Master`s Thesis
Contents
1. 45 2 T O on Energy keV Figure 4 6 Comparison between calibration factors calculated with and without vegetation above the ground based on the multiple slabs model 4 2 The Field of View of the Detector Figure 4 7 4 8 and 4 9 present the detector s field of view for several photon energies when assuming different deposition model In these figures the contribution of full energy peak count rate from remote region was plotted as a function of the field of view of the detector The full energy peak count rate contribution from remote region was defined as the ratio between the photons emitted from remote region that are registered by the 26 detector and the photons emitted from the whole plane The field of view of the detector for some typical energies are tabulated in Appendix D It can be seen in Figure 4 7 and 4 8 that the photon contribution from remote region is decreasing more drastically for the emergency preparedness model Also the field of view of the detector is larger for the surface deposition model for all photon energies These effects depend on that the photon fluence rate is smaller for the emergency preparedness model where the attenuation in soil occurs However the surface deposition model is a simplified model so the detector field of view is overestimated E 0 1 MeV E 0 5 MeV P E 1 MeV zZ 2 Q Cc 2 z 10 20 30 40 50 60 70 80 90 100 110 Dete2. Filnamn untitled Filformat MATLAB Figure fig v MATLAB Figure fig Figure F 9 LALA The results of the combined uncertainty associated to the calibration factor calculation are saved in the sub folders with the same name as the deposition model that was chosen These sub folders can be found in the folder named Results There are three columns in the text file photon energy given in keV the nominal calibration factor and the combined uncertainties k 1 given in An example is shown below 100 00 122 00 140 00 160 00 180 00 3 482E 03 4 160E 03 4 430E 03 4 539E 03 4 528E 03 4 476 4 458 4 444 4 430 4 418 11
3. mined by setting r Htan and dr H cos0 d0 Then the following equation is obtained dps p E C E drdz 2 7 Atan 2 By rearranging Equation 2 1 the factor C E in Equation 2 8 is obtained Co p E C E d dz 2 8 C E h exp pr 2 9 Because this factor is also depending on the material which the photon is passing through and the vertical distance between the detector and the source hence in this report the Detector Air Vegetation Soil Figure 2 1 A schematic description of the arrangement of the slabs attenuation factor is written as id C d exp 44 2 10 where j is the current material and d is the vertical distance in m If one considers the vegetation as one of the slabs the total attenuation factor from slab 7 can be expressed as i 1 Ctot i Cair H d Cj ilui II Crnldn 2 11 n 1 where j can be either vegetation or soil Photon Attenuation A general description of the mass attenuation coefficient for soil so with unit m was developed earlier 8 Psoil mr 1 26 10587427 0 142E 9 2 1075 2 12 Psoil where the soil density poi is given in kg m and the energy E in MeV This description is valid for most types of soil and gives good results for photon energy within the range 0 3 to 3 MeV In order to approximate the attenuation coefficient for the vegetation one can use a linear combination between the attenuation of air and the attenua
4. Appendix B Appendix C Appendix D Appendix E Appendix F 31 32 34 35 37 40 41 42 44 1 Introduction Radioactivity has always been present in the environment due to the presence of natural radionuclides There are three types of these radionuclides primordial cosmogenic and anthropogenic 1 Since World War II the radioactivity in the environment has been increased due to the release of anthropogenic radionuclides mainly from nuclear weapons testing and nuclear accidents Because the radioactivity may affect human health it is essential to characterise and determine the level of the activity after a nuclear contamination as soon as possible There are many kinds of radioactivity measurement methods However gamma ray spectrometry on site or in situ is an important technique regarding to these purposes An in situ measurement can identify the radionuclides on site and provide the amount of it directly after a completed measurement Traditionally sodium iodine Nal scin tillators had been used but since the development of detectors with higher resolution e g the High Purity germanium HPGe detector these are today the primary choice for gamma ray spectrometry 2 1 1 Background In situ gamma ray spectrometry using HPGe detectors is a powerful method to measure deposition of radionuclides The HPGe detector is a semiconductor detector which work similarly to a reverse biased diode 1 When a gamma pho
5. The results are then saved in an external text file for further use Getting Started Find the file main m and open it in MatLab by a double click Click on the icon run to run the script software However depending on the MatLab version this icon will have different appearance After you had started the software a menu window appears See Figure F 1 for how the run button and the menu window appears in the MatLab version R2014b J manan 20145 R R R T 1 Surface m 1 Main program 2 i clear E clc 4 global Defaults l Defaults zeros i 1 6 EA i modelChoice menu Please gi e Surface i 9 Volume e o E p ct e H M 11 Exponential model 12 Cancel Figure F 1 The run icon and the main menu Menu There are five option buttons in the menu window four deposition model buttons and one cancel button Models Choose the desired model by clicking the corresponding button then a graphical user interface where you do the inputs for the chosen deposition model is opened Cancel You will receive a request if answer Yes the software shuts down Graphical User Interface One of the Graphical user interfaces GUI is shown in figure F 2 The interfaces have different layout depending on the selected deposition model but the differences are small The input boxes are arranged in panels in order to give you a better input overview There are already defau
6. a7 8 10449 ag 0 215457 ag 6 83275 aio 11 5236 a11 0 848338 35 Table A 2 Mass attenuation coefficients for water that were used to obtain the parameters in Eq 2 14 The density of water was assumed to be 1 g cm 4 Energy MeV u plem g 0 1 1 707 107 0 15 1 505 1071 0 2 1 370 107 0 3 1 186 107 0 4 1 061 107 0 5 9 687 107 0 6 8 956 1072 0 8 7 865 107 1 0 7 072 107 1 25 6 323 107 1 5 5 754 107 2 0 4 942 107 3 0 3 969 107 36 Appendix B 80 s 0 0003966 60 40 3 O 20 0 8 8 9 9 2 9 4 9 6 9 8 10 10 2 10 4 1 PPPE Hair J x10 Figure B 1 Hair for photon energy E 661 keV calculated when the pressure was fixed The standard deviation of the results is shown in the corner 80 s 0 00054861 Counts 9 9 5 10 10 5 1 and Hair J x10 Figure B 2 Hair for photon energy E 661 keV calculated when the temperature was fixed The standard deviation of the results is shown in the corner s 0 00067848 Counts 8 8 5 9 9 5 10 10 5 11 11 5 4 403 Hair M x10 Figure B 3 Hair for photon energy E 661 keV calculated when the pressure was fixed The standard deviation of the results is shown in the corner 80 s 0 00027684 60 fa E 40 3 O 20 0 6 6 2 6 4 6 6 6 8 7 7 2 1 403 Hair M x10 Figure B 4 Hair for photon energy E 1048 keV calculated when the relative humidity was fixed The standard deviation of the re
7. 13 W L Dunn and J K Shultis Exploring Monte Carlo Method Elsevier 14 K Jareteg Monte carlo simulations Available from http klas nephy chalmers se teaching montecarlo2013 documents Slides pdf Lecture Hand out 2013 15 M D McKay R J Beckman and W J Conover A comparison of three methods for selecting values of input variables in the analysis of output from a computer code Technometrics 16 Palisade Latin Hypercube vs Monte Carlo Available from http www palisade com downloads help risk35 faq_html latinhypercubevs montecarlo htm 10 Oktober 2014 17 J A Rice Mathematical Statistics and Data Analysis Third Edition Thomson Higher Education 18 Swedish Meteorological and Hydrological Institute Lufttryck Available from http www smhi se kunskapsbanken meteorologi lufttryck 1 657 19 September 2014 written in Swedish 19 Swedish Meteorological and Hydrological Institute Luftfuktighet Avail able from http www smhi se kunskapsbanken meteorologi luftfuktighet 1 3910 19 September 2014 written in Swedish 34 Appendix A Table A 1 Values for parameters in Eq 2 3 6 Six significant figures are retained for further calculation These parameters are valid for this particular detector since different detectors will have different energy response as well as angular response Parameter Value ay 33 9245 a2 0 0392096 a3 0 0353600 a4 0 00132088 as 487 125 a6 0 0671579
