Mathematics – Probability
Scientific paper
Jun 2005
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2005e%26psl.235..244a&link_type=abstract
Earth and Planetary Science Letters, Volume 235, Issue 1-2, p. 244-260.
Mathematics
Probability
8
Scientific paper
This paper presents a new approach to quantify sediment mixing based on the mixing of U Pb zircon age distributions within sediment. Two statistical techniques are presented to determine the proportion in which two known age distributions combine to create a known mixed age distribution. These techniques are then used to determine relative erosion rates between adjacent drainage basins above and below the Main Central Thrust (MCT) in the central Nepal Himalaya. The MCT region is coincident with an abrupt north south change in geomorphic character and mineral cooling ages that are thought to represent an erosional response to higher rock uplift rates north of the MCT zone. However, it is unclear whether the ongoing deformation responsible for the differential uplift rates is: (1) focused on the MCT; (2) at depth along a crustal scale ramp; or (3) along newly mapped thrust faults south of the MCT. Our study explores this issue by comparing modern erosion rates with longer-term erosion rates determined from mineral cooling ages. Zircons were separated from modern river sand and dated by LA-MC-ICPMS before the measured isotopic ratios and ages were used in 1-d and 2-d mixing calculations. The 1-d technique creates probability density functions of zircon ages for each sample and then uses both an iterative and inverse approach to estimate mixing between samples. In contrast, the 2-d technique estimates mixing between probability “fields” defined by the measured 238U/206Pb and 207Pb/206Pb ratios. Given a finite mixture with perfect sample representation, both techniques produce perfect mixing estimates across a range of mixing proportions. Modeling results demonstrate that given imperfect subsample representation of the complex parent age distribution, differing degrees of subsample smoothing may be required to achieve an accurate mixing estimate. Using mixing of zircon ages as a quantitative proxy for sediment mixing requires a correction for the concentration of zircon in the river sediment. Two new methods for establishing zircon concentration in river sediment are presented demonstrating the existence of 2- to 5-fold differences in zircon concentration between adjacent drainages. Relative erosion rates are estimated by determining the zircon mixing ratio between adjacent drainages which are then normalized by the ratio of zircon concentrations and the ratio of drainage areas. Results show ˜ 3 times higher modern erosion rates south of the MCT in the northernmost Lesser Himalaya. Future applications of this new technique may include reach-scale sediment transport dynamics, improved sedimentary basin analysis, and better interpretation of foreland mineral cooling ages.
Amidon William H.
Burbank Douglas W.
Gehrels George E.
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