ics 61 (2007) 227–234www.elsevier.com/locate/jappgeo

Journal of Applied Geophys

Multi-transmitter multi-receiver null coupled systems for inductivedetection and characterization of metallic objects

J. Torquil Smith ⁎, H. Frank Morrison, Lawrence R. Doolittle, Hung-Wen Tseng

Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA

Received 1 November 2005; accepted 26 May 2006

Abstract

Equivalent dipole polarizabilities are a succinct way to summarize the inductive response of an isolated conductive body atdistances greater than the scale of the body. Their estimation requires measurement of secondary magnetic fields due to currentsinduced in the body by time varying magnetic fields in at least three linearly independent (e.g., orthogonal) directions. Secondaryfields due to an object are typically orders of magnitude smaller than the primary inducing fields near the primary field sources(transmitters). Receiver coils may be oriented orthogonal to primary fields from one or two transmitters, nulling their response tothose fields, but simultaneously nulling to fields of additional transmitters is problematic. If transmitter coils are constructedsymmetrically with respect to inversion in a point, their magnetic fields are symmetric with respect to that point. If receiver coils areoperated in pairs symmetric with respect to inversion in the same point, then their differenced output is insensitive to the primaryfields of any symmetrically constructed transmitters, allowing nulling to three (or more) transmitters. With a sufficient number ofreceivers pairs, object equivalent dipole polarizabilities can be estimated in situ from measurements at a single instrument sitting,eliminating effects of inaccurate instrument location on polarizability estimates. The method is illustrated with data from a multi-transmitter multi-receiver system with primary field nulling through differenced receiver pairs, interpreted in terms of principalequivalent dipole polarizabilities as a function of time.© 2006 Elsevier B.V. All rights reserved.

Keywords: Electromagnetic induction; Unexploded ordnance (UXO); Receiver nulling; Multi-transmitter multi-receiver systems

1. Introduction

Detection of secondary magnetic fields due to cur-rents induced in an object by time varying magneticfields from a source current distribution is often themethod of choice for detection of buried metallic objectssuch as unexploded ordnance (UXO). Detection of the

⁎ Corresponding author.E-mail addresses: JTSmith@LBL.gov (J.T. Smith),

HFMorrison@Berkeley.edu (H.F. Morrison), LDoolitt@LBL.gov(L.R. Doolittle), HWTseng@LBL.gov (H.-W. Tseng).

0926-9851/$ - see front matter © 2006 Elsevier B.V. All rights reserved.doi:10.1016/j.jappgeo.2006.05.011

secondary magnetic fields is challenging as they may beas much as six orders of magnitude smaller than theprimary inducing fields. One method of diminishing theproblem of primary magnetic fields is to choose receiverlocations and orientations such that the receiver coils arenull coupled to the primary magnetic fields; that is, theyhave no net primary field flux passing through them, or,given a finite accuracy of manufacture, the net primaryfield flux through them is greatly diminished. For asingle transmitter, or a pair of independent transmittercoils, for small loop receivers this can be achieved byorienting each receiver so that the receiver axis (i.e.,

Fig. 1. Geometry of simple symmetric loop, showing differential loopsegment dl at point q, and complimentary differential loop segment−dl at −q. Magnetic fields of current in loop, at any point r andcomplimentary point −r are the same.

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receiver loop normal vector) is at right angles to themagnetic fields from each transmitter. A second methodof diminishing the relative size of the primary magneticfields is to transmit over a finite length of time, andto measure secondary magnetic fields after the primarymagnetic fields have stopped (e.g., time domain sys-tems). In general, to be sensitive to the smaller sec-ondary magnetic fields, the receiver outputs must beamplified, and the front end of the receiver amplificationsystem must be designed to withstand the much largervoltages due to the primary magnetic field signals. Soeven in time domain systems it can be advantageousto reduce the primary fields seen by the receiver by(approximately) null coupling them to the primarymagnetic fields.

