Magnetic models of unexploded ordnance

Transcription

1 1 Magnetic models of unexploded ordnance Stephen D. Billings, Catherine Pasion, Sean Walker and Laurens Beran Abstract Magnetometery is widely used for characterization of areas contaminated by unexploded ordnance (UXO). To successfully discriminate hazardous UXO from non-hazardous clutter requires accurate models of the ordnance response. Here we develop an ordnance library with fifteen different items using total-field magnetic data collected over a test-stand. The induced and remanent magnetizations were obtained by varying the 3-D orientation of each item and measuring the magnetic field on a horizontal plane in the dipolar regime. Replicate measurements using multiple specimens of the same ordnance returned very similar induced magnetizations. The fitted moments were used to estimate the detection depths for different sensor noise floors. A prolate spheroid with a 3.5 aspect ratio was used to provide a good approximation to the detection depths for many of the ordnance items. Assuming a 1 nt noise floor,these orientation dependent detection depths ranged from 1 to 17 times the object s diameter. Index Terms Discrimination, magnetics, unexploded ordnance, inversion, classification I. INTRODUCTION Unexploded ordnance (UXO) contamination is a significant, world-wide problem that prevents productive use of affected areas. In the United States alone 1 million acres are potentially contaminated and the military is creating more UXO than it is clearing [1]. Digital geophysics is playing a major role in UXO clean-up, with the predominant techniques based on magnetostatics and electromagnetics [2]. Both have particular strengths and weaknesses and the optimum technology varies from site-to-site. Increasingly, both datasets are collected simultaneously (or sequentially) and interpreted cooperatively to produce improved interpretations [3]. Accurate models of the response of different UXO are essential to the success of any discrimination procedure. Furthermore, models are required to quantify the maximum detection depths for different ordnance types. Previous work concerning magnetometery and unexploded ordnance have included theoretical modelling studies [4], [5], collection of magnetic signature data [6] and statistical [7], [8], [9] and rule-based classification [1] of dipole-parameter fits to magnetometer data. This paper focuses on the development of magnetic models for fifteen different ordnances from detailed measurements taken over a test-stand. The previous measurements of [6] were collected under the assumption that the magnetic response was invariant to rotation about the symmetry axis. This assumption is correct for ordnance that have no remanent magnetization. However, as soon as there is a component of Submitted to IEEE Transactions on Geoscience and Remote Sensing February 7, 26

2 2 remanence perpendicular to the symmetry axis, the ordnance response is no longer axially symmetric. In collecting magnetic signature data, one then has to take account the full 3-D orientation and rotation of the ordnance. The work presented here is essentially a follow-on from work presented previously [1]. The following summarizes relevant observations from that paper: 1) Most UXO are steel and therefore ferromagnetic with a susceptibility χ > 2, so that self-demagnetization effects cannot be ignored when modeling the ordnance magnetic signature; 2) The magnetization of a UXO is a combination of the magnetization induced by its presence in the Earth s field and any remanent magnetization the body has acquired and retained throughout its history; 3) UXO undergo a significant shock at the time of impact and this impact is sufficient to cause shock demagnetization, so that the amount of remanence of impacted UXO is generally small [4]; 4) The source-detector geometry in most UXO clearance scenarios is such that the response is dominated by the dipole component and a dipole model is often sufficient to fully characterize the data to within the limits imposed by noise; 5) There is an inherent non-uniqueness of magnetic dipoles whereby objects of many different sizes and orientations can represent the data equally well. With the above observations in mind, a magnetic discrimination method was developed based on the model m = V µ o A T χ d Ab o + A T m r. (1) where m is the fitted dipole moment of the anomaly, m r is the remanent magnetization of the body, V is its volume, A is the Euler rotation matrix (defined fully later), χ d is the diagonalized matrix of effective susceptibilities and b o is the Earth s magnetic field. Given the moment m the objective is to find which UXO drawn from a library of ordnance items produces the lowest percentage remanent magnetization, i.e. 1 m r m. (2) The volumes and effective susceptibilities required in Equation 1 were estimated by modeling each UXO as an equivalent spheroid. The spheroid dimensions were obtained by approximately the length and diameter of the UXO as closely as possible. Using this method, effective discrimination capability was demonstrated on datasets collected in Montana, USA. The purpose of this paper is four-fold: 1) Verify the validity of Equation 1; 2) Provide accurate estimates of the product V χ d for a range of different ordnance by detailed test-stand measurements; 3) Determine the extent of any variability in V χ d for different specimens of a given ordnance; and 4) Quantify the detection depths for different ordnance. II. TEST-STAND DATA MEASUREMENT METHODOLOGY The test-stand data collection occurred in two phases February 7, 26

