The effects of spatial autoregressive dependencies on inference in ordinary least squares: a geometric approach

There is a common belief that the presence of residual spatial autocorrelation in ordinary least squares (OLS) regression leads to inflated significance levels in beta coefficients and, in particular, inflated levels relative to the more efficient spatial error model (SEM). However, our simulations show that this is not always the case. Hence, the purpose of this paper is to examine this question from a geometric viewpoint. The key idea is to characterize the OLS test statistic in terms of angle cosines and examine the geometric implications of this characterization. Our first result is to show that if the explanatory variables in the regression exhibit no spatial autocorrelation, then the distribution of test statistics for individual beta coefficients in OLS is independent of any spatial autocorrelation in the error term. Hence, inferences about betas exhibit all the optimality properties of the classic uncorrelated error case. However, a second more important series of results show that if spatial autocorrelation is present in both the dependent and explanatory variables, then the conventional wisdom is correct. In particular, even when an explanatory variable is statistically independent of the dependent variable, such joint spatial dependencies tend to produce “spurious correlation” that results in over-rejection of the null hypothesis. The underlying geometric nature of this problem is clarified by illustrative examples. The paper concludes with a brief discussion of some possible remedies for this problem.     

Old stellar population synthesis： new age and mass estimates for Mayall Ⅱ = G1

Mayall Ⅱ = G1 is one of the most luminous globular clusters （GCs） in M31. Here, we determine its age and mass by comparing multicolor photometry with theoretical stellar population synthesis models. Based on far- and near-ultraviolet GALEX photometry, broad-band UBVRI, and infrared JHKs 2MASS data, we construct the most extensive spectral energy distribution of G 1 to date, spanning the wavelength range from 1538 to 20 000A. A quantitative comparison with a variety of simple stellar population （SSP） models yields a mean age which is consistent with G1 being among the oldest building blocks of M31 and having formed within ～1.7 Gyr after the Big Bang. Irrespective of the SSP model or stellar initial mass function adopted, the resulting mass estimates （of order 10^7M⊙） indicate that GI is one of the most massive GCs in the Local Group. However, we speculate that the cluster＇s exceptionally high mass suggests that it may not be a genuine GC. Our results also suggest that G1 may contain, on average, （1.65±0.63） × 10^2L⊙ far-ultraviolet-bright, hot, extreme horizontal-branch stars, depending on the adopted SSP model. In addition, we demonstrate that extensive multi-passband photometry coupled with SSP analysis enables one to obtain age estimates for old SSPs that have similar accuracies as those from integrated spectroscopy or resolved stellar photometry, provided that some of the free parameters can be constrained independently.     

Mutual replacement reactions in alkali feldspars I: microtextures and mechanisms

Intracrystal microtextures formed by a process of mutual replacement in alkali feldspars record fluid–rock reactions that have affected large volumes of the Earth’s crust. Regular, ≤1 μm-scale ‘strain-controlled’ perthitic microtextures coarsen, by up to 10³, by a dissolution–reprecipitation process, producing microporous patch or vein perthites on scales >100 μm. We have developed earlier studies of such reactions in alkali feldspar cm-scale primocrysts in layered syenites from the Klokken intrusion, South Greenland. We present new hyperspectral CL, SEM images, and laser ICPMS analytical data, and discuss the mechanism of such replacement reactions. The feldspars grew as homogeneous sodic sanidines which unmixed and ordered by volume diffusion during cooling into the microcline field at ~450°C, giving regular, fully coherent ‘braid’ cryptoperthite. At ≤450°C the crystals reacted with a circulating post-magmatic aqueous fluid. The braid perthite behaved as a single reactant ‘phase’ which was replaced by two product phases, incoherent subgrains of low albite and microcline, with micropores at their boundaries. The driving force for the reactions was coherency strain energy, which was greater than the surface energy in the subgrain mosaic. The external euhedral crystal shapes and bulk major element composition of the primocrysts were unchanged but they became largely pseudomorphs composed of subgrains usually with the ‘pericline’ and ‘adularia’ habits (dominant {110} and subordinate {010} morphology) characteristic of low T growth. The subgrains have an epitactic relationship with parent braid perthite. Individual subgrains show oscillatory zoning in CL intensity, mainly at blue wavelengths, which correlates with tetrahedral Ti. Regular zoning is sometimes truncated by irregular, discordant surfaces suggesting dissolution, followed by resumption of growth giving regular zoning. Zones can be traced through touching subgrains, of both albite and microcline, for distances up to ~500 μm. At ≤340°C, the microcline subgrains underwent a third stage of unmixing to give straight lamellar film perthites with periodicities of ~1 μm, which with further cooling became semicoherent by the development of spaced misfit dislocations. Sub-grain growth occurred in fluid films that advanced through the elastically strained braid perthite crystals, which dissolved irreversibly. Braid perthite was more soluble than the strain-free subgrain mosaics which precipitated from the supersaturated solution. Some volumes of braid texture have sharp surfaces that suggest rapid dissolution along planes with low surface energies. Others have complex, diffuse boundaries that indicate a phase of coherent lamellar straightening by volume diffusion in response to strain relief close to a slowly advancing interface. Nucleation of strain-free subgrains was the overall rate-limiting step. To minimise surface energy subgrains grew with low energy morphologies and coarsened by grain growth, in fluid films whose trace element load (reflected in the oscillatory zoning) was dictated by the competitive advance of subgrains over a range of a few tens of mm. The cross-cutting dissolution surfaces suggest influxes of fresh fluid. Removal of feldspar to give 2 vol% porosity would require a feldspar:fluid ratio of ~1:26 (by wt). The late reversion to strain-controlled exsolution in microcline subgrains is consistent with loss of fluid above 340°C following depressurization of the intrusion. A second paper (Part II) describes trace element partitioning between the albite and microcline subgrains, and discusses the potential of trace elements as a low-T geothermometer. This paper and the Part II are dedicated in memory of J.V. Smith and W.L. Brown, both of whom died in 2007, in acknowledgement of their unrivalled contributions to the study of the feldspar minerals over more than half a century.     

