Borehole measurements within highly magnetic bodies corrections of measured magnetic fields and gradients

Transcription

1 Borehole measurements within highl magnetic bodies corrections of measured magnetic fields and gradients David A Clark* CSIRO Manufacturing & CSIRO Minerals PO Bo 8, Lindfield NSW 7 Davidclark@csiroau *presenting author SUMMARY This paper gives eplicit epressions for the internal field and gradient components for a laered earth, a laer with gradational susceptibilit, a dipping sheet, a sphere and a clinder, that are eposed to an eternal field with a uniform gradient owever, the internal field and gradient components cannot be measured directl, as magnetic sensors must be placed within a cavit in the magnetic medium This modifies the measured field and gradients For low to moderate susceptibilities, the cavit effect can be calculated assuming that the magnetisation of the surrounding medium is essentiall unperturbed b the presence of the cavit This assumption is unacceptable when the surrounding medium has high susceptibilit I also give epressions that allow the true field and gradient components within a high susceptibilit bod to be calculated from measurements made in clindrical cavities, such as boreholes, or in spherical or disc-like cavities Ke words: Downhole magnetics, magnetic field, magnetic gradient tensor, self-demagnetisation, cavit fields INTRODUCTION Forward modelling of magnetic sources is usuall based on calculating the eternal field and gradient components produced b a bod of specified shape and magnetic properties The magnetic properties of the source are generall taken to be homogeneous This does not necessaril impl, however, that the magnetisation of the source is uniform, because the self-demagnetising field of strongl magnetic sources is generall non-uniform, ecept for the special case of homogeneous ellipsoidal bodies (Clark et al, 98) The non-uniform resultant internal field (applied field plus self-demagnetising field) produces a non-uniform induced magnetisation in the source, even though its susceptibilit is uniform Bodies with gradational magnetic properties, such as oned intrusive sills or plugs, oned alteration sstems, or detrital magnetite-bearing sedimentar laers with graded bedding, generate internal magnetic gradients, even though the applied field ma be uniform It is usuall assumed when modelling the eternal and internal effects of a magnetic source that the applied field is the regional geomagnetic field, which can be taken as uniform When making gradient measurements, however, it is important to understand the effect of the local magnetic medium on the background gradient Furthermore neighboring strongl magnetic sources can perturb the regional field and impose gradients on the target source For this reason, it is useful to stud the effects of the local magnetic environment on imposed gradients, as well on the ambient field Measurement of magnetic gradients, especiall measuring the full gradient tensor, has man advantages (Pedersen and Rasmussen, 99; Schmidt and Clark, ) over conventional magnetic surves, particularl when spatial coverage is sparse This is especiall true for borehole magnetic measurements, which provide a single string of data Measuring TMI downhole provides a profile of onl a single magnetic component, whereas measuring the field vector provides three components at each measurement location, but these tend to be ver nois due to orientation uncertainties Measuring the full gradient tensor provides five independent components at each observation point, with much less sensitivit to orientation errors, which allows better targeting of nearb sources (Pedersen and Rasmussen, 99; Schmidt and Clark, ; Clark,, 3) Borehole magnetic measurements, in particular, can be ver useful for targeting subsurface sources (Levanto, 93; Bosum et al, 988; oschke, 99; illan et al, ) and can provide useful information about the source magnetisation, especiall when the borehole intersects the magnetic source (Clark, 4) It is therefore important to (i) model the internal field of magnetic sources correctl, and (ii) calculate the field and gradients that are actuall measured in a borehole, or other cavit, inside a magnetic bod so that borehole magnetic data can be interpreted correctl Leslie et al (5) describe a downhole tool capable of measuring the full magnetic gradient tensor that is being developed to assist mineral eploration Within a medium