## Measurement techniques

Measuring techniques depend on the tracers’ radiological characteristics (beta, gamma or stable chemical ones), but all of them include some sample treatment prior to undertaking the measurement itself.

When counting a radioactive sample, it is well known that the instrument reading is a measure of the sample activity plus the background activity. The latter must be subtracted in order to evaluate the actual net sample activity. The background activity is usually taken to be the activity measured by using the sample taken before the injection (blank sample). If, however, the tracer does not appear immediately (there are no canalizations), a more representative value of the background activity is obtained by measuring several of the samples and averaging the results, taking into account that the more samples, the lower the background’s variation coefficient will be. The variation coefficient is the ratio between the standard deviation and the mean value.

Radioactive decay is an inherently random phenomenon that follows, strictly speaking, the binomial distribution. Nevertheless, the Poisson distribution is an excellent approach that takes into account some of the radioactive decay characteristics (the random event ‘disintegration’ is repeated many times and the individual probability of an atom disintegrating is very low).

Poisson distribution depends on just one parameter, generally symbolized by the Greek letter a and the distribution mean value and the variance are both equal to a This property is very useful in radioactive measurements. Once the count rate has been determined, its numerical value can be used as the expected average value and its square root as the standard deviation.

Furthermore, in the case that the number of events approaches infinity, the binomial distribution and the Poisson distribution converge towards anothers statistical distribution known as the normal distribution or Gaussian distribution, which is continuous and symmetrical around its mean value. In a normal distribution, the probability for the random variable to take values close to the mean value is very high while it approaches, asymptotically, zero for large values located in the positive and negative distribution ‘tails’.

As a ‘rule of thumb’ it is common to require that all random variable values fall within a 2.0 standard deviation interval around the mean value. In such a case, a confidence level of 95% for the measurement is established. This means that there is a 5% probability that the ‘true’ mean value is outside the range given by the measured mean value by +2.0 and -2.0 standard deviations. Consequently, two measurements may be said to belong to different populations when their measured mean values differ by at least five standard deviations. This criterion is also applied to determine whether a sample is active or not, namely, that a sample has some radioactivity of its own when its count rate is five standard deviations greater that the background.

Generally, the following condition is established to calculate the lower detection limit (minimal detectable concentration), LD, on the basis of the instrument background:

RN > 2 SRB (5)

This means that the sample count rate should be at least twice its own standard deviation in order to be distinguished from the background. The standard deviation is given by the following expression:    (6)

where

<rRN is the standard deviation for the net count rate RN (cps);

Rg is the gross count rate (cps);

tc is the counting time (s);

RB is the background count rate (cps).    After some operations and approximations the following expression is obtained for LD:

where

Ld is the lower detection limit (or minimum detectable activity concentration)

(Bq/L);

RB is the background count rate (cps);

tc is the counting time;

є is the detection efficiency (counts per disintegration);

V is the sample volume.

As a consequence of statistical dispersion, some preprocessing of experimental data is usually needed in addition to the subtraction of background values in order to filter noise and smooth the response curves.

Finally, radioactive decay correction is needed, although in the case of tritium its half-life is long enough to avoid this kind of correction when the sampling periods last only a few months. In a general situation, an interwell study implies more than a year of sampling and tritium decays at a rate of 0.45% per month.