important design considerations for inboard airborne magnetic gradiometers

GEOPHYSICS, VOL. 49, NO. 11 (NOVEMBER 1984); P. 2W2018, 14 FIGS., 2 TABLES

Important design considerations for inboard

airborne magnetic gradiometers

C. D. Hardwick*

ABSTRACT

The advantages of magnetic gradiometry as an ad- with long-wavelength anomalies. The second source of junct to total field mapping are generally recognized error is the frequency-counting technique usually em- and a few aircraft have been equipped with gradi- ployed to convert a Larmor frequency to ambient total ometers. These gradiometers are derived from high- field. The counting process is somewhat analogous to sensitivity total-field magnetometer systems that are in digital sampling at a relatively low rate and as such themselves subject to certain errors that can usually be affords little protection against aliasing from higher fre- tolerated in conventional surveys. However, in a gradi- quency interference sources, including components at ometer, where very large total-field values are differ- aircraft maneuvering frequencies. enced, these errors can, in many cases, greatly exceed This paper, using examples, illustrates the two types the basic accuracy required of the system. of error. A list of design criteria is presented and several

There are two principal sources of error in inboard techniques are described for realizing these criteria. Fin- gradiometer systems. The first, and most significant, re- ally, compensation and survey line results are shown for sults from the inevitable magnetic interference of the a three-axis gradiometer system in the National Re- aircraft or from the inability of currently available com- search Council of Canada’s Convair 580. This aircraft pensation systems to deal with the magnetic interference uses nonoriented cesium magnetometers, one in each adequately. Passive methods of compensation are not wingtip and one at the tip of the tail fin. Compensations sufficiently comprehensive for gradiometry and the over the entire normal maneuver envelope of the air- active compensation systems currently in use, which craft on all headings give typical standard deviation were designed for military applications, cannot guaran- errors of 3 my/m from dc to 1 Hz. Thus, the system is tee compensation at zero frequency (dc) or at the very capable of measuring gradients down to nongeologic low frequencies of interest to the geophysicist concerned background levels.

INTRCiDUCTlON

The value of gradiometry as a source of additional infor- can be used to classify suprabasement structures of interest in petroleum exploration, can be effectively estimated using mea-

mation m total held aeromagnetic surveys is generally recognized; and advantages of flying a gradiometer can be briefly summarized on an axis-by-axis basis as follows.

Vertical

Increased definition of near-surface features such as verti- cally dipping fault zones is possible, while contributions from deeper features such as basement structures are suppressed (Hood, 1971). The fall-off exponent n in Euler’s equation, which

sured vertical gradient (Slack et al., 1967). The vertical gradient can also be used to correct total field data for a nonconstant flight path height over rough terrain.

Lateral

For a given spacing of survey lines, higher resolution total- field contouring is possible (Breiner, 1982). Conversely (and perhaps of more importance), wider spacing of flight lines is possible for a given specification of contour resolution.

Manuscript received by the Editor November 29, 1982; revised manuscript received May 21, 1984. *Flight Research Laboratory, National Research Council, Montreal Road, Ottawa, Ontario, Canada KlA 0R6. This paper was prepared by an agency of the Canadian government.

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Design of Inboard airborne Gradiometers 2005

Longitudinal

If the longitudinal gradient is directly measured, temporal variations, such as diurnal shifts, in the total field can be removed from survey data without the need for ground magnetometers and/or extensive tie-line leveling calculations (Breiner, 1981).

A gradiometer is essentially two total-field magnetometers, separated by as long a baseline within the aircraft structure as is possible, whose outputs are simultaneously differenced. (Tensor gradiometers that measure gradients of the orthogonal components of the Earth’s field are in use for such applications as magnetotellurics, but considerable development will be necessary before such devices can be usefully flown in aircraft.)

When the National Aeronautical Establishment (NAE) start- e& ‘buildirrg gradi- irr 1977 them was no commonly agreed-upon requirement for resolution and accuracy of gradient measurement. However, there were some benchmarks: Slack et al. (1967) had achieved a vertical gradient resolution equivalent to 1.64 my/m with a helicopter-towed gradiometer; and the Geological Survey of Canada began publishing vertical gradient maps contoured at 25 my/m intervals, implying a resolution of about 5 my/m (Hood, 1980). In the absence of

more explicit guidelines, for the NAE gradiometer system it was decided to set as a design objective a resolution and overall accuracy that would allow measurements of gradients down to the “background” or nongeologic level. Typical International Geomagnetic Reference Field (IGRF) background values given by the 1975 model for an altitude of 300 m are for the vertical, about 15 to 30 my/m, while horizontal gradients vary from about 2 to 5 my/m.

This design objective was achieved only with considerable effort because of two sources of error in current methods of total-field measurement. These errors are due to the inevitable motion-related magnetic interference of the aircraft (or to inaccuracies in the interference compensation system) and to a lesser extent, to the methods of measuring the magnetometer signals. These errors are usually insignificant in total-field surveys, but depending upon the intended use of the gradiometer data, can becomes quite significant. Tom illustrate this point, consider the following example.

Given two high-sensitivity total-field magnetometers, individually compensated, each with a dc (zero frequency) error of four gammas (4~) standard deviation (0): in a total field of 50 000 y, this would be considered reasonably good compensation, about 0.008 percent.

1OKM IOOOM 1ooM 10M - WAVELENGTH @ 160 KNOTS

I 1 I

I I , ’ I

I j !

; 30KM DATA PROCESSING HIGH.PASS

i i I

-

TYPICAL D.P. LOW-PASS FILTERS I

POSSIBLE GEOLOGICAL SPECTRA

I I I

- TYPICAL ASW COMPENSATOR

MOTION-RELATED MAGNETIC

INTERFERENCE

I I

4 RECOMMENDED

LOWER LIMIT OF 1 DATA SAMPLING

SJGNAUNOISEUMIT QF I I ----_ --_-

MAGNETOMETER I

FREQUENCY. (Hz)

FIG. 1. The aeromagnetic spectrum.

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2006 Hardwick

Next, assume a short baseline of 2 m, which would be representative for the vertical axis in a small aircraft. If the two errors were uncorrelated, after differencing to form a gradient signal, the resulting error would be Jo:++&= 5 66 y Thus, the gradient error is 5.66 y/2m = 2 830 my/m. This is many times greater than the typical values given above for the background vertical gradients.