with magnetisation M, the magnetic field intensit, and the flu densit B are related b B = µ( + M), where µ is the permeabilit of free space Assuming no remanent magnetisation and an induced magnetisation M = that is linear in the field intensit, then B = µ(+) = µµ, where is the susceptibilit and µ = + is the relative permeabilit of the medium This paper eamines how fields and field gradients within a highl magnetic medium, due to eternal magnetic sources, are affected b the shape and permeabilit of the magnetic bod within which measurements are made Figure illustrates the simple relationship between the measured magnetic field in a borehole that intersects an initiall uniforml magnetised bod (eg a homogeneous ellipsoid in a uniform eternal field) and the unperturbed internal field and magnetisation of the bod It will be shown in this paper that the effects of self-demagnetisation on gradients are somewhat more complicated than its effects on field components The field vectors and their gradients cannot be measured directl within a permeable medium; rather, the fields and gradients in the medium must be inferred from measurements made b instruments situated in a cavit, such as a borehole, within the medium This paper shows how measurements made within a spherical or disc-like cavit or within a borehole, approimated as an infinitel long clindrical cavit, can be corrected to infer the fields and gradients within the surrounding magnetic medium AEC 8: Sdne, Australia

2 MANETIC SCALAR POTENTIAL OF AN APPLIED FIELD WIT A UNIFORM RADIENT The magnetic scalar potential is onl defined to within an arbitrar additive constant, so for simplicit can be set to ero at the origin of co-ordinates Then, in terms of Cartesian co-ordinates (,, ), the magnetic scalar potential associated with an applied field with a superimposed uniform gradient tensor is: ( ) ( ) ( ) ( ) ( ) ( ) ( ), () where is the field, averaged over all space, which is also equal to the field vector at the origin, and the components of the gradient tensor are ij = i/j = ²/ij (i,j =,, ) The matri of Cartesian elements of the uniform gradient tensor is ( ) () The mathematical form of equation () ensures that the corresponding gradient tensor, given b (), is smmetric and traceless, as required b Mawell s equations for the magnetostatic field, in the absence of conduction currents This implies that there are onl five independent gradient tensor components, eg,,,, In () the functions of,, associated with each tensor element are harmonic and homogeneous functions of order two Note that the magnetic gradient tensor is defined here, and throughout this paper, as the vector gradient of the magnetic field intensit, rather the gradient of the flu densit B, and is epressed in units of A/m² In a linear magnetic medium with no remanence (or a uniform remanence) the gradient of the flu densit is B = µ = µ radiometer measurements are made in a locall non-magnetic environment (air, water, oil, outer space), for which B = µ, so interconversion between measured gradients of B and is straightforward (ij = A/m² (B) ij = 4 7 T/m = 57 nt/m) As a function of spatial position, the field corresponding to the potential in (), is (,, ) r [( ) ]ˆ [( ) ]ˆ (3) [( ) ]ˆ where ˆ, ˆ, ˆ are unit vectors along the co-ordinate aes With respect to spherical polar co-ordinates (r,,), is: ( ) r cos sin ( ) r sin sin ( ) r cos r ( 3cos sin ) r sin sin (4) ( ) r cos sin r ( 3sin sin ) r sin sin r ( 3cos ), and with respect to clindrical co-ordinates (,, ) ( ) cos ( ) sin ( ) cos sin 4 ( ) cos cos sin ( ) 4 (5) INFINITE SEET WITIN A PERMEABLE MEDIUM EOMANETIC FIELD WIT A UNIFORM RADIENT Consider the case of a magnetic subsurface of permeabilit µ, from the surface (or the top of the magnetic basement) at = to a depth = 3, with an embedded horiontal laer of different permeabilit µ over the depth range 3 The boundar conditions impl that the vertical component of B and the horiontal components of are continuous through the horiontal interfaces This implies that the vertical component of undergoes step changes at each interface between laers of different permeabilit, but gradient tensor components that onl involve or are unaffected b the horiontall laered structure It turns out that the diagonal gradient tensor components in all ones are unperturbed b the laering owever a geomagnetic gradient tensor, or a gradient tensor produced b a neighbouring source, with nonero or components is perturbed b the magnetic laering AEC 8: Sdne, Australia