8. Detector The HPGe detector named defaultDetector which was produced by Ortec Inc USA redJa man kan l gga till nya detectorer sedan ar det bara att anropa den i program met You can add another detector by writing a MatLab function file for the detector efficiency calculation Give the function the same name as the detector There must be two input argument to the detector efficiency function set the photon incidence angle with unit radian as the first input argument to the function and set the photon energy with unit MeV as the second input argument There is an example below Example function y defaultDetector theta e defaultDetector determines the intrinsic efficiency detector for the default detector from empirical studies defaultDetector Theta E returns the detector efficiency with photon incidence angle Theta in rad and the photon energy E in Mev A parameters A 33 9245 0 0392096 0 0353600 0 00132088 487 125 0 0671579 8 10449 0 215457 6 83275 11 5236 0 848338 E e 1000 convert to keV y exp A 1 A 2 theta 2 A 3 theta A 4 E A 5 E A 6 cos A 7 theta E A 8 A 9 A 10 log E A 11 log E 72 end Input for the name of the uncertainty result Regarding the uncertainty analysis the result will be saved as a text file and the desired file name will be given in this panel You can use any symbol when you do your input but plea
9. H J Beck J DeCampo and C Gogolak In situ Ge Li and Nal Tl gamma ray spectrometry HASL 258 Health and Safety Laboratory US Atomic Energy Commission J Boson H Ramebiack T Nyl n and K Lidstr m Kalibrering av en HPGe detector f r gammaspektrometri i f lt FOI R 2914 SE FOI Umea Sweden 2010 J Boson K Lidstr m T Nyl n G gren and L Johansson In situ gamma ray spectrometry for environmental monitoring A semi empirical calibration method Radiation Protection Dosimetry W Sowa E Martini K Gehreke P Marschner and M J Naziry Uncertainty of in situ gamma ray spectrometry for environmental monitoring Radiation Protection Dosimetry 27 2 93 101 1989 G Sibbens and T Altzitzoglou Preparation of radioactive sources for radionuclide metrology Metrologia 44 1 71 79 2007 K Lidstr m and T Nyl n Beredskapsmetoder f r m tning av radioaktivt nedfall FOA R 98 00956 861 SE FOA Umea Sweden 1998 Joint Committee for Guides in Metrology JCGM The guide to the expression of uncertainty in measurement GUM Available from http www bipm org utils common documents jcgm JCGM_100_2008_E pdf 33 12 Joint Committee for Guides in Metrology JCGM Evaluation of measurement data supplement 1 to the guide to the expression of uncertainty in measurement propagation of distributions using a monte carlo method Available from http wuw bipm org en publications guides gum html
10. aa Ge ee dee nes LOS COPE hin ass tk Bie te ee ee ea ase a tee le Baa 2 Theory 2 1 Gamma Ray Spectrometry 2 0 ee ee ee 2 1 1 Ground Level Gamma Ray Spectrometry 2 1 2 Detector Characteristics 2 e 2 1 3 Field of view of a Detector 2 0000 2 2 Radioactivity Deposition Models 0 20000 2 2 1 Photon Fluence Rate 2 2 2 2 0202000002 eee 2 2 2 Multiple Slabs Model 02 0008 2 2 3 Surface Deposition Model 2 208 2 2 4 Volume Deposition Model 2 0208 2 2 5 Exponential Model 0 020002 eee 2 3 Statistics and Data Analysis 0 0 0 0000 eee eee 2 3 1 Monte Carlo Method 20 a 2 3 2 Latin Hypercube Sampling 4 2 3 3 Uncertainty Analysis 2 2 0 00 00 000 eee eee 3 Method 3 1 Sensitivity Analysis i p 26 4 ein ee Rs ee a a ae 3 1 1 Results and Discussions 0 0 000002 ee 3 2 Accuracy Investigation 2 2 ee 3 2 1 Results and Discussions 0 0 0 0002 eee 4 Results and Discussions Als Calibration Hactor so stea aao ah Ped ec teed ae he aoe a Bae 4 1 1 The Effects from Vegetation 20 4 4 2 The Field of View of the Detector 20 4 3 Combined Uncertainties 2 2 ee ee 4 4 Graphical User Interface 2 2 20 02 0000002 ee eee 15 15 16 18 19 5 Conclusions 6 Further Work References Appendix A
11. and the detector field of view are also expectation values For calculation of the combined uncertainty associated to the calibration factor determi nation the square root of the total number of calculations was taken and round to the closest integer This integer will be the number of iterations as well as the number of calculations per iteration Because the uncertainty calculation time is long the progress is shown in an external window during calculations When the calculation is completed the user will be reminded regarding the file name with the results Outputs Two kinds of outputs are given A figure with calibration factors and a table with detector field of view see figure F 8 These figures are not saved automatically In order to save them click Save As under File in the menu in the figure window see figure F 9 Note that the default file type is fig which must be opened in MatLab Therefore if you want to open the figure in a common photo viewer it is convenient to choose other file type that is more general such as jpg or png Energy keV Vision m 100 52 4364 x10 Surface Deposition Model 122 57 9196 140 62 0256 45 180 70 1680 a 200 73 8246 2 4 244 81 1119 E 35 344 94 9055 5 444 106 2104 z 3 661 125 9115 amp 25 779 134 8790 964 147 3137 2 1086 154 6785 15 1112 156 1762 0 500 1000 1500 1408 171 7598 Energy keV Figure F 8 Examples of the outputs one plot and one table 10
12. parameters of the detector used in this work that are obtained after curve fitting can be found in Table A 1 in Appendix A 2 1 3 Field of view of a Detector Ideally the field of view of a detector is infinite if the surface is perfectly plane Since the photons that are emitted from remote regions may be attenuated before they reach the detector the contribution from the remote region decreases Within a distance Rmaz the contribution of number of counts are a certain percentage of the total number of counts from the whole area 3 For example if 95 of the detector counts origin within a radius of 10 m the detector should then be places at least 10 m away from anything that might interfere the measurement This will make measurement over a large area more reliable The distance Rmaz hereafter called the detector field of view can easily be expressed with the photon incidence angle Onyx Rmaz H tan Omax 2 4 where H is the detector height over the ground in m 2 2 Radioactivity Deposition Models As stated in an earlier section the photon flux will depend on how the radioactivity is distributed in and or on the ground The distribution of radionuclides in the soil will depend on many factors 3 e g the time after deposition the properties of the soil the weather and human activities on the site In this project four models were set up for description of possible source distributions e Surface deposition model where the
13. al x Sim Calculation time s S D 100 x 50 275 0 0443 100 x 100 550 0 0414 120 x 50 330 0 0368 120 x 100 660 0 0409 21 4 Results and Discussions In this section results from calibration factor calculation detector field of view calcu lation and the combined uncertainties associated to calibration factor calculations are presented Also a brief description of the developed graphical user interface is given 4 1 Calibration Factor Different calibration factors depending on the radioactivity deposition on in the ground are shown in Figure 4 1 4 2 and 4 3 In order to be able to compare different models the same conditions were assumed for the models plotted in the same figure lt 10 Surface deposition Emergency preparedness Calibration Factor 0 500 1000 1500 Energy keV Figure 4 1 Calibration factors for surface deposition model and the emergency prepared ness model plotted as function of photon incidence energy The calibration factors that were obtained using the surface deposition model and the emergency preparedness model can be seen in Figure 4 1 The results are similar to the ones that were obtained from a earlier study 6 though with small differences These differences might depend on different description of the density of air that was used As can be seen in Figure 4 1 the calibration factors calculated using surface deposition model are higher than those ones that were calculate
14. alues of quantities X i 1 N are selected randomly from their PDFs p Using these M values for each input quantity an out put set Y k 1 M is obtained This process can be seen as a repetition of the same experiment many times Out of these Y s the estimates of Y and its standard deviation s can be determined using Equation 2 33 respective 2 34 1 M 1 M PS Yr ef Xk X24 o XN 2 33 k 1 k 1 1 amp 2 Z 2 y 2 2 34 aay 2 k Yp aaa Due to this random sampling the parameter values with low occurrence probability might be excluded from the input set if M is not large enough Therefore a large number of samples must be drawn to ensure that the input sets are representative for the parameter distributions and in turn avoid clusters in the output set A large number of samples requires large computer memory and also means a long calculation time However these problems can be reduced by using a stratified sampling method 15 e g Latin Hypercube sampling 2 3 2 Latin Hypercube Sampling The Latin Hypercube Sampling LHS method is a special stratified sampling method that was developed by McKay et al in 1979 15 Assume that the PDF for input quantity x is OO Pr E Jr d 1 2 35 0 The PDF for each input quantity is divided into M disjoint intervals i e stratifications so that pal f gm G dg k Ayn 2 36 Ik is equal for each interval I4 Within every interval I one and o
15. alysis of series of observations 11 The combined uncer tainty associated with Y u y can be determined analytically as shown in Equation 2 32 11 This combined uncertainty will give a perception about the quality of the measurement result of Y On 18 2 P ww gt FL Pa 2 32 i 1 However the function f is not always differentiable In case of a complex relation between the input quantity and the measurand a numerical approach may be convenient 12 For input quantities X1 X2 Xy that are characterized by specific probability density functions PDFs the output will get a certain probability distribution Then the combined uncertainty u y is simply the standard deviation of the outputs A useful numerical method for the propagation of distributions is Monte Carlo methods 12 2 3 1 Monte Carlo Method Monte Carlo MC methods are a selection of methods that uses random samplings to solve problems 13 12 14 Samples from predetermined PDFs are used in simulations 10 to obtain the probability distribution and other statistical properties of an unknown quantity It is an old idea scientists tried to determine the value of 7 using this idea centuries ago 13 Nowadays the MC methods are widely used within many scientific areas e g physical science engineering and finance When using the MC method one must deal with the precision and the accuracy of the simulation results The MC method works as follow M v
16. as function of photon incidence energy The soil density was set to 1500 kg m and the activity on the ground surface was constant 4 1 1 The Effects from Vegetation Figure 4 4 4 5 and 4 6 present the calibration factors calculated in the presence of radioactivity in the vegetation The vegetation conditions were set to the same for all deposition models and the values are presented in Table 4 1 Table 4 1 Values of vegetation condition used in the calculation of calibration factor in presence of vegetation Parameter Value Height m 0 1 Surface mass ke m 1 Activity content 30 The calibration factors are always higher for calculation with radioactivity containing 24 vegetations than those without This difference is barely visible for the surface deposition model though The attenuation coefficient for the vegetation under the conditions given in Table 4 1 is slightly higher than the coefficient for dry air When the radioactivity is only deposited on the surface the vegetation on the ground has small impact on the photon fluence rate that reaches the detector The attenuation coefficient for the vegetation increases if the surface mass increases However the attenuation coefficient will be limited by the water content in the vegetation a on S Without vegetation With vegetation gt Calibration Factor Ww wn 0 500 1000 1500 Energy keV Figure 4 4 Comparison between calibration fa
17. ation factor calculation for some typical photon energies based on total 2000 calculations Energy keV Combined Uncertainty Surface dep Preparedness Multi slabs 122 4 45 36 64 6 17 344 4 34 31 40 5 64 661 4 28 28 58 5 38 779 4 27 27 92 5 32 964 4 25 27 09 5 24 1112 4 24 26 55 5 20 43 Appendix X User Manual Software for Calibration in In situ Gamma Ray Spectrometry This manual is aimed to give guidance for using the software for calibration of gamma ray spectrometric in situ measurements MatLab version R2012b or later is required to run this software since it was designed and comprises MatLab GUI The software is designed to be able to handle photons with energy up to 3 MeV in other words it can be used for most relevant photon energies in environmental measure ments However one limitation is the energy range for which the intrinsic calibration of the HPGe detector was done for For each input energy the software has three outputs the detector field of view the calibration factor and the combined standard uncertainty for these measurands The calibration factor is the total measurement efficiency which is an important parameter when comes to activity determination on site For calculation of the combined standard uncertainties the method Latin Hypercube sampling is used Parameters that contribute to the combined standard uncertainty can be sampled from three continuous probability distributions
18. cantly resulting in a decreased combined measurement uncertainty for the emergency preparedness model The combined uncer tainty for the multiple slabs model and the exponential needs to be validated 31 6 Further Work Due to the lack of empirical data during the time of this project some quantities should be validated in the future They are e the calibration factor and its combined uncertainty based on the multiple slabs model and the exponential model e the calibration factor for models that include vegetations on the ground e the field of view of the detector for all models Also some improvements should be done for a more user friendly software such as functions that can handle incorrect inputs 32 References G Choppin J O Liljenzin and J Rydberg Radiochemistry and Nuclear Chem istry Third Edition Butterworth Heinemann ICRU Gamma ray spectrometry in the environment icru report 53 Technical report International Commission on Radiation Units and Measurements 1994 J P Laedermann F Byrde and C Murith In situ gamma ray spectrometry the influence of topography on the accuracy of activity determination Journal of Environmental Radioactivity 38 1 1 16 1998 J H Hubbell and S M Seltzer X ray attenuation and absorption for materials of dosimetric interest Technical report The National Institute of Standard and Technology NIST Available from http www nist gov pml data xraycoef
19. ctor field of view m Figure 4 7 Full energy peak count rate contribution from remote region as function of the detector field of view for three photon energies Calculation based on the surface deposition model The field of view of the detector calculated based on exponential model are shown in Figure 4 9 Due to the fact that the radioactivity will diffuse and homogenise as time goes by several relaxation lengths were tested in order to see how the photon contribution from remote regions varies with time As can be seen in the figure the field of view of the detector decreases as the relaxation length grows The radionuclides penetrate deeper into the soil when the relaxation length is larger which means that the photons emitted from deeper regions might be attenuated by the soil before the detector does response 27 E 0 1 MeV E 0 5 MeV E 1 MeV 0 20 40 60 80 100 Detector field of view m Figure 4 8 Full energy peak count rate contribution from remote region as function of the detector field of view for three photon energies Calculation based on the emergency preparedness model Om 0 003 m 0 20 40 60 80 100 Detector field of view m Figure 4 9 Full energy peak count rate contribution from remote region as function of the detector field of view for photon energy E 660 keV Calculation based on the exponential model with four different photon relaxation lengths 4 3 Combined Uncerta
20. ctors calculated with and without vegetation above the ground based on the surface deposition model Compared to the surface deposition model the differences in calibration factors calcu lated with and without vegetation are more pronounced for the models which include radioactivity deposition in the ground The reason for this is that the vegetation has much lower attenuation coefficient than the soil and that in some extent the activity accumulated in the vegetation has shorter distance to the detector Both these factors give rise to increased photon fluence rate and in turn increased calibration factor due to the proportionality between these to quantities For the multiple slabs model the soil conditions were taken from an earlier study 7 The difference is even larger compare to the surface and volume deposition model The soil densities are much higher than the density assumed in the emergency preparedness model And also the thickness of the layers are larger in the multiple slabs model which gives larger attenuation effects These factors result in that the difference in calibration factors is even larger for the multiple slabs model see Figure 4 6 25 S Without vegetation With vegetation Calibration Factor Energy keV Figure 4 5 Comparison between calibration factors calculated with and without vegetation above the ground based on the emergency preparedness model 3 3 X10 5 2 5 O Lay u 2
21. d with emergency preparedness 22 model This is due to the fact that no attenuation in soil occurs in the surface deposi tion model In Figure 4 2 the calibration factors for exponential respective multiple slab model are shown for the case where the same detector might have been used In order to obtain a description of how the radioactivity penetrates into the soil empirical values 7 for ac tivity contents were used An exponential function was adapted to the empirical values so that the activity in the soil can be described in the form as in Equation 2 22 The data and the adaption of the data points is shown in Figure C 1 which can be found in Appendix C lt 10 3 b e gt Multiple slab Exponential Calibration Factor oo N A D 0 500 1000 1500 Energy keV Figure 4 2 Calibration factors for multiple slabs model and the exponential model plotted as function of photon incidence energy The relaxation length was adapted to empirical data from Boson et al 7 From Figure 4 2 one can see that the curves have similar shape which is expected For the same conditions the exponential model gives higher calibration factors about 30 more than calibration factors calculated using multiple slab model It is because that there had been an overestimation of the activity near the ground surface in the data adaption And in combination of low attenuation the photon fluence rate for th
22. distance between the detector and the source The combined uncertainties for calculations based on the emergency preparedness model have larger variations compare to the surface deposition model They vary from 27 to 37 k 1 depending on the photon energy and the total number of calculations Because the difference between the two models is the soil attenuation these extra un certainties could only come from the uncertainty of the soil density In order to cover the most types of soil the uncertainty in the soil density was assumed to be large This large uncertainty propagates further and results in a large combined uncertainty The combined uncertainties are also in agreement with results from an earlier study 6 As stated above the uncertainty of the soil density has a large impact on the com bined uncertainty i e by lowering the uncertainty of the soil density the combined uncertainty will decrease There is a lack of empirical data for the calibration factor as suming multiple slabs model using the HPGe detector that is considered in this project But if one uses the detector characterised by Equation 2 3 and soil conditions taking from Boson et al 7 the combined uncertainty for calculations based on the multiple slabs model will vary from 5 2 to 6 2 k 1 depending on the photon energy and the total number of calculations In the multiple slabs model the soil column sample was divided in several sections In this way t
23. e activity is As ki Av Ves di 2 19 where d is the thickness of slab and k is a proportional factor that describes the relative activity content in slab i For total N slabs the factor k can be expressed as Av di TN yA 7 BF Ay jd Then according to Equation 2 17 the calibration factor for the multiple slab model is ki 2 20 N N E S ki A Edet E 0 a d 1 I Edet E 8 Ctot i tan Odu d 2 21 2 2 3 Surface Deposition Model The radionuclides will initially after a deposition be deposited on the surface In this model assumption of uniformly distributed radionuclides on a perfectly flat surface is made This is an ideal model because in reality the radionuclides transported by the atmospheric process will not be distributed uniformly on the surface To determine the calibration factor for a such model take N 1 in equation 2 21 and assume simply that the soil slab is extremely thin The vegetation above the ground surface can be assumed to be one of the slabs in multiple slab model In such cases take N 2 in order to take the vegetation into account 2 2 4 Volume Deposition Model The radioactivity distribution may also be considered as uniform in the soil Therefore the calibration factor for such a model can be obtained by taking N 1 in equation 2 21 If the vegetation above the ground surface is desired to be included take instead N 2 However soon after a radioactive fallout radionuc
24. e corner The standard deviation of Hair is largest when the relative humidity was fixed This means that the relative humidity is the least important parameter Note that the relative humidity describes the relation between the amount of moisture or water and the maximal amount in the air at a certain temperature 19 the higher the relative humidity is the more moist the air is It is known that water has good attenuation ability therefore the relative humidity should have significant impact on Hair However this relation can not be seen in the results from this sensitivity analysis One might use an other description for Hair where the relative humidity has more significance A linear combination of Ugirdry aNd water Might be used compare this idea with equation 2 15 140 120 100 80 60 Counts 40 20 0 0 019 0 02 0 021 0 022 0 023 0 024 0 025 0 026 0 027 0 028 m H air Figure 3 3 Hair for photon energy E 100 keV calculated when the relative humidity was fixed However when determining Hair using equation 2 15 it results in that the relative hu midity is not a significant parameter This means that it has a small contribution to the uncertainty for calculation of the Hair in turn the calculation of the calibration factor Therefore the relative humidity will be designed to be an un sampled parameter in the calibration calculation program Parameters that contribute to the combined uncertainty are shown in
25. e expo nential model might be overestimated and in turn the calibration factor However it is difficult to say how realistic the exponential model is due to the lack of empirical data of the calibration factors The calibration factor calculated using the exponential model will vary depending on the exponential function that was adapted to the data points and also the soil density that was assumed Since soil has a good attenuating ability by assuming homogeneous soil density in depth will result an incorrect estimation of the photon fluence rate and thereby the calibration factor This problem can be reduced by using relaxation mass depth instead of relaxation length 2 23 The calibration factors for exponential model with several relaxation lengths are shown in Figure 4 3 Note that the surface deposition model can also be described as en expo nential model with zero relaxation length The calibration factors are decreasing with increasing relaxation lengths The greater the relaxation length is the deeper the ra dionuclides penetrate into the soil 5 When the radionuclides penetrate deeper in the soil it means that the possibility for them to be detected is lower because the attenuation of the soil Therefore the calibration factors are low for long relaxation lengths Calibration Factor 0 500 1000 1500 Energy keV Figure 4 3 Calibration factors for the exponential model with varying radionuclide relax ation lengths plotted
26. e see figure F 4 m a m mta m a m m a Figure F 4 The probability density functions for uniform and triangular distribution m is the expectation value or the medium and a is the half width of limits Input for the detector distance to the ground Detector Height Enter detector distance to the ground in meters Choose the probability distribution and fill in the half width limits or standard uncertainty Default value for the detector distance to the ground is 1m Expected Value Distribution Detector Conditions Height m 1 Please Choose v Air Conditions Pressure kPa 101 325 Please Choose v Temperature C 20 Please Choose Figure F 5 The panel for detector and air condition inputs Input for the air conditions Pressure Input the air pressure in kPa Choose the probability distribution and fill in the half width limits or stan dard uncertainty Default value for the air pressure is 101 325 kPa Temperature Input the air temperature in C Choose the proba bility distribution and fill in the half width limits or standard uncertainty Default value for the air tem perature is 20 C Input for the vegetation conditions Due to the algebraic limitations the vegetation height must be non zero If there is not any vegetation set the surface mass to zero instead The activity content in the vegetation slab will then be set to zero automatically as well as their ranges or variances Expected Value Distributio
27. ector For ev ery input photon energy the program will provide the measurement efficiency including its combined uncertainty and also the detector s field of view A graphical user interface was constructed in MatLab in order to give a more user friendly program Fluctuations of the ground surface influence the measurement results and are difficult to handle 3 In this work the surface is assumed to be perfectly plane the activity and the density distribution in any compartment in the soil are assumed to be homogeneously distributed and any object above the ground is not included in the models 2 Theory The following theories give basic knowledge about in situ gamma ray spectrometry and hence a deeper understanding of the development of different models In later part of this chapter there is some information about statistics used in this project 2 1 Gamma Ray Spectrometry Monoenergetic photons that traveling though a uniform material attenuate according to an exponential function 2 IT Ipe 2 1 where J is the number of photons transmitted without change of the original energy Io is the number of original photons u is the linear attenuation coefficient with dimension m7 and r is the length of the path m The mass attenuation coefficient j1 p is also convenient to use because its values can easily be found in databases from e g the National Institute of Standards and Technology NIST 4 2 1 1 Ground Level Gamma Ray Spectr
28. every parameter and they were paired randomly to form input sets to the calculation of Hair Standard deviation were then taken for the airs the parameter that resulted the smallest standard deviation was the most important one Table 3 1 Values used to examine the sensitivity of the linear attenuation coefficient of air 18 19 All parameters were assumed to be uniformly distributed Average Limits Pressure kPa 100 10 Temperature C 5 20 Relative humidity 80 20 3 1 1 Results and Discussions The results of sensitivity analysis of Hair are shown in Figure 3 1 3 2 and 3 3 Similar figures for two other photon energies can be found in Appendix B The standard devia tions for respective results are also shown in the figures It is shown that the Hairs for fixed air pressure were least dispersed which means that the air pressure is the most important parameter for the Hair calculation 80 s 0 00097337 60 40 Counts 20 0 0 0215 0 022 0 0225 0 023 0 0235 0 024 0 0245 0 025 0 0255 1 H air m Figure 3 1 Hair for photon energy E 100 keV calculated when the pressure was fixed The standard deviation of the results is shown in the corner 16 80 s 0 0013464 60 2 54 a 0 O 20 0 0 02 0 021 0 022 0 023 0 024 0 025 0 026 1 H air m Figure 3 2 Mair for photon energy E 100keV calculated when the temperature was fixed The standard deviation of the results is shown in th
29. every slab Enter the values as a list separated by space or comma When you fill in the number of slabs the software will remind you how to enter the soil conditions Expected Value Distribution Soil Slab Conditions Thickness m 0 02 Please Choose Densi oe 500 Please Choose v Activity Content Bqim43 Please Choose v Figure F 7 The panel for soil condition inputs for the volume deposition model Thickness Enter the soil slab thickness in m Choose the prob ability distribution and fill in the half width limits or standard uncertainty Density Enter the density in kg m Choose the probability distribution and fill in the half width limits or stan dard uncertainty Activity Content Enter the activity content in Bq m or relative activity content in the soil slab or slabs Choose the prob ability distribution and fill in the half width limits or standard uncertainty Input for the exponential model In this case activities penetrate exponentially into the soil The vegetation contains no activity The soil density is assumed to be uniformly distributed Relaxation Length Enter the relaxation length in cm Choose the prob ability distribution and fill in the half width limits or standard uncertainty Calculations For parameters that consist of uncertainties the expectation nominal values are used for calculation of the calibration factor and the detector field of view This means that both the calibration factor
30. he uncertainty of the soil density in each 29 section can be lowered Due to the lowered uncertainties the combined uncertainty for the multiple slabs model is much lower compare to the emergency preparedness model even though there are more input quantities that are associated with uncertainties 4 4 Graphical User Interface User friendly graphical user interfaces GUIs were designed for each deposition model Figure 4 10 shows one of the GUIs The GUIs have similar appearance and the execution options are the same for all of the models Input quantities that can be sampled are shown in Table 3 2 For every input photon energy the program provides the calibration factor and the detector s field of view in external figures The combined uncertainty is saved as a text file tzt for further use More details about the program can be found in the User Manual in appendix F F Volume Calibration Calculation for Volume Deposition Model Expectation Value Distribution Detector Conditions Enter a list separated by space or comma Height m 1 Please Choose Choose default values TO Default Energies Pressure kPa 101 325 Please Choose Temperature C 20 Please Choose POOE ESEN Vegetation Conditions Detector Name Type the Detector Name Here Height m Please Choose Default Detector Surface Mass A Please Choose Contribution of Counts Ikgim 2 95 Activity Content Bqim 3 Please Choose Combined Uncertianty Numbe
31. hese all other conditions were taken the same for all models Energy keV Detector Field of View m Surface dep Preparedness Multi slabs Exponential 100 50 56 17 82 14 00 122 56 14 19 59 12 88 15 29 140 60 32 20 88 13 68 16 24 160 64 63 22 17 14 49 17 19 180 78 62 23 36 15 22 18 05 200 72 34 24 46 15 89 18 84 244 79 74 26 61 17 13 20 39 344 93 70 30 63 19 52 23 20 444 105 10 33 87 21 34 25 41 661 124 91 39 43 24 32 29 09 779 134 00 41 93 25 62 30 70 867 140 06 43 62 26 49 31 79 964 146 38 45 37 27 37 32 90 1086 153 76 47 40 28 38 34 18 1112 155 27 47 82 28 58 34 44 1408 170 90 52 14 30 70 37 12 41 Appendix E Table E 1 The combined uncertainty k 1 for the calibration factor calculation for some typical photon energies based on total 500 calculations Energy keV Combined Uncertainty Surface dep Preparedness Multi slabs 122 4 46 37 45 6 23 344 4 14 32 16 5 68 661 4 28 29 29 5 41 779 4 27 28 62 5 35 964 4 27 27 78 5 28 1112 4 26 27 73 5 23 Table E 2 The combined uncertainty k 1 for the calibration factor calculation for some typical photon energies based on total 1000 calculations Energy keV Combined Uncertainty Surface dep Preparedness Multi slabs 122 4 47 37 09 6 20 344 4 37 31 80 5 66 661 4 30 28 95 5 39 779 4 30 28 28 5 33 964 4 26 27 44 5 26 1112 4 25 26 90 5 21 42 Table E 3 The combined uncertainty k 1 for the calibr
32. ides may penetrate a bit into the ground In order to get a quick result of the calibration factor for a so called emergency preparedness model 10 values in table 2 1 are assumed Table 2 1 Values used in calibration factor calculation for the emergency preparedness model Ingnore the last three values and set the relative activity content in the soil to 100 if there is no vegetation Parameter Value Soil layer thickness m 0 02 Soil density kg m3 500 Relative activity content 70 Vegetation height m 0 1 Surface mass kg m 0 5 Relative activity content 30 2 2 5 Exponential Model Another model that may be applied in in situ gamma ray spectrometry is when the concentration of radionuclides can be assumed to decrease exponentially with depth 5 A z Ape 2 22 where Ao is the activity on the ground surface in unit Bq m and a the reciprocal of the relaxation length of unit m for the radioactivity in the soil It is convenient to make a projection of the total activity in the soil on the surface by integration of equation 2 22 from 0 to co which gives Aa Ao a Insert equation 2 22 in equation 2 6 and set again r H z tan 0 The fluence rate is then obtained 1 dy P E aAge tan 0C E d dz 2 23 The attenuation factor above the ground is determined by an equivalent attenuation coefficient My My Ls Hair 120 2 24 Heq Te arr Hpm0 2 and the fluence ra
33. ie amp WANN CHALMERS x as UNIVERSITY OF TECHNOLOGY Software for Calibration in Gamma Ray Spectrometric n situ Measurements Master s thesis in Nuclear Engineering YE YUAN JOSEFSSON Department of Chemical and Biological Engineering CHALMERS UNIVERSITY OF TECHNOLOGY Gothenburg Sweden 2014 Software for Calibration in Gamma Ray Spectrometric In situ Measurements YE YUAN JOSEFSSON Department of Chemical and Biological Engineering CHALMERS UNIVERSITY OF TECHNOLOGY Gothenburg Sweden 2014 Master s Thesis Software for Calibration in Gamma Ray Spectrometric In situ Measurements YE YUAN JOSEFSSON OYE YUAN JOSEFSSON 2014 Department of Chemical and Biological Engineering Division of Nuclear Chemistry CHALMERS UNIVERSITY OF TECHNOLOGY SE 412 96 Gothenburg Sweden Telephone 46 0 31 772 10000 Abstract A gamma ray spectrometric measurement on site or in situ in Latin can identify and quantify the radionuclides after a radioactive fall out and provide results quickly The efficiency of such a measurement also called the calibration factor is depending on many parameters on the site These parameters may consist of uncertainties and the quality of the measurement result is given by the combined uncertainty A software including graphical user interfaces was developed in MatLab R2014b to provide the calibration factor and its combined uncertainty for in situ gamma ray spec trometric measureme
34. iew for corresponding energies is opened Change Model Back to the main menu for model change Exit Exit the GUI and the software shuts down How to Enter Input Data Follow the advice below in order to avoid any unsuccessful calculations Figure F 3 show the left part of a GUI Photon Property Energy Enter a list separated by space or comma Choose default values D Default Energies Detector Property Relative Humidity Detector Name Type the Detector Name Here 80 Combined Uncertianty Default Detector Contribution of Counts 95 Number of Calculations per Simiation Save the Uncertainty Result Number of Simulations Type the File Name Here Please remember the file name Figure F 3 The left part of a GUI Input for the photon property Energy Input desired photon energies as a list separated by space or comma in the unit keV Defaults Choose the preprogrammed photon energies by pressing the radio but tons The default energies are 100 122 140 160 180 200 244 344 444 661 779 867 964 1086 1112 1408 keV These energies will be displayed in the boxes under the input boxes for energy Please do not change any number in this box Input for the detector name Due to the fact that all detectors are unique the detector efficiency will depend on the detector characteristic Default detector in this case is a HPGe detector made by Ortec Inc USA Detector Name Input the name of the detector Default