To fully characterize the inductive response of anisolated conductive object, one needs to measure itsresponse to stimulation by primary magnetic fields inthree linearly independent (e.g., approximately orthog-onal) directions (Khadr et al., 1998; Baum, 1999; Smithand Morrison, 2004). This can be achieved either bymeasuring the response to magnetic fields of threeindependent transmitters arranged to have magneticfields that are linearly independent, or by measuring theresponse to a single transmitter which is moved to illu-minate prospective object locations with magnetic fieldswhich are linearly independent. In the latter case, systemlocation and orientation errors are a major source oferror (Barrow and Nelson, 2001; Smith and Morrison,2005), and given current size errors in differential GPSlocation (3 cm), one would do better to use multipletransmitters and receivers of known relative positionand orientation on a single platform than to combinemultiple sittings of a single transmitter system witherrors in location (Smith and Morrison, 2005). Adding athird transmitter makes it impossible, at most locations,to null couple receivers to all three transmitters, at leastwhen receivers are considered individually.

Huang et al. (2005) observe that for a pair of axiallyoriented circular loop receivers located symmetricallyon axis of a circular loop transmitter, one above, onebelow, contributions due to the primary fields cancel inthe differenced output of the two receivers. Here, themethod is extended to allow cancellation of primaryfields from multiple transmitters simultaneously, withmore complicated transmitter and receiver geometries.When transmitter systems are constructed symmetri-cally with respect to (inversion in) a central point, andreceiver pairs are similarly constructed, the differencesbetween receiver pairs are insensitive to the primarymagnetic fields, and thus null coupled in a differencemode, for as many transmitter loops as needed. Or,

because of source receiver reciprocity, one can similarlyconstruct transmitter systems that are anti-symmetricwith respect to the central point, and use sums of outputfrom corresponding receiver pairs.

2. Construction of suitably symmetric transmittersystems

Under a quasi-static approximation, the contributionto the magnetic field dB(r) at point r due to a currentelement Idl in the dl direction at point q (along path a(α)tracing out a transmitter loop as α is varied) is

dBðrÞ ¼ l0Idl� ðr−qÞ4kjr−qj3 ð1Þ

(Biot-Savart law). For simplicity of exposition, wechoose the center of a prospective ensemble of receiversand transmitters as the coordinate origin. To constructtransmitters that are symmetric with respect to inversionin the origin, for each section of transmitter loop indirection dl at point q, we also include a correspondingsection in direction −dl at point −q so that the field atpoint r due to the two sections is

dBðrÞ þ dB ′ðrÞ ¼ l0Idl� ðr−qÞ4kjr−qj3

−l0Idl� ðrþ qÞ

4kjrþ qj3 : ð2Þ

A simple example of a single loop so constructedwould be a circular loop in the x–y plane centered at theorigin, of some radius c, diagrammed in Fig. 1. If acurrent I is flowing counter clockwise when viewed

Fig. 3. Geometry of simple symmetric receiver loop pair, one receiverloop centered at r with loop normal p, and the other centered at −rwith loop normal −p. Primary magnetic fields at any point r andcomplimentary point −r are the same, so summed response ofcomplimentary receiver loops to magnetic fields due to currents intransmitter loop (Tx) is zero.

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from above, a current element at (x,y)= (c cosα,c sinα)would be Idl(x,y)= I(−sinα,cosα), with α the angle ofthe current element from the x axis. Adding π to α flipsthe sign of both (x,y) and dl(x,y) as needed. This singleloop example can be trivially extended to loops in they–z and x–z planes by interchanging x and y with y andz or z and x.