To achieve gradient sensitivities of less than 10 my/m over a 2 m baseline requires very high-resolution sensors, implying the use of some type of nuclear resonance magnetometer where a Larmor frequency proportional to the total field is produced. Cesium and metastable helium possessing nominal sensitivities of 5 my are well suited; rubidium is slightly less so. Proton precession magnetometers of this order of sensitivity might be used, but as will be shown subsequently, there is a requirement for data rates that could be slightly beyond the capability of these magnetometers.

This paper describes the problems of compensation and magnetometer processing related to accurate total-field measurement as required for gradiometry and then shows two- system configurations that have been used to measure gradients down to the Earth’s field background level. Measurement results are also presented.

TOTAL FIELD MEASUREMENT ERRORS

Motion-induced magnetic interference and compensation errors

To help understand this problem, let us look at the aircraft motions that produce magnetic interference as shown in the aeromagnetic spectrum of Figure 1. At the top of the figure, the frequency scale has been translated into wavelengths of (hypo- thetical) sinusoidal data for an aircraft flying at a ground speed of 160 knots. The wavelengths generally of interest to the geologist are from about 200 m up to as high as 30 km. The geologic power spectral densities shown are also quite hypo- thetical; the steep portions are associated with the distance to and the magnetization of the basement rocks, while the less steep portions represent surface geology (Erickson, 1975).

The various types of aircraft motion are discussed individually in the subsequent section of the text as follows.

Short period-When an aircraft (or helicopter flying at survey speeds) is perturbed, either by pilot input or by atmo- spheric turbulence, the first response of the vehicle (about its pitch, roll, and yaw axes) is in the short-period mode. The frequencies involved, which are somewhat air speed-dependent, can be considered to be those at which the aircraft can be maneuvered with a minimum of control force.

Phugoid.-This is a lightly damped mode in which air speed and height are exchanged with one another resulting in a slow pitch oscillation. This motion is present to some degree in all aircraft, its amplitude being dependent upon a number of factors, especially the altitude-hold mechanization of the autopilot. Figure 2 shows an example of the effect of the phugoid. The magnetometer spectrum shown is for a survey line flown without autopilot. Crosscorrelation of magnetometer and vertical acceleration result in a squared coherence function that

FRCOUENCY lHl,

FIG. 2. Phugoid motion example.

shows significant correlation at the phugoid period of about 40 seconds.

Turning.-When the pilot (or autopilot) makes a heading or altitude correction, the aircraft moves slowly to achieve the required condition. (The “Rate 1” turn of Figure 1 is 180 degrees of heading change per minute.)

Air mass.-This very low-frequency motion is difficult to define. It is associated with long wavelength barometric pressure changes which can certainly cause very low-frequency vertical motion in an aircraft whose autopilot is holding a constant pressure contour. For surveys that are flown at a constant height above ground using a radar altimeter, air mass motion may not be relevant, but for those flown at constant barometric altitudes it could be a problem.

The motions described produce magnetic interference that is seen by a total-field sensor, even in the most scrupulously magnetically “clean” aircraft. In cleaning an aircraft, there is a definite point of diminishing returns; not all magnetic sources can be practically removed from an aircraft. Permanent magnetic fields are unavoidably associated with ferrous metals in the airframe and engines, and with the magnets of dc motors. Induced magnetic fields are associated with nonferrous metals and paramagnetic steel fasteners; these fields are heading- dependent. Finally, large conducting skin surfaces present an unavoidable source of eddy current interference as the aircraft maneuvers in the Earth’s field. The frequency band over which

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Design of Inboard Airborne Gradiometers 2007

Table 1. Two magnetometers, each individually compensated.

Mag 1 Mag 2

o uncompensated 0.535 y 0.3746 y o compensated 0.0369 y 0.0277 y Improvement ratio (IR) 14.50 13.52

the interference occurs is shown in Figure 1, and I note that it extends well beyond the highest maneuver frequency. This is because of harmonics in the spectral content of the short period maneuvers (many control inputs tend toward being impulse- shaped) and because of harmonic products (especially the second) associated with the interference components themselves.

Motion-related magnetic interference can be represented very satisfactorily by the linear model described by Leliak (1955, 1961). Attempts to use empirical, less complete models have not been successful for high-sensitivity magnetometry. It is true that low-sensitivity magnetometers can be compensated for gross sources of interference by so-called passive methods; permanent magnets can cancel permanent fields, pieces of permalloy can oppose induced fields, and eddy current sources can be reduced by short-circuited coils near the magnetometer. However, arriving at the right size and orientation of compensating components is a frustrating and time-consuming process; the Leliak equations are too complicated to be solved by trial and error.

The type of compensator referred to as “active” uses the Leliak equations or a subset of them and produces an electrical analog of the magnetic interference. These systems were orig- inally designed for use with military magnetic detection systems and perform a very adequate job of compensating in their specific role. The CAE-9-Term Compensator (CAE, 1968) is a good example of such compensators. However, the character- istics of military detection systems are quite different from those of geophysical systems and consequently, military-type compensators may not be particularly suited for geophysical work.’

In the military application only anomalies such as sub- marines, whose signal wavelengths are less than about 1 000 m, are of interest. High sensitivity and large dynamic range are achievable over a relatively small bandwidth by sharply filtering out as much of the lower frequency geologic signal as possible. Figure 3 is a block diagram of a conventional military type of compensator. The three-axis vector magnetometer measures the direction cosines H between the body axes of the aircraft and the Earth’s field vector. These, with their first derivatives k, are combined to form terms A corresponding to permanent, induced, and eddy-current terms in the Leliak model. Since the majority of such compensators are analog- mechanized to save hardware, only the most significant terms for a particular installation are formed (typically nine out of a possible eighteen). Predetermined compensation coefficients i

‘Several military compensators are currently being flown in vertical gradient systems over Precambrian geology, and useful maps are thereby produced. However, because of bandwidth and other considerations, this type of compensation is less than ideal for the broader applications of gradiometry outlined in this paper.

