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Physics of the Earth and Planetary Interiors, 42 (1986) 246-254 Elsevier Science Publishers B,V., Amsterdam - Printed in The Netherlands 246 Theoretical investigation of the o c e a n - c o a s t effect at a passive continental margin Gaston Fischer and J.T. Weaver * Observatoire Cantonal, CH-2000 Neuchhtel (Switzerland) (Received August 28, 1985; revision accepted December 23, 1985) Fischer, G. and Weaver, J.T., 1986, Theoretical investigation of the ocean-coast effect at a passive continental margin. Phys. Earth Planet. Inter., 42: 246-254. The idea that oceanic lithosphere is thinner than continental lithosphere is widely accepted even though one would like to see clearer evidence to support it. In fact, the very concept of lithosphere is still a matter of some debate. If there is indeed a variation in the thickness of the lithosphere at continental margins and if this change is associated with a lateral variation in electrical conductivity one may envisage detecting it with electromagnetic soundings methods. A model of a passive continental margin has therefore been investigated to test whether this would be feasible. It has been found that the well-known but strong ocean-coast effect masks the minor lithospheric effect in magnetotelluric soundings performed on the shore. Inductive soundings, on the other hand, are highly sensitive to lateral variations in electrical conductivity. An analysis in terms of the induction arrow has shown that such soundings carried out on land would be perfectly suitable to reveal a changing lithospheric thickness, if the continents merely extended to the oceanic coast. However, the presence of only a narrow continental shelf of 100 km width under 250 m of sea-water produces an overriding coast effect ahead of the margin, and thus renders electromagnetic methods unsuited to reveal a changing lithospheric thickness. 1. Introduction T h e past few years have seen a n u m b e r of papers dealing with model calculations of the o c e a n - c o a s t effect. F o r the most part these models were t w o - d i m e n s i o n a l (2-D) a n d the ocean was simulated with a perfectly c o n d u c t i n g semi-infinite sheet. Bailey (1977) gave a n analytic solution of the B-polarization (B-POL) response of such a simple ocean at the surface of a u n i f o r m half-space. Nicoll and Weaver (1977) extended this work to include a perfect conductosphere at typical m a n t l e depths of 5 0 - 6 0 0 kin. The Epolarization (E-POL) response of the simple model was solved semi-analytically by Fischer et al. (1978, 1980) a n d a n analytical solution in closed form * On leave from the University of Victoria, Victoria, B.C., V8W 2Y2 Canada. 0031-9201/86/$03.50 © 1986 Elsevier Science Publishers B.V. was then given by Raval et al. (1981). Paralleling these developments great progress was made i n analytical a n d n u m e r i c a l calculations with models involving superficial thin sheets of finite conductance. These new methods are often used to tackle 3-D problems (cf. Vasseur a n d Weidelt, 1977; D a w s o n a n d Weaver, 1979b; Weaver, 1979, 1982; M c K i r d y a n d Weaver, 1983; M c K i r d y et al., 1985) in c o n n e c t i o n with regional studies a n d are very suitable for looking at various forms of the transition from l a n d to ocean. G r e e n a n d Weaver (1978) considered a model simulating a c o n t i n e n t a l m a r g i n out at sea a n d M c K i r d y a n d Weaver (1984) generalized this m e t h o d to include a stratified substratum. D a w s o n a n d Weaver (1979a) a n d D a w s o n et al. (1982), respectively, solved analytically the B-POL p r o b l e m s of two u n i f o r m thin half-sheets a n d of two generalized thin sheets over a u n i f o r m half-space, and Daw- 247 Thin 8beet with conductance "l" × Ef~ I~H y Om o 3 I Z model 1 : P3 = model 2 : pz=p1, modal 3 : P3 = Pz = P3-- P2 PI PI/1~ -- P l / I ~ Fig. 1. Sketch of the models considered. The thin