For more complicated loop shapes the same sym-metry may be obtained by using a loop and a mirrorimage of the loop, as diagrammed in Fig. 2. If one iscentered at (x,y,z) with ‘normal’ oriented in the (u,v,w)direction, centering the other at (−x,−y,−z) orientedwith ‘normal’ in the (−u,−v,−w) direction, with the looprotated so that an ‘up’ bump on the first at a point (x1,y1,z1) corresponds to a ‘down’ bump on the second at point(−x1,−y1,−z1). More precisely, if the first loop is de-scribed by curve a(α), the second is described by −a(α).For some loop shapes and positions, after the mirrorcopy has been repositioned and oriented, the two loopscoincide with current in the same direction in each, soonly one is needed (e.g., the loop of Fig. 1). Otherwisethe two may be wired in series to form a single trans-mitter loop with the proper symmetry (neglecting anyfields due to their leads).

3. Suitably symmetric placement of receiver pairs

The magnetic fields given by Eq. (2) are symmetricon change of sign of r; at point −r the fields point in thesame direction as the fields at r, with the same mag-nitude. This suggests differencing the output of pairs of

Fig. 2. Geometry of less simple (non-coplanar) symmetric loop pair,showing differential loop segment dl at point q, and complimentarydifferential loop segment −dl at −q. Magnetic fields of current in loop,at any point r and complimentary point −r are the same.

receivers placed at mirror points to eliminate theirresponse to primary fields. For inductive receivers thatare of small dimension, a receiver is sensitive to themagnetic field normal to the plane of the receiver, or forsolenoidal receivers, the magnetic field in its axial di-rection. A simple system is shown in Fig. 3. If a receiverat point r sensitive to changes in magnetic fields in the pdirection, is coupled with a receiver at point −r orientedat 180° from the first, so that it is sensitive to changes inmagnetic fields in the −p direction, for the duplicatedcurrent element of Eq. (2) (Idl at q and − Idl at −q), thesum of the outputs from the two receivers is sensitive tochanges in the p component of

dBðrÞ þ dB ′ðrÞ−dBð−rÞ−dB ′ð−rÞ

¼ l0Idl� ðr−qÞ4kjr−qj3 −

l0Idl� ðrþ qÞ4kjrþ qj3 −

l0Idl� ð−r−qÞ4kj−r−qj3

þ l0Idl� ð−rþ qÞ4kj−rþ qj3 : ð3Þ

All terms cancel, so with transmitters that are sym-metric (on inversion in the origin) and symmetricallyplaced receivers with opposing orientations summed, orsymmetrically placed receivers with a common orienta-tion differenced, the summed (or differenced) receivercoil response to the primary fields vanishes, so the pair ofreceiver coils, as a unit, is null coupled to the primaryfields of the transmitter coil. Thus such paired receivercoils are null coupled to any transmitter coils that aresymmetrically constructed, so can be made to be null

Fig. 4. Geometry of less simple symmetric receiver loop pair, onereceiver loop centered at r with loop ‘normal’ p, and the other centeredat −r with loop ‘normal’ −p. Primary magnetic fields at any point rand complimentary point −r are the same, so summed response ofcomplimentary receiver loops to magnetic fields due to currents intransmitter loop (Tx) is zero. Schematic wiring for symmetrictransmitter loop pair shown.

Fig. 6. Practical 8 receiver pair system with symmetry on inversion inorigin, appropriate for null coupling to symmetric transmitter system,such as shown in Fig. 5. Each receiver pair consists of one lowerreceiver (a), and upper receiver diagonal across from it (b), withreceiver outputs differenced.

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coupled to a plurality of transmitter coils providing aplurality of source magnetic field polarizations.

The use of receivers in a difference mode as in theprevious paragraph has the advantage of cancelling outnoise that is common to the two receivers, such asmotion noise from changing orientation in the Earth'smagnetic field, or magnetic field noise due to distantcurrent sources. Cancellation of primary transmitterfields may also be obtained if the duplicate section of

Fig. 5. Practical 3 transmitter system with symmetry on inversion inorigin, appropriate for null coupling receiver pairs to all transmitters.Loops Tx1 and Tx2 are run independently. Loops Tx3a and Tx3b arerun together as a unit.

transmitter loop at point −q is in the +dl direction. Thiscreates source magnetic fields that are anti-symmetricon change of sign of an observation point r; fields that atpoint −r are in the opposite direction as the fields at itsmirror point r, with equal magnitude. With such a sourceconfiguration the receiver coil at point −r needs to besensitive to changes in the magnetic fields in the +pdirection instead of in the −p direction (its sign isreversed), so both receiver coils in a pair are sensitive tochanges in the same direction. Such a configurationvariant lacks the common mode noise cancellation ofthe configuration of the previous paragraph so is moresusceptible to external noise and motion noise.

