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.
An inverse method for obtaining the attenuation profile and small variations in the sound speed and density profiles of the ocean bottom Rajan, Subramaniam D. (Massachusetts Institute of Technology and Woods Hole Oceanographic Institution, 1985-05)The acoustic properties of marine sediments have a direct effect on the propagation of sound in the ocean. In the frequency range of interest (50 - 500 Hz) the sediment can be modelled as a fluid. Assuming horizontal ...
Poole, Travis L. (Massachusetts Institute of Technology and Woods Hole Oceanographic Institution, 2007-02)This thesis introduces an algorithm for inverting for the geoacoustic properties of the seafloor in shallow water. The input data required by the algorithm are estimates of the amplitudes of the normal modes excited by ...
Geoacoustic inversion in laterally varying shallow-water environments using high-resolution wavenumber estimation Becker, Kyle M. (Massachusetts Institute of Technology and Woods Hole Oceanographic Institution, 2002-02)Sound propagation in shallow water is highly dependent on the interaction of the sound field with the bottom. In order to fully understand this problem, it is necessary to obtain reliable estimates of bottom geoacoustic ...