Abstract
Abstract. To enable the separation of pre- and post-depositional components of the length distribution of (partially annealed) horizontal confined fission tracks, the length distribution is corrected by deconvolution. Probabilistic least-squares inversion corrects natural track length histograms for observational biases, considering the variance in data, modelization, and prior information. The corrected histogram is validated by its variance–covariance matrix. It is considered that horizontal track data can exist with or without measurements of angles to the c axis. In the latter case, 3D histograms are introduced as an alternative to histograms of c-axis-projected track lengths. Thermal history modelling of samples is not necessary for the calculation of track age distributions of corrected tracks. In an example, the age equations are applied to apatites with pre-depositional (inherited) tracks in order to extract the post-depositional track length histogram. Fission tracks generated before deposition in detrital apatite crystals are mixed with post-depositional tracks. This complicates the calculation of the post-sedimentary thermal history, as the grains have experienced different thermal histories prior to deposition. Thereafter, the grains share a common thermal history. Thus, the extracted post-depositional histogram without inherited tracks may be used for thermal history calculation.
Highlights
Where λ0 is the present track normalized length, ε is the fission-track production rate, and n(λ) is the measured number of fission tracks of length λ produced per volume
Three major biases appear to be important when deriving the equation for track age: 1. the surface track density bias, reflecting the likelihood that a track is exposed to etching on the surface
The deconvolution method presented here is used to identify the post-depositional part of a track length histogram from Jameson Land, Greenland
Summary
Fission of uranium-238 (U-238) in apatite, titanite, and zircon creates tracks in the crystal lattice. Forwardcalculation examples are given by Bertagnolli et al (1983) On this basis, Keil et al (1987) developed an inversion procedure in which the temperature history is derived from either the length distribution of tracks within the crystal or from the length distribution of projected tracks intersecting the surface. Hansen: Deconvolution of fission-track length distributions track is calculated by counting the number of shorter tracks plus one This age is determined without the use of an annealing model. The model by Keil et al (1987) does not include blurring of track length histograms caused by the initial distribution of fission fragment energy (Jungerman and Wright, 1949), annealing and etching anisotropy, mineral composition, the uncertainty of measurement (Ketcham, 2003), and track selection biases (Jensen et al, 1992).
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