A general inversion for end-member ratios in binary mixing systems
Sohn, Robert A.
MetadataShow full item record
Binary mixing is one of the most common models used to explain variations in geochemical data. When the data being modeled are ratios of elements or isotopes, the mixtures follow hyperbolic trends with curvatures that depend on a cross-term representing the relative concentrations of the elements or isotopes under consideration in the mixing components. The inverse problem of estimating mixing components is difficult because of the cross-term in the hyperbolic equation, which requires the use of nonlinear methods to estimate the mixing parameters, and because the end-member ratio values are intrinsically underdetermined unless the mixing proportions of the samples are known a priori, which is not generally the case. I use maximum likelihood methods to address these issues and derive a general inversion for binary mixing model parameters from ratio-ratio data. I apply the method to synthetic test data and a global compilation of 230Th/232Th versus 87Sr/86Sr data from oceanic basalts and find that the concentration ratio parameter is well-constrained by the inversion while the end-member ratio estimates are strongly dependent on the initial guesses used to start the iterative solver, reflecting the underdetermined nature of the end-member positions on the mixing hyperbola. Monte Carlo methods that randomly perturb the initial guesses can be used to improve error estimates, and goodness-of-fit statistics can be used to assess the performance of the mixing model for explaining data variance.
Author Posting. © American Geophysical Union, 2005. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Geochemistry Geophysics Geosystems 6 (2005): Q11007, doi:10.1029/2005GC000975.
Showing items related by title, author, creator and subject.
Poole, Travis L.; Frisk, George V.; Lynch, James F.; Pierce, Allan D. (Acoustical Society of America, 2008-02)This paper introduces a perturbative inversion algorithm for determining sea floor acoustic properties, which uses modal amplitudes as input data. Perturbative inverse methods have been used in the past to estimate bottom ...
Hernandez-Guerra, Alonso; Joyce, Terrence M.; Fraile-Nuez, Eugenio; Velez-Belchi, Pedro (2009-08-06)Using a variety of oceanographic data, including direct volume transports in the Florida 19 Strait, and Argo float profiles and drift velocities at 24 and 36N in the North Atlantic, inverse calculations are presented in ...
Meridional circulation during the Last Glacial Maximum explored through a combination of South Atlantic δ18O observations and a geostrophic inverse model Gebbie, Geoffrey A.; Huybers, Peter (American Geophysical Union, 2006-11-15)The vertical profile of meridional transport in the South Atlantic is examined by combining paleoceanographic observations with a geostrophic circulation model using an inverse method. δ18Ocalcite observations along the ...