3 3 Phase 1: Eight different ordnance items were measured at fifteen different orientations. This phase was primarily conducted to verify the suitability of Equation 1 and to verify the utility of the measurement methodology; and Phase 2: Three representatives of twelve different ordnance types were measured at four orientations. The objectives of this phase were primarily to increase the size of the ordnance database and to determine the extent of any variability amongst specimens of a given ordnance. 1) Equipment and Setup: Measurements were conducted on a non-metallic, fibreglass, test-stand at the United States Army Corps of Engineers - Engineer Research and Development Center (USACE-ERDC) Laboratory in Vicksburg, Mississippi. The measurement platform is elevated approximately three meters above the ground and has a usable measurement area of three by four meters in extent. Automated controls are used to position an ordnance item at an accurate depth (within 1 cm) below the sensor. The sensor is mounted on a robotic arm that can be moved around the test stand using control software running on a PC. The sensor can be positioned with an accuracy of approximately 1 millimeter. A Geometrics G-858 magnetometer was used to collect magnetic data on a fine grid on a 2-D plane above the ordnance. The magnetometer performed ten measurements per second as it was slowly scanned over the ordnance item. A base-station magnetometer was positioned at a magnetically quiet location 15 meters from the test-stand. It performed a measurement every five-seconds and was used to monitor and correct for temporal variations in the Earth s magnetic field. 2) Coordinate System: The ordnance items are all radially symmetric (or at least almost radially symmetric), but their magnetic response may not be symmetric due to the possible presence of a remanent magnetic component. Therefore, before measurement each ordnance was marked with a strip of masking tape and a felt-tip pen to establish a reference orientation parallel to the symmetry axis. The magnetic signature was then measured on a regular horizontal grid as each item was rotated through a number of different orientations. For each orientation, a systematic procedure was followed. First, the item was rotated about its symmetry axis by an angle γ. Next, the item was rotated to a dip of θ degrees above or below horizontal (upwards dip is positive). Last, the item was rotated to an azimuthal angle of φ degrees relative to magnetic North. A graphical representation of the geometry is shown in Figure 1. For the Earth s field we use geographical coordinates; b o =(b ox,b oy,b oz ), i.e. x is positive to the East, y is positive to the North and z is positive upwards. Note that this differs from the definition used to specify the International Geomagnetic Reference Field (IGRF) where x is positive to the North, y is positive to the East and z is positive downwards. The test-stand was oriented with magnetic North so that b ox =, the inclination was o and the magnitude of the field was 5,15 nt. February 7, 26

4 4 With the above conventions, the Euler rotation matrix for an ordnance with orientation (θ, φ, γ) is, cos φ cos γ sin φ cos φ sin γ cos θ sin φ cos γ +sinθsin γ cos θ cos φ cos θ sin φ sin γ +sinθcos γ A =. (3) sin θ sin φ cos γ +cosθsin γ sin θ cos φ sin θ sin φ sin γ +cosθcos γ 3) Sensor to Target Separation: The objective of the measurements was to isolate the dipole moment contribution to the magnetic signature for the purpose of determining the induced and remanent contributions to magnetization. At a measurement-plane to target separation distance of less than approximately 2 times the length of the ordnance major axis (2L), the contribution of the quadrupole (if present) and octupole moments to the magnetic signature bias the fitted dipole model. At larger distances, the signal-to-noise ratio (SNR) decreases, the areal extent of the anomaly increases and the accuracy of the recovered dipole parameters degrades. On the basis of these constraints, the center of the ordnance was first positioned at 2L from the measurement-plane and the magnetic field was measured. If a dipole model could be fit to the data with a correlation coefficient of.99 that sensor-target separation was accepted. If not, the distance was increased to 2.5L and the measurements were repeated. Almost all of the measurements reported here were collected at 2L from the ordnance. 4) Measurement spacing and area: Magnetometer measurements were collected on North-South transects separated by 1/4 times the distance from the magnetometer to the center of the ordnance. The sampling strategy was always arranged so that one transect passed directly over the ordnance center. The measurement area was a square with a side length at least five times the sensor-source distance (and centered at the ordnance). Along each transect the data were collected continuously with a minimum sample spacing of 1/4 times the sensor-source distance. 5) Background Magnetic Field Measurements: The background magnetic field on the test-stand was measured at the start and end of each day and before the first measurement of each new ordnance type. This involved collecting data on the measurement grid with no ordnance in the holder. The background was found to be approximately constant each day and varied by about 55 nt over the region the measurements were taken (e.g. Figure 3). The background could be approximated by a 3rd degree polynomial and its contribution to the data was removed before any additional analysis took place. The 55 nt variation in background magnetic field is caused by a stationary motor that is used to automatically change the height of the ordnance between measurements. Because this motor does not move during sample measurement, the background does not vary with time. 6) Phase I ordnance and orientations: In Phase I, signature data at fifteen different orientations (Table I) were collected over the each of the following eight ordnance items (Figure 2): 4 mm projectile MKII; 57 mm projectile APC M86; 6 mm mortar M49A3 Standard; 2.75 in rocket M23 Standard; 76 mm AP projectile; 81 mm mortar; 9 mm AP projectile; and 15 mm projectile M6. All the rounds except the 76 and 9 mm projectiles and the 81 mm mortar were part of the standardized target repository made available by the Aberdeen Test Center (ATC), U.S. Department of Defense. The exceptions were representatives of inert rounds supplied by the Montana Army National Guard from sites in the Helena Valley, Montana. February 7, 26

