Optimized formulas for the gravitational field of a tesseroid

Various tasks in geodesy, geophysics, and related geosciences require precise information on the impact of mass distributions on gravity field-related quantities, such as the gravitational potential and its partial derivatives. Using forward modeling based on Newton’s integral, mass distributions are generally decomposed into regular elementary bodies. In classical approaches, prisms or point mass approximations are mostly utilized. Considering the effect of the sphericity of the Earth, alternative mass modeling methods based on tesseroid bodies (spherical prisms) should be taken into account, particularly in regional and global applications. Expressions for the gravitational field of a point mass are relatively simple when formulated in Cartesian coordinates. In the case of integrating over a tesseroid volume bounded by geocentric spherical coordinates, it will be shown that it is also beneficial to represent the integral kernel in terms of Cartesian coordinates. This considerably simplifies the determination of the tesseroid’s potential derivatives in comparison with previously published methodologies that make use of integral kernels expressed in spherical coordinates. Based on this idea, optimized formulas for the gravitational potential of a homogeneous tesseroid and its derivatives up to second-order are elaborated in this paper. These new formulas do not suffer from the polar singularity of the spherical coordinate system and can, therefore, be evaluated for any position on the globe. Since integrals over tesseroid volumes cannot be solved analytically, the numerical evaluation is achieved by means of expanding the integral kernel in a Taylor series with fourth-order error in the spatial coordinates of the integration point. As the structure of the Cartesian integral kernel is substantially simplified, Taylor coefficients can be represented in a compact and computationally attractive form. Thus, the use of the optimized tesseroid formulas particularly benefits from a significant decrease in computation time by about 45 % compared to previously used algorithms. In order to show the computational efficiency and to validate the mathematical derivations, the new tesseroid formulas are applied to two realistic numerical experiments and are compared to previously published tesseroid methods and the conventional prism approach.     

Compaction localization in the Earth and the laboratory: state of the research and research directions

Localized compaction in porous rocks is a recently recognized phenomenon that has been shown to reduce permeability dramatically. Consequently, the phenomenon is relevant to a variety of technologies involving fluid injection or withdrawal. This article summarizes current understanding of localized compaction and impediments to further progress. The article is based on discussions at a small workshop on localized compaction sponsored by the Office of Science, U. S. Department of Energy.     

Latitudinal variation in the aerial/aquatic ratio of oxygen consumption of a supratidal high rocky‐shore crab

The colonisation of the terrestrial environment by crustaceans is more apparent in tropical latitudes because of the high diversity of semi‐terrestrial and terrestrial crabs. However, in temperate regions there are also great numbers of crustaceans that inhabit ecological niches at the water–air interface. Grapsidae crabs (Decopoda) are especially important in studies of water‐to‐land transition as the family contains species occupying the intertidal and adjacent regions. A way to evaluate the ability of intertidal invertebrates to breathe air is to measure the aerial/aquatic oxygen consumption ratio. The objective of this study was to test the effect of thermal variation on the aquatic and aerial metabolism. We selected as study model the decopoda crab Cyclograpsus cinereus Dana and utilised five populations of the species spread over 2000 km along the Chilean coast. To determine the compensation capacity in respiration with respect to latitude, we evaluated metabolic rate at the same temperature in a common garden design in the laboratory, to examine the extent to which variation in crab physiology is environmentally determined. Whereas in our study, m_b (body mass) varied significantly with latitude, the difference in mass‐independent metabolism both in air and water persisted, indicating that observed differences in MR (Metabolic Rate) were not an effect of differences in body size. We demonstrated that C. cinereus is able to breath oxygen from air and water as expected for an amphibious crab. Almost all the studied populations of C. cinereus show a aerial/aquatic metabolism ratio near 1. The pattern found indicates an increase in metabolic rate, both aerial and aquatic, in low latitudes and therefore does not support the latitudinal compensation hypothesis for temperate habitats. Finally, these kinds of studies are required to make the necessary link between ecological physiology and macroecology and to help develop a global understanding of organismal function in marine systems.     

Observations of hysteresis in solar cycle variations among seven solar activity indicators

We show that smoothed time series of 7 indices of solar activity exhibit significant solar cycle dependent differences in their relative variations during the past 20 years. In some cases these observed hysteresis patterns start to repeat over more than one solar cycle, giving evidence that this is a normal feature of solar variability. Among the indices we study, we find that the hysteresis effects are approximately simple phase shifts, and we quantify these phase shifts in terms of lag times behind the leading index, the International Sunspot Number. Our measured lag times range from less than one month to greater than four months and can be much larger than lag times estimated from short-term variations of these same activity indices during the emergence and decay of major active regions. We argue that hysteresis represents a real delay in the onset and decline of solar activity and is an important clue in the search for physical processes responsible for changing solar emission at various wavelengths. The High Altitude Observatory is sponsored by the National Science Foundation.     