3 For a surface geomagnetic field = (X, Y, Z) with a superimposed uniform gradient tensor, the corresponding fields within the i th depth one (i =,,3,4) can be calculated b noting that within each laer of relative permeabilit µi the gradient tensor components in the permeable medium are related to the gradient tensor above the surface b: i / / i i / i / i, () and b tracking the step changes in vertical field across each interface, which are given b: i i i i i i Z Z ; (7) Starting at the surface or just above the top of the first nonmagnetic laer, the fields within each laer are etrapolated to the net interface b substituting the gradient components in () into (3) (where in this case represents the increment in depth within that laer), to the field just below the previous interface, which in turn is determined b adding the step change given b (7) to the field just above the previous interface These results ma also be applied to the relativel common case of a dipping magnetic sheet of relative permeabilit µ = + in a nonmagnetic half-space, provided the gradient tensor components are epressed in terms of Cartesian aes with down-dip, along strike, and normal to the plane of the sheet Then, for points within the sheet that are several sheet-thicknesses awa from the top and bottom edges so that edge effects are negligible, the gradient of is continuous across the boundar of the sheet for all components ecept for and, which are decreased b a factor /(+) within the sheet The same principles that appl to infinite sheets ma also be applied to measurements made in a thin disc-like or slot-like cavit ( = ) within a medium of permeabilit µ In this case the gradient tensor in the surrounding medium is related to the measured gradient tensor cav b: cav cav cav cav cav cav / / cav cav cav / /, (8) where the and aes lie in the plane of the disc and the ais is normal to the disc Thus the gradient tensor elements in the surrounding medium can be inferred from the measured gradient tensor in the cavit, if the susceptibilit of the medium is known The and components in the cavit must be divided b the relative permeabilit; the other components are unchanged b the presence of the cavit For a disc-like cavit the eternal field components in the plane of the disc are unchanged within the cavit, but the cavit field normal to the disc must be divided b µ to obtain the normal component of the eternal field SPERICAL BODY OR CAVITY WITIN A PERMEABLE MEDIUM Consider a spherical homogeneous magnetisable bod of radius a, with relative permeabilit µ, within an effectivel infinite magnetisable medium with relative permeabilit µ We assume that there is no permanent magnetisation in either medium If the unperturbed applied field has a uniform gradient, we ma convenientl emplo spherical polar co-ordinates with origin at the centre of the sphere and the polar () ais chosen to be parallel to the unperturbed field at the position of the sphere The unperturbed scalar potential, far from the cavit, is then given b (4) with () = () = The boundar conditions on the scalar potential are: (i) continuit of the potential across the spherical boundar, (ii) continuit of the normal (ie radial) component of the magnetic flu densit B = µµ across the spherical boundar, (iii) regularit of the potential inside the sphere, and (iv) convergence of the eternal potential to epression (4) as r Solving Laplace s equation with these boundar conditions and calculating the fields from the scalar potentials ields: 3 r a) 5, 3 ( r (9) for the internal field Equation (9) shows that the internal field also has a uniform gradient The field at the centre of the sphere is multiplied b a factor of 3µ/(µ +µ) compared to the unperturbed field at the same location For the case of a permeable sphere, with µ = +, in a nonmagnetic medium (µ = ) the internal field at the centre is reduced with respect to the applied field, due to selfdemagnetisation: ( r ;, ) () / 3 AEC 8: Sdne, Australia 3

