On Modelling Discrete Geological Structures as Markov Random Fields

The purpose of this paper is to extend the locally based prediction methodology of BayMar to a global one by modelling discrete spatial structures as Markov random fields. BayMar uses one-dimensional Markov-properties for estimating spatial correlation and Bayesian updating for locally integrating prior and additional information. The methodology of this paper introduces a new estimator of the field parameters based on the maximum likelihood technique for one-dimensional Markov chains. This makes the estimator straightforward to calculate also when there is a large amount of missing observations, which often is the case in geological applications. We make simulations (both unconditional and conditional on the observed data) and maximum a posteriori predictions (restorations) of the non-observed data using Markov chain Monte Carlo methods, in the restoration case by employing simulated annealing. The described method gives satisfactory predictions, while more work is needed in order to simulate, since it appears to have a tendency to overestimate strong spatial dependence. It provides an important development compared to the BayMar-methodology by facilitating global predictions and improved use of sparse data.     

最大效果测度值法研究矿井突水水源

为了快速准确地查清矿井突水水源，排除水患对生产的影响，利用最大效果测度值燕子山矿14-2＃煤层顶板砂岩裂隙水，其导水通道为工作面所在盘区发育的F23和F38正断层。最大效果测度值为矿井防治水工作提供了一个新的思路。     

Late Neoproterozoic crustal growth in the European Variscides: Nd isotope and geochemical evidence from the Sierra de Córdoba Andesites (Ossa-Morena Zone, Southern Spain)

Because the Hercynian overprint was extremely weak, the Sierra de Córdoba (southeastern Ossa-Morena Zone, OMZ) provides an excellent opportunity to study the tectonic evolution of sequences deposited close to the Late Neoproterozoic–Early Palaeozoic boundary. In order to put constraints on the sources and geodynamic significance of the Late Proterozoic magmatism, a representative set of 18 igneous rocks, and 3 interbedded sedimentary rocks from the San Jerónimo Formation have been studied for major and trace element geochemistry and for the Sm–Nd isotopic systematics. The igneous rocks are generally porphyritic to microporphyritic andesites, with abundant plagioclase (±amphibole) phenocrysts. With the exception of two intrusive rocks, possibly not related to the Late Proterozoic episode, all the samples display positive _{Nd550 Ma} values, ranging from +2.9 to +7.6. Most of them, with +4<_{Nd550 Ma}<+6, exhibit LREE enrichment, high La/Nb ratios, and elevated Zr/Nb ratios ranging from 21 to 32. There is no obvious correlation between the shape of REE patterns, La/Nb ratios and _{Nd550 Ma} values, precluding simple models of late-stage interaction with typical crustal components having low _Nd and high LREE/HREE and La/Nb ratios. Based on their major element composition and enriched, continental crust-like trace element characteristics, combined with distinctly positive _Nd initial values, the Córdoba andesites document an episode of crustal growth through the addition of calc-alkaline magmas, extracted from a mantle reservoir which was strongly depleted in LREE on a time-integrated basis. The occurrence of interlayered sediments of continental provenance (negative _Nd values) does not favour a purely ensimatic arc setting, remote from continental land masses, for this subduction-related magmatism, but the geochemical data suggest an active margin environment located on relatively juvenile crust. In any case, the Córdoba andesites document the addition of materials chemically similar to the bulk continental crust which were extracted from mantle sources with strong time-integrated LREE depletion. Therefore, they provide evidence for crustal growth related to Cadomian orogenic events during Late Proterozoic times.     

Book Review: Vadose Zone Science and Technology Solutions. By Brian B. Looney and Ronald W. Falta. Battelle Press, 2000, 1540p, $95 (hardback), ISBN 1-57477-085-3

Mathematical Geosciences -     

A ‘core-complex-like structure’ formed by superimposed extension,folding and high-angle normal faulting. The Santi Petri dome (western Betics,Spain)

The Santi Petri dome (western Betics, southern Spain) shows a core-complex-like structure, where migmatitic gneisses and schists outcrop below low-grade slates and phyllites, all of which form the basement of the Neogene Málaga basin. The migmatites and schists suffered a coaxial-flattening event during isothermal decompression and were later exhumed by ductile ESE non-coaxial stretching. Further exhumation was achieved by W- to SW-transport brittle low-angle normal faulting. Subsequently these extensional structures were gently folded in the core of a NE/SW-oriented antiform during the Tortonian. Finally the Santi Petri domal geometry was accentuated by the interference of orthogonal high-angle faults with ENE–WSW and NNW–SSE orientation. This core-complex-like structure, formed by superposition of extensional and compressive tectonic events, does not represent a classical, purely extensional core complex, which shows that metamorphic structure and geometry are not decisive criteria to define a core-complex.     

Vortex–ridge interaction in a rotating fluid

The evolution of barotropic vortices interacting with a topographic ridge on a f-plane is studied by means of laboratory experiments in a rotating tank and numerical simulations. The initial condition in all experiments is a cyclonic vortex created at a certain distance from the ridge. The results are presented in two main scenarios: (a) weak interactions, which occur at early stages of the experiments, when the vortex is far from the ridge, and thus weakly experiences the influence of the topography. In these situations, the vortex slowly drifts towards the ridge with a leftward inclination due to the ascending slope of the topography. Such a behaviour is similar to the “northwestern” motion of cyclones over a weak sloping bottom. The circular shape of the monopolar vortex is preserved. (b) Strong interactions, in which the vortex core reaches the ridge and presents a more complicated evolution. The cyclone “climbs” to the top of the topography and crosses to the other side. Once the vortex experiences the opposite slope, it moves backwards trying to return to the original side of the ridge. For strong enough vortices, this process may be repeated a number of times until the vortex is dissipated by viscous effects. During these interactions the shape of the vortex is strongly deformed and several filaments are produced. In some cases the vortex is cleaved in two parts when crossing the ridge, one at each side of it and moving in opposite directions.Weak and strong interactions are numerically simulated by using a quasi-two-dimensional model. The results confirm that the vortex behaviour is governed by stretching and squeezing effects associated with changes in depth over the ridge and, at latter stages, by Ekman damping due to the solid bottom. The main results observed during strong interactions on a f-plane are also found on preliminar topographic β-plane experiments.