FIG. 3. Conventional compensator for military magnetic detection systems.

are multiplied with their respective A terms to form a compensation signal which is resolved into signals for compensation coils that produce compensation fields in the same axes as the vector magnetometer. Actually, the resolver is drawn for convenience of explanation; in practice, the terms are arranged to form three separate, axis-ordered signals.

When this military type of compensator is applied to a geophysical system, two problems arise. The first (which is also applicable to military systems) is related to the coils. Because for practical reasons they must be mounted some distance from the sensor, sometimes as far as several meters, it is difficult to determine their respective scale factors and to assure orthogonal alignment with the vector magnetometer. This results in interaxis cross couplings which are not accounted for in the model. Because these cross couplings are small, compensation solutions are certainly possible, but if the latter are obtained by a formal process (as in a digital mechanization), several iter- ations of maneuvering and solution computation are necessary, while in an analog compensator, there is a great deal of tedious “cut-and-try.” Anyone who has been aboard an aircraft during compensation maneuvers will appreciate the disadvantage of any technique that does not lead to a minimization of maneuvering.

Compensation coils can cause an additional problem when used in short-baseline gradiometer systems, in that the two sets of coils create interacting fields which further obscure the solution process.

The solution to the coil problem is, quite simply, to compensate the magnetometer signal after it has been converted from Larmor frequency to a digital (or analog) format.

The second problem associated with the military-type compensator is caused by the fact that a solution for the interference coefficients is obtained using band-pass filtered data. Such a solution cannot, in general, be used to compensate over the frequency band of interest to the geologist, i.e., 0 to about 0.15 Hz without introducing significant errors. The reason for this is explained by Leach (1980) in a very comprehensive treatment of aeromagnetic compensation. A brief explanation is that the equations associated with the Leliak model tend to

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2008 Hardwick

be somewhat ill-conditioned. Because compensation data cannot practically include 360 degree maneuvers about all three aircraft axes (only about the vertical), certain near-linear relationships can exist among terms, leading to solutions that are certainly valid for the data from which they are derived, but which do not necessarily hold up well in predicting and cancel- ing the interference for a slightly different set of data. In early studies it was found that one of the factors to which solutions were particularly sensitive was bandwidth of data. Changes of as little as half an octave in the low-frequency break-point of the band-pass filter produced huge changes in compensation coefficient values, and coefficients calculated at one bandwidth gave poor results when applied to the same data at a slightly different bandwidth. Thus, it is not surprising that coefficients computed at detection bandwidths that are typically 0.06 to 1.0 Hz do not hold up at 0 Hz.

Before this effect is illustrated with an example, it is necessary to explain the criterion used by NAE to assess the effectiveness of compensation. At NAE, compensation maneuvers consist of a series of pitches, rolls, and yaws on four orthogonal headings, with 30 degree bank turns between each heading. This procedure takes about six minutes of flying time The effectiveness of compensation is evaluated in terms of the standard deviation (o) of the magnetometer or gradiometer signal during the compensation maneuvers. The improvement ratio (IR) is the ratio

of the standard deviation of the uncompensated signal to that of the compensated signal. The use of standard deviation is a departure from the commonly used “Figure of Merit” (FOM) criterion; the rationale for this choice is given in Appendix A. The term “FOM” is often applied to the set of compensation maneuvers, and in this paper, it is used in this sense.

The example consists of two magnetometers that were each compensated using data band-pass filtered between 0.06 and 1.6 Hz. The results given in Table 1 indicate that each magnetometer was very well compensated.

The resulting coefficients were then used to compensate the magnetometers in a gradiometer pair, i.e., their compensated outputs were dilTerenced. The same maneuver data were used to evaluate this gradiometer, but they were only low-pass filtered, giving wide-band content from 0 to 1.6 Hz (an appropri- ate bandwidth for geophysical purposes). The result is shown in Figure 4, and it can be seen immediately that the compensated difference signal has a dc bias (BI) of over 36 y. Furthermore, the IR of 3.428 is very low (an IR of 10 to 20 is considered acceptable). It can be seen that the low IR is due to low- frequency compensation errors associated with the turning frequency of the aircraft. In contrast, the compensation result using wide-band data for the solution has an IR of 15 and a dc bias shift of 0.010 y, both of which are much more in keeping with gradiometry requirements.

FLT 79.15

FOR COMPENSATION

UNCOMPENSATED

u = 4.2697

2 s 0.0 - 81 - 0.259 7

9

COMPENSATED - BANDPASSED COEFFS. U = 40.0 I.2457 -

or 39.60 my/m

81 = 36.500 7

or 1217.00 my/m

30.0 - IR = 3.426

25.0

COMPENSATED - WI DE-BAND COEFFS.

?$ _jj~R~I ffj$g;;:

4 5 6 7 0

DIFFERENCE MAGl MAG2 time (minutes)

FIG. 4. Comparison of band-pass coefficient results versus wide- band coefficient results.

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Deslgn of Inboard airborne Gradiometers 2009

To summarize, this example shows that compensation coef- in an area of significant uniform gradient, one way to ensure

ficients calculated using band-passed data can cause errors at that the average value of gradient as seen by the lateral gradi-

dc and at frequencies below the band-pass when applied to ometer is zero is to fly the FOM pattern in such a way that each

wide-band data. However, coefficients calculated using wide- of the four legs covers the same distance. However, at high band data give satisfactory compensation when used on wide- altitude in nonzero wind conditions, such a pattern could be

band data. beyond the capability of many navigation systems.

The frequency (and wavelength) range over which compensation errors have been observed as the result of using coefficients derived from band-pass filtered data is shown in Figure 1. One method intended to circumvent the problem of low-frequency compensation errors is to sharply high-pass filter gradient data at approximately 30 km as shown in the figure. This does not eliminate the errors above the high-pass, but it does remove the dc bias. Such data high-pass filtering could be acceptable for making vertical gradient anomaly maps in geologically active areas where long wavelength information is not considered to be necessary. However, in processes involving integration of a gradient, such as total-field contouring using lateral gradient or using measured longitudinal gradient to remove diurnal variations, it is essential to know the dc value of the gradient.