5 5 7) Phase II ordnance and orientations: For Phase II, the signature data were collected over six of the eight ordnance items measured in Phase I (the 4 and 57 mm projectiles were not measured) as well as the following additional seven items: 2 mm M55 projectile; M42 submunition; BDU-26 submunition; BDU-28 submunition; 81 mm M374 mortar; 15 mm heat round M456; and 155 mm M483A1 projectile. Each ordnance in Phase II was measured at four different orientations (where mark refers to the reference point marked on the ordnance); 1) Horizontal, nose-east, mark South (φ =9 o, θ = o, γ = 9 o ); 2) Horizontal, nose-east, mark North (φ =9 o, θ = o, γ =9 o ); 3) Horizontal, nose-west, mark South (φ = 9 o, θ = o, γ =9 o ); and 4) Parallel to Earth s field, nose-down, mark South (φ = o, θ = o, γ = 18 o ); From analysis of Phase I data, we determined that the above four orientations were sufficient to resolve the two effective susceptibilities and three components of remanent magnetization for each item. The first three orientations have the long axis of the ordnance perpendicular to the Earth s field, while the last orientation has it parallel. A. Data fits III. ANALYSIS OF PHASE I DATA For each of the 15 different orientations of the ordnance, a dipole model was fit to the data recorded on the test-stand. In all cases, there was close agreement between modeled and observed data (see the example fit given in Figure 4). The fit correlations were generally better than.99 (better than.999 for the larger projectiles), and were only smaller than that (.97) for the 4 mm projectile where the magnetic field from the projectile had a low amplitude. Linearized estimates of the errors in recovery of the dipole moments were less than 1% of the dipole magnitude. We now endeavor to fit the models defined by Equation 1 to the dipole parameters recovered over each of the orientations of the ordnance. The first case we consider is where the magnetization is assumed to be entirely due to induced means (that is, there is no remanence). In that case, if we assume radial symmetry, we have two unknowns to solve for: 1) the induced moment with the ordnance axis parallel with the Earth s field (m a axial excitation); and 2) the induced moment with the ordnance axis perpendicular to the Earth s field (m t transverse excitation). Each of the 15 different orientations of the ordnance corresponds to a different Euler rotation matrix (via Equation 3). We solve for the best-fitting values of the two unknowns so that there is minimum discrepancy, in a weighted leastsquares sense, N min m(ω n, α) m o (Ω n ) 2 α σ(ω n ), (4) n=1 between the recovered moments, m o and the predictions, m, of Equation 1. In the above equation Ω n =(θ n,φ n,γ n ) is the n-th orientation set, N is the number of orientations and σ(ω n ) is the standard deviation estimated when February 7, 26

6 6 inverting for the moment at the n-th orientation. The standard deviation will be different for each of the threecomponents of the recovered moments and the divide operation above is meant to be executed on an element by element basis. For the case of induced magnetization, m r =, and the parameter set to minimize over is α =(m t,m a ). In the second case we consider, the model includes both induced and remanent magnetization (Equation 1) and there are five unknowns, α =(m a,m t,m rt1,m rt2,m ra ). The first two are the same as the model above, the remaining three are the remanent magentizations in three orthogonal directions of the ordnance. m rt1 and m rt2 are along the short (transverse) axis of the ordnance, while m ra is along the long (axial) axis of the projectile. The values of the unknowns are again found by a least-squares procedure. Table II lists the fitted models and fit model errors for each of the ordnance items measured on the test-stand. The fitted moments for the induced magnetization can be converted to V χ by multiplying by b o /µ o =39.98 (because the field at Vicksburg on the teststand was 5,15 nt). The percentage errors in the induced magnetization were calculated by a Monte Carlo (MC) analysis. This involved repeating the following procedure 1 times: 1) Add normally distributed errors to the modeled moments (that is, the moments predicted by Equation 1 and not the moments recovered from the test-stand data); 2) Add normally distributed errors to all three orientation angles; 3) Solve for the best fitting induced and remanent magnetization using the perturbed moments and angles; The error in the recovery of the induced and remanent moments were then estimated by calculating the standard deviation between the 1 MC simulations and the recovered induced and remanent moments. For the MC analysis the standard deviation of the errors for each moment were estimated when fitting the moment to the test-stand data. For the orientation angles we estimated that we could orient the ordnance within an accuracy of 2 o and used that number as the standard deviation in the MC analysis. Table II has a column called remanence, which was calculated as the size of the remanence (vector sum of the 3 components of remanence) divided by the induced magnetization with the ordnance axis parallel with the Earth s field. The resulting percentage value provides an indication of the significance of the remanent magnetization relative to the induced. We define the induced magnetization curve for a given ordnance as the family of dipole moments that can be produced by induced magnetization alone. The induced magnetization curves and fits to the observations are shown in Figures 5 and 6. In each plot we show the following: (i) the component of the moment parallel to the Earth s field; (ii) the component that is perpendicular to the Earth s field and within the plane that includes the long-axis of the ordnance; and (iii) the component along the remaining orthogonal direction. The induced magnetization curve lies within the plane spanned by the first two coordinate directions. This occurs because the last coordinate direction is orthogonal to both the Earth s magnetic field and the long-axis of the ordnance and there can be no induced moment in that direction due to the radial symmetry of the ordnance. It is only when remanent magnetization is present that a moment can lie off the plane containing the induced magnetization curve. If that is the case, the fitted or observed moment is plotted with a solid line, with a length proportional to the size of the moment in the 3-rd February 7, 26