35. ill converge towards the expec tation value as the number of samples increases i e 1 E X Xn lim 5 X 2 38 Consider that the PDF for every input quantity is stratified in N intervals then N calibration factors CF will be obtained after calculations According to the LLN the estimate of the CF will converge towards the expectation value of the CF when N gt oo Also the estimation of the uncertainty of the CF will converge towards the standard deviation of the CF The relative uncertainty associated with calculations described in Equation 2 37 can be determined by the ratio between the standard deviation of the CF and the expectation value of the CF i e Ucalculation Sn Yn 2 39 14 3 Method Initially a simple sensitivity analysis was performed for the linear attenuation coeffi cient of air in order to reduce the amount of input quantities if possible Models for the calibration factor calculation with different deposition types were implemented in MatLab version R2014b together with other necessary functions The models were then modified to be able to be used for different purposes Some user friendly graphical user interfaces GUIs were build using a build in interactive GUI construction kit the GUI development environment GUIDE To generate sample sets using the LHS method build in MatLab functions were used with some modifications By assuming independence between all parameters the co variance
36. inties The combined uncertainties are shown in Table E 1 E 2 and E 3 which can be found tables in Appendix E In order to obtain the combined uncertainty associated to the cal culation based on the surface deposition model and the emergency preparedness model values in Table 4 2 were used For calculation based on the multiple slabs model values 28 for soil conditions were taking from an earlier study 7 while the other conditions were taking as shown in Table 4 2 Table 4 2 Values used in the combined uncertainty investigation for the surface deposi tion model respective the emergency preparedness model Parameters were assumed to be uniformly distributed Parameter Medium Limits Pressure kPa 100 5 Temperature C 7 5 22 5 Relative humidity 80 0 Detector height m 1 0 05 Soil density kg m3 900 800 Soil slab thickness m 0 03 0 02 Activity content in soil 100 0 For the surface deposition model the combined uncertainties for the whole calibration measurement were between 4 2 to 4 9 k 1 depending of the photon energy and the number of calculations performed Note that the uncertainty contribution from the detector efficiency determination was 4 This means that the contribution of the un certainty associated with the calibration factor calculation to the combined uncertainty is very small because there are only uncertainties in the detector efficiency calibration the air density and the
37. ion of the sample is also given Figure 2 3 shows two input sets containing samples that were generated according to the MC method respective the LHS method Both parameter A and B were assumed to distribute according to the uniform distribution U 0 1 As can be seen in Figure 2 3 the inputs generated according to the LHS method are more dispersed over the whole sample space and each stratification for the these two parameters had been represented once In this way clusters in the output set can be avoided 12 Parameter B 0 0 2 0 4 0 6 0 8 1 Parameter A Figure 2 3 Two input sets containing 70 samples generated according to the MC method respective the LHS method Both parameter A and B were assumed to distribute uniformly between 0 and 1 2 3 3 Uncertainty Analysis The total uncertainty of the calibration factor consists of two components the com bined uncertainty of the detector efficiency calculation and the uncertainty from the calculations According to Equation 2 32 the total uncertainty can be determined by 2 n2 2 Utotal Udetector Ucalculation 2 37 The combined uncertainty of the detector efficiency is a Type B uncertainty and was calculated to be 4 6 In order to determine the uncertainty from calculations the following two concepts are useful 13 Law of Large Numbers 17 The Law of Large Numbers LLN is a mathematical formulation which states that the sample mean of random variables X w
38. lations per simulation was investigated for energies E 100 779 1048 keV in order to get an idea about how the relative uncertainty in the uncertainty associated with the calculation of the CF varies with different combina 18 tions The investigation was performed using the emergency preparedness model with inputs according to table 3 3 All parameter values were assumed to be uniformly distributed For definition of the half width of limit see figure 3 4 Table 3 3 Values used in the accuracy investigation All parameter values were assumed to be uniformly distributed Parameter Medium Half width of limits Pressure kPa 100 5 Temperature C 20 10 Relative humidity 80 0 Detector distance to the ground m 1 0 05 Veg height m 0 Surface mass ke m 0 Activity content in veg 0 Soil density ke m 3 900 800 Soil slab thickness m 0 03 0 02 Activity content in soil 100 0 m a m m a m a m m a Figure 3 4 The probability density functions for uniform and triangular distribution m is the expectation value or the medium and a is the half width of limits 3 2 1 Results and Discussions Figure 3 5 shows the relative uncertainty of the combined uncertainty associated with the calibration factor The number of calculations per simulation and the number of simulations were varied It is possible to see in Figure 3 5 that the relative uncertainty 19 of the combined uncertainty is lower for large
39. lt values in some of the boxes the calculations will be performed using these values if you do not change them E Volume Calibration Calculation for Volume Deposition Model Expectation Value Distribution Detector Conditions Enter a list separated by space or comma Height m 1 Please Choose Choose default values Air Conditions Default Energies Pressure kPa 101 325 Please Choose Temperature C 20 Please Choose Detector Property Relative Humidity Detector Name Type the Detector Name Here 80 Combined Uncertianty Vegetation Conditions Height m Please Choose Default Detector Surface Mass Contribution of Counts kgim 2 Activity Content Bqim43 Please Choose Please Choose Number of Calculations per Simlation Soil Slab Conditions Save the Uncertainty Result Thickness m Please Choose Density a E E Type the File Name Here ad Please Choose Please remember the file name Activity Content rete i Please Choose Figure F 2 User interface for a volume deposition model There are always five execution options see the colored push buttons in figure F 2 Their functions are described briefly below Plot Calibration Factors An external window with plot of calibration fac tor versus photon energy is opened Do Uncertainty Analysis Simulate the combined standard uncertainty for each input energy Detector Field of View An external window with a table showing the detector field of v
40. n Vegetation Conditions Height m 0 1 Please Choose v Surface Mass kgim 2 Please Choose v Activity Content Bq m 3 Please Choose Figure F 6 An example of the panel for vegetation condition inputs Height Surface Mass Activity Content Input the vegetation height in meters Choose the probability distribution and fill in the half width lim its or standard uncertainty Default value for the veg etation height is 0 1m Input the surface mass in kg m Choose the proba bility distribution and fill in the half width limits or standard uncertainty Set surface mass to 0kg m if there is not any vegetation on the ground Input the activity content in Bq m or proportion in the vegetation slab Choose the probability distribu tion and fill in the half width limits or standard un certainty Set activity content to 0 if there is not any activity content in the vegetation on the ground Input for the soil conditions The panels where you enter soil condition inputs have different appearance depending on the selected deposition model The default values will also be different For the surface deposition model the soil slab thickness is infinite small and the soil density is 1000 kg m For the volume deposition model the soil slab thickness is 0 02m and the soil density is 500kg m which are the values for calculation using emergency prepared ness model For multiple slab model the soil condition must be specified for
41. nly one sample is drawn randomly By doing this M samples are taken for each input quantity The order of samples for each input quantity is shuffled randomly Then the samples for each input quantity are randomly paired to form M input sets which in turn give an output set Yk k 1 M The outputs can then be analysed as in the case of using MC method The LHS method has several benefits compared to the MC methods Using LHS the 11 samples with low probability are forced to be represented in the input set In this way clusters in the output set are avoided even if a small number of calculations is performed Earlier study has shown that it requires about 1 3 as many Latin Hypercube iterations as MC iterations to get equal results 16 Comparison between MC and LHS Methods Figure 2 2 shows two sets of sample drawn using MC method respective LHS in his tograms The samples were drawn from the same normal distribution with u 0 and o 1 It can be seen that there is some clusters in the case of using the MC method These clusters may cause clusters in the output set which can affect the statistical properties of the outputs and that is not desirable 30 30 s 0 99971 LHS f 20 2 20 5 10 10 0 0 4 2 0 2 4 4 2 0 2 4 Sample value Sample value Figure 2 2 1 500 samples generated according to the MC method respective the LHS method from the same normal distribution with u 0 and 1 The standard deviat
42. nts The field of view of the detector was also provided by the software Depending on how the radionuclides were deposited on and or in the soil four deposition models were considered in this work In order to estimate the combined uncertainty a numerical approach was used The samples for each input quantities were taken according to the Latin Hypercube Sampling LHS Moreover the samples could be assumed to have either uniform triangular or normal distribution The software gave reliable results about the calibration factor and its combined un certainty Also the detector s field of view that was calculated was reasonable However validations need to be performed for some of the models KEYWORDS 4 spectrometric in situ measurement combined uncertainty Latin Hypercube Sampling Acknowledgements I would like to thank my examiner Chistian Ekberg and my supervisors Henrik Rameb ck and Torbj rn Nyl n for giving me the opportunity to have this interesting project A special thank to my supervisors for rewarding discussions and also advice and help they had given me during the this work I would also like to thank Patrik Fredriksson for helping me with the MatLab Finally I would like to thank my family and my friends for their support Ye Yuan Josefsson Gothenburg January 2015 Contents 1 Introduction ill isl Background scana Yh os aoe hoe fee OR Wee ee Ao Pa heh Ae See 12 gt Purpose 2 5 4 3 Pokey aes Ae ee be RRS
43. number of calculations and also larger number of calculations per simulation Also the relative uncertainties for simulations containing 100 and 120 calculations per simulation did not vary much For increasing number of simulations the relative uncertainty of the combined uncertainty should be decreasing which means better estimation of the combined uncertainty However such trend could not be seen in Figure 3 5 0 1 S 50 per sim 8 80 per sim gt 100 per sim 120 per sim Number of simulations Figure 3 5 The relative uncertainty of the combined uncertainty associated with the calibration factor based on the preparedness model and the photon energy E 100keV The number of calculations per simulation and the number of simulations were varied Tabel 3 4 shows the calculation time and the standard deviation of the standard un certainty associated with the calibration factor for some combinations of calculations As can be seen in the Table 3 4 the standard deviation would not necessarily be re duced when the number of total calculations was increased but the calculation time was increased much Therefore it is up to the user to decide about the the number of calculations per simulation and the number of simulations and thereby the accuracy of the estimation of the combined uncertainty associated with the calibration factor 20 Table 3 4 Calculation results for photon energy E 100keV C
44. ometry The total efficiency also called the calibration factor CF of a detector for in situ measurements can be expressed as 5 N oN M 2 2 A No Ag a where N is the full energy peak count rate in cps No the full energy peak count rate sT for photon incidence that is normal to the detector surface y the fluence rate per unit soil concentration m s or m 3s and A the source activity which can have different dimensions The first ratio on the right hand side can be expressed as a correction factor due to the unparalleled incidence of the photon the second one the peak response and the last one the fluence The photon fluence rate y is depending on the chosen deposition model and will be discussed later in this section 2 1 2 Detector Characteristics The first two ratios in Equation 2 2 can be denoted as the detector efficiency and de pends on the detector characteristics e g detector diameter and length This is often determined empirically for a particular detector For the HPGe detector used in this project the detector efficiency as a function of energy and angle of incidence had been developed by curve fitting of measurement results 6 see Equation 2 3 a Edet 0 E exp ax a20 a30 a4 E r 0 ag cos a aoln E a11 nE 2 3 where a a11 are parameters without physical interpretations 0 is the photon incident angel in rad and E the photon energy in keV The values for the
45. r of Calculations per Simlation Soil Slab Conditions Save the Uncertainty Result Thickness m Please Choose Density Number of Simulations Type the File Name Here Ikgm 3 Please Choose Please remember the file name Activity Content Bqim43 Please Choose Figure 4 10 The GUI for the calculation for the volume deposition model 30 5 Conclusions The designed software calculated the calibration factor well for the surface deposition model and the emergency preparedness model Validation of the calibration factor must be performed for the multiple slabs model and the exponential model The results of the effect of the vegetation and the field of view of the detector were reasonable although validation need to be performed The combined measurement uncertainty based on the surface deposition model was cal culated to be between 4 2 to 4 9 k 1 depending on the photon energy For the emergency preparedness model the total measurement uncertainty was in the range 27 to 37 k 1 depending on the photon energy The high uncertainty in the soil density estimation contributed to a high combined measurement uncertainty when the calculation performed was based on the emergency preparedness model This high uncertainty is due to the fact that the density assumed in the emergency preparedness model should cover many ground types If the density is measured for soil samples the uncertainty of the density will be reduced signifi
46. radioactivity is assumed to be homogeneously distributed on the ground surface e Volume deposition model where the radioactivity is assumed to be homogeneously distributed within a soil volume e Multiple slabs model where the radioactivity containing soil volume is divided in several layers where each layer has a homogeneous activity distribution e Exponential model where the radioactivity is assumed to penetrate into the soil and decreases exponentially 2 2 1 Photon Fluence Rate The fluence rate of the photon at energy E is given by 2 Ay 2 5 where p E is the photon emission probability for energy E in C is the attenuation factor for photon energy E and R is the distance between the source and the detector in m In order to describe the activity contribution more realistically the whole radioactiv ity containing volume can be divided in several sub volumes 7 Each sub volume or slab has individual thickness d uniformly distributed radioactivity and consists of a fraction of the total activity see Figure 2 1 According to Equation 2 5 the fluence rate from an infinitesimal volume is Apl E C E dgy 4r R2 dV 2 6 where A is the activity per unit volume and dV rdrdd dz with as the azimuthal angle When integrating over the azimuthal angle a factor 27 is introduced and the equation above becomes Ayr QR The photon fluence rate which depends on the photon incidence angle can be deter
