Abstract
Laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS) provides the spatial distribution of elements within crystals and therefore can constrain the rates of geological processes. Spatial resolution of LA-ICP-MS is limited by the requirement to ablate sufficient material to surpass the detection limit of the instrument: too little material and the concentration cannot be measured; too much material from the same spatial location and the possibility of depth dependent variations in concentration increases. Because of this requirement and typical analytical setup, this commonly places a lower bound on the diameter of an ablation ‘spot’ size of approximately 20μm for elements with ppm concentration. Here we present a means to achieve sub-spot size resolution using inverse methods. We discretize the space sampled in an analysis into pixels and note that the average concentration of the pixels sampled by a spot equals the measured concentration. As multiple overlapping spots sample some of the same pixels, we can combine discrete expressions for each spot as a system of linear equations. Through linear inversion with smoothness constraints we can solve for unknown pixel concentrations. We highlight this approach with two natural examples in which diffusive processes are important: magmatic ascent speeds and (U-Th)/He noble gas thermochronometry. In these examples, accurate results require that the true concentration gradients can be recovered from LA-ICP-MS data. We show that the ability to infer rapid rates of magma ascent is improved from months to weeks and that we are able to interpret previously un-interpretable thermochronometric data.
Highlights
Understanding how composition varies across an individual mineral elucidates numerous geological problems, ranging from understanding magmatic systems (e.g. Davidson et al, 2007; Streck, 2008; Bussweiler et al, 2015) to measuring rates of metamorphic processes (e.g. Lasaga and Jiang, 1995; Morgan et al, 2014) to understanding the production and diffusion of noble gases (e.g. Farley et al, 2011; Flowers and Farley, 2012; Fox et al, 2014)
During the last two decades, LA-ICP-MS has advanced significantly to emerge as a cost effective and time-efficient choice, especially when making elemental distribution maps (Ubide et al, 2015, and references therein)
The radial distance parameter is the main parameter that controls the averaging length-scale (Farley et al, 2011; Tripathy-Lang et al, 2015). This approach treats a spot measurement, which represents the average concentration across an ablated circle, as a single point measurement located at the center of the circle
Summary
Understanding how composition varies across an individual mineral elucidates numerous geological problems, ranging from understanding magmatic systems (e.g. Davidson et al, 2007; Streck, 2008; Bussweiler et al, 2015) to measuring rates of metamorphic processes (e.g. Lasaga and Jiang, 1995; Morgan et al, 2014) to understanding the production and diffusion of noble gases (e.g. Farley et al, 2011; Flowers and Farley, 2012; Fox et al, 2014). Previous studies have explored converting LA-ICP-MS data collected across laser spots or line-scans of known size to continuous functions of concentration These approaches do not account for the smearing of information due to the potentially large spot size with respect to concentration gradients. The radial distance parameter is the main parameter that controls the averaging length-scale (Farley et al, 2011; Tripathy-Lang et al, 2015) This approach treats a spot measurement, which represents the average concentration across an ablated circle, as a single point measurement located at the center of the circle. Individual locations may be associated with multiple spot concentration values This redundant information can either be averaged to produce smooth maps or exploited to infer subspot size concentration variation. We present our inverse approach and highlight its application with the two examples described above: Ni diffusion in olivines to infer the time scale of magma flux and He diffusion in apatite to infer cooling associated with exhumation
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