This JavaScript calculator demonstrates the process of calculating equivalent ground concentrations of potassium (K), uranium (U) and thorium (Th) from measured raw count rates and spectrometer/system constants.

This calculator is for educational/demonstration purposes only. A complete description of the techniques for processing gamma-ray spectrometry data can be found in:

1. The top two sections (Spectrometer/system constants & Measured field data) are already pre-filled with sample values. Note that these values are specific to a particular system (consisting of a spectrometer, set of NaI detectors and an aircraft) and can not be used on other systems. Proper calibration is required.

2. You can modify any of the values in the top two sections if you wish to experiment with different values.

3. Press the Calculate button in the third section to calculate the equivalent ground concentrations.

4. The Spectrometer/system constants can be reset to the original values with the Restore constants button. The Measured field data can be reset to the original values with the Restore data button.

5. HTML/JavaScript limitations:
   • Read-only/display-only fields are not available. Although the values in the Calculate concentrations section can be edited, the changes are ignored and are always over-written with calculated values when the Calculate button is clicked.
   • Functions to format floating-point numbers are limited: I have made an arbitrary decision to display results with 2 decimal places.

Spectrometer/system constants

Stripping ratios at ground level α:    a: β:    b: γ:    g: The forward (α,β,γ) and reverse (a,b,g) stripping ratios are used to correct for Compton scattering. The ratios are obtained by calibrating the spectrometer+aircraft package using calibration pads of known concentrations. These values are applicable to 'infinite' sources at ground level. Variation (increase) of stripping ratios with height above ground α:  /m β:  /m γ:  /m At increased height, the additional air mass between detector and source causes more Compton scattering to lower energies, so the forward stripping ratios (α,β,γ) are higher. The corresponding decrease in reverse stripping ratios (a,b,g) is negligible. Sensitivities Survey height:  m K:  cps/% U:  cps/ppm Th:  cps/ppm The sensitivities are valid only for a specific (planned) survey height (terrain clearance). During the calibration procedure, a series of measurements is obtained at various heights (60-200 m) over a test strip (using the same spectrometer+aircraft package that will be used in the actual survey). These data are compared to the equivalent ground concentrations (obtained from ground measurements using a properly-calibrated spectrometer) and the sensitivities are calculated for the planned survey height (typically ~120 m). Attenuation of count rate with increasing height K:  /m U:  /m Th:  /m Count rates decrease with distance from source. The attenuation factors are obtained by making measurements over a test strip (see above) over the range of possible flying heights (i.e. 60-200 m).

Measured field data

Background count rate K:  cps U:  cps Th:  cps Background count rates are measured by flying over a body of water such as a small lake or a wide river. The background counts include contributions from the aircraft, radon and cosmic scattering. In areas with no water, background count rates can also be determined using upward-looking detectors. Measured count rate K:  cps U:  cps Th:  cps The measured counts depend on the volume of the detectors (NaI crystals) and the terrain clearance, and include contributions from the background (radon, aircraft, cosmic scattering) and of course, the source (geological or man-made, such as a nuclear reactor). Other measured values Radar altimeter:  m Ambient temperature:  C Barometric pressure:  kPa The ambient temperature and pressure are required for correction of the measured radar altimeter to STP.

Calculate concentrations

1. Subtract background count rate from measured count rate K:  cps U:  cps Th:  cps This removes the background counts attributable to the aircraft, radon and cosmic scattering. 2. Radar altimeter at STP (0 C, 101.325 kPa) STP altimeter:  m The radar altimeter (terrain clearance or height) is corrected to STP using the measured temperature and pressure. 3. Stripping ratios at observed STP height α: β: γ: The stripping ratios obtained from the calibration procedure are only applicable at ground level, so higher stripping ratios are computed which are valid at the observed STP height. 4. Apply stripping ratios to background-corrected counts K:  cps U:  cps Th:  cps Application of the forward & reverse stripping ratios to the measured count rates is a complex mathemetical procedure described by: 5. Apply attenuation factors (to adjust for variation from planned survey height) Δh:  m K:  cps U:  cps Th:  cps Since the sensitivities are only applicable at the planned survey height, the count rates at the observed height must be adjusted to equivalent values at the planned survey height. Counts measured below the planned survey height will be higher than those that would have been measured at the planned survey height. 6. Apply sensitivities to compute equivalent ground concentrations K:  % eU:  ppm eTh:  ppm The final corrected count rates are converted to equivalent ground concentrations using the sensitivities acquired during the calibration. Note that negative values are not necessarily 'wrong', even though a negative concentration is physically impossible. Gamma-ray spectrometry measures a statistical process and negative values are a legitimate part of the set of calculated data values. The statistics of the data set will be skewed if negative values are set to 0. There is valuable information in the presence, magnitude and number of negative values: it might indicate an error in stripping ratios (calibration), a questionable background value, or a damaged detector (crystal). 7. Useful derived ratios for analysis eU/eTh: eU/K: ppm/% eTh/K: ppm/% The relative concentrations of K, U, Th are useful diagnostics for analyzing the survey data.