4 This is consistent with the well-known formula for the induced magnetisation in a uniform applied field, of a permeable sphere in a vacuum, M = =, for which the effective susceptibilit, corrected for self-demagnetisation, is = /(+/3) On the other hand, the field inside a spherical cavit within a permeable medium (µ = +, µ = ) is given b: ( r ;, ) () /3 Thus the field at the centre of the spherical cavit is amplified b a factor of (+)/(+/3) with respect to the unperturbed applied field at that point For relativel small susceptibilities ( << ), this amplification factor is, to a good approimation, equal to (+/3), which is the cavit field calculated b assuming a uniform magnetisation equal to in the eternal medium For 5, there is a significant difference between the eact calculation and the uniform-magnetisation approimation, due to the perturbation of the applied field b the presence of the cavit The eternal field of the sphere is equivalent to that produced b point dipole plus point quadrupole sources at the centre of the sphere The dipole term is produced b the average applied field, the quadrupole term arises from the applied gradient The magnetic moment of the equivalent dipole is: 3( ) m ( ) ( ) ( ) / 3 () Note that, if > (in particular, for a cavit in a magnetic medium), then the dipole moment is directed opposite to the applied field The total magnetic moment arises from both the magnetisation of the material in the sphere and from the distribution of magnetic poles induced on the inner surface of the spherical cavit that has been carved out of the surrounding permeable medium in order to accommodate the sphere For a spherical cavit within an infinite permeable medium (µ = +; µ = ), the internal gradient tensor is amplified with respect to the applied gradient: ( r a;, ) (3) 3 / 5 For a spherical permeable bod within an infinite nonmagnetic medium (µ =, µ = +), the internal gradient tensor is somewhat shielded with respect to the applied gradient: ( r a;, ) (4) /5 Thus the shielding factor for first-order gradients inside a magnetisable sphere, /(+/5), differs from the shielding factor for the applied field, which is /(+/3) CYLINDRICAL BODY OR CAVITY WITIN A PERMEABLE MEDIUM Consider a magnetisable bod in the form of a ver long clinder of radius a, with relative permeabilit µ, within an effectivel infinite magnetisable medium with relative permeabilit µ We assume that there is no permanent magnetisation in either medium If the unperturbed applied field has a uniform gradient, we ma emplo clindrical polar co-ordinates with origin on the ais of the clinder, which coincides with the ais The potentials and fields in this case are independent of Continuit of the field component across the walls of the clinder ensures that this component is unperturbed b the presence of the clinder Thus we onl need to consider the applied field components that lie in the plane perpendicular to the clinder ais Let the polar ais, for which =, coincide with the unperturbed applied field direction at the origin The unperturbed scalar potential, far from the cavit, is then given b (5) with () = () = Solving Laplace s equation with the appropriate boundar conditions and calculating the fields from the scalar potentials ields: a), ( r (5) for the internal field, where the modified gradient tensor inside the clinder is: (3 ) ( ) ( ) ( ) ( ) ( ) (3 ) ( ) ( ) ( ) ( ) ( ) () AEC 8: Sdne, Australia 4

5 Equations (5) and () show that the internal field also has a uniform gradient The aial field and its aial gradient are unperturbed b the presence of the clinder The transverse field on the ais of the clinder is multiplied b a factor of µ/(µ +µ) compared to the unperturbed transverse field at the same location For the case of a permeable clinder, with µ = +, in a nonmagnetic medium (µ = ) the internal transverse field on the ais is reduced with respect to the applied transverse field, due to self-demagnetisation:, ;, ) ( ) ( ) (7) /, (, This is consistent with the well-known formula for the magnetisation induced b a uniform applied transverse field in a permeable clinder in a vacuum, M = =, for which the effective susceptibilit, corrected for self-demagnetisation, is = /(+/) The anomalous eternal potential and field are identical to those produced b an infinite line of dipoles along the clinder ais, aligned with the transverse component of the applied field, plus a line of quadrupoles that are associated with the applied gradient, and a line of poles associated with the aiall smmetric portion of the gradient tensor ( = = /) The latter gradient configuration produces an aiall smmetric distribution of magnetic poles, associated with the radial magnetisation contrast across the walls of the clinder, that lines the surface of the clinder and is evenl distributed along the length of the clinder Such a pole distribution produces no internal field Eternall, the