For receivers of large enough extent that changes inthe primary field over the receiver coil are significant,the same symmetry arguments hold. For transmittersthat are constructed to be symmetric on inversion in theorigin, as leading to Eq. (2), receiver loop pairs arearranged symmetrically on inversion in the origin, so ifone receiver loop path is described by a path Γ(α) itscomplimentary receiver loop is described by path−Γ(α). In practical terms, this means that if an arbitrarilyshaped loop is centered at r with ‘normal’ p, its com-pliment is a mirror image centered at −r, rotated 180°about an axis through their centers, with ‘normal’ −p: an‘up’ wiggle on one corresponds to a ‘down’ wiggle onthe ‘far’ side of the other. A symmetric system witharbitrarily shaped receivers is shown in Fig. 4. Theelectromotive force in the first is then

V ¼ −ddt

ZsBdda; ð4Þ

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where the integral is over a surface S bounded by theloop path Γ(α), and da is a surface differential (normal),and in the second is

V ′¼ −ddt

Z−sBdda; ð5Þ

where −S is the same surface with reversed coordinates(bounded by curve −Γ(α)), and da points in the oppositedirection for the surface of the second integral. Fortransmitter loops that are symmetric on inversion in theorigin, the primary magnetic fields are symmetric on

Fig. 7. Response of 75 mm mortar with center 86 cm below system. (upper)response to By transmitter (vertical loop with normal in y direction). (lowedirection).

change of sign of position r, so integrals (4) and (5)cancel for the primary magnetic fields, and the summedpair is null coupled to the transmitter coils.

4. Construction of multiple transmitter multiplereceiver pair systems

The method of constructing transmitters that aresymmetric (on inversion in the origin) given in theearlier section on symmetric transmitter construction,and the symmetric receiver placement method of theprevious section are entirely general. To make a multi-transmitter multi-receiver pair system one merely

Object response to Bz transmitter (horizontal loops). (middle) Objectr) Object response to Bx transmitter (vertical loop with normal in x

Fig. 8. Principal equivalent dipole polarizabilities of 75 mm mortar, estimated from data of Fig. 7.

232 J.T. Smith et al. / Journal of Applied Geophysics 61 (2007) 227–234

includes several suitably symmetric transmitters givingprimary magnetic of desired orientations, and an arrayof symmetrically placed receiver pairs. An examplethree transmitter array is shown in Fig. 5. The twovertical transmitters loop operated independently givemagnetic fields oriented primarily in the x and y direc-tions below the transmitter assembly, the pair of hori-zontal transmitter loops gives magnetic fields primarilyin the z direction. (A single horizontal transmitter loopat the height of the assembly center would also be anacceptably symmetric source of vertical magnetic field,but gives smaller amplitude fields at depth for the samenet magnetic moment.) An example receiver pair arrayis shown in Fig. 6. Eight pairs of receiver coils are

Fig. 9. Axial direction of mortar es

shown, with one element of each pair in the lower plane,and the other element in the upper plane diagonallyacross from it. The lower receiver plane is slightly belowthe lowest transmitter coil so that together the trans-mitters and half the receivers are as close as possible toobjects to be detected. The receivers shown are orientedto be sensitive to vertical magnetic fields, as verticalmagnetic fields tend to be a bit more sensitive to objectsbelow the sensors.

5. Example

Data was collected using a three orthogonal transmit-ter loop, eight receiver coil pair system, with transmitter

timated from data of Fig. 7.

