the Earth in the area studied as shown in Fig. 10. The first layer has resistivity pl = 100 SZm and thickness h l = 0.5 km. The second layer is conductive and has resistivity from about 1 to 6 SZm and thickness about 1km. The third layer is highly resistive and thick, having resistivity p3 = 10000 SZm and when we assume that this layer has a relative permeability of 1 then the thickness varies from 12 km in the east to 44km in the west. The bottom half-space is relatively conductive having resistivity of about 100SZm on average. Because the periods of the electromagnetic fields measured are greater than 30 s, the data give clearer information concerning deep crustal structure than about the near surface rocks. 336 D.Kao and D.Orr A structural boundary lying approximately north-south through MW was indicated by the principal directions of the rotated apparent resistivities and of the transfer functions as shown in Fig. 11. To the east of MW, the major principal directions of these two specific quantities are perpendicular, and the major principal directions of the apparent resistivities are approximately north-south. To the west of MW at site 3 the major principal direction of the apparent resistivity tends to point east-west and is also closely parallel to that of the transfer function. In general, the signal level of the vertical component of the magnetic field, H, was rather low and contaminated by noise, thus the transfer function analysis is not as significant as the rotated resistivity work in which the signal to noise ratio was very much better. In the future we plan to make measurements at higher frequencies; without these data it is difficult to interpret whether the boundary is lying within the top few kilometres of the surface or if it is lying at depth. As the periods of these data are from 100 t o 500 s, it may be reasonable to postulate that the boundary lies below the first few kilometres of the crust, either a conductivity contrast or a permeability contrast, or both. The conductive basement at depth may arise from high temperature. The relatively small depth (12 km at site 6) of the conductive basement under eastern sites may be explained if granite intrudes from the east of MW. The coastal effect may also be important and such an effect can be examined by MT soundings along a profile parallel to the coast line. These future measurements will be interpreted with the help of the numerical modelling of the coast effect undertaken by Mbipom (1 980). To summarize, in this initial survey and analysis of the data in terms of a 1-D model a resistive layer, which is more than 1 km below the surface, has been detected (the third layer of resistivity 10 000 R m in the model). We have drawn attention to the way the apparent thickness of this layer decreases towards the east; it should also be noted that at site 3, some 6 km to the north of the main east-west traverse, the thickness of this third layer increases to a depth close to the position of the Moho for the typical continental crust which underlies Britain (Bamford ef al. 1976). This large change in thickness between sites 5 and 8 may arise from a structural change associated with the northern boundary of the granite batholith postulated by Bott et al. (1978), and points to the need to undertake 2-D modelling of the region. We are planning a further MT project to investigate the crustal structure in this area in more detail, this will include an examination of the coastal effect and 2-D modelling of the data. Acknowledgments This study was supported by the Natural Environment Research Council of UK under project GR3/308 1. The authors gratefully acknowledge this support and also that from the Department of Physics at the University of York; particularly valuable contributions have been made by David Coulthard, Greg Wadman and Adrian Tatnall. We also thank local farmers for their friendly cooperation in allowing measurements on their land. 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Monogr. Am. geophys. Un., 14,279-301. 12