Total field frequency counting

Wide-band compensation of a gradiometer is fairly straight- forward to mechanize. The wide-band (non-high passed) uncompensated magnetometer signals are differenced and the resultant signal is used in a regression analysis as described by Leach (1979) to obtain compensation coefficients “Ridge regression,” which entails a small modification to the conventional least-squares regression, should be used to ensure maximum insensitivity of the solution vector to such factors as the uncorrelated noise statistics of the data. All 18 terms of the Leliak model should be solved, plus a constant (19th) term to account for the zero-frequency component (dc bias).

This is the second potential source of total-field measurement error. For a nuclear resonance magnetometer, the most logical way to measure the Larmor frequency is to count it directly or to average a finite number of its signal periods (period averaging), which is equivalent to frequency counting. One of these techniques is always used in current geophysical magnetometer systems. Usually, to capitalize on a magnetometer’s resolution, the Larmor frequency is premultiplied by some integer before counting. For cesium, for example, to get 10 my resolution in a 1 s counting period, the Larmor frequency signal, which is scaled at 3.498 Hz/y, must be multiplied by a factor n to satisfy the inequality

(10 x 10m3) x 3.498 x n 2 2

to have 10 my represented by 2 counts. For this case, n would be 57.

In collecting wide-band compensation data, it is essential that they be taken in an area of minimum, uniform (constant) gradient. A compensation pattern flown in nonuniform gradient conditions will give rise to low-frequency gradiometer signals that the regression procedure will cause to be compensated, while other low-frequency signals from aircraft maneuver interference will be less well-compensated. For an aircraft flying at its lowest safe handling speed in a representative survey configuration, a square FOM pattern with one-minute sides does not require a very large area. Satisfactory uniform horizontal gradient areas can always be found over sedimentary geology with the aid of magnetic maps, and usually the magnitude of the gradient over such an area decreases steadily up to the aircraft’s maximum operating altitude. The magnitude and uniformity of the horizontal gradient can easily be measured by flying a “mapping square” over the intended FOM pattern and observing the total field. Mapping the vertical gradient is some- whatmore diifcuit in that it invoives mapping the total field for two FOM patterns using repeatable navigation at two different altitudes that straddle the altitude at which the FOM data will finally be collected. Once a uniform vertical gradient area has been mapped, it is a good idea to record its coordinates.

With present day silicon chip technology, large multiplication factors and short counting times are easily achieved. However, the problem is that a counter is essentially an avera- ger and a process similar to digital aliasing can occur, causing its count to be subject to error whenever signal components are present at anything above one-half the sampling frequency (Nyquist’s criterion). Unfortunately, the Larmor signal contains frequency modulated (FM) information that corresponds to all the higher frequency fields seen by the magnetometer, and as shown in Figure 1 there are various unwanted components in the signal in the high-frequency part of the spectrum. Schemes to remove these FM components by means of phase-lock filters are generally only partially effective. Phase-lock loops acting as filters can be effective provided they only have to operate over a very limited range of frequency. Because of the large range of the Earth’s field, Larmor frequencies vary over greater than a 4 : 1 range, thus requiring a wide tracking bandwidth which is in conflict with the requirement for narrow-band response to unwanted FM components.

Solution of the 19th (dc) term simply involves removal of any residual bias in the compensation solution, on the assumption that the compensation data were taken in an area of zero gradient. Even if the gradient for the FOM is uniform, unless it is very low, it will distort the value obtained for the dc term. Thus, for vertical gradiometer compensation, the dc term should be modified by the actual mapped vertical gradient for the compensation area. For lateral gradiometer compensation

Figure 5 shows a spectrum of the higher frequency components in a typical airborne magnetometer signal; those at power frequencies are clearly evident, as are beats between 60 Hz and 400 Hz, while the strong second harmonic of 60 Hz is due to onboard dc-to-60 Hz inverters which cause a strong i~20 Hz modulation of the aircraft’s dc system. In addition to power-related higher frequency components, as shown in Figure 1, there can be contributions from propellers which may not be entirely nonmagnetic; these occur between 16 and 33 Hz and in addition, for multiengine aircraft whose propellers are not phase-synchronized, there can be very low-frequency beats at slowly varying frequencies throughout the aeromagnetic band. For helicopters, there is certain to be a large magnetic signal from the rotor, occurring between 10 and 15 Hz, depending upon the number of blades and type of machine.

Another type of spurious FM can occur at the high end of the frequency range of Figure 1, in that some magnetometers are

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FIG. 5. A magnetometer spectrum containing power frequency components.

self-orienting by means of 1 000 Hz quadrature components that modulate the Earth’s magnetic field as seen by the sensor cell. Finally, the higher frequency portions of the maneuver interference can cause aliasing if the Nyquist frequency of the counter is lower than the highest interference frequency.

Counter aliasing effects can be overcome by raising the sampling rate to above twice the highest expected spurious frequency, but when this is as high as 400 Hz, the required counting speeds would be beyond the state of the art. However, a counter differs from a pure digital sampler in that aliasing effects can be reduced by lowering the sampling rate (i.e., in- creasing the counting time). The worst case for single-frequency aliasing occurs when a spurious frequency has an odd multiple of one-half cycle within the counting period; all complete cycles within the period have no net effect. For a given counting period T and spurious signal A sin (27rj’)t where A is amplitude in y’s andfis frequency, the worst case aliasing error (E) can be calculated as

1 tnfr=n

E=-

T s A sin (2ajI) dt

2n/r = 0

For example, for a 2 s counting period, if the spurious response of 60 Hz is to be kept below 10 my, the maximum allowable safe amplitude of 60 Hz would be 3.78 y. Thus, it can be seen that with a counting period of this order, the effect of higher frequency spurious components could be kept under control. However, the effects of maneuver interference at frequencies above half the sampling frequency are much harder to control (e.g., for the 2-s counter, components above 0.25 Hz).

A second potential problem with total-field counting is that the six signals for compensation, H and H must be carefully phase matched to each other and to the magnetometer signal,

since in any linear compensation process where sinusoidal components are supposed to cancel to zero small errors in phase are very significant. It is convenient to anti-alias filter the analog signals with second (or higher) order filters with break frequencies between about 1 and 2 Hz (depending, of course, on sampling rate). The amplitude response of a counter can be shown to be

1 sin (2@)T 1

t&f )T

where T is the counting period. The phase characteristic corresponding to this amplitude function is quite unlike that of any analytical second-order filter. Phase compensation could be applied to the counter signal after digitization, but great care would have to be taken in the digital filter design to assure acceptable accuracy. An alternative technique to obtain phase- matching between counter and compensation signals is to sample the latter at a relatively high rate and then average them over the counting period of the magnetometer to simulate the “period average” response of (2).