7 7 orthogonal direction. For example, if m =(m 1,m 2,m 3 ) then the line will have length m 3 and will intersect the plane containing the induced magnetization at (m 1,m 2 ). Note that remanent magnetization will generally cause m 1 and m 2 to deviate from the induced magnetization curve (as occurs for instance in Figure 5d). For the 76 and 9 mm projectiles, the results for the induced and the induced plus remanence models are indistinguishable within the limits imposed by the measurement precision. This shows that these rounds, which were recovered from the Limestone Hills area of Montana and were never specifically degaussed, have little or no remanent magnetization. The 4 and 57 mm projectiles (which were degaussed at ATC) also have a relatively small remanent magnetization. There are then a number of rounds that have a modest level of remanent magnetization and which cannot be fit very well with the induced only model. From lowest to highest remanence these are the 6 mm mortar, the 2.75 inch rocket, the 81 mm mortar and then the 15 mm projectile. Except for the 81 mm mortar (which was recovered from Limestone Hills) and the 15 mm projectile, each of these rounds were degaussed. The fact that several of the degaussed rounds have a significant remanent magnetization implies either that: 1) the degaussing procedure is flawed; or 2) the rounds acquire a remanent magnetization due to exposure to shock and or large magnetic fields during transport and storage; One last point to take away from these results is the close agreement between the recovered dipole moments and the induced/remanent magnetization model. This confirms the validity of the model expressed in Equation 1. B. Calculation of equivalent spheroids We store our ordnance library in the form of equivalent spheroid models because the response from a spheroid of arbitrary dimensions at an arbitrary orientation can be rapidly calculated for any orientation of the Earth s field. For m 3 >m 2 it is always possible to find a prolate spheroid model that will reproduce the induced magnetization curve. To see how this is obtained, assume the spheroid has a diameter a, length L = ae (where e>1 is the aspect ratio) and a magnetic susceptibility, χ. A solution of a boundary value problem [11] shows that the effective susceptibility is constant throughout the body and given by the expression χ χ i = (5) 1+n i χ where n 1 = n 2 and n 3 are self-demagnetization factors that are dependent on the aspect ratio, e (see [1], [5]). Thus, with this equation and Equation 1 it is possible to solve for a spheroid that will reproduce the induced models given in Table II. The resulting spheroids are listed in Table III. Note that we obtained these spheroids assuming an arbitrary value of χ = 1. This choice is not important as long as we always use the same value in the calculations. February 7, 26

8 8 IV. ANALYSIS OF PHASE II DATA A. Data fits The data for Phase II were analyzed in the same was as the Phase I data. The main difference was in the number of orientations for each item, with only four having been collected in Phase II. Example fits to the moments for six different ordnance are shown in Figure 7. The results for the 2.75 inch rocket show that the round had large remanent magnetization around 1 times larger than the maximuduced magnetization. The induced magnetization curve for this item is significantly different from that obtained in Phase I which we attribute to uncertainty due to the large remanence. For the other ordnance with repeat measurements, the induced moments agree to within a few percent (Table II and the 81 mm round in Figure 7), with the exception of the 6 and 81 mm ATC mortars, and the 9 mm projectile (Figure 7). This particular 9 mm had an intact ballistic windshield, whereas the original round had no ballistic windshield. This difference could likely explain the relatively small discrepancy in the 9 mm measurements. We postulate that the differences observed with the ATC mortars could result from uncertainty due to relatively large remanent magnetizations. For the 6 mm mortars, the other possible explanation is the presence and variation in the relatively large ferrous tail-fins on the rounds which introduce an unmodeled asymmetry into the induced magnetization. Table II includes results for several small ordnances with very small moments (BDU-26, BDU-28 and M42 submunition). We expect that the actual induced magnetizations will have a larger error than indicated by the Monte Carlo predictions given in the table; the signal-to-noise ratio for these items is low and the linearized predictions of the errors in the recovered dipole moments are underestimated. Table III lists the equivalent spheroids for both the Phase I and II data collection efforts. We do not include the equivalent spheroids for the BDU-26, BDU-28 or 2.75 projectiles as the uncertainty in the induced magnetization models are large. For the other items (with the exception of the 6 and 81 mm ATC mortars), the replicate measurements are all within several percent of each other. V. DETECTION LIMITS FOR DIFFERENT ORDNANCE ITEMS At this point, we have obtained magnetic models of fifteen different ordnance items. Using these models we can now place constraints on the detection limits for different ordnance. Obviously, the specific detection depths depend on a number of variables, such as the ordnance s orientation with respect to the earth s field, the remanent magnetization, the geological setting etc. We will therefore seek to provide estimates for certain endmembers, specifically for parallel and perpendicular orientation (relative to the earth s field) and with no remanent magnetization. We proceed by first recognizing that for a fixed shape (assumed to be a body of revolution), the magnitude of the dipole moment will scale as the cube of the diameter. We assume θ is the dip and φ the azimuth of the object and that the object s symmetry axis makes an angle γ with the Earth s magnetic field. In that case, the induced moment for the body will be m(θ, φ) =d 3 m u (γ) ˆm u (θ, φ) (6) February 7, 26