anomalous potential corresponds to that of a line of poles uniforml distributed along the clinder ais The potential associated with such a line of poles has a logarithmic dependence on radial distance, but is independent of There is a seeming parado due to an apparent ecess of poles on the outer surface of the clinder This can be eplained b noting that the missing poles (which are required to ensure that the total pole strength produced b the magnetisation distribution sums to ero) are to be found at the ends of the clinder, which are assumed to be sufficientl distant that their fields can be neglected The dipole moment per unit length of the clinder is MA A A (8), where A = a² is the cross-section area of the clinder and M is its effective transverse magnetisation This differs from the internal transverse magnetisation M = (µ ) of the clinder, because the magnetisation contrast across the walls of the clinder produces a surface densit of magnetic charge that also contributes to the anomalous potential and field Note that the effective magnetisation of the clinder is not simpl proportional to the susceptibilit contrast between the eternal and internal media owever, if the eternal medium is non-magnetic (µ = ), and the internal permeabilit is µ = +, then the internal field is = /(+/) and the magnetisation of the clinder is /(+/) =, where is the demagnetisation-corrected effective susceptibilit for an infinite clinder in a non-magnetic medium If the susceptibilit of the clinder is less than that of the surrounding medium, the equivalent line of dipole moments is oriented opposite to the applied field On the other hand, the transverse field on the ais of a clindrical cavit within a permeable medium (µ = +, µ = ) is given b: ( ), ;, ) ( ) (9) /, (, Thus the field along the ais of the clindrical cavit is amplified b a factor of (+)/(+/) with respect to the applied field For relativel small susceptibilities ( << ), this amplification factor is, to a good approimation, equal to (+/), which is the cavit field calculated b assuming a uniform magnetisation equal to in the eternal medium For 5, there is a significant difference between the eact calculation and the uniform-magnetisation approimation, due to the perturbation of the applied field b the presence of the cavit Appling the tracelessness propert to (), the gradient tensor measured within a clindrical cavit within a permeable medium is: ( ) ( / ) ( ) ( ;, ) a ( / ) ( ) ( / ) / 4 ( ) ( / ) ( ) ( / ) ( ) ( / ) / 4 ( ) ( / ) ( ) ( / ) () Equation () shows that the,, and components of the gradient tensor inside a permeable clinder (µ = +) within a nonpermeable medium (µ = ) are attenuated b self-demagnetisation, with a shielding factor of /(+/), which is identical to the shielding factor for and On the other hand, equation () shows that for a clindrical cavit in a permeable medium, these components of the applied gradient within the surrounding medium are amplified b a factor of (+)/(+/) Thus the shielding/amplification factors for the off-diagonal components of the applied gradient tensor are the same as for the transverse components of the field The component of the gradient is unaffected b the presence of the clindrical bod or cavit owever the responses of the other diagonal components of the gradient tensor are more complicated than a simple shielding/amplification AEC 8: Sdne, Australia 5

6 Manipulation of equation () gives the following epressions for the true gradient tensor in the surrounding medium, corrected for the effects of the borehole cavit, epressed in terms of the tensor elements measured in the borehole: ( / ) / 4 ( / ) ( / ) ( ) ( ) ( ) () ( / ) ( / ) / 4 ( / ) ( ) ( ) ( ) ( / ) ( / ) ( ) ( ) Within a medium that has relativel low susceptibilit, such as most sedimentar rock units, the required corrections to the measured gradient tensor elements are approimatel: ii ( / ) ii /4, ( i, ) ( / ) ij ij, ( i j), ( ) () BOREOLE WITIN A REMANENTLY MANETISED PERMEABLE MEDIUM Ecept near the boundaries of a magnetic rock unit, a borehole can be modelled as a long, effectivel infinite, clindrical cavit Figure illustrates the relationship between the measured magnetic field in a vertical borehole that intersects a horiontal laer and the unperturbed field and magnetisation in the laer, in the simple case of homogeneous properties and a uniform eternal field If the permeable medium (relative permeabilit µ) surrounding the borehole has a uniform remanent