The Ascraeus Mons fan-shaped deposit: Volcano-ice interactions and the climatic implications of cold-based tropical mountain glaciation

Amazonian-aged fan-shaped deposits extending to the northwest of each of the Tharsis Montes in the Tharsis region on Mars have been interpreted to have originated from mass-wasting, volcanic, tectonic and/or glacial processes. We use new data from MRO, MGS, and Odyssey to characterize these deposits. Building on recent evidence for cold-based glacial activity at Pavonis Mons and Arsia Mons, we interpret the smaller Ascraeus fan-shaped deposit to be of glacial origin. Our geomorphological assessment reveals a number of characteristics indicative of glacial growth and retreat, including: (1) a ridged facies, interpreted to be composed of drop moraines emplaced during episodic glacial advance and retreat, (2) a knobby facies, interpreted to represent vertical downwasting of the ice sheet, and (3) complex ridges showing a cusp-like structure. We also see evidence of volcano-ice interactions in the form of: (1) an arcuate inward-facing scarp, interpreted to have formed by the chilling of lava flows against the glacial margin, (2) a plateau feature, interpreted to represent a subglacial eruption, and (3) knobby facies superimposed on flat-topped flows with leveed channels, interpreted to be subglacial inflated lava flows that subsequently drained and are covered by glacial till. We discuss the formation mechanisms of these morphologies during cold-based glacial activity and concurrent volcanism. On the basis of a Mid- to Late-Amazonian age (250-380 Ma) established from crater size-frequency distribution data, we explore the climatic implications of recent glaciation at low latitudes on Mars. GCM results show that increased insolation to the poles at high obliquities (>45°) forces sublimation of polar ice, which is transported to lower latitudes and deposited on the flanks of the Tharsis Montes. We assess how local orographic effects, the mass balance of the glacier, and the position of equilibrium line altitudes, all played a role in producing the observed geomorphologies. In doing so, we outline a glacial history for the evolution of the Ascraeus Mons fan-shaped deposit and compare its initiation, growth and demise with those of Arsia Mons and Pavonis Mons.     

Bleaching of the post‐IR IRSL signal: new insights for feldspar luminescence dating

Post‐infrared (pIR) stimulated luminescence dating of sedimentary feldspar largely avoids the effects of anomalous fading that affect conventional infrared stimulated luminescence (IRSL) dating. However, optical resetting of pIR signals is more difficult than resetting the conventional IRSL signal, which may undermine the crucial assumption that pIR signals were effectively bleached upon deposition and burial of sediment grains. In this study, we quantify the bleaching properties of several pIR signals on various samples using laboratory‐simulated bleaching in full sunlight and water‐attenuated sunlight. Our data show that bleaching is most efficient under full spectrum conditions for all pIR signals and that pIR signals measured at elevated temperature are increasingly harder to bleach than IR and pIR signals measured at low temperature (e.g. IR at 50°C). All bleaching curves exhibit a very slow and steady decrease, indicating that a fixed un‐bleachable residual level cannot be reached within the 11 days of solar simulator exposure undertaken here. We show that the magnitude of a laboratory‐determined residual dose depends on the adopted bleaching protocol and cannot be used as a proxy for the dose that remains in the sample at the time of burial (remnant dose). Our data emphasize the importance of finding a balance between sufficient signal stability and a minimized contribution of a remnant dose when using pIR procedures for feldspar luminescence dating.     

Civil engineering meets geology: at the Panama Canal

The Panama Canal ranks high among the world's greatest feats of civil engineering. The sheer scales of its ground excavations, its concrete structures and its economic significance are truly spectacular. It is also remarkable for the geology of the massive landslides that developed within its Culebra Cut.     

An Alternative Classification Scheme for Uncertain Attribute Mapping

The reality of uncertain data cannot be ignored. Anytime that spatial data are used to assist planning, decision making, or policy generation, it is likely that error or uncertainty in the data will propagate through processing protocols and analytic techniques, potentially leading to biased or incorrect decision making. The ability to directly account for uncertainty in spatial analysis efforts is critically important. This article focuses on addressing data uncertainty in one of the most important and widely used exploratory spatial data analysis (ESDA) techniques—choropleth mapping—and proposes an alternative map classification method for uncertain spatial data. The classification approach maximizes within-class homogeneity under data uncertainty while explicitly integrating spatial characteristics to reduce visual map complexity and to facilitate pattern perception. The method is demonstrated by mapping the 2009 to 2013 American Community Survey estimates of median household income in Salt Lake County, Utah, at the census tract level.