9 9 where m u (γ) is the magnitude of the induced moment for a unit diameter shape, and ˆm u (θ, φ) is the corresponding unit vector. Note that we have explicitly emphasized that the magnitude of the induced magnetization depends on the angle the object makes with the Earth s field, while the direction of the moment depends on the object s orientation in geographic space. We now seek to non-dimensionalize the equation for the dipole moment, b(x) = µ ( ) o 3 4πr 3 [r m(θ, φ)]r m(θ, φ) (7) r2. We non-dimensionalize the distance units using the height of the sensor above the object, so that r = hr u with r u =(x/h, y/h, z/h). The equation for the dipole then becomes ( ) b(x) = d3 m u (γ) µ 3 h 3 4πru 3 ru 2 [r u m u (θ, φ)]r u m u (θ, φ), (8) which shows that the amplitude of the magnetic field scales as d 3 m u (γ)/h 3. This means that to achieve a fixed amplitude threshold, the height above the object will scale linearly with the object diameter. We assume that we are measuring the total-magnetic-field b t, which for anomalies that are small relative to the Earth s field can be approximated by b t (x) =ˆb o b(x) (9) where ˆb o is the unit-vector for the Earth s magnetic field. Without loss of generality we can assume our coordinate system is aligned with magnetic north, so that the first component of ˆb o will be. Later, we will refer to the non-dimensionalized total magnetic field, b tu which is obtained from Equations 8 and 9 by ignoring the leading d 3 m u (γ)/h 3 term. We estimate the detection thresholds using the SNR. For N observations contaminated by Gaussian noise, ɛ, with a standard deviation of σ the expected noise power will be and the expected signal power of the total magnetic field, will be [ N ] E[b 2 t ]=E b t (x i ) 2 E[ɛ 2 ]=Nσ 2 (1) i=1 where x i represents the location of the i-th observation. In order to estimate the signal power, we assume that observations were collected on a roughly uniform grid with spacings ( x, y). We will consider only those points that lie within a square box centered over the object which encompasses a certain fixed percentage of the signal energy. We assume that for a unit height above the object that this box encompasses an area of A u = l l. Now using the mid-point rule for integral approximation, E[b 2 t ]= 1 b 2 t x y = d6 m 2 u(γ) l 2 h 2 [ ] 1 x y A h 6 x y l 2 b 2 tu x u y u. (12) A u (11) February 7, 26

10 1 The box will contain N = lh/ x times M = lh/ y points so that E[b 2 t ]= d6 m 2 u(γ) h 6 NMg(p, θ, φ, β) (13) where g(p, θ, φ, β) is the ter square brackets in the previous equation and contains only dimensionless quantities. Its value depends on the orientation of the object (θ, φ), the Earth s field inclination β (we elected to use a coordinate system with zero declination) and on the percentage of signal energy, p we choose to encompass. Now the noise energy will scale with N M as well, so that the SNR in decibels (db) will be [ d 3 ] m u (γ) SNR = 2 log 1 h 3 +1log σ 1 [g(p, θ, φ, β)]. (14) Some pertinent observations from this equation 1) The detection depth will scale linearly with the object diameter; 2) The detection limit h d 1/ 3 σ so that an 8-fold reduction in the noise level is required to double the detection depth; 3) At a fixed height, the SNR will increase with the cube of the object diameter; We now proceed to some specific calculations of detection depths assuming the moment is parallel with the Earth s field so that θ = β and φ =. We use a SNR criterion of 6 db to declare a valid detection and a noise floor of σ =1nT. Results for different SNR criterions or noise floors can easily be obtained through the scaling relationship evident in Equation 14. For instance, for σ =1nT, h 1 = h 1 / 3 1, where h σ is the detection limit for a noise floor of σ. We evaluate g(p, β,,β) using a square integration area that comprises p = 95% of the signal energy. This results in 1 log 1 g(95%,β,,β)= cos(β) (15) For an inclination of β =65 o (relevant to much of North America and Europe) this evaluates to 36.3 with l =2. By substituting this value into Equation 14 and using m = d 3 m u, the relationship between the detection depth and moment is h d =3.2 3 m. (16) This means that a dipole of moment 1 Am 2 can be detected at SNR =6dB to a depth of 3.2 m with a noise floor of 1 nt. Note that if we had instead assumed a noise floor of 5 nt, the coefficient in the above equation would have been 1.87; if 1 nt, it would have been The detection depths do depend relatively weakly on the orientation of the dipole moment, through the function g(p, θ, φ, β). For instance, at β =65 o, g varies by less than 13% as φ is varied from 18 to +18 o and by less than 26% as θ is varied from 9 to +9 o. The function takes on its minimum value for a horizontal, north facing dipole, while its maximum value is for a vertically oriented dipole. As the orientation of the moment changes, the detection depth for a 1 Am 2 dipole will vary from a minimum of 2.69 to a maximum of 3.55 meters (compared February 7, 26

11 11 to the 3.2 meters reported above). Thus there will be about a 15% variation in the detection depths we report depending on the orientation of the induced moment. Due to the significant variation of ordnance shapes, no fixed relationship of detection depth with diameter can be derived. Instead, for any given shape there will be a linear relationship between detection depth and diameter for a fixed orientation. To provide a consistent point of comparison, we use as a standard shape a prolate spheroid with an aspect ratio of 3.5 and a susceptibility of χ = 2 (we choose this spheroid, because as will be evident later it provides a good match to the test-stand data). For a 1 m diameter spheroid the moment is 77 Am 2 when the axis is parallel to the Earth s field. From Equations 6 and 16 this means the detection depth will be 29.4 times the diameter. For the same 1 m diameter spheroid perpendicular to the Earth s field, the moment is Am 2 and the detection depth is 17.3 times the diameter. Values for noise floors of 5 and 1 nt are given in Table IV, while in Table V we list the detection depths for the test-stand ordnance. In Figure 8 we plot the variation in detection depth for the spheroid considered above, as well as for each of the items modeled on the test-stand. In each case, we show the best-case and worst-case corresponding to transverse and axial orientation relative to the Earth s field. The prolate spheroid provides a reasonable approximation to the depths of most of the ordnance. Exceptions include the submunitions which have an aspect ratio closer to 1, and the 2.75 rocket which has a larger aspect ratio of around 5. The detection depths were calculated under the assumption that the noise is Gaussian. If this is not the case, then one would need to modify the expression for the noise power in Equation 1 and propagate the σ equivalent quantity through the rest of the calculations. We also make no claim that 1 nt is the only noise floor to use, and in fact selection of a specific noise floor will depend on number of factors. We simply derive and present our results because conversion to other noise floors is simply achieved by scaling the results by 1/ 3 σ. We stress that the height relation we derive refers to the height of the sensor above the object. Therefore, if the sensor is.5 m above the ground, then the detection depth below the ground will be reduced by.5 m from our predictions. By reference to Table V, it is evident that detection of several of the smaller items at any depth will be difficult or impossible at a noise floor of 1 nt or greater. VI. DISCUSSION In this paper we have demonstrated a technique to estimate the induced and remanent dipole moments of a compact metallic object. Accurate measurements of the total magnetic field are required on a horizontal plane above the item which is rotated through a number of non-redundant angles. For axi-symmetric objects with remanent magnetization, it is essential to record the full 3-D orientation of the item. Care must be taken to ensure that the item is in the dipolar regime, otherwise non-dipolar effects will bias the estimation of the moment at any given angle. For the smaller objects there is a delicate balance to strike between getting too close, and measuring too far away where the SNR is low. We found that a distance of twice the longest ferrous dimension of the item was ideal. There was close agreement between Equation 1 and the recovered dipole moments, even when there was substantial remanent magnetization. When the remanence was large, accurate recovery of the induced magnetization February 7, 26

12 12 was not always possible due to the large uncertainty (e.g. the 2.75 rockets). One could conceivably degauss the items prior to measurement if this were found to be problematic. For many of the items in the standardized target repository there was a substantial remanence; in one case (the 2.75 rocket) the remanence was 1 times the size of the induced magnetization. These items had never been fired but most had been degaussed, which may point to a problem with the degaussing procedure, or alternatively an acquisition of remanence during transport and storage. All the 76 and 9 mm projectiles and one of the 81 mm mortars from Montana had very low remanence. These had been fired and presumably shock demagnetized. However, this may not be a universal phenomena, as two of the 81 mm mortars had a modest remanence. The equation of the field from a dipole can be non-dimensionalized, which simplifies the task of estimating detection depths assuming different noise floors. However, the specific detection depth of any given UXO depends on the amount of remanence and the orientation of the round. Therefore, exceptions to the general rules derived here will apply, and we stress that our results are only meant to be indicative. We also note that our calculations dealt solely with SNR and did not deal with specifics such as sampling densities. Obviously, for a detection to be declared there must be sufficient observations within the area spanned by the anomaly. The results presented in this paper are intended to provide researchers with useful information for constraining discrimination techniques. We note that any such discrimination method (statistical or analytic) that is based on analysis of the dipole field is at the mercy of remanent magnetization. This can cause a small item to have a substantially increased moment (e.g. the 2.75 rocket), and conversely can cause a large object to have a much smaller moment. Constraints on the prevalence and level of shock induced demagnetization are required before dipole-based discrimination techniques can be relied upon. Lastly, none of the ATC items measured had been fired and all the ordnance from Montana were intact and of identical size and shape to their unfired form. The models derived here will strictly apply only to rounds that are in equivalent condition. At live-sites, rounds may be rusted or deformed (e.g. many of the 81 mm mortars in [1] were deformed due to detonation of a spotting charge). Any variations in item shape or condition will cause the induced magnetization of the round to differ from the models calculated here. This will result in an apparent remanent magnetization for that round even when it has no actual remanence. We expect that this variability will be no more significant than remanent magnetization. For instance, all the deformed 81 mm rounds in [1] were recovered at an apparent remanence that still allowed the majority of clutter items to be rejected. ACKNOWLEDGMENT This research was supported by the U.S. Department of Defense, through the Strategic Environmental Research and Development Program (SERDP), project number UX-138 and by the USACE Engineer Research and Development Center through contract W912HZ-4-C-39. The work benefited greatly from the support of Dr Clifton Youmans from the Montana National Guard who supplied several of the ordnance items used; from Larry Overbay and George Robitaille of the Army Environmental Center who supplied the standardized target items and from Morris Fields and Clif Morgan from USACE-ERDC who assisted with the collection of the test-stand data. February 7, 26

13 13 REFERENCES [1] W. P. Delaney and D. Etter, Report of the defense science board on unexploded ordnance, Office of the Undersecretary of Defense for Acquisition, Technology and Logistics, Tech. Rep., December 23. [2] D. K. Bulter, E. R. Cespedes, C. B.Cox, and P. J. Wolfe, Multisensor methods for buried unexploded ordnance detection, discrimination and identification, SERDP, Tech. Rep. 98-1, September [3] L. R. Pasion, S. D. Billings, and D. W. Oldenburg, Joint and cooperative inversion of magnetics and electromagnetic data for the characterization of UXO, in Proceedings of the Symposium on the Application Geophysics to Engineering and Environmental Problems, San Antonio, Texas, September 23. [4] T. W. Altshuler, Shape and orientation effects on magnetic signature prediction for unexploded ordnance, in Proc UXO Forum, Williamsburg, VA, Mar 1996, pp [5] J. E. McFee, Electromagnetic remote sensing; low frequency electromagnetics, Defence Research Establishment Suffield, Tech. Rep. 124, January [6] H. H. Nelson, T. W. Altshuler, E. M. Rosen, J. R. McDonald, B. Barrow, and N. Khadr, Magnetic modeling of UXO and UXO-like targets and comparison with signatures measured by MTADS, in Proc UXO Forum, Anaheim, CA, May 1998, pp [7] L. Collins, Y. Zhang, J. Li, H. Wang, L. Carin, S. Hart, S. L. Rose-Phersson, H. Nelson, and J. R. McDonald, A comparison of the performance of statistical and fuzzy algorithms for unexploded ordnance detection, IEEE Trans. Fuzzy Systems, vol. 9, pp. 17 3, 21. [8] S. J. Hart, R. E. Shaffer, S. L. Rose-Pehrsson, and J. R. McDonald, Using physics based modeler outputs to train probabilistic neural networks for unexploded ordnance (UXO) classification in magnetometry surveys, IEEE Trans. Geoscience & Remote Sensing, vol. 39, pp , 21. [9] Y. Zhang, L. Collins, H. Yu, C. E. Baum, and L. Carin, Sensing of unexploded ordnance with magnetometer and induction data, IEEE Trans. Geoscience & Remote Sensing, vol. 41, pp , 23. [1] S. D. Billings, Discrimination and classification of buried unexploded ordnance using magnetometry, IEEE Transactions Geoscience & Remote Sensing, vol. 42, pp , 24. [11] J. Stratton, Electromagnetic theory. McGraw Hill, February 7, 26

14 14 LIST OF TABLES I Range of orientations measured during Phase I II Recovered models from the test-stand data. The first eight rows are from Phase I measurements with the rest obtained in Phase II. The remanence column represents the total remanence divided by the maximuduced moment III Dimensions of equivalent spheroids with a susceptibility of 1 obtained by fitting the test-stand models in Table II along with errors estimated by the Monte Carlo analysis IV Relationship of detection depth with diameter for a prolate spheroid with aspect ratio 3.5, χ = 2 and with an inclination of β =65 o V Variation of detection depths (in centimeters) with diameter for each of the items measured on the test-stand assuming an inclination of β =65 o and an ambient field of 5, nt LIST OF FIGURES 1 Coordinate system used for the teststand measurements, with y-aligned with magnetic North, and z vertically up Ordnance items measured during Phase I Example background magnetic field recorded over the teststand Dipole fit to the 15 mm heat-round at an orientation of θ = o, φ = 24 o and γ = o. The location of the center of the round is marked by a plus sign. The data and model fit are shown with a linear color stretch from -5 to 85 nt (the colorbar) while the residual stretch is from -3 to 5 nt. Note the small dipolar feature in the residual plot which is present in most images and is likely due to a small ferrous object on the teststand (such as a nail) Dipole fits to projectiles with calibers between 4 mm and 2.76 diameter. The black circles are the recovered moments, the black triangles are for a model fit including induced and remanent magnetization (model 1) while the gray stars are for a model with induced magnetization alone (model 2). The solid black curve is the induced magnetization curve for model 1 and the dashed gray curve the same for model Results for projectiles with calibers between 76 and 15 mm (for explanation of symbols see Figure 5) Example fits to 6 different items measured during Phase II (for explanation of symbols see Figure 5). For the Montana 81 and 9 mm rounds and the 2.75 rocket the induced magnetization curves derived from the 24 data are plotted as dashed lines Detection depths for the test-stand items and a 3.5 aspect ratio prolate spheroid for a noise floor of 1 nt and β =65 o. We only show labels for items with equal or nearly equal diameters February 7, 26

15 15 θ φ γ TABLE I: Range of orientations measured during Phase I. February 7, 26

16 16 m t m a m rt1 m rt2 m ra Caliber (Am 2 ) Error (Am 2 ) Error (Am 2 ) (Am 2 ) (Am 2 ) Remanence Phase I 4 mm %.481.6% % 57 mm %.117.6% % 6 mm % % % % % % 76 mm (MT) % % % 81 mm (MT) % % % 9 mm (MT) % % % 15 mm % % % Phase II 2 mm.16 2.% % % 2 mm.14 2.% % % 2 mm % % % m % % % m % % % BDU % % % BDU % % % BDU % % % BDU % % % BDU % % % 6 mm % % % 6 mm % % % 6 mm % % % % % % % % % % % % 76 mm (MT) % % % 76 mm (MT) % % % 81 mm (MT) % % % 81 mm (MT) % % % 81 mm (ATC).73 2.% % % 81 mm (ATC) % % % 81 mm (ATC) % % % 9 mm (MT) % % % 9 mm (MT) % % % 15 mm HR % % % 15 mm HR % % % 15 mm HR % % % 155 mm % % % 155 mm % % % TABLE II: Recovered models from the test-stand data. The first eight rows are from Phase I measurements with the rest obtained in Phase II. The remanence column represents the total remanence divided by the maximuduced moment February 7, 26

17 17 Diameter Aspect ratio Caliber (mm) error value error Phase I 4 mm % % 57 mm % % 6 mm % % % % 76 mm (MT) % % 81 mm (MT) % % 9 mm (MT) % % 15 mm % % Phase II 2 mm % % 2 mm % % 2 mm % % m % % m % % 6 mm % % 6 mm % % 6 mm % % 76 mm (MT) % % 76 mm (MT) % % 81 mm (MT) % % 81 mm (MT) % % 81 mm (ATC) % % 81 mm (ATC) % % 81 mm (ATC) % % 9 mm (MT) % % 9 mm (MT) % % 15 mm HR % % 15 mm HR % % 15 mm HR % % 155 mm % % 155 mm % % TABLE III: Dimensions of equivalent spheroids with a susceptibility of 1 obtained by fitting the test-stand models in Table II along with errors estimated by the Monte Carlo analysis. Noise floor Transverse Axial TABLE IV: Relationship of detection depth with diameter for a prolate spheroid with aspect ratio 3.5, χ = 2 and with an inclination of β =65 o. February 7, 26

18 18 Noise floor 1nT 5nT 1 nt Caliber Transverse Axial Transverse Axial Transverse Axial 2 mm mm m mm mm BDU BDU mm (MT) mm (ATC) mm (MT) mm (MT) mm HR mm mm TABLE V: Variation of detection depths (in centimeters) with diameter for each of the items measured on the test-stand assuming an inclination of β =65 o and an ambient field of 5, nt. February 7, 26

19 19 Fig. 1: 6 mm 15 mm 76 mm 2.75 in 57 mm 81 mm 4 mm 15 mm 9 mm Fig. 2: February 7, 26

20 2 Fig. 3: February 7, 26

21 Northing (m) Easting (m) (a) Data.8.6 Northing (m) Easting (m) (b) Model fit Northing (m) Easting (m) (c) Residuals Fig. 4: February 7, 26

22 22 x 1 3 x 1 3 = = (a) 4 mm projectile (b) 57 mm projectile = = (c) 6 mm mortar (d) 2.75 rocket Fig. 5: February 7, 26

23 23 = 5.25 x 1 3 = (a) 76 mm projectile (b) 81 mm mortar = = (c) 9 mm projectile (d) 15 mm projectile Fig. 6: February 7, 26

24 24 x 1 4 = = (a) 2 mm projectile (b) 2.75 rocket = = (c) ATC 81 mm mortar (d) MT 81 mm mortar 1 = = (e) 9 mm projectile (f) 155 mm projectile Fig. 7: February 7, 26

25 Spheroid (transverse) Spheroid (axial) Test stand (transverse) Test stand (axial) 4 Detection depth (cm) " 81 mm (MT) 15 mm 15 mm HR 2 81 mm (ATC) 15 mm 15 mm HR 1 4 mm 2.75" 81 mm (MT) 81 mm (ATC) m42 4 mm BDU26 BDU28 BDU Ordnance diameter (mm) Fig. 8: February 7, 26