conducting sheet represents the ocean whose resistivity is taken to be 0.25 f~m. The various oceanic depths assumed correspond respectively to a continental margin (d = 250 m, ~"=1000 S) an intermediate ocean ( d = 1000 m, ~-= 4000 S) and a deep ocean (d = 4000 m, "r = 16000 S). With model 1 the perfect conductor (~" ~ o0, d --, 0) is also considered for comparison. In addition a fourth model is studied, similar to models 2 and 3 with ~"= 16000 S, but involving a 100 km continental shelf where ~-= 1000 S and extending over the continent from its right-hand edge. son (1983) o b t a i n e d the a n a l y t i c solution for the c o r r e s p o n d i n g E - P O L p r o b l e m of two u n i f o r m half-sheets. I n the p r e s e n t p a p e r we e x a m i n e the coast-effect when oceans of different d e p t h s are s i m u l a t e d with u n i f o r m thin sheets of various c o n d u c t a n c e s . F o r the s u b s t r a t u m we choose either a h o m o g e neous half-space ( m o d e l 1) or a s s u m e an a s t h e n o sphere with a ten-fold increase in conductivity. In m o d e l 2 this a s t h e n o s p h e r e is p l a c e d at a c o m m o n d e p t h of 100 k m a n d in m o d e l 3 its d e p t h is set at 100 k m u n d e r the l a n d a n d at 50 k m u n d e r the ocean. These various m o d e l s are sketched in Fig. 1. A fourth m o d e l is then considered, involving a c o n t i n e n t a l shelf b e t w e e n the coast a n d the deep ocean. W h a t we have in m i n d for the p r e s e n t s t u d y is to investigate w h e t h e r it might b e p o s s i b l e with m a g n e t o t e l l u r i c a n d / o r i n d u c t i o n s o u n d i n g s to resolve changes in the structure of the l i t h o s p h e r e a n d the u p p e r m a n t l e at a passive c o n t i n e n t a l margin. T h e thickness of the c o n t i n e n t a l lithos p h e r e has in general b e e n taken to be in the range of 7 0 - 1 0 0 k m a n d for the oceans figures as low as 2 0 - 3 0 k m (cf. Maxwell, 1984) have often b e e n p r o p o s e d . In a recent s t u d y b a s e d on the r e s p o n s e o f the p l a n e t to the last d e g l a c i a t i o n Peltier (1984) c a m e f o r w a r d with c o n t i n e n t a l lithospheric thicknesses in excess o f 200 km. If there is i n d e e d an i m p o r t a n t r e d u c t i o n of this thickness at passive c o n t i n e n t a l margins, a n d if this change is associa t e d with a m a r k e d v a r i a t i o n in electrical resistivity, it is w o r t h verifying whether e l e c t r o m a g n e t i c s o u n d i n g m e t h o d s could c o n f i r m it. H i t h e r t o the o c e a n - c o a s t effect has b e e n s t u d i e d p r i m a r i l y w i t h a view to investigating the influence of highly c o n d u c t i n g oceans on m a g n e t o t e l l u r i c or i n d u c t i v e responses. These effects are so large (cf. the re- 248 views by Fischer, 1979 and Parkinson and Jones, 1979) that they are likely to mask the much less significant effect of a changing lithospheric thickness. In principle the oceanic lithosphere and upper mantle can be studied by sea-floor magnetotelluric soundings like those of Filloux (1980, 1982). However, such experiments are technically difficult and the shielding effect of the conducting ocean water reduces the available magnetic signal. Measurements on land would be far easier to carry out, but it remains to show whether they are likely to provide the information necessary to elucidate the structure of passive continental margins. itself was only one cell in thickness in the case of the smallest conductance value used, no numerical problems arose in the finite-difference treatment of this extreme model. The finite difference method was also used in models 1 and 2 when computing the deep ocean response (d = 4 km), as this depth would violate the thin sheet approximation which presupposes that d is much less than the skindepth. 3. The magnetotelluric response In Figs. 2, 3 and 4 the respective responses of the three models are reproduced. Assuming a sea- 2. Method of computation COAST EFFECT MODEL 1 6~ A series of analytical solutions (Dawson and Weaver, 1979a; Raval et al., 1981; Dawson, 1983) have provided exact results for the response of model 1 to a uniform field. However, since it has been established (Dawson and Weaver, 1979a; Dawson, 1983) that the numerical method of Green and Weaver (1978) in both the E- and B-polarization modes is extremely accurate, and since the numerical method is much faster on the computer than the evaluation of the closed form integrals in the analytic solution, it was decided to use this program to calculate the responses of model 1. Only for a perfectly conducting ocean were analytical results used since these have been tabulated by Raval et al. (1981). The calculations for model 2 were made with the aid of the computer program developed by McKirdy and Weaver (1984) which is based on an extension of the Green and Weaver theory to include a layered half-space beneath the thin sheet. The only difficulty occurred with model 3 because, at present, the thin sheet programs cannot accommodate a substructure which includes lateral variations of conductivity. Thus these calculations were performed by using the full 2D finite-difference program of Brewitt-Taylor and Weaver (1976). The thin sheet representing the ocean was simulated by a layer of finite thickness with a given resistivity of 0.25 £m. Even though grid cells representing this ocean were extremely elongated in some parts of the model and the layer /" SB B-POL 30 20 [,::. . . . . . . . 10 0 I -3 "2 21 ~ l 2 DISTANCE B-POL v ~@@@ / J DISTANCE Fig. 2. M T response of model 1. To avoid crowding the graph the curves corresponding to ~-= 16000 S have not always been plotted. We recall that the horizontal distances are given in terms of the skin-depth in lithospheric material. One unit therefore amounts typically to 100 km for material of 100 ~2m resistivity at a period of 40~r2 = 400 s. The same scale length applies to all the following figures. 249 COASTEFFECT COASTEFFECT MODEL 2 66 MOOEL 3 ...... 70 ~ttt~:::c:L[-',,I 56 60 46 50 30 40 E-POL ~.-, _~<:222]--.,', B POL C~ 20 ]0 20 ! I ~ 6 22 -]6 Z1 i0 i' } - 0_3 - -2 -1 8 1 B-PDL POL "RL' -,. ,,,., o~ E-POL ~,.,.,~, ~ " '~ I ~'<,',,I '0,,I "'~'--. . . . . . . . n-. -: "2 Jl 2 DISTANCE OISTANCE 0 OISTANCE 1 4¢8~ T. loao s s 2 '< 03 - -'z -'l 6 DISTANCE 1 Fig. 3. MT response of model 2. To avoid crowding the graph some curves are left out. Fig. 4. MT response of model 3. To avoid crowding the graph part of the z=16000 S curve is left out in the apparent resistivity plot. water resistivity of 0.25 f~m the assumed ocean conductances of ~"= (1, 4, 16) x 103 S correspond to bathymetric depths of d = (2.5, 10, 4 0 ) × 102 m, i.e., respectively, a very shallow sea (e.g., a typical continental margin), an intermediate and a deep ocean. In Fig. 2 (Model 1) we have also plotted for reference the response of a perfectly conducting ocean (~" = oo, d = 0). The distance scale is given in terms of the skin-depth 81 in lithospheric material, and at the chosen period of T = 2rr/¢0 = 40~r 2 s yields a unit of 100 km for the assumed lithospheric resistivity of Pl = 100 ~2m. The apparent resistivities in Figs. 2 - 4 have been normalized with respect to their value at infinity on the left, and the horizontal scale is in units of skin-depth 81 - { ( 2 P l / ~ # 0 ) SO that the various graphs can, to some degree at least, be scaled to other periods and other resistivities. For, if the dimensions of the model measured in units of 81, the resistivity ratio p 3 / / P l = 1/10, and the conductance of the ocean measured in units of 81/01 are all held invariant then the curves plotted in Figs. 2 - 4 will remain unchanged for all models obtained by varying T and Pl- (Note that since the sea-water resistivity must have the same value 0.25 S m -1 in all models, holding the dimensionless conductance of the ocean constant causes the ocean depth to scale like ~ .) The most striking feature of the ocean-coast effect, as displayed in Fig. 2, is the large anisotropy of the apparent resistivity on land close to the shore, even for a very shallow ocean, and the abrupt change of the B-POL apparent resistivity Os (or Pyx) at the coast. Just on the landward side 250 of the coastal boundary ( y ~ 0 - ) the electric field has a singularity like 1/I y l 1/2, whereas on the seaward side (y---, 0 + ) it remains finite (Dawson and Weaver, 1979a). It follows that since P~ = Z (1) the apparent resistivity exhibits a similar behaviour. These properties are easily understood. In B-POL the surface magnetic field is uniform whereas the current, which is distributed to depths of order 6 a far inland, tends to accumulate at the coast to concentrate in the ocean. This results in a strong increase of the electric field on land near the shore. Crossing into the sea the large discontinuity of conductivity produces a great drop in the surface electric field. These features are further magnified in the apparent resistivity PB as this parameter is proportional to the square of the electric field amplitude. As ~-~ ~ , PB becomes smaller over the ocean, and vanishes altogether on a perfectly conducting ocean. The phase falls below 45 °, as expected for a structure with a highly conducting overburden (cf. Fischer, 1985). With E-POL the surface magnetic field is no longer uniform near the coast, but the behaviour of Pe (or Oxy) is still controlled largely by the electric field. Continuity of its tangential component means continuity of Ex, which must drop steadily to the low values typical of the ocean surface. Again this translates into stronger variations for PE. However, the ocean edge is a point of jump discontinuity for By (Dawson, 1983) and since PE is given by °le pe = - j ture of any structural change of the lithosphere and upper mantle which may occur at the transition associated with a passive continental margin. 4. The induction arrow Whereas the magnetotelluric apparent resistivity and phase describe the relation between horizontal electric and magnetic fields the induction arrow depends only on the vertical and horizontal components of the magnetic field. Soundings of the three magnetic components are usually performed with arrays of synchronous stations and are called induction soundings. With Bx and B v the horizontal and B: the downward pointing vertical components we define the induction arrow in the horizontal plane e r = (ReA, ReB) Pi = (ImA, ImB) (3) where A and B are given by (4) B, = A B x + BBy Here we note that we have assumed a time dependence of the form exp( + iwt) (cf. Lilley and Arora, 1982; Chen and Fung, 1985). For the simple 2-D geometry that we have chosen in Fig. 1 the E-POL configuration involves only the magnetic components B), and B,; so MODEL i 0.5 / I / IZZZ 2 (2> "" 0 r,-- it experiences a jump discontinuity at the coast as well. This is also true for the phase. What is most striking in a comparison of Figs. 2 - 4 is their similarity. The dominant effect by far is the presence of the ocean; variations in the structure of lithosphere and upper mantle have only a minor influence on the response curves of apparent resistivity and phase. Magnetotelluric measurements on land near an ocean coast are therefore unlikely to shed much light on the na- -os! z "2 21 ml DISTANCE Fig. 5. The inductive response of model 1 represented in terms of the induction arrow. 251 MODEL 2 MODEL 3 ~:-0"51 ;", 0 ~-~-----~ . . . . . ........ , " " "'-, .I. . . '. . .~. . . .". . ~°\ \ , , : ~ \ \',i c- -~.S -t -3 -'2 { -'1 j 3 DISTANCE Fig. 6. The inductive response of model represented in terms of the induction arrow. For the sake of clarity the intermediate curve with z = 4000 S is left out. there is no factor A. In the B - P O L configuration there is only a B x c o m p o n e n t and thus no arrow at all. The induction vector is therefore directed along the y axis, i.e. it is perpendicular to our assumed straight coastline. Figures 5, 6 and 7 display the behaviour of the real and imaginary parts of the induction arrow for our three models. While there are again obvious similarities a m o n g these three figures, there are also important differences. O n land the real c o m p o n e n t always points away from the sea, but the range over which there is an important c o m p o nent is m u c h larger in model 3 than in model 1. With the deep ocean (~ = 16000 S) for example one has - P, > 0.5 for - y < 0.30, 0.36 and 0.65 for models 1 to 3, respectively, and - P, > 0.2 for - y < 0.78, 0.82 and 1.44. At sea the real c o m p o nent reverses direction at some distance from the coast, except for T --- o0 when there is no induction arrow over the perfect conductor. Since B z = 0 on the surface of a perfect conductor, it is to be expected that the greater the c o n d u c t a n c e of the ocean, the smaller the length of the induction arrow. In other words we expect to find a longer induction arrow over a shallow sea than over a deep one. The magnitude of the imaginary c o m p o n e n t of -: -2 -1 8 1 2 3 DISTANCE Fig. 7. The inductive response of model 3 represented in terms of the induction arrow. For the sake of clarity the intermediate curve with z = 4000 S is left out. the induction vector is, in general, smaller on land, and larger at sea, than the magnitude of the corresponding real component. F o r a deep ocean it points toward the coast on land, except for a short range close to the coast where it reverses direction and becomes very large. This reversed range widens for shallower seas, but the c o m p o nent then weakens. A nearly antisymmetric behaviour occurs at sea: the imaginary vectors generally point away from shore, except in a narrow range close to the coast. For shallow seas this range is only slightly wider, but here it exhibits a stronger amplitude. Beyond the narrow range of reversed imaginary c o m p o n e n t s the arrows at first are stronger for deep oceans, but far out to sea the arrows for shallow oceans again predominate. For a perfect c o n d u c t o r the width of the coastal ranges narrows to zero and the imaginary arrow completely vanishes over the ocean. As with the real c o m p o n e n t the imaginary arrow undergoes an important change between model 2 (Fig. 6) and model 3 (Fig. 7), suggesting that induction soundings m a y indeed be suitable to resolve variations in the structure of the lithosphere and upper mantle at a passive continental margin. 252 5. The effects of a submerged continental margin In the m o d e l s discussed so far we have set the edge of the c o n t i n e n t at the s e a - c o a s t . As is well known, however, these two edges d o n o t coincide, especially at passive margins. I n m o s t instances the c o n t i n e n t a l m a r g i n is situated several h u n d r e d kilometres on the s e a w a r d side of the coast. O n l y a l o n g the shores of A f r i c a can long coastal sections be f o u n d where the c o n t i n e n t a l shelf is less t h a n a b o u t 100 k m in width. But the coast effect of even a shallow ocean is so strong that a subm e r g e d c o n t i n e n t a l shelf of only 100 k m c o u l d well d e s t r o y any h o p e of observing a changing lithosphere at the true m a r g i n of the continent. T o test this hypothesis we have a n a l y s e d a fourth m o d e l involving a 100 k m shelf. M o d e l 4 is therefore identical with models 2 a n d 3, except that now the thin c o n d u c t i n g sheet is p r o l o n g e d a d i s t a n c e of 100 k m to the left. F r o m its new left edge the sheet c o n d u c t a n c e is set at ~- = 1000 S for the first 100 k m a n d then at • = 16000 S to the r i g h t - h a n d m o d e l b o u n d a r y . In the actual 2-D MEASUREMENTS MODEL 4 ON S H E L F m o d e l the ocean resistivity is m a i n t a i n e d at p = 0.25 t i m b u t the b a t h y m e t r i c d e p t h is taken as 250 m over the shelf a n d 4000 m a b o v e the oceanic crust. Magnetotelluric or induction m e a s u r e m e n t s w o u l d be difficult to p e r f o r m at the surface of the ocean. A t the same time, however, these measurements will have to be carried out as close to the c o n t i n e n t a l m a r g i n as possible if one hopes to derive any i n f o r m a t i o n a b o u t the oceanic lithosphere. W e have, therefore, c o m p u t e d the m o d e l responses in the c o n t i n e n t a l shelf area b o t h at the ocean surface a n d at the ocean floor. O u r c o m p u tations show, as expected, that magnetotelluric soundings would be totally i n a d e q u a t e to reveal a changing lithospheric thickness, regardless of whether the m e a s u r e m e n t s in the shelf area are carried out at the ocean b o t t o m or at its surface. U n f o r t u n a t e l y , as Fig. 8 shows, the same conclusion is also o b t a i n e d for i n d u c t i o n soundings when m e a s u r e m e n t s are carried out at the ocean floor over the shelf area (the answer is also negative for sea-surface soundings over the shelf). FLOOR l i CI_ L IMAG -1_: -'2 -- 0 2 3 DISTANCE Fig. 8. The inductive response of model 4 represented in terms of the induction arrow. Over the continental shelf the arrow is computed at the ocean floor. The full line corresponds to an extension of model 3, i.e. with a changing lithospheric thickness. The dashed line arises from an extension of model 2. Note the minute difference between the two curves. 253 6. Conclusions C o n t i n e n t a l l i t h o s p h e r e is u s u a l l y t a k e n to b e thicker than oceanic lithosphere, although even t o d a y t h e r e are h i g h l y d i v e r g e n t o p i n i o n s as to w h a t c o n s t i t u t e s the l i t h o s p h e r e a n d h o w t h i c k it r e a l l y is ( M a x w e l l , 1984; Peltier, 1984). If the c h a n g i n g l i t h o s p h e r i c t h i c k n e s s at a p a s s i v e c o n t i n e n t a l m a r g i n is a s s o c i a t e d w i t h a m a r k e d varia t i o n o f t h e d e p t h p r o f i l e of t h e e l e c t r i c a l resistivity, e l e c t r o m a g n e t i c s o u n d i n g m e t h o d s m a y b e d e e m e d c a p a b l e o f r e v e a l i n g this m a r g i n s t r u c t u r e . H o w e v e r , the s i m u l t a n e o u s o c c u r r e n c e o f the s t r o n g o c e a n - c o a s t e f f e c t m a s k s the l i t h o s p h e r i c effect. T h i s is e s p e c i a l l y t r u e for t h e m a g n e t o t e l l u r i c r e s p o n s e w h i c h is t h e r e f o r e ill-suited to reveal the changing lithospheric thickness through m e a s u r e m e n t s o n land. T h e i n d u c t i v e r e s p o n s e , o n t h e o t h e r h a n d , is well k n o w n for its s e n s i t i v i t y to lateral changes within conductive structures and w e h a v e s h o w n t h a t in t h e a b s e n c e o f a c o n t i n e n tal shelf u n d e r t h e o c e a n s u r f a c e it c o u l d c o n s t i t u t e a s u i t a b l e m e t h o d to r e v e a l a c h a n g i n g l i t h o s p h e r i c thickness. H o w e v e r , a n a r r o w subm e r g e d shelf of o n l y 100 k m w i d t h u n d e r 250 m of sea-water produces such a strong coast effect ahead o f t h e c o n t i n e n t a l m a r g i n , t h a t it also r e n d e r s i n d u c t i v e m e t h o d s u n s u i t e d to r e v e a l a c h a n g i n g l i t h o s p h e r i c thickness, e v e n w h e n t h e s e m e a s u r e m e n t s are c a r r i e d o u t at sea o n the shelf f l o o r f i g h t up to the e d g e o f the c o n t i n e n t . Acknowledgements This research project received financial support f r o m the Swiss N a t i o n a l S c i e n c e F o u n d a t i o n a n d the Natural Sciences and Engineering Research C o u n c i l of C a n a d a . It was b e g u n w h i l e o n e of us ( J . T . W . ) was a v i s i t o r at the O b s e r v a t o i r e C a n t o n a l o f N e u c h ~ t e l . T h e a u t h o r s are also g r a t e f u l to B.V. L e Q u a n g w h o c a