Opportunistic natural experiments using digital telemetry: a transit disruption case study

ABSTRACT

In the past decade society has entered a technological period characterized by handheld computing that supports input and processing from numerous sensors. Today’s mobile phones offer the ability to integrate input from sensors monitoring various external and internal sources (e.g., accelerometer, magnetometer, microphone, GPS, wireless Internet, and Bluetooth). Furthermore, these raw inputs can be integrated and processed in ways that can offer novel representations of human behaviour. As a result, new opportunities to examine and better understand human spatial behaviour are available; one such application is the constant monitoring of a group of people over an extended period of time. Such a research setting lends itself to natural experiments that emerge as a result of regular and on-going observations. We report here on the observation of a natural experiment that took place in the context of a month-long monitoring study of 28 participants using mobile phone-based ubiquitous sensor monitoring. The implications for public health and transportation planning are discussed.     

Microbial–silica interactions in Icelandic hot spring sinter: possible analogues for some Precambrian siliceous stromatolites

Silicified deposits, such as sinters, occur in several modern geothermal environments, but the mechanisms of silicification (and crucially the role of microorganisms in their construction) are still largely unresolved. Detailed examination of siliceous sinter, in particular sections of microstromatolites growing at the Krisuvik hot spring, Iceland, reveals that biomineralization contributes a major component to the overall structure, with approximately half the sinter thickness attributed to silicified microorganisms. Almost all microorganisms observed under the scanning electron microscope (SEM) are mineralized, with epicellular silica ranging in thickness from < 5 μm coatings on individual cells, to regions where entire colonies are cemented together in an amorphous silica matrix tens of micrometres thick. Within the overall profile, there appears to be two very distinct types of laminae that alternate repeatedly throughout the microstromatolite: ‘microbial’ layers are predominantly consisting of filamentous, intact, vertically aligned, biomineralized cyanobacteria, identified as Calothrix and Fischerella sp.; and weakly laminated silica layers which appear to be devoid of any microbial component. The microbial layers commonly have a sharply defined base, overlying the weakly laminated silica, and a gradational upper surface merging into the weakly laminated silica. These cyclic laminations are probably explained by variations in microbial activity. Active growth during spring/summer allows the microorganisms to keep pace with silicification, with the cell surfaces facilitating silicification, while during their natural slow growth phase in the dark autumn/winter months silicification exceeds the bacteria’s ability to compensate (i.e. grow upwards). At this stage, the microbial colony is probably not essential to microstromatolite formation, with silicification presumably occurring abiogenically. When conditions once again become favourable for growth, recolonization of the solid silica surface by free‐living bacteria occurs: cell motility is not responsible for the laminations. We have also observed that microbial populations within the microstromatolite, some several mm in depth, appear viable, i.e. they still have their pigmentation, the trichomes are not collapsed, cell walls are unbroken, cytoplasm is still present and they proved culturable. This suggests that the bulk of silicification occurred rapidly, probably while the cells were still alive. Surprisingly, however, measurements of light transmittance through sections of the microstromatolite revealed that photosynthetically active light (PAL) only transmitted through the uppermost 2 mm. Therefore the ‘deeper’ microbial populations must have either: (i) altered their metabolic pathways; (ii) become metabolically inactive; or (iii) the deeper populations may be dominated by different microbial assemblages from that of the surface. From these collective observations, it now seems unequivocal that microstromatolite formation is intimately linked to microbial activity and that the sinter fabric results from a combination of biomineralization, cell growth and recolonization. Furthermore, the similarities in morphology and microbial component to some Precambrian stromatolites, preserved in primary chert, suggests that we may be witnessing contemporaneous biomineralization processes and growth patterns analogous to those of the early Earth.     

La constante solar

Zusammenfassung Aus der Temperatur der Sonnenoberfläche und der Entfernung Sonne-Erde ergiebt sich die Solarkonstante 2.4 in Uebereinstimmung mit dem rohen Wert, der die Instrument-Temperatur berücksichtigt. Da an den meisten Observatorien die mittägliche Sonnenhöhe nicht ausreicht für eine genaue Bestimmung der Solarkonstante, wird 2.4 als rohe vorläufige Solarkonstante vorgeschlagen, bis im Laufe der nächsten 2 Jahre eine genauere Bestimmung vorliegt. Vermutlich ist auch die Strahlungskonstante von dem Temperaturfehler beeinflusst.     

Fluid-induced mineral composition adjustments during exhumation: the case of Alpine stilbite

Stilbite is locally present as a very late mineral on fractures and fissures of granitic basement in the Central Swiss Alps. Stilbite samples from the Gotthard rail base tunnel provide evidence that they originally formed as a K-absent variety at depth. However, all stilbite samples from surface outcrops above the tunnel display significant potassium concentrations. Interestingly, water from fractures in the tunnel (at 50 °C) is oversaturated with respect to stilbite and essentially potassium-free whereas waters from high-Alpine brooks above the tunnel (and at other high-Alpine areas) have unusually high K/Na ratios. The data suggest that stilbite that may actively form on fissures at tunnel level as a K-absent variety by precipitation from water. Older stilbