A new technique for processing airborne gamma ray spectrometry data for mapping low level contaminations

Applied Radiation and Isotopes 51 (1999) 651±662

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A new technique for processing airborne gamma ray spectrometry data for mapping low level contaminations H.K. Aage a,*, U. Korsbech a, K. Bargholz a, J. Hovgaard b a

Department of Automation, Building 327, Technical University of Denmark, 2800 Lyngby, Denmark b Exploranium, 6108 Edwards Blvd., Mississauga, Ont., Canada L5T 2V7 Received 4 March 1999; received in revised form 23 April 1999; accepted 27 April 1999

Abstract A new technique for processing airborne gamma ray spectrometry data has been developed. It is based on the noise adjusted singular value decomposition method introduced by Hovgaard in 1997. The new technique opens for mapping of very low contamination levels. It is tested with data from Latvia where the remaining contamination from the 1986 Chernobyl accident together with fallout from the atmospheric nuclear weapon tests includes 137Cs at levels often well below 1 kBq/m2 equivalent surface contamination. The limiting factors for obtaining reliable results are radon in the air, spectrum stability and accurate altitude measurements. # 1999 Elsevier Science Ltd. All rights reserved.

1. Introduction In 1996 a team from the Technical University of Denmark (DTU) measured a number of areas in Latvia with airborne gamma-ray spectrometry (AGS) equipment belonging to the Danish Emergency Management Agency. The equipment included 16 l NaI(Tl) detectors and a 512 channel analyser. Flying at 80 m nominal altitude a spectrum was recorded and stored on hard disk each second together with GPS co-ordinates. The line spacing in general was 500 m and the velocity was around 120 km/h. The aims were to search for unauthorised gamma sources and to check and map the 137Cs contamination levels caused by the release of radioactivity from the 1986 accident at the Chernobyl nuclear power plant. Further the

* Corresponding author. Tel.: +45-4525-3459; fax: +454588-7133. E-mail address: [email protected] (H.K. Aage)

measurements should form a basis for mapping the levels of natural radioactivity. Except for observing some contaminated chimney bricks from a factory that incidentally had melted a 137 Cs source no unauthorised sources were found. The Chernobyl accident contamination levels in Latvia were found to be very low. Often less than 1 kBq/m2 equivalent surface concentration of 137Cs was observed and this also includes the remains of the 137Cs fall-out from the atmospheric nuclear weapon tests. These low levels are below the detection level for standard methods for processing AGS data obtained with NaI(Tl) (Bourgeois et al., 1997; Bargholz, 1998). In order to produce maps with low level 137Cs contamination a more sensitive method therefore had to be developed. An unstable altimeter and a varying amount of radon daughters in the air and on the ground complicated the data processing and a 137Cs contamination of the aeroplane used caused additional `spectrum noise'. In 1997 Hovgaard (1997a,b) introduced the noise adjusted singular value decomposition (NASVD) tech-

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Fig. 1. Spectral component No.'s. s0 (gross average spectrum) and s1 for NASVD processed data, South-western part of Latvia, logarithmic scale.

nique for analysing large sets of gamma spectra. This technique is today in common use by several AGS groups for improving AGS data for mapping natural radioactivity, i.e. U, Th and K (Grasty, 1998; Minty and McFadden, 1998). The NASVD technique can, however, also be basis for other types of analysis of AGS data (Hovgaard, 1997b; Hovgaard and Grasty, 1997, 1998; Bargholz et al., 1998; Korsbech et al., 1998). Here we describe the use of the NASVD technique for mapping very low levels of 137Cs contamination by a method we call the pseudo concentration method.

2. Theory The basic principles of the NASVD method are described in some detail elsewhere (Hovgaard, 1997a,b). Therefore, only a short introduction is given here. The NASVD technique could be considered an extension of the ordinary singular value decomposition method (Mardia et al., 1979; Krzanowski, 1996) where the statistical noise of the spectra has been taken into account in the decomposition. Consider a data set with J NaI(Tl) spectra each including N channels with counts. The NASVD technique then extracts a set of spectral components, s0, s1, s2,, etc., also spectra with N channels. The spectral components contain all spectral information of the whole set of data. By building linear combinations of the spectral components one is

able to reconstruct all measured spectra. Eq. (1) describes the reconstruction of the measured spectra. rj ˆ s0 ‡ …s1 bj1 ‡ s2 bj2 ‡ . . . ‡ smax bjmax †=LTj

…1†

where rj is the reconstructed spectrum number j. It is considered a vector with elements (channel count rates) rj,n with unit counts per second (cps). bji is the amplitude (amount) of si to be included in the reconstruction of measured spectrum number j. si is also considered a vector. The `unit' of si is counts except for s0 that has the unit cps. LTj is the live time (in seconds) for measurement number j. The LT's are slightly less than 1 s due to dead time losses. Spectral component number zero, s0, is equivalent to the average of all spectra in the set of data. In principle there are as many spectral components as there are channels, i.e. N, and by including all spectral components an exact reconstruction of all measured spectra can be performed. However, in order to avoid most of the statistical noise one in general only uses spectral component number zero together with the next 4 to 9 components. Spectral components of low numbers are more important than those of higher numbers. The average spectrum, s0, is the most important component, s1 is the second most important, etc. The reconstructed spectra rj then can be processed by standard methods as for example the three windows method commonly used for determination of the concentrations of Th, U and K from AGS data (IAEA, 1991; Grasty, 1998). By using a four windows method

H.K. Aage et al. / Applied Radiation and Isotopes 51 (1999) 651±662

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Fig. 2. Spectral components No.'s. s2 and s3 for NASVD processed data, South-western part of Latvia. 137

Cs can in principle also be mapped (ICRU, 1994; Sanderson et al., 1997a). However, due to the low levels of 137Cs contamination in Latvia and due to the not optimal quality of the data, a new method had to be developed. Figs.1±3 show the spectral components s0, s1, s2, s3, s4 and s5 for area 5a, one of the areas mapped. (Area 5a is the upper third of Fig. 6 covering the area 5(a+b+c).) In the average spectrum s0 one may identify the peaks due to thorium (208Tl), uranium (214Bi), potassium (40K) and caesium (137Cs). The same peaks

are contained in s1; however, in a slightly di€erent relative amount. The spectral components s2 and s3 shown in Fig. 2 have both positive and negative channel counts; and peaks due to 40K and 137Cs are easily identi®ed. In an ideal situation one should only observe real signals in a number of spectral components equal to the number of independent gamma emitters, i.e. Cs, Th, U and K. The other spectral components then only contain noise. However, any factor that in¯uences the spectrum shape may cause an additional spectral com-

Fig. 3. Spectral components No.'s. s4 and s5 for NASVD processed data, South-western part of Latvia.

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Fig. 4. Average measured spectrum and reconstructed average spectrum calculated from six 1 s spectra, logarithmic scale.

ponent. This could be spectrum drift and altitude variations. The spectral components s4 and s5 are shown in Fig. 3. It is seen that s4 contains some information in the 137 Cs peak region (around channel 118). From spectral component s5 and upwards the signals are reduced to noise. Fig. 4 shows a spectrum based on the average of six reconstructed spectra together with the average of the corresponding six measured spectra from area 5a. The reconstruction is based on s0 and further 4 spectral components. (Due to the logarithmic count rate scale channels with no counts are not indicated and the lowermost channel count rate for the measured spectrum is 1/6=0.17 cps.) It is easily seen that the reconstructed spectra contain less noise than the measured spectra.

3. Synthetic spectra The spectral components contain all spectral information about the measured gamma spectra. Therefore, if the measured spectra contain a `caesium signal' in amounts that vary independent of the content of the other signals, it is possible to construct a 137Cs spectrum, v1, by linear combinations of spectral components. A criterion for construction of a `clean', synthetic 137Cs spectrum is that the channels above the 137 Cs full energy peak contain no counts. In an (almost) ideal situation one should be able to construct further only three linearly independent spectra, v2, v3 and v4, without a 137Cs signal, i.e. only containing Th, U and K signals. (One may try to construct `clean' spectra of Th, U and K, respectively. That is not needed here, and any three linearly independent spectra with mixtures of Th, U and K can be used.) This could be expressed by:

Fig. 5. `Clean', synthetic 137Cs spectrum and real 137Cs spectra measured in the laboratory for equivalent heights of 117 and 146 m. The real spectra have been scaled so the full energy peaks around channel 118 overlap with the peak of the synthetic spectrum.

v1 v2 v3 v4

ˆ a11 s1 ‡ a12 s2 ‡ a13 s3 ‡ a14 s4 ˆ a21 s1 ‡ a22 s2 ‡ a23 s3 ‡ a24 s4 ˆ a31 s1 ‡ a32 s2 ‡ a33 s3 ‡ a34 s4 ˆ a41 s1 ‡ a42 s2 ‡ a43 s3 ‡ a44 s4

…2†

In order to determine the synthetic 137Cs spectrum, v1, one has to know the a1i values. The value of aj1 may in practice arbitrarily be selected to 1 and the other constraints could be that the counts of the standard (or modi®ed) Th, U and K windows for the three windows method should be zero for a 137Cs spectrum, i.e. the constraints should be uTh ˆ a11 f1,Th ‡ a12 f2,Th ‡ a13 f3,Th ‡ a14 f4,Th ˆ 0 uU ˆ a11 f1,U ‡ a12 f2,U ‡ a13 f3,U ‡ a14 f4,U ˆ 0 uK ˆ a11 f1,K ‡ a12 f2,K ‡ a13 f3,K ‡ a14 f4,K ˆ 0

…3†

where uX is the nuclide X window counts for v1 and fj,X is the window counts of the nuclide X window for spectral component number j. Thus, Eq. (3) states that the synthetic spectrum v1 should be built up from spectral components in a way that ensures no counts in the Th, U and K windows. The resulting v1 synthetic 137Cs spectrum for area 5a is shown in Fig. 5. One recognises a 137Cs spectrum including photons Compton scattered in soil, grass, trees, air and aeroplane, i.e. an environmental 137Cs spectrum. This spectrum corresponds to the signal from a certain ground level 137Cs contamination (in kBq/m2) called one H-unit; please confer the section on calibration. Also shown in Fig. 5 are two 137Cs spectra measured in a laboratory calibration set-up at DTU simulating airborne measurements at 117 and 146 m equivalent altitude (Korsbech, 1993; Haase, 1999). The counts of the spectra from the laboratory measurements have been scaled in order to get the same full energy peak counts (around channel 118) as has the synthetic 137Cs spectrum. It is observed that

H.K. Aage et al. / Applied Radiation and Isotopes 51 (1999) 651±662 Table 1 Matrix A, constants for construction of synthetic spectra

v1 v2 v3 v4

s1

s2

s3

s4

0.9137 0.5 0.8 1.0

4.1508 ÿ0.27 ÿ0.62 ÿ1.05

0.5558 ÿ0.1 0.7 2.0

1.0 0.5 ÿ0.3 1.0

this also almost gives `correct' channel counts around the channels 90 to 110 where forward scattered photons are detected. However, it is also observed that the synthetic spectrum has a higher number of counts in the lower channel numbers than have the laboratory 137 Cs spectra. Obviously many multiple Compton scattered photons are lost from the laboratory set-up. The slope of the curve (versus channel number) at the lower channel numbers is almost equal to the slope of the average spectrum curve. This re¯ects the fact that after a few scatterings in air, the di€erential photon ¯uence rate, f(E ), has an energy dependency almost solely dependent on the relative magnitude of Compton and photo absorption cross sections of the air. An extrapolation of the laboratory results to around 160 m equivalent altitude gives count rates equal to those of the synthetic 137Cs spectrum from channel 70 to channel 125. With 113 m equivalent ¯ying altitude the di€erence, around 47 m of air, could be equated to an average depth (zav) of burial of 137Cs in the ground, i.e. a `mass depth' (zavr ) of around 5.6 g/cm2 with estimated accuracy +/ÿ1.2 g/cm2. (113 m equivalent altitude includes 80 m real altitude, 30 m equivalent attenuation in the aeroplane and 3 m equivalent vegetation).

4. The pseudo concentration method The synthetic spectrum, v1, shown in Fig. 5 corresponds to a certain amount of 137Cs ground level contamination called one H-unit. The next step now is to determine the amount of v1 that is included in each reconstructed spectrum. This amount is termed the pseudo concentration of 137Cs for the reconstructed spectrum in question. The ®rst step is to calculate the amount of v1 that is contained in each of the spectral components si. In Table 1 are listed the a1i values for construction of the synthetic 137Cs spectrum v1 for area 5a. Also shown are the aji values for construction of v2, v3 and v4. The aji values for v2, v3 and v4 have been found by trial and error. The criteria are that v2, v3 and v4 should be linearly independent and that the spectra

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Table 2 Matrix D, contents of synthetic spectra in spectral components

d1,i d2,i d3,i d4,i

dj,1

dj,2

dj,3

dj,4

0.11960 0.20763 0.04813 0.00214

0.92845 ÿ0.25334 ÿ0.96782 0.74118

0.91848 0.01630 0.00378 ÿ0.90892

ÿ0.30828 ÿ0.07607 0.43691 0.35459

should have no sign of a peak at the channels for the 137 Cs full energy peak. (In Section 7 an additional constraint for aji is mentioned). Now Eq. (2) is rewritten as a matrix equation, V ˆ AS or Aÿ1 V ˆ S and D ˆ Aÿ1 ˆ SVÿ1

…4†

where D is the inverse of matrix A, and the di1 values are the amount of v1 that is contained in spectral component number i. (For example d11 is the content of v1 in spectral component s1). By solving Eq. (4) one gets the dij values listed in Table 2. Next a pseudo concentration hj1 of (ground level) 137 Cs is de®ned by hj1 ˆ h01 ‡ …bj1 d11 ‡ bj2 d21 ‡ bj3 d31 ‡ bj4 d41 †=LTj

…5†

where hj1 is the amount (fraction) of the synthetic Cs spectrum v1 (Fig. 5) that is contained in reconstructed spectrum number j. As mentioned earlier this spectrum corresponds to the signal from one H-unit; therefore Hhj1 is the physical equivalent ground level concentration of 137Cs corresponding to measured spectrum number j. In a similar way h01 is the amount of v1 that is contained in the average spectrum s0 (excluding a possible 137Cs contamination of the aeroplane). The other symbols have the same meaning as described earlier. The pseudo concentrations corresponding to the terms bjidi1/LTj of Eq. (5) are calculated from the spectral component amplitudes bji and the dij values found above. The h01 value has to be calculated in another way. One notices that for measurements taken above the sea or above another large body of water the hj1 values should be zero. For these `background spectra' Eq. (5) can be written as 137

h01 ˆ ÿ…bj1 d11 ‡ bj2 d21 ‡ bj3 d31 ‡ bj4 d41 †=LTj

…6†

By using the average spectral component amplitudes and live times for a large number of measurements above the sea one gets for area 5a h01=0.0939 H-units of 137Cs contamination. (It is later shown that for area 5a one H-unit is equal to 15.84 kBq/m2; therefore, for area 5a the 137Cs `content' of the mean spectrum s0 is c0=h01H = 0.0939  15.84 kBq/m2=1.49 kBq/m2.)

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In a similar way the amount of the synthetic spectra v2, v3 and v4 contained in each reconstructed (and measured) spectrum could be determined. This was not done for the Latvian data because the mapping of Th, U and K concentrations has already been done by the standard three windows method (Bargholz, 1998). 5. Calibration One may map the pseudo concentrations, hj1, of Cs calculated by the method described above. However, in order to map the physical concentrations (kBq/m2) one has to perform a calibration. The AGS equipment used was calibrated for 137Cs ground level surface contamination by measurements in laboratory calibration set-ups (Bargholz, 1995). However, in order to check the calibration, and to include the in¯uence of the aeroplane carrying the detector system, a calibration area was selected in the Western part of Latvia. The area was over¯own many times and a number of samples were collected by both Danish and Latvian scientists (Bute, 1997). The area was not supposed to have been ploughed since the Chernobyl fall-out in 1986. However, the laboratory measurements of samples later unveiled that an e€ective depth mixing had occurred, presumably due to ploughing. Furthermore, the average 137Cs speci®c concentration for the upper 20 cm soil (minus the uppermost turf) along a ¯ight line at the centre of the calibration area was 6.7 Bq/kg (mass including natural moisture) with variations from 5.5 to 7.7 Bq/kg. Half of this 137Cs may be due to the atmospheric nuclear weapon tests. Assuming homogeneous distribution down to at least 20 cm one can calculate an equivalent surface concentration ceq of around 0.57 kBq/m2. (The equivalent surface concentration of 137Cs is that surface contamination that would cause the same detector count rates as the actual amount of 137Cs present on and in the soil). The calculated equivalent surface concentration of 0.57 kBq/m2 is a too low value for a calibration. Therefore, another calibration method had to be used. It is based on a knowledge on the 137Cs window sensitivity for a four windows method at the ¯ight altitude(s), i.e. the 137Cs window net count rate (cps) per contamination unit (kBq/m2 equivalent surface contamination). Based on own experiences (Bargholz, 1995) and similar experiences by others (Sanderson et al., 1997a) a sensitivity s137 Cs =9.68 cps/(kBqmÿ2) at 100 m equivalent altitude can be assumed. (The equivalent altitude includes attenuation in air, aeroplane and vegetation). The sensitivity at other altitudes can be calculated from our laboratory experiments giving an e€ective attenuation of 0.0142 mÿ1 (Bargholz, 1995) not much di€erent from 0.0126 mÿ1 observed by 137

Ronning and Smethurst (1997). The calibration then was performed as follows. The peak net count number of the synthetic 137Cs spectrum (v1) corresponds to an equivalent surface contamination of H (kBq/m2). H is height dependent and relates to the average equivalent altitude for the data series. H is not a ®xed number; the concentration corresponding to one Hunit is di€erent for di€erent synthetic spectra (i.e. di€erent series of measurements). For the synthetic 137Cs spectrum of Fig. 5 constructed from measurements with an equivalent altitude of 113 m the peak net count number is 127.6 counts. For a 1 s measurement and a sensitivity of s137 Cs =8.06 cps/(kBq mÿ2) at 113 m altitude this corresponds to an equivalent surface contamination of H = 15.84 kBq/m2. Therefore, for this series of measurements one H-unit is 15.84 kBq/m2 and for a conversion from the pseudo concentrations, hj, to real contamination concentrations the hj values from Eq. (5) should be multiplied with 15.84 kBq/m2, i.e. the physical concentration cj corresponding to reconstructed (and measured) spectrum number j becomes cj ˆ hj H

…7†

6. Maps In Figs. 6±8 maps are shown for the calculated equivalent 137Cs concentrations for three of the surveyed areas. Areas with di€erent levels of contamination have been selected for presentation. The colour scales, therefore, are di€erent for the ®gures. Fig. 6 covers the South-western part of Latvia (area 5a+b+c) that is the only part of the country having received a 137Cs contamination from the Chernobyl accident that to some extent might have been mapped with standard AGS data processing methods. The maximum equivalent surface contamination is around 3.6 kBq/m2. The total inventory in the ground is somewhat higher. Fig. 5 indicates that the typical 137Cs spectrum for area 5a corresponds to 137Cs activity buried at an equivalent mass depth (zavr ) around 5.6 g/ cm2. Dependent on the vertical distribution of 137Cs in the ground and taking the uncertainties into account the actual, maximum total inventory of 137Cs in the ground may be from around 4 kBq/m2 to more than 7 kBq/m2. The higher equivalent surface concentrations are found in forests and peat bogs. This can be seen when comparing with a topographic map. Especially, the peat areas show high concentrations. The large blue inland area is a lake with adjacent wetland areas. Below the lake is seen another blue area. This is not

H.K. Aage et al. / Applied Radiation and Isotopes 51 (1999) 651±662

another lake; during the survey it was observed that the peat here has been dug up recently. Obviously the 137 Cs has been removed together with the peat. The distribution observed is in accordance with ICRU (1994) and with Bergman (1994) who describes that in Boreal forests the humus layer retains a major fraction of the caesium fallout for many years. Bergman also mentions that some peatland plants are e€ective in accumulating caesium. The distribution is similar to that around GaÈvle in Sweden where AGS measurements in 1997 showed a distinct di€erence between forest areas and cultivated areas (Mellander, 1999). Fig. 7 shows an area in the Western part of Latvia (area 2). It is characteristic that the shapes of the areas with higher (than average for the whole area) concentrations of 137Cs are in agreement with the `forest areas' of a topographic map of the same area. The equivalent surface concentrations of 137Cs are found to be in the interval 0±2 kBq/m2. Another interesting aspect is the relationship between the concentrations of 137Cs and 40K. Maps showing the concentrations of K for the surveyed areas have been produced by Bargholz (1998) using the three windows method. Where the K concentration within the area is high (relative to other K concentrations within that area), the 137Cs concentration is often low and vice versa. First this was assumed to be an artifact caused by an error in the data processing; but no error could be found. There are, however, reasons to expect the observed `anti correlation'. The lower K concentrations are found in forest areas and similar areas. Here the soil often is of `low quality', i.e. with a low content of clay and thus also a low content of K. Further the K in the ground in pine and spruce forests is covered with a layer of needles containing almost no K. The 137Cs concentrations are high in forests, etc., because the earth has not been cultivated and because `biologic activity' may keep 137Cs close to the surface. Higher K concentrations are found on agricultural soils because of a higher content of clay. (Clay-based soil, which is preferred for agricultural activities in general contains more K than sandy soil.) On agricultural soil the equivalent surface 137Cs concentrations are found to be very low, supposedly due to ploughing which changes the 137Cs distribution in the soil. In Fig. 8 an inland area around Saldus (area 4) is shown with very low levels of 137Cs contamination. The equivalent surface concentrations were found to be in the interval from 0±0.5 kBq/m2, i.e. well below the detection limit for normal methods for processing of AGS data. This area is also covered by a great deal of vegetation, however, the concentrations are very low probably due to wind and weather conditions around the time of deposit of Chernobyl fall-out;

657

indeed most of the 137Cs activity observed may originate from the atmospheric nuclear weapon tests. Again the `high concentration' areas (red) are peat bogs except for one spot around the co-ordinates 4592300, 6274600 which does not match with any feature in a topographic map. (This spot is marked with a blue triangle on the map.) During a visit to Latvia by one of us in March 1999, the spot was identi®ed as leftovers from a sawmill. Large piles of bark, needles and smaller branches were found there. Obviously, several years accumulation of needles with 137Cs deposits from the Chernobyl accident in 1986 has taken place. This is bound to give a contamination level higher than for a usual forest in that area and the spot should be visible on the colour map. And it is. 7. Discussion The planned ordinary calibration of the spectral components (Korsbech et al., 1998) based on sampling and airborne measurements could not be carried out for 137Cs due to a too low equivalent surface contamination. A synthetic 137Cs spectrum could not be determined from the calibration area measurements alone, indicating that the 137Cs concentration is low and almost constant for the selected area. However, by including measurements also from the surrounding areas a synthetic 137Cs spectrum could be determined, and the Pseudo Concentration method could be used. This method indicates that the equivalent surface contamination for the calibration area is between 0.2 and 0.5 kBq/m2. By using the results for the measured samples from the calibration area a value around 0.57 kBq/m2 equivalent surface contamination was estimated. The turf without 137Cs may have reduced a little the radiation from 137Cs mixed homogeneously in the clayey soil below the grass. The reliability of the pseudo concentration method is dependent on the ability to calculate a `clean', synthetic 137Cs spectrum from linear combinations of the spectral components derived from the NASVD processing of the measured AGS data. Further one should be able to produce three linearly independent spectra without 137Cs. The synthetic 137Cs spectrum (Fig. 5) used for mapping of area 5a is easily recognised as an environmental 137Cs spectrum including photons scattered in the ground, air, etc. By comparisons with spectra obtained in a laboratory calibration set-up one observes that the synthetic 137Cs spectrum compares well with a laboratory spectrum for around 160 m equivalent altitude, except for a signi®cant de®cit of low energy photons in the laboratory spectrum. The de®cit is ascribed to loss of multiple scattered photons from the laboratory calibrations set-up. One may also calculate that this spectrum corresponds to an equival-

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ent surface contamination of 15.84 kBq/m2 for an equivalent altitude around 113 m. For other areas synthetic spectra similar to that of Fig. 5 could be calculated, some of which, however, included a signi®cant amount of noise. For a few areas it was not possible to calculate a recognisable 137Cs spectrum and a mapping could not be done. This may be ascribed to low levels of 137Cs contamination combined with inferior data caused for example by varying amounts of radon daughters in the air, on the aeroplane or on the ground (after rain). Spectrum drift

caused by malfunctioning spectrum stabilisation also sometimes gave low quality data. The aeroplane used for the measurements in 1996 was slightly contaminated with 137Cs giving a constant, false signal corresponding to around 2 kBq/m2 ground level contamination. Although the signal from this contamination is extracted from the calculations, it will produce additional noise. Problems with the altimeter probably caused that the planned ¯ying altitude of 80 m was not always obtained. In principle the NASVD technique is able to handle,

Fig. 6. 137Cs, equivalent surface concentrations map, Area 5 in the South-western part of Latvia. (Area 5a is the upper third part of area 5.) Concentration scale from 0±3 kBq/m2. The large blue inland area is a big lake with uplands.