NAE has carried out limited experiments with various counter configurations and has found phase matching by means of simulated period averaging to be generally satisfactory under carefully controlled conditions, although the compensation results in terms of improvement ratio (IR) are somewhat unpre- dictable. This technique will be discussed in more detail in a later section on system configurations.

SUMMARY OF GRADIOMETER DESIGN REQUIREMENTS

If the errors in the total-field measurement as discussed above are to be avoided to the extent that gradients can be measured accurately to the background level, certain design criteria are implicit. These can be summarized as follows.

Compensation

(1) Compensation should be comprehensive; the full l&term Leliak model with a 19th term for dc (common mode) bias should be used.

(2) Compensation should be wide-band; dc to approximately 1 Hz.

(3) Solutions for compensation coefficients should provide maximum predictive performance throughout the full, normal maneuver envelope of the aircraft and for varying levels of nonmaneuver related noise in the magnetometers. Thus, solution should be by means of ridge regression (Leach, 1979) or an equivalent method, in order to minimize the sensitivity of the solutions to the data used.

(4) Compensation should be highly accurate. Compensation coils should not be used, but rather, compensation should be applied directly to the magnetometer signals, preferably after differencing.

(5) Measured direction cosine signals and their first derivatives must be carefully phase-matched to each other and to the magnetometer signals.

(6) Compensation data should be taken in an area of mini- mally low, constant gradient where the magnitude of the gradient has been determined by total-field mapping.

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FIG. 6. The NAE Convair 580 research aircraft, showing wingtip and tail magnetometers.

Magnetometer signal measurement

(1) Magnetometer signals should be wide-band processed (dc to about 1 Hz).

(2) Signal processing transfer functions should be carefully matched in amplitude and phase to those of the compensation signals.

(3) Signal measurement should be immune to all aliasing from spurious signal components at frequencies above those of geophysical interest.

Gradient calcuiatioa

Signal processing for the magnetometer must provide high accuracy and high resolution until after differencing to form a gradient signal.

GRADIOMETER SYSTEM CONFIGURATIONS

There are many possible mechanizations that can be used to meet the design requirements outlined above. By way of illus- tration, three systems that have been successfully flown by NAE are presented along with some representative results. The three systems differ from each other mainly in their methods of processing the input signals from the magnetometer.

The first employs digital “complementary filtering” to provide wide-band, high-accuracy magnetometer signals, while the second employs more hardware-oriented methods to produce difference signals before digitization, thus allowing less strin-

gent accuracy requirements on the digital signal processing than with the complementary filter approach. The third process is a much simpler system, using frequency counters, that ap- pears capable of meeting the design criteria under the right circumstances.

The test bed for these systems is the NAE Convair 580 research aircraft (Hardwick, 1978) pictured in Figure 6, which is flown as a three-axis gradiometer, the baseline geometry for which is sketched in Figure 7. The magnetometers used are all of the optically pumped type, employing cesium vapor, with a resolution of about 5 my. In the wingtip pods either self- oriented ASQ-501 magnetometers (CAE) are used, or (inter- changeably) nonoriented (“strap-down”) type VIW 2321-A2 (Scintrex) magnetometers are used. For the tail-fin tip, because of space and weight limitations, only the strap-down type of unit can be fitted.

In the system drawings that follow, in addition to gradient measurement, total-field measurement per se is shown. This will be discussed in a later section.

Complementary filter system

This mechanization is shown in Figure 8. The Larmor frequency signal from each magnetometer is split into two processing paths, one of which is a conventional frequency counter with a 2-s counting gate, long enough to provide immunity to higher frequency aliasing. The other path is a “Delay Line Discriminator” (DLD) which is essentially a very high- resolution frequency-to-voltage converter (Baker et al., 1970).

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The analog output of the DLD can be made to have infinite dynamic range (in terms of amplitude) by means of a high-pass filter (HP) as shown in Figure 8, or it can work over a limited range of field strength that corresponds to dc analog limits. Thus, each complementary filter is supplied with two signals, one (from the DLD) of high resolution but with no dc component and the other (from the counter) that is accurate at dc but which has no appreciable high-frequency information. The operation of the complementary filter (Hardwick, 1980) can be described briefly as follows.

FIG. 7. Gradiometer geometry of the NAE Convair 580.

DIFFER-

ENTIATOR ::

! z

The high-frequency side (DLD) is sampled at 8 Hz and the low-frequency counter signal at 0.5 Hz is interpolated to form a matching 8 Hz data stream. These two data streams are oper- ated- on, repectively by second-order high-pass and iow-pass filters and then summed. The transfer functions of the filters are chosen to be complementary to each other so that the transfer function of the summed output will be unity, i.e., it will have an absolutely flat frequency response characteristic. Because the interpolation of necessity involves a delay (which in this case cannot be less than 3 s), the DLD sample stream must be delayed to keep the two streams in step.

The break (or “cross-over”) frequency of the complementary filter is set sufficiently low (0.022 Hz) to ensure that the higher frequency part of the counter response [equation (2)], which

COMPENSATION _

L--1

!JSEC. DELAY! I

v

IBSEC. DELAY)

GROUND

SPEED

I3 SEC. DELAY)

ITFl + TFZVZ

1 ,+ DELAYS1

TOTAL

-- FIELD1

3 LATERAL

- GRADIENT

‘; VERTICAL b

* GRADIENT

*; LONG.

t GRADIENT

FIG. 8. NAE gradiometer system: complementary filter version.

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could contain spurious components and which would be hard to complement analytically, is heavily attenuated. Thus, the output of the filter is a wide-band, high-fidelity representation of the total field, delayed by 3 s.

