Éditeur(s) : HAL CCSD American Geophysical Union
Résumé : Solidus phase relations of carbon dioxide-saturated (CO2 vapor) model peridotite in the system CaO-MgO-Al2O3-SiO2-CO2 in the 1.1-2.1 GPa pressure range are reported. The solidus has a positive slope in pressure-temperature (PT) space from 1.1 to 2 GPa. Between 2 and 2.1 GPa, the melting curve changes to a negative slope. From 1.1 to 1.9 GPa, the liquid, best described as CO2-bearing silicate liquid, is in equilibrium with forsterite, orthopyroxene, clinopyroxene, spinel, and vapor. At 2 GPa, the same crystalline phase assemblage plus vapor is in equilibrium with two liquids, which are silicate and carbonatitic in composition, making the solidus at 2 GPa PT invariant. The presence of two liquids is interpreted as being due to liquid immiscibility. Melting reactions written over 1.1-1.9 GPa are peritectic, with forsterite being produced upon melting, and the liquid is silicate in composition. Upon melting at 2.1 GPa, orthopyroxene is produced, and the liquid is carbonatitic in composition. Hence, the invariance between 1.9 and 2.1 GPa is not only the reason for the dramatic change in the liquid composition over an interval of 0.2 GPa, but the carbonated peridotite solidus ledge itself most likely appears because of this PT invariance. It is suggested that because carbonatitic liquid is produced at the highest solidus temperature at 2 GPa in PT space in the system studied, such liquids, in principle, can erupt through liquid immiscibility, as near-primary magmas from depths of approximately 60 km.
ISSN: 0148-0227

hal-00939406
https://hal.archives-ouvertes.fr/hal-00939406
DOI : 10.1002/jgrb.50249

Éditeur(s) : HAL CCSD
Résumé : 28 pages, 6 figures
We study a universal object for the genealogy of a sample in populations with mutations: the critical birth-death process with Poissonian mutations, conditioned on its population size at a fixed time horizon. We show how this process arises as the law of the genealogy of a sample in a large class of critical branching populations with mutations at birth, namely populations converging, in a large population asymptotic, towards the continuum random tree. We extend this model to populations with random foundation times, with (potentially improper) prior distributions g_i: xmapsto x^{-i}, iinZ_+, including the so-called uniform (i=0) and log-uniform (i=1) priors. We first investigate the mutational patterns arising from these models, by studying the site frequency spectrum of a sample with fixed size, i.e. the number of mutations carried by k individuals in the sample. Explicit formulae for the expected frequency spectrum of a sample are provided, in the cases of a fixed foundation time, and of a uniform and log-uniform prior on the foundation time. Second, we establish the convergence in distribution, for large sample sizes, of the (suitably renormalized) tree spanned by the sample genealogy with prior g_i on the time of origin. We finally prove that the limiting genealogies with different priors can all be embedded in the same realization of a given Poisson point measure.
https://hal.archives-ouvertes.fr/hal-01053343

hal-01053343
https://hal.archives-ouvertes.fr/hal-01053343
ARXIV : 1407.7720