<p>Lu-Hf isotopic analysis of zircon is becoming a common way to characterise the source signature of granite. The data are collected by MC-LA-ICP-MS (multi-collector laser ablation inductively coupled plasma mass spectrometry) as a series of spot analyses on a number of zircons from a single sample. These data are often plotted as spot analyses, and variable significance is attributed to extreme values, and amount of scatter.

<p>Lu-Hf data is used to understand the origin of granites, and often a distribution of εHf values is interpreted to derive from heterogeneity in the source or from mixing processes. As with any physical measurement, however, before the data are used to describe geologic processes, care ought to be taken to account for sources of analytical variability. The null hypothesis of any dataset is that there is no difference between measurements that cannot be explained by analytical uncertainty. This null hypothesis must then be disproven using common statistical methods.

<p>There are many sources of uncertainty in any analytical method. First is the uncertainty associated with the counting statistics of each analysis. This uncertainty is usually recorded as the SE (standard error) uncertainty attributed to each spot. This uncertainty commonly underestimates the total uncertainty of the population, as it only contains information about the consistency of the measurement within a single analysis. The other source of uncertainty that needs to be characterised is similarity over multiple analyses. This is very difficult to assess in an unknown material, but can be assessed by measuring well-understood reference zircons.

<p>Reference materials are characterised by homogeneity in the isotope of interest, and multiple analyses of this material should produce a single statistical population. Where these populations display significant excess scatter, manifested as a MSWD value that far exceeds 1, this means that counting statistics are not the sole source of uncertainty. This can be addressed by expanding the uncertainty on the analyses until the standard zircons form a coherent statistical population. This expansion should then be applied to the unknown zircons to accommodate this ‘spot-to-spot-uncertainty’ or ‘repeatability’ factor. This approach is routinely applied to SHRIMP U-Pb data, and here is similarly applied to Lu-Hf data from granites of the northeast Lachlan Orogen.

<p>By applying these uncertainty factors appropriately, it is then possible to assess the homogeneity of unknown materials by calculating weighted means and MSWD factors. The MSWD is a measure of scatter away from a single population (McIntyre et al., 1966; Wendt and Carl, 1991). Where the MSWD is 1, the scatter in data points can be explained solely by analytical means. The higher the MSWD, the less likely it is that the data can be described as a single population. Data which disperses over several εHf units can still be attributed to a single population if the uncertainty envelopes of analyses largely overlap each other. These concepts are illustrated using the data presented in Figure 1. Four out of five of the εHf datasets on zircons from granites form statistically coherent populations (MSWD = 0.69 to 2.4).

<p>A high MSWD does not necessarily imply that variation is due to processes occurring during granite formation. Although zircon is a robust mineral, isotopic disturbances are still possible. In the U-Pb system, there is often evidence of post-crystallisation ‘Pb-loss’ which leads to erroneously young apparent U-Pb ages. The Lu-Hf system in zircon is generally thought to be more robust than the U-Pb system, but that does not mean that it is impervious to such effects. In the data set presented in Figure 1, the sample with the most scatter in Lu-Hf (Glenariff Granite, εHf = -0.2 ± 1.5, MSWD = 7.20) is also the sample which had the most rejections in the SHRIMP U-Pb data due to Pb-loss. The subsequent Hf analyses targeted only those grains which fell within the magmatic population (i.e., no observed Pb-loss), but the larger volume excavated by laser Hf analysis means that it is likely that disturbed regions of these grains were incorporated into the measurement. This gives an explanation for the scatter that has nothing to do with geological source characteristics.

<p>This line of logic can similarly be applied to all types of multi-spot analyses, including O-isotope analyses. While most of the εHf datasets presented here form coherent populations, the O-isotope data are significantly more scattered (MSWD = 2.8 to 9.4). The analyses on the unknowns scatter much more than on the co-analysed TEMORA2 reference zircon. This implies a source of scatter additional to those described above. In addition to the above described sources of uncertainty, O-isotope analysis by SIMS is also extremely sensitive to topography on the surface of the epoxy into which zircons are mounted (Ickert et al., 2008). O isotopes may also be susceptible to post-formation disturbance and so care should also be taken when interpreting O data, before assigning geological meaning.

<p>While it is possible for Lu-Hf and O analyses of zircons in granites to reflect heterogeneous sources and/or complex formation processes, it is important to first exclude other sources of heterogeneity such as analytical sources of uncertainty, and post-formation isotopic disturbances.