The antialiasing filters for all inputs in Figure 8 are third order with components that allow phase matching to within k5 degrees at the break frequency of 1.6 Hz. The direction cosine signals for compensation [H] are corrected for small permanent and induced magnetic errors in the vector magnetometer as well as for any slight null, scale factor or axis alignment errors, using a simple 12-term error model. This was found to contribute somewhat to the dc stability of gradient solutions. The compensation coefficients, which are computed off-line, are used by a real time algorithm (Jordan, 1980) to form compensation signals that are delayed by 3 s to match the outputs of the complementary filters.

The lateral gradient signal (I-,) is obtained by differencing the wingtip magnetometers with compensation being applied after differencing. The vertical gradient signal (r,) is derived by taking the average of the wingtip magnetometers and then subtracting the tail magnetometer signal. Because of the longitudinal separation between the tail magnetometer and those in the wingtips, in addition to vertical gradient this signal will

pt.--&+ DIFF.

TOTAL FIELD

METER (TFM)

contain longitudinal gradient information. The latter is removed by subtracting a fraction K of the computed longitudinal gradient to give a pure vertical gradient signal. The scaling fraction K is a function of the gradiometer geometry shown in Figure 7.

The longitudinal gradient (r,) is calculated by differentiating the compensated total field (TFI) and dividing by ground speed (GS), using the simple relationship

d(TF1) d(TF1)

dt dt d(TF1) -=-=-=I-,

GS dX dX x (3)

dt

It should be noted that the three gradient outputs TX, Tu, arid rL are measured in aircraft axes and, depending upon the use for which they are intended, may have to be transformed to some earth-fixed coordinate frame, such as True North-East- Vertical, etc. Fortunately, for most aircraft flying survey lines, pitch and roll attitudes are close to zero and the Z-aircraft axis is close to the earth-vertical. However, because of drift, TX and rY will not, in general, be referenced to the flight track and must be resolved through the drift angle (8). Although not

, DIFFER- L

ENTIATOR

i

SOFTWARE

COMPENSATION

TOTAL

FIELD 1

LATERAL

GRADIENT

f X ) LONG.

GRADIENT

FIG. 9. NAE gradiometer system: hardware preprocessing version.

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shown in the sketches, the NAE systems resolve the gradient quantities into the earth-level/flight track frame using pitch, roll, and drift angles.

Hardware preprocessing system

The complementary filter system as just described has been validated and was used operationally by NAE from 1978 to 1982. It does, however, have some slightly inconvenient features that can be overcome with a modest amount of hardware preprocessing. Furthermore, tests to date show that the preprocessing gives slightly improved compensation performance over the complementary filter system.

The 3 s delay inherent in the complementary filter poses no problem for geophysical work, although it might not be acceptable for military applications. However, the three notable weak points of the mechanization include the following.

Transient response.PAlthough the filter can track all normal total-field changes, a random data error in one of the inputs, because of the large time constant associated with the cross- over frequency, can cause “ringing” in the output that can persist for an inconveniently long time Even the best of instru-

10.0

FDHC

OAYYA5

833

K(HZ

FIG. 10. Hardware preprocessing: derivation of lateral and vertical gradient signals.

COMPENSATED FOT SIGNAL: 0 = 0.160 y(0.194 7)

BIAS = Oy IO 71

IRg = 18.54 l16.701

0 @O 1 LO 180 L40 500 5e0 4LO ID0 I40 time ISECSl

FIG. 11. Lateral gradient compensation result using hardware preprocessing.

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mentation is subject to the occasional data drop out or other suitable reference frequencies_&,&, ,fR3 and then down-mixed transient error. to give finite audio frequencies corresponding to zero gradient.

Analog overscaling of the high-passed DLD signal.-It is desirable to have a high analog gain in this leg of the signal processing for low gradient areas, but in high gradient areas, it must be reduced to prevent exceeding analog limits. Because of the large dynamic range of the total field, it is difficult to select a gain that is ideal for all circumstances. An overscale causes a ringing transient as described previously.

The vertical gradient is again derived from the average of the two wingtip magnetometers, but the averaging is done at the frequency level as shown. In all other respects, the mechanization is essentially the same as that for the complementary filter.

dc stability,To ensure long-term dc stability, extreme care must be taken in the signal processing up to the point of gradient subtraction. In particular, any small dc bias between the DLD high-pass and the A/D conversion can cause substan- tial shifts in the dc value of gradient.

The arithmetic of the frequency mixing is shown in Figure IO. Figure 11 shows the results of a Tr compensation using hardware preprocessing with the same results for complementary filtering. Note the slightly better Improvement Ratio (IR) for the hardware preprocessing (lg.54 versus 16.70); these numbers typify the slight quantitative advantage of the hardware method.

Total-field counter system

The system shown in Figure 9 avoids these problems by doing gradient subtraction of the Larmor frequencies h&n-e

any signal conversion or processing. The DLD’s are still used to give a high frequency-to-analog-to-digital resolution, but the difference signals they now see vary over a very limited range compared to the total field. Thus, even before compensation the difference frequency stays within the analog range of the DLD, and dc reference can be obtained without the use of counters and complementary filtering. Because the DLD’s will not operate at zero input frequency (corresponding to zero gradient), the various Larmor frequencies are offset upward by means of

This mechanization, shown in Figure 12, represents a considerable simplification over the previous two configurations, but it should be used with caution because of the risk of aliasing errors as explained previously. The compensation inputs must be sampled at a high enough rate to simulate the period averaging of the counter. The output data will be delayed by half a sampling period. The counting period must be long enough to meet the antialiasing criterion of equation (1) for all expected spurious higher frequencies in the magnetometer signals, and yet must be short enough to meet the geologists’ specifications for short-wavelength data. If these criteria can be met, it ap-

MULTIPLIERS Z-SECOND

COUNTERS I

COUNTER GATE PULSE I

_

COMPENSATION ’ !

T

DELAY

0.5 Hz I ‘;

NOTE A DELAY? REMOVES LONGITUDINAL GRADIENT FROM I-.

FIG. 12. NAE gradiometer system: total field counter version.

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FIG. 13. Typical gradiometer data, Kane basin, 1981.

pears that the counter method can give satisfactory results, but with one reservation: there is no way of handling the aliasing effects of maneuver interference components at frequencies above half the counting period.