magnetisation R, the remanence produces an additional uniform field within the borehole The aiall directed component of R has no effect The transverse field in the cavit produced b the remanence of the surrounding medium is proportional to and parallel to the transverse component R of R Solving the elementar boundar value problem for this case shows that the transverse anomalous field vector in the borehole is: R M M, (3) where M is the transverse component of the vector sum of the induced and remanent magnetisations The component of magnetisation parallel to the borehole can be estimated from the fairl abrupt step-like change in the aial component of that occurs over a distance of several borehole diameters as the borehole sensor passes into the sheet (see Figure 3) In order to estimate the magnetisation vector, the orientation of the sheet must be known, so that the direction of the self-demagnetising field (normal to the sheet) can be ascertained If the susceptibilit of the formation that is intersected b the borehole is known, b borehole logging or measurements on samples of the formation, then the total magnetisation and remanent magnetisation can be estimated from measurements of the anomalous magnetic field vector in the borehole: M ) ( ) ; R M (4) ( If the susceptibilit of the sheet is known to be reasonabl low ( << ), (µ+) can be set equal to and the magnetisation can be inferred directl from the borehole field measurements Otherwise, reliable estimation of the transverse components of magnetisation requires an independent measurement of the susceptibilit of the sheet EFFECTS OF ZONED SUSCEPTIBILITIES ON BOREOLE FIELD AND RADIENT MEASUREMENTS A rock unit with oned susceptibilit has non-uniform magnetisation and produces internal gradients, even when the applied field is uniform Eamples of such units include thick intrusive sills that have undergone crstal settling, laered mafic/ultramafic intrusions, alteration ones, and detrital magnetite-bearing sandstones with graded bedding For simplicit consider a horiontal unit of thickness T, in which the susceptibilit varies linearl from to between its upper and lower boundaries at and The vertical component of B is continuous across the upper and lower boundaries of the unit and is constant within the magnetic unit This implies that = B/µ(+) varies sstematicall with depth For a vertical borehole well within the magnetic unit (ie several borehole diameters from either interface) in the borehole is equal to in the adjacent rock, so in the borehole the measured vertical component of the flu densit, B = µ, varies sstematicall with depth If there is no imposed gradient, ie the eternal field is uniform, the measured vertical component of the field and its vertical gradient are given b: B B B ( ) ( )( ) / T B B( / ) B( / ) [ ( )] [ ( / )( )] B, ( / )( ) (5) AEC 8: Sdne, Australia

7 Thus the gradient in susceptibilit produces a field gradient inside the borehole If the eternal vertical field has a superimposed uniform vertical gradient B then B() = B() + ( )B along a vertical profile through the sheet In a vertical borehole well within the sheet the measured vertical field and its vertical gradient are given b: B( ) B( ) B( ) B( ) B( ) B ( ), ( / )( ) B B( )( / ) B [ B( ) B( )]( / ) B ( ) ( ) [ ( )] ( ) ( ) () Thus the eternal gradient is attenuated b factor of /[+()], which is the standard shielding factor for this geometr, and the gradient in susceptibilit contributes an additional field gradient inside the borehole The latter term can be substantial, when there is a significant gradient in the susceptibilit Sstematic changes in remanent magnetisation with depth produce similar effects and can be calculated using these formulas b converting the magnetisation M() into an equivalent susceptibilit equal to M()/() If the susceptibilit of the intersected rock units is known, or is logged during drilling, simple corrections can be made to measured field and gradient data if either (i) the susceptibilit is fairl uniform throughout a given stratigraphic interval (even if it is fairl high), or (ii) the susceptibilit varies graduall and is measured through the stratigraphic interval On the other hand, large susceptibilit variations over short stratigraphic intervals will introduce substantial noise into magnetic measurements Similarl, measurements within a strongl magnetic rock unit that has highl heterogeneous magnetic properties will be afflicted b