Fig. 10. Principal equivalent dipole polarizabilities of irregular piece of shrapnel.

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loops as in Fig. 5 and receiver pairs as in Fig. 6. Trans-mitter loops were two nestled orthogonal vertical loops0.941×0.680 m and 0.942×0.651 m driven with 611.and 563. amp-turns current (peak) respectively and a pairof 0.983×0.983 m horizontal loops separated 0.642 mvertically with 307. amp-turns current (peak) each. Re-ceivers were 500 turn 6ʺ inside diameter solenoids ap-proximately critically damped with a nominal resonancefrequency of 20 kHz, on the diagonals of the twohorizontal transmitter loops, with centers at 27.3 and50.2 cm laterally from the transmitter loop centers. Thetransmitters were operated with a 340 μs half sine pulsewaveform repeated every 1852 μs with alternating pola-rity, with a series of nine pulses to each of the threetransmitters in turn, and stacked over 20 such sequences,cancelling harmonics of 60 Hz. Data from the first pulsein each series to a transmitter was omitted from the stack.In the system as built, null coupling by receiver pairdifferencing reduces the magnitude of the primary fieldsignals by factors between 0.006 and 0.16 compared tovalues calculated for what would appear in single coilmeasurements, for the various receiver coils operatedwith the three transmitters. This gives maximum primaryfield transients of 0.3 to 13 V.

To distinguish the response of a target object, from thebackground response of other objects in the room wheremeasurement were made, background reference mea-surements were made, and subtracted from subsequentmeasurements with a target object near the detectionsystem. Data from the system operated above a horizontal75 mm mortar shell (empty) oriented in the x direction isshown in Fig. 7, as a function of time after transmittercurrent shut-off, with separate traces for each of the eight

differenced receiver pairs. The measured object responseto the horizontal loops (upper panel) is roughly sym-metric as the mortar is horizontal and directly below thesystem, with a greater response measured by the innerreceiver pairs. Object response to the two vertical loops(middle and lower panels) is smaller in magnitude, andchanges sign on opposite sides of the object in the di-rection of the primary (transmitted) fields.

The data of Fig. 7 was smoothed using a variablelength half-sine window, with length 10% of the timeafter transmitter shut-off, and equivalent dipole polariz-ability (rates) and dipole position estimated using themethods of Smith and Morrison (2004). Estimated prin-cipal equivalent dipole polarizability as a function of timeis shown in Fig. 8. The close agreement of two estimatedprincipal polarizabilities (transverse) is consistent with anobject symmetric about an axis of rotation. The consid-erably greater other principal polarizability (axial) isconsistent with an elongate magnetic (ferrous) object at‘late’ time. Object axis orientation estimated as a functionof time shown in Fig. 9 agrees with the true orientation.Equivalent dipole position was estimated as (−0.022,0.000,−0.837)±(0.001, 0.001, 0.001) m which differsfrom the actual center position by 0.032 m. Similarlyestimated principal equivalent dipole polarizabilities foran asymmetric piece of shrapnel is shown in Fig. 10. Lackof axial symmetry of the shrapnel is immediately evidentin its three widely separated principal polarizabilities.

6. Conclusion

Differenced outputs from symmetrically placed recei-vers offer a viable means of reducing system response to

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primary fields due to multiple symmetrically constructedtransmitters. Response of objects to such a system allowsestimation of polarizability responses from measure-ments with the system at a single location relative to thedetected object, allowing direct evaluation of objectsymmetries.

Acknowledgements

This work was supported by the US Department ofthe Army contract No. W74RDV93447299, under theauspices of the Strategic Environmental Research andDevelopment Program (SERDP). The authors aregrateful to A. Becker, A. Ratti, J.B. Greer, H. Yaver,Z. Radding, J.F. Beche, R.E. LaFever, S. Zimmerman,and E. Gasperikova for assistance in system design andconstruction and/or logistics support.

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