47. s could be set to zero The samples were generated as vectors except for the soil condition parameters e g the thickness and the density where the samples were generated as matrices In order to be able to use LLN and CLT the number of calculations must be large enough So several tests were done in order to investigate how the relative uncertainty associated with calculations varies with the number of calculations Also how the re lation between the number of iterations and the number of calculations per iteration affects the uncertainties was investigated 3 1 Sensitivity Analysis Sensitivity analysis is performed in order to identify the most important ones among a large number of input parameters In this project how the linear attenuation coefficient of air Hair was affected by its input parameters was examined Hair is a function of the photon energy and is proportional to the air density see Equation 2 15 The air density is in turn depending on three parameters e the air pressure e the air temperature e the relative humidity in the air 15 There are many ways to perform a sensitivity analysis In this project the variation of Mair Was investigated by fixing one of the three parameters of the air density an letting the other two vary The variation range for the three parameters are shown in Table 3 1 and these ranges were chosen to adjust to the Swedish conditions 18 19 10 000 samples were taken using LHS method for
48. se do remember the name of the file File Name Input desired name for the file in where the uncertainty analysis result is saved If the name already exists the content of the old one will be overwritten Other inputs Number of Calcula Enter the desired number of calculations per sim tions per Simulation ulation The probability density functions of every input quantities are divided into the number that is entered here Number of Simulation Enter the desired number of simulations Contribution of Counts Enter the desired field of view in percent The de tector field of view is defined as the radius of a cir cle where the contribution of counts from its area is a certain percentage of the number of the counts from a circle with infinite radius Relative Humidity Enter the relative humidity for the air density cal culation Default value 80 can be used since this parameter does not have a significant effect on the result The middle part of the interface is constructed as a table with three columns A gen eral rule is to first input the expectation value or the nominal value of the parameter Thereafter you choose the distribution in the pop up menus The parameters can have uniform triangular and normal distributions Depending the selected distribution you are asked to enter either the half width of limits or standard uncertainties of the distri bution in the third column For the meaning of half width of limits pleas
49. sults is shown in the corner 38 80 s 0 00038295 40 Counts 20 5 8 6 6 2 6 4 6 6 6 8 7 7 2 7 4 4 ore Hair M x10 Figure B 5 Hair for photon energy E 1048 keV calculated when the temperature was fixed The standard deviation of the results is shown in the corner 150 s 0 00047038 8 m x10 Figure B 6 Hair for photon energy E 1048 keV calculated when the relative humidity was fixed The standard deviation of the results is shown in the corner Appendix C Table C 1 Values from Boson et al 7 that were used to obtain the inout data for the exponential model Slab Thickness Density Fraction of total em kg m activity 1 2 0 1210 80 5 0 1460 16 3 9 4 1720 4 500 z g 400 300 x 200 z 100 0 0 0 02 0 04 0 06 0 08 0 1 0 12 Depth m Figure C 1 Adaption of an exponential function to data points from Boson et al 7 Table C 2 Input values that were used in the exponential model for comparison between the multiple slabs model and the exponential model Density kg m 1500 Ao Bq m 500 Relaxation length m 0 015 40 Appendix D Table D 1 The field of view of the detector corresponding to 95 contribution of full energy peaks for all models Soil conditions for multi slab model were taken from an earlier study 7 Relaxation length was taken as 0 3cm and the soil density 1500kg m for the exponential model Beside t
50. table 3 2 By assuming independence between all parameters their individual contributions to the uncertainty can be determined Set uncertainties of other parameters to zero the devi ation of the results will then only come from the parameter in question Table 3 2 table showing whether the parameter is contributing or not to the uncertainty of the calibration factor for different models The y indicates Yes and x No Parameters Models Surface Volume Multiple slabs Exponential Detector height Air pressure Air temperature Vegetation height Surface mass Activity content in veg Soil slab thickness Soil density KORA i Re Se SG ee Ae a es S hs seg RL EAER XR K K RARAS Activity content in soil 3 2 Accuracy Investigation As described in section 2 3 3 the relative uncertainty associated with the calculations can be obtained by using Equation 2 39 However the estimate of the uncertainty is depending on how many calculations that are performed The more calculations that are performed the better estimation of the uncertainty Therefore in the calibration software there has to be a compromise between time and accuracy According to the LLN both the number of iterations and the number of calculations per iteration should be large However it is not realistic to spend too long time to perform CF determination calculation for in situ spectrometry measurements Different combination of simulations and calcu
51. te can be rewritten as p E aAa a acos soil dy 5 Ceq H exp z tan 6d dz 2 25 cos 0 Integrating z from 0 to oo the previous equation becomes p E aAasin 2 a cos soit dy Coq H d0 2 26 and finally the calibration factor for the exponential model is N 7 2 p E sin8 Ag et Bi O Ceql Had 2 2 Aa i 2 cos 0 aay I E 0 Ceq H d 2 27 2 3 Statistics and Data Analysis First of all two important statistical quantities are defined For total N samples the sample mean and the sample variance are pak B a 2 28 ea and 1 x 2 ay J mi z 2 2 Oy Zo T 2 29 In many measurements the measurand is not measured directly but is expressed as a function of other measurement quantities In practice a measurement result is only an estimate of the value of the measurand Therefore the uncertainty of that estimate must be included to give a complete measurement result 11 Assume that the measurand Y can be written as a function of measurement quantities X1 X2 XN VS FOG A co XN 2 30 After N identical measurements the estimate of Y can be taken as the mean of Y 1 n DA Yp 2 31 ea i l Further assume that every input estimate of measurement quantity X consists of a standard uncertainty u 2 This uncertainty can be of Type A which is obtained by the statistical analysis of series of observations and Type B which is obtained by other methods than the statistical an
52. tion of water 3 Con sider a vegetation height of h in m and the mass per unit area of m kg m Further assume that the density of the vegetation is ppo when compressed Then the attenua tion coefficient can be expressed as My My e ee a hie a 2 13 we mts ne E 2 219 The observed values for linear attenuation coefficient for water and air 4 0 and air respectively can be found in the NIST database 4 The following equation was obtained after plotting values in log log scale and then a curve fitting was applied For photon energy E in MeV the upo is umol E 100exrp 0 04 InE 0 48InE 2 65 2 14 The Hair is described as Equation 2 15 taken from Boson et al 7 Hair E pair0 0623E 4 2 15 These us are given in m7 and pair in kg m The air density is assume to be a function depending on three parameters 9 the air pressure P given in kPa the temperature T in C and the relative humidity h in a 3 348444 parameters b 2 52 1075 2 16 c 2 0582 1074 aP bT c h T 273 16 Pair To summarize the photon fluence contribution from slab 7 with thickness d can then be expressed as Apl E pi Ae f Crot tan Odu dd 2 17 with integration intervals lt u lt di Osu lt di 2 18 0 lt 6 lt 7 2 2 2 2 Multiple Slabs Model The activity in each slab can be written in terms of total activity per unit area A The relation between the surface activity and the volum
53. ton enters the depleted layer in the detector crystal electron hole pairs are formed and thereby charged are created which are collected and a signal can be measured for its amplitude This amplitude is proportional to the energy of the incoming gamma photon 1 However in order to achieve reliable measurement result with respect to activity the efficiency of an HPGe detector needs to be calibrated for different gamma energies In order to calibrate an HPGe detector in a laboratory a standard solution containing a mixture of known radionuclides is often used For an in situ measurement the calibra tion is more difficult to perform because a source with known activity is not always available Moreover the measurement result on site depends on many parameters which may contain uncertainty and the combined measurement uncertainty is a measure of the quality of the measurement result 1 2 Purpose In this project the total efficiency of an in situ gamma ray spectrometry measurement was calibrated for models with different radionuclide deposition models i e how the radioactivity is distributed in and or on the ground This efficiency is for a specific detector a function of incoming photon energy and its angle of incidence Moreover since the measurement uncertainty is an important component of the measurement result this is also calculated by the software 1 3 Scope A MatLab program was designed for efficiency calculations of an HPGe det
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