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Section II: Dose Rates and How They Are Obtained

The rate at which trapped electrons are accumulated is proportional to the energy absorbed during burial. Several components are needed for an accurate DR; 1). measurement of K , U, Th and Rb 2). calculation of moisture content in field at time of collection and saturation potential of the sample sediment and 3). cosmic ray component calculation.

DR's are taken from the combination of material around each site to be dated. These include neutron activation (INAA), atomic absorption, X-ray fluorescence (XRF), flame photometry (K only) and inductively coupled plasma mass spectrometry (ICP-MS). The fundamental disadvantage of these methods is they do not account for U and Th being in disequilibrium.

Equilibrium can be checked by using alpha spectrometry or high-resolution gamma spectrometry, since these methods measure the activities of several individual radionuclides in the decay chains. Usually the facilities required for these techniques are expensive and measurement time can be long.

Another routine approach that minimizes possible error due to disequilibrium is thick source alpha counting (TSAC) which determines the Th and U and the K as above. TSAC can also be used to count only for alpha contribution and the beta contribution can be determined by a beta TLD or particle counter (high sensitivity TL dosimetry phosphor).

The method in use at the USGS lab is gamma ray spectrometry, due to an inherited collection of NaI crystals from radioactive chemistry labs. High-resolution gamma-spectrometry is carried out on a 600-gram sample (the ideal weight since less material means higher counting errors); admittedly a lot of sample, but the crystals date from the early 1980's. However, this amount of sample more adequately represents the variations and mix that the collected sample might have absorbed during deposition, rather than relying on the one or two gram quantity normally counted in other techniques. Apart from elemental quantification, this technique enables the checking of radioactive equilibrium (see assumption #1). The samples are measured on four (4) different crystals for ten (10) hours per crystal.

Moisture and radon migrations are not factors because the bulk sample has been dried and sealed for a month and radon allowed to equilibrate before counting. We collect gamma spectra and then fitted to standard spectra of K , U, and Th using the least square criterion. Elements measured in standard materials provide quality assurance as they run alongside the unknown samples. Comparisons between the USGS luminescence laboratory and published NBS (now NIST) and USGS Open-Files literature values for these standards show excellent agreement. Most of the scatter can be attributed to counting statistics.

Occasionally, the lab will compare the K concentration of samples using X-ray fluorescence (XRF). General agreement, within 1 sigma, provides another check on secular equilibrium. If the lab suspects the sample to be high in Rb, this element will be analyzed on the XRF as well.

It is most desirable to measure the gamma dose-rate on-site. This is so that if there is any doubt about uniformity of radioactivity within the 30-cm sphere of influence of the surrounding sample, the readings will show such variations, even if a laboratory high-resolution gamma spectrometer is available to count after collection. The USGS lab keeps a portable NaI crystal for this purpose and will loan it out if the USGS scientist is unable to collect the samples. The sample site should be counted for an hour or more, to provide high resolution and account for present field moisture or large stones. The lab crystals are unable to reproduce moisture conditions or stone placement, since the sample is usually dried and sieved before measurement.

The annual DR to the sample is computed from the concentrations of K , U and Th by the method described in several literature sources, Aitken, 1985 (Thermoluminescence Dating, M.J. Aitken, 1985, Academic Press, London, pp. 10-12 and pp. 282-288). The lab initially assumes secular equilibrium in the U decay series, unless comparisons in randomly picked samples show otherwise. The measurements must now include alpha, beta, and cosmic radiation and factor in the reduced effect of alpha radiation relative to gamma and beta radiation. Annual radiation doses in Gy/Ka taken from Aitken, 1985 are adapted as shown in Table 1.

Table 1
	Alpha	Beta	Gamma
1% Rb	--------	4.00	--------
1% K	--------	0.83	0.24
1 ppm U	2.78	0.15	0.11
1 ppm Th	0.74	0.03	0.05

A reasonable estimate is made of the moisture content through geologic time with the understanding that this estimate carries a large uncertainty. Ages are calculated using field moisture percentage, unless unusual conditions prevailed at the time of sample collection, i.e. sustained rain over a period of time, drought or human disturbance. Water attenuation corrections for each type of radiation are made using moisture correction factors taken from Aitken, 1985. The actual equations used can be found in USGS Open-File Report 94-249 pp.18-21.

In comparison with silicates, water has a significantly higher mass absorption coefficient for alpha, beta and gamma rays, but negligible radioactivity; hence it more or less attenuates the DR and can significantly change the radiation a sample may have absorbed. Therefore, the lab also calculates ages based on the sample being fully saturated. In the final report there will be listed a "halfway" value; that is the sample moisture content may have had dry and wet frequencies during deposition of unknown duration, but somewhere between conditions at time of collection and a fully saturated value. There will be three ages listed for each sample for each technique, each age corresponding to a different water moisture value. It is the client's prerogative to quote which age best fits their carefully researched scenario.

The lab then calculates the dose rates for element/radiation combination using the annual radiation doses in Table 1, the corrections for attenuation of water, and the alpha k-effective value (0.10 ± 0.03). (Equations can be seen in USGS Open-File Report 94-249 pp. 18). The dose rate for the various element/radiation combination are combined to give the dose rates for the radioelements as follows:

Rb, K , U, and Th for the three types of radiation.">

Table 2
	Alpha	Beta	Gamma
Total DR Rb	--------	DR Rb	--------
Total DR K	--------	DR K	DR K
Total DR U	DR U	DR U	DR U
Total DR Th	DR Th	DR Th	DR Th

The final component of cosmic ray value is added now to the dose rate calculations. The value, 0.291 Gy/Ka, is the cosmic ray dose at sea level and latitude 38° South and is taken from Prescott and Hutton, 1988. This value is valid for latitude greater than 40°, but must be corrected for the sample elevation above sea level and depth within the sediment. Aitken, 1985 p. 298 present a graph of the elevation factor versus elevation for different latitudes. The low elevation portion of the curve (about 3,000 meters or 9,000 feet.) is approximately linear with slopes shown in Table 3.

Table 3
Latitude	Slope
>40°	8.2-5/foot
25°	6.1-5/foot
0°	4.0-5/foot

Values for the depth factor are taken from Prescott and Hutton, 1988 and may be read from USGS Open-File Report 94-249, p. 19. Finally, the total DR of the sample is computed using DR of cosmic ray, DR of Rb, DR of U, DR of Th and DR of K .

Errors are calculated in a separate program to 2 sigma, using standard formulas from Taylor, 1982 (An Introduction to Error Analyses, University Science Books, 1982, pp. 148-150).

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