To date at NAE, a limited number of variations of the counter method have been tried. The most successful of these was a 2-s counter (with a 32 x multiplication of the Larmor frequency) and 8 Hz sampling of the compensation signals, giving 16 samples of simulated period averaging over the two second counting period. Variants that did not give satisfactory results were a l-s counter with similar processing of the compensation signals and ones that did not use simulated period averaging of the compensation signals.

Comparative results between the 2-s counter system and the other two systems (complementary filtering and hardware preprocessing) do not show a consistent trend to date, although improvement ratios for the vertical gradient as high as 93 have been obtained, compared to 33 for the complementary filter for the same data. The lack of consistency may be due to aliasing errors from the higher frequency maneuver interference components as discussed above.

TYPICAL GRADIOMETER RESULTS

Figure 13 shows typical three-axis gradient time histories with corresponding total held for a survey line. This particular line was selected because of the interesting anomaly (starting at about 64 minutes) and for the high-frequency definition in the gradient traces (starting at l$ minutes) that is hardly evident in the total field. Note the change in signal at 10 minutes indicated by the sharp FZ minimum and its subsequent change in character; this would be difficult to infer from the total field by itself.

Figure 14 shows the Fr compensation for the Convair that was used during the survey in question. The compensated o of 3.47 my/m is close enough to the nongeologic background horizontal gradient of 2.3 my/m calculated for the area. A small amount of residual error may be seen from the compensation maneuvers. This is typical of wide-band compensations in that

FIG. 14. Lateral gradiometer compensation, Kane basin, 1981

some high-frequency compensation capability is sacrificed for very tight compensation at the low-frequency end of the spectrum where it is needed. The small-amplitude high-frequency components are above the geophysical band and would nor- mally be taken out by the low-pass filtering in data processing.

The Fz compensation for the survey was not as good as that for Fr. The compensated o was 44.6 my/m while the background vertical gradient for the area was 22.5 my/m. Thus in this case, the design objective was missed by a factor of about two. The reason for the poorer Iz performance is that in the Convair, the tail-fin magnetometer is mounted quite close to the tail structure in an area that is difficult to make sufficiently magnetically clean. Thus, there is a very heavy burden on the compensation system. When compensation coefficients become large, a simplifying approximation in the Leliak equations leads to inaccuracies in the compensation. A study is currently underway to find a numerical method that will improve the accuracy of the interference model.

TOTAL-FIELD MEASUREMENT- IMPROVED ACCURACY

The reduction of total field measurement errors for the pur- pose of gradiometry leads indirectly to a useful byproduct, in that the absolute value of total field can be measured more accurately than might otherwise be possible. A magnetometer calibrated for absolute total-field measurement is useful for surveying secularly changing anomalies and for investigations supporting updates to the IGRF model. It can also be used to tie two magnetic surveys to the same datum.

Total field is, of course, a dc measurement, but it is exceed- ingly difficult to do total-field compensation at dc in the same manner as is done for the gradient signals; one has to rely on a

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Design of Inboard Airborne Gradiomeiers 2017

Table 2. Total field calibration. Ref. point BOURGET, Ont., 57 570 y, corrected for diurnal for four

cardinal headings, Feb. 27,198l.

Mag 1 Mag 2 Mag 3

Mean error (E) 1.53 y -0.83 y 27.18 y Standard

deviation (cr) 0.95 y 1.49 y 2.60 y Band-pass

compensation

band-passed compensation. Band-passed magnetometer signals can be easily compensated to a standard deviation (o) in the order of the magnetometer’s resolution (to about 10 my for cesium), but as outlined previously in the section on gradiometer compensation, there is no guarantee that the compensation will hold outside the frequency band, particularly at dc. However, it turns out rather fortuitously that if a comprehensive compensation model is used in conjunction with a stabil- ized solution such as ridge regression, quite good dc compensation is usually achievable for total field.

Table 2 shows typical airborne total-field calibration results that are routinely obtainable. The reference point is corrected for diurnal variation using ground magnetometers; altitude corrections are applied, and aircraft positioning was within &20 m. The significant result is for Mag 1, which was band- pass compensated (0.06 to 1.6 Hz). The other two magnetometers were wide-band compensated before differencing to give minimum gradient interference; in this configuration the dc compensation of the individual magnetometers can vary con- siderably.

In Table 2, the mean error for Mag 1 can be taken out as a dc term and the residue, characterized by cr, is under 1 y in 57 570.

The reason that wide-band compensation cannot be applied directly to a total-field signal is that although it is possible to find constant gradient areas for gradiometer compensation, areas of zero gradient are almost nonexistent. As an aircraft flies a square FOM compensation pattern in a constant gradient, the total-field magnetometer sees a low-frequency quasi- sinusoid, whose period corresponds to the 360 degree heading change of the aircraft and whose positive p.eak occurs at the heading corresponding to the positive direction of the uniform horizontal gradient. (The uncompensated FOM trace of Figure 11 shows this effect.) A wide-band compensation algorithm will treat this low-frequency gradient in the total-field signal as aircraft magnetic interference, producing a distorted set of coefficients whose predictive capability for the real interference will be greatly reduced.

The mechanization of total-field measurement in the NAE systems is shown in the system drawings, Figures 8 and 9. In the complementary filter version, software total-field compensation can be applied to any one of the wideband signals. In the hardware preprocessing version, the “total field meter” (TFM) is used (Hardwick, 1984). Its principle of operation can be described briefly as follows.

The delay line discriminator (DLD) is a very high- resolution, linear frequency-to-analog converter whose input range is 0 to 4 kHz. The counter, modulo 4 000 Hz, divides the Larmor frequency (f,) by this number to

produce N, the closest integer multiple of 4 000 Hz tof,. N drives a synthesizer to produce a frequency such that the input to the DLD is always within the range 0 to 4 kHz. The analog output of the DLD is antialias filtered and phase-matched to the analog compensation signals before A/D conversion at 16 bits. N is fed directly to the digital processor, where it is combined with the DLD output to form a wide-band, high-resolution measure of total field, with infinite dynamic range. The resolution and absolute accuracy of the TFM is +O.Ol y. With both total-field measurement methods, the compensated total field is processed by a digital high-pass filter to form a “synthetic” DLD signal, which because of its high resolution and compressed dynamic range, provides a good means of monitoring the quality of the compensated field.