substantial geological noise, which could mask the signatures of nearb target sources CONCLUSIONS The internal magnetic field of a magnetised bod is affected b self-demagnetisation, which in general depends both on its shape and on the susceptibilities of the bod and its host rock The effects of self-demagnetisation on the internal gradient tensor differ from the effects on the internal field Measured magnetic field vectors and gradient tensor components in a borehole or other cavit differ from the corresponding quantities in the surrounding rock Inferring the eternal field and its gradient in the adjacent material from measurements that are necessaril made in a cavit within the magnetised rock, requires knowledge of, or assumptions about, the geometr of the magnetic bod within which the measurements are made Furthermore the susceptibilit of the rock surrounding the borehole affects the correction that is required to infer the field and gradients in the surrounding rock A rock unit with gradational magnetic properties has internal magnetic gradients (in addition to imposed gradients from eternal sources), which are detectable within a borehole that intersects the unit This paper gives epressions that relate measured fields and gradients to the corresponding quantities in the surrounding rock, which should assist interpretation of borehole data, in particular, in highl magnetic environments REFERENCES Bosum, W, Eberle, D, and Rehli, J, 988, A gro oriented 3 component borehole magnetometer for mineral prospecting, with eamples of its application: eophsical Prospecting, 3(8), Clark, DA,, New methods for interpretation of magnetic vector and gradient tensor data I: eigenvector analsis and the normalised source strength Eploration eophsics, 43, 7 8, Clark, DA, 3, New methods for interpretation of magnetic vector and gradient tensor data II: Application to the Mount Leshon Anomal, Queensland, Eploration eophsics, 44, 4 7 ( Clark, DA, 4 Methods for determining remanent and total magnetisations of magnetic sources - a review Eploration eophsics, 45, Clark, DA, Saul, SJ, and Emerson, DW, 98, Magnetic and gravit anomalies of a triaial ellipsoid: Eploration eophsics, 7, 89- illan, D, Foss, C, Austin, J, Schmidt, P, and Clark, D,, Direction to magnetic source analsis of single string of down-hole magnetic tensor data: 8nd Annual Meeting Societ of Eploration eophsicists; 4-9 November ; Las Vegas, Nevada oschke, T, 99, eophsical discover and evaluation of the West Peko copper-gold deposit, Tennant Creek: Eploration eophsics,, Leslie, K, Foss, C, illan, D, and Bla, K, 5, A downhole magnetic tensor gradiometer for developing robust magnetisation models from magnetic anomalies: Iron Ore 5; 3-5 Jul 5; Perth, WA, Australia Australasian Institute of Mining and Metallurg (AusIMM); Levanto, AE, 93 On magnetic measurements in drill holes: eoeploration, (), 8- Pedersen L B, and Rasmussen T M 99, The gradient tensor of potential anomalies: Some implications on data collection and data processing of maps: eophsics, 55, AEC 8: Sdne, Australia 7

8 Schmidt, PW and Clark, DA,, The magnetic gradient tensor: Its properties and uses in source characteriation: The Leading Edge, 5(), Figure : Relationship between the uniform unperturbed internal magnetic field for a homogeneous ellipsoidal bod and the field measured within a borehole that intersects the bod Figure : Relationships between the unperturbed eternal and internal magnetic fields for a uniforml magnetised horiontal laer and for the field measured within a borehole that intersects the laer Figure 3: Anomalous vertical field and its vertical gradient along the ais of a cm ( inch) diameter borehole as it passes from a non-magnetic formation into a thick horiontal sheet with a vertical magnetisation of A/m Laterall awa from the borehole the field undergoes a sharp step change across the upper surface of the magnetic sheet owever the borehole produces a clindrical one of missing magnetisation which smooths the measured field in the borehole, but the measured aial field anomal in the borehole asmptoticall approaches the theoretical step change as the sensor penetrates a distance equivalent to several borehole diameters into the sheet The corresponding gradient anomal has a large amplitude sharp peak around the interface, which drops to negligible values over a distance of several borehole diameters, as a uniforml magnetised sheet has no internal gradient AEC 8: Sdne, Australia 8