Fig. 7. 137Cs, equivalent surface concentrations map, area 2 in the South-western part of Latvia. Concentration scale from 0±2 kBq/m2. A large forest area spreads across the North-western part of the map (higher equivalent concentrations; humus ®xes the caesium and keeps it close to the surface).

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659

Fig. 8. 137Cs, equivalent surface concentrations map, area 4 Saldus. Concentration scale from 0±0.5 kBq/m2. The concentrations are below the detection limit for normal methods for processing AGS data. Two of the `high' concentration areas (red) are bogs.

and to separate out, all parameters that in¯uence the spectra. Therefore, in theory the problems mentioned above could be taken care of, and eliminated, except for the additional noise caused by aeroplane contamination. However, for each parameter one has to include an additional spectral component. Furthermore, one has to be able to identify the in¯uence on the spectra from the additional parameter. The equivalent, total altitude, including the depth distribution of 137Cs in the ground, could be such a parameter. The laboratory measurements of `buried' 137Cs (Fig. 5) tell that the equivalent altitude has a simple relation to the ratio between full energy counts and counts in the channels at lower energies. Hovgaard (1997c) used NASVD processed AGS data for mapping the depth distribution of 137Cs in an area in Finland. The 137Cs concentrations for that area, however, varied between 10 kBq/m2 and 100 kBq/m2 and the signal to noise ratio for the Finnish data was much better than for the Latvian data. Here we only are able to estimate the average depth for an area. We have in general only used the ®rst four spectral components corresponding to four `parameters' namely the concentrations of Cs, K, U and Th. The rationale behind this also is that for most of the measured areas a visual examination of the other spectral components unveiled none or very little 137Cs signal. However, for some areas there were some 137Cs signals also in the spectral components No.'s 5 to 8. Due to diculties in including more than 4 spectral components, they were neglected. Without a useful calibration area for test of the calculated 137Cs concentrations we have to rely on other indications. Prior to the AGS measurements it was

known (Dambis, 1995) that the Western part of Latvia had a higher contamination than other areas. Our mapping con®rmed this. The variations in equivalent surface contamination (Figs. 6±8) have been examined and many details have been understood. The edges of old forests bordering on cultivated areas are easily seen on the contamination maps; and rivers, lakes and the sea are also clearly identi®ed as `non-radioactive areas'. Peat bogs, even small ones, show their existence by having higher equivalent surface contamination than have the neighbouring areas. Further, by comparing the average 137Cs concentration over an area calculated by the Pseudo Concentration method with the average concentration calculated from the mean (net) spectrum for that area together with the sensitivity known from the windows method, one gets a check of the calculations. It has been observed that this comparison is very sensitive to the construction of the synthetic spectra without 137Cs, i.e. v2, v3 and v4; and on several occasions a reconstruction of the spectra v2, v3 and v4 was needed (Aage, 1999).

8. Uncertainties and accuracy Due to the conditions for the surveys it is dicult to get reliable values for the uncertainty and accuracy of the measurements. Some parts of the calculations can be evaluated by standard statistical methods, e.g. the standard deviations of the amplitudes of the spectral component and parameters derived from the spectral components. However, the in¯uence of other factors as for example the in¯uence of radon daughter, altitude

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errors and spectrum drift cannot (at present) be quanti®ed. An evaluation of the ®nal results may, however, give some estimates of accuracy and uncertainties. As mentioned above the distribution of the calculated equivalent surface contamination ®ts well with the topographic map; the sea, lakes and wetlands show up with no 137Cs. The borders between forests and cultivated areas are easily observed. Peat areas also can easily be identi®ed by their high equivalent surface concentration. Due to the less than optimal `calibration area' it was not possible to perform an `on the spot' absolute calibration of the equipment. Instead the synthetic spectra were calibrated by using parameters for the standard four windows method. An equivalent altitude of 113 m was assumed for the synthetic spectra. Due to altimeter problems this may have introduced a scaling error in¯uencing all calculations of concentrations based on synthetic spectra. It is estimated that the scaling error is not larger than 15% for Fig. 6 and around 25% for Figs. (maps) 7 and 8. For each area an average spectrum was calculated and based on the net count rate of the 137Cs peak the average equivalent surface concentration was calculated. Also here an equivalent altitude of 113 m was assumed. Due to the inclusion of a large number of spectra, the net count rate in general could be determined with an accuracy better than or equal to that of the matching synthetic spectrum. The average concentration based on the pseudo concentration method then was compared to that calculated from the mean spectrum. If a discrepancy was observed, the non-caesium synthetic spectra were adjusted until agreement was obtained. Thus, the average concentration for the mapped areas is determined as accurate as is possible with the windows method for the average spectrum. The samples from the `calibration area' indicated an equivalent surface concentration of around 0.57 kBq/ m2. The uppermost turf may reduce the signal a little. Mapping of the area showed equivalent surface concentrations between 0.2 and 0.5 kBq/m2. This indicates that there may possibly be an error or scattering of around one colour scale unit. From the mapping of the background measurements above the sea one may get an estimate of the scatterings of the results around the mean value, i.e. 0 kBq/ m2 for the background measurements. An examination of the upper third of the background measurements of Fig. 7 tells that the sample standard deviation is around 0.3 kBq/m2, i.e. around 1.5 colour scale unit. This is in agreement with the colours of the map. For the other part of the background measurements of Fig. 7 the colours tell that the sample standard deviation here is signi®cantly smaller. The di€erence is assumed to be caused by di€erent spectrum drift and radondaughters in the air.

For inland areas it is possible to select areas with one or two colours based on measurements for two or three adjacent ¯ying lines covering some hundred single measurements. Assuming that the contamination level is almost constant for this area one may conclude that the sample standard deviation is around or less than one colour unit. For a few other of the surveyed Latvian areas (not shown in the ®gures) the scatterings of results are so large that the maps are almost without information. In total one may estimate that for results not strongly in¯uenced by spectrum drift, radon daughters and altitude errors the accuracy of the measurements could be stated as a scaling error not larger that 15± 25%. The `scatterings' typically correspond to one colour scale unit; both for low and for `high' concentrations. 9. Conclusion Based on the NASVD technique developed by Hovgaard (1997a,b) we have tested a new method, the pseudo concentration method, for mapping low levels of contamination. This method cannot yet be considered mature and the limitations for its use have not yet been fully clari®ed. The limitations we have observed concern the quality of the data. However, even with data of less than optimal quality it has been possible to perform contamination mapping at levels below the detection limits for the standard methods for examining AGS spectra. The basis for the pseudo concentration method is that the spectral components contain all information about the shapes of the measured spectra. By mixing the most important spectral components in a way that excludes the contributions from Th, U and K one ends up with a linear combination of spectral components giving a synthetic caesium spectrum. This spectrum is the typical caesium spectrum for the surveyed area. By using the sensitivity for the standard windows method one recognises that for 113 m equivalent altitude the synthetic spectrum (Fig. 5) corresponds to 15.84 kBq/ m2 equivalent surface concentration of 137Cs. The ®nal step then is by simple matrix calculations to determine the amount/fraction of the synthetic caesium spectrum that is `contained' in each of the reconstructed spectra; this is also the fraction of 15.84 kBq/m2 137Cs that is found at the position corresponding to the reconstructed spectrum in question. The decomposition of a set of 10000 spectra by the NASVD technique takes about 3±5 min when a standard Pentium PC is used. The following processing of spectral components and amplitudes was performed `manually' in a spread sheet program, and has been very time consuming. However, with some experience

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a low level contamination map (with 10000 spectra) may be produced within 4±5 h. At contamination levels signi®cantly higher than those observed in Latvia a 1 h production time could be expected because the non-caesium spectra can be constructed without iterations. Neither the NASVD technique nor the pseudo concentration method and similar methods can yet be considered fully developed; and the techniques may have a much wider application than just for processing AGS data. We have applied similar techniques to spectra from borehole logs and to spectra from Early Warning Stations that continuously record the environmental gamma ray intensities in Denmark and some East European countries. We feel that some of the techniques described above may have applications in many other areas where a large number of gamma spectra or similar spectra are being processed with the aim of `measuring' di€erent physical parameters.

Acknowledgements Thanks to Frank Andersen (DTU) for having performed several of the airborne surveys. Thanks to Maris Dambis (Latvian Nuclear Safety Inspectorate) and Ojars Ulskis (Regional Environmental Board of LiepajaÂ) for having co-ordinated the AGS surveys and thanks to Vija Bute (Latvian Environmental Data Centre) and Dorte Eide Paulsen (DTU) for sampling and measurements for the planned calibration.

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