r r i e d o u t m u c h o f the c o m p u t a t i o n a l work. References Bailey, R.C., 1977. Electromagnetic induction over the edge of a perfectly conducting ocean: the H-polarization case. Geophys. J. R. Astron. Soc., 48: 385-392. Brewitt-Taylor, C.R. and Weaver, J.T., 1976. On the finite-difference solution of two-dimensional induction problems. Geophys. J. R. Astron. Soc., 47: 375-396. Chela, P.F. and Fung, P.C.W., 1985. Significance of the sign changing of the imaginary arrows in geomagnetic induction investigation. Geophys. J. R. Astron. Soc., 80: 257-263, Dawson, T.W., 1983. E-Polarization induction in two thin half-sheets. Geophys. J. R. Astron. Soc., 73: 83-107. Dawson, T.W. and Weaver, J.T., 1979a. H-Polarization induction in two thin half-sheets. Geophys. J. R. Astron. Soc., 56: 419-438. Dawson, T.W. and Weaver, J.T., 1979b. Three-dimensional induction in a non-uniform thin sheet at the surface of a uniformly conducting Earth. Geophys. J. R. Astron. Soc., 59: 445-462. Dawson, T.W., Weaver, J.T. and Raval, U., 1982. B-Polarization induction in two generalized thin sheets at the surface of a conducting half-space. Geophys. J. R. Astron. Soc., 69: 209-234. Filloux, J.H., 1980. Magnetotelluric soundings over the northeast Pacific may reveal spatial dependence of depth and conductance of the asthenosphere. Earth Planet. Sci. Lett., 46: 244-252. Filloux, J.H., 1982. Magnetotellurie experiments over the ROSE area. J. Geophys. Res., 87B: 8364-8378. Fischer, G., 1979. Electromagnetic induction effects at an ocean coast. Proc. IEEE, 67: 1050-1060. Fischer, G., 1985. Some remarks on the behavior of the magnetotelluric phase. Geophys. Prosp., 33: 716-722. Fischer, G., Schnegg, P.A. and Usadel, K.D., 1978. Electromagnetic response of an ocean-coast model to E-polarization induction. Geophys. J. R. Astron. Soc., 53: 599-616. Fischer, G., Schnegg, P.A. and Usadel, K.D., 1980. Electromagnetic induction at a model ocean coast. J. Geomagn. Geoelectr., 32: 67-71. Green, V.R. and Weaver, J.T., 1978. Two-dimensional induction in a thin sheet of variable integrated conductivity at the surface of a uniformly conducting Earth. Geophys. J. R. Astron. Soc., 55: 721-736. Lilley, F.E.M. and Arora, B.R., 1982. The sign convention for quadrature Parkinson arrows in geomagnetic induction studies. Rev. Geophys. Space Phys., 20: 513-518. Maxwell, J.C., 1984. What is the lithosphere. EOS, 65: 321-325. McKirdy, D.M. and Weaver, J.T., 1983, A numerical study of the channelling of induced currents between two oceans. J. Geomagn. Geoelectr., 35: 623-641. McKirdy, D.M. and Weaver, J.T., 1984. Induction in a thin sheet of variable conductance at the surface of a stratified Earth--I. Two-dimensional theory. Geophys. J. R. Astron. Soc., 78: 93-103. McKirdy, D.M., Weaver, J.T. and Dawson, T.W., 1985. Induction in a thin sheet of variable conductance at the surface of a stratified Earth--lI. Three-dimensional theory. Geophys. J. R. Astron. Soc., 80: 177-194. Nicoll, M.A. and Weaver, J.T., 1977. H-polarization induction over an ocean edge coupled to the mantle by a conducting crust. Geophys. J. R. Astron. Soc., 49: 427-442. 254 Parkinson, W.D. and Jones, F.W., 1979. The geomagnetic coast effect. Rev. Geophys. Space Phys., 17: 1999-2015. Peltier, W.R., 1984. The thickness of the continental lithosphere. J. Geophys. Res., 89B: 11303-11316. Raval, U., Weaver, J.T. and Dawson, T.W., 1981. The ocean-coast effect re-examined. Geophys. J. R. Astron. Soc., 67: 115-123. Vasseur, G. and Weidelt, P., 1977. Bimodal electromagnetic induction in non-uniform thin sheets with an application to the northern Pyrenean induction anomaly. Geophys. J. R. Astron. Soc., 51: 669-690. Weaver, J.T., 1979. Electromagnetic induction in thin sheet conductivity anomalies at the surface of the Earth. Proc. IEEE, 67: 1044-1050. Weaver, J.T., 1982. Regional induction in Scotland: an example of three-dimensional numerical modelling using the thin sheet approximation. Phys. Earth Planet. Inter., 28: 161-180.