CONCLUSIONS

High sensitivity gradiometry using pairs of sensitive total- field magnetometers mounted on an aircraft presents definite challenges, especially for short baselines; certain refinements of conventional aeromagnetic instrumentation methods are necessary. The key element in gradiometry is compensation, particularly with respect to bandwidth, and a uniform gradient area for collecting compensation data is essential. The second key element is front-end processing of the magnetometer signals, with emphasis on performing magnetometer signal subtraction as early in the processing chain as possible.

The design criteria outlined in this paper can be realized with algorithms that are well within the current state-of-the-art for digital signal processing and the associated hardware need not be very extensive, as illustrated by the system configurations used in the NAE Convair.

The results achieved to date show that gradient measurement down to background levels is achievable.

Looking to the future, a new generation of more sensitive optically pumped magnetometers is being considered, most notably one employing potassium vapor. Higher sensitivity would, in principle, allow shorter, more convenient gradiometer baselines and increased gradiometer sensitivity. How- ever, compensation will always be the limiting factor, and with the present interference models it is doubtful that the improvement ratios given in this paper as being typical can be pushed much higher. If the compensation methods suggested here come into wider use, experience may result in compensation model refinements and experimental effort should be so direc- ted. This, in conjunction with possible changes in design or modification of survey aircraft specifically for high-sensitivity gradiometry, could result in the effective utilization of more sensitive magnetometers.

ACKNOWLEDGMENTS

The techniques and instrumentation described in the paper were developed by the Convair Projects Group at the Flight Research Laboratory. The author wishes to express his appreci- ation to Dr. B. W. Leach, who was responsible for much of the theoretical work, particularly in the area of compensation and who has made valuable suggestions with respect to this paper; to J. E. Jordan for many of the on-line mechanizations; to R. A.

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Low and M. E. Bower for their support in data gathering and Quart. Bull., no. 1979(4), National Res. Council of Canada, Ottawa.

processing; to G. Hoftyzer who developed much of the pre- ~ 1984, The NAE Total Field Meter: Nat. Res. Council of

processing hardware; and finally, to R. W. Lee who had overall Canada. Ottawa.

Hood, P. J., 1971, Geophysical applications of high resolution magne- responsibility for digital hardware design. tometers, in Encyclopedia of physics: Springer-Verlag, 49(3), 422-

460. 1980, Aermagnetic gradiometry: a superior geological mapping

tool for mineral exploration programs: Proc. of the workshop on SQUID applications to geophysics, June 1980, Los Alamos Sci. Lab., New Mexico, 73.

REFERENCES

Baker, R. C., Davis, N., Bronstein, L., and Lowe, J., 1970, High resolution frequency to analog converter: U.S. patent no. 3,538,416.

Breiner, S., 1981, Horizontal magnetic gradient methods for airborne

Jordan, J. E., 1980, The NAE software aeromagnetic compensation system: LTR-FR-78, Nat. Aeronautical Establishment, NRC, Ottawa.

and marine geophysical exploration: Presented at the Slst Annual International SEC Meeting, in Los Angeles.

Leach, B. W., 1979, Automatic aeromagnetic compensation: LTR-FR- 69, Nat. Aeronautical Establishment, NRC, Ottawa.

~ 1982, Airborne transverse gradiometer-a new outlook on mapping: Geoprofiles 5, no. 1 EC&G Geometries, Sunnyvale, CA.

CAE, 1968, Study guide for the 9-term compensator: Tech. Dot. TD- 2501, Mark 1, CAE Electronics Div., Montreal.

Ericson, R. E., 1975, Preliminary analysis of MAD noise samples obtained on North Star flights: TM 75-5, Dept. of Nat. Defense of Canada.

Hardwick, C. D., 1978, The NAE Convair 580 research aircraft-an update for potential users: LTR-FR-64, Nat. Aeronautical Estab- lishment, NRC, Ottawa.

~ 1980, NAE Convair 580 aeromagnetics program: DME/NAE

~ 1980, Aeromagnetic compensation as a linear regression problem: Information linkage between applied mathematics and industry 11: Academic Press Inc.

Leliak, P., 1955, Identification and evaluation of magnetic field sources of MAD equipped aircraft: Electr. Div., the Martin Company, Balti- more, MD., Rept. no. ER7362.

~ 1961, Identification and evaluation of magnetic field sources of magnetic airborne detector equipped aircraft: Inst. Radio Eng. Trans., Aerospace and Navigational Electr., 8,95-105.

Slack, H., Lynch, V., and Langan, L., 1967, The geomagnetic gradiometer: Geophysics, 32,877-892.

APPENDIX CRITERION FOR DETERMINING EFFECTIVENESS OF

COMPENSATION

In military detection systems, because of their limited bandwidth, a measure of residual interference at the compensation maneuver frequency is a sufficient measure of compensation performance. The accepted method is the “Figure of Merit” (FOM), which is the absolute sum after compensation of the magnetometer signal for pitches, rolls, and yaws on the four (magnetic) cardinal headings. “Standard” FOM maneuvers as defined by the United States Navy are f5 degrees for pitches and yaws, and & 10 degrees for rolls. The FOM criterion has been generally accepted for airborne geophysical magnetometer and gradiometer systems even though it does not necessarily reflect the parameter in which the geophysicist is most interest- ed, namely the compensation of the system at dc.

To evaluate wide-band compensation, PJAE measures the standard deviation (0) of the residual magnetometer signal after compensation. To assess the actual effectiveness of compensa-

tion, the ratio of cr before and after compensation, termed the “Improvement Ratio” (IR) is calculated. The same FOM maneuver pattern is used except that the maneuvers are half the amplitudes listed above (“Half Standard”), which are much easier for the aircrew to tolerate. Turns between headings are done at 30 degrees to 35 degrees of bank angle.

The o criterion has an advantage over the FOM in that it is representative of magnetic conditions over the entire normal maneuver envelope of the aircraft for the entire frequency band of interest, which includes dc. Two additional advantages are that the FOM must always be evaluated by hand from an analog chart, whereas o is automatically available in a digital solution, and that o is much less dependent upon the accuracy of the short-period maneuvers, whereas the FOM is directly proportional to maneuver amplitudes.

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important design considerations for inboard airborne magnetic gradiometers

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