WellCAD Basics - Advanced Logic Technology

1.5.13.7 Window Based Model
BOOK 1 - WELLCAD BASICS - 159
the model information and measured data set. For further information about the
window based model refer to 1.5.13.7 Window Based Model.
Theory of calibration and computation of elemental content
The natural spectral gamma tool calibration involves the measuring of the counting
rates in different enriched zones of a calibration pit. For each zone the
concentration of radioactive isotope must be known. The counting rates are read out
of designated energy windows of the recorded spectrum. From the known
concentrations and measured counting rates a set of calibration coefficients can be
computed. These are applied later to the counting rates measured in the field to
determine a concentration of isotopes.
Calibration:
The counting rate in window i and when the tool is placed in zone j is called W ij .
For a KUT (Potassium, Uranium and Thorium) calibration model these counting
rates are related to the contents of K j , U j , Th j by the linear equations:
W � a K � bU
� c Th
ij
i
j
Where K j , U j , Th j are known (actually it is the concentrations of daughter products
or isotopes that are known, e.g. K-40, Ra-226 and Th-232) and W ij is measured.
Assuming 3 enriched zones and 3 energy windows we will get 9 coefficients a i , b i
,c i which can be computed from the 3 equations system:
Wi1 ai
K1
� biU1
� ci
i
� Th (Zone 1)
Wi 2 aiK
2 � biU
2 � ci
� Th (Zone 2)
Wi3 ai
K3
� biU
3 � ci
� Th (Zone 3)
The determination of these 9 coefficients (if 5 energy windows would be used there
would be 15 coefficients) can be considered as the master calibration of the tool.
The coefficients are combined in a calibration matrix:
� a
�
K
� �a
�
� a
1
2
3
b
b
b
1
2
3
j
1
2
3
c1
�
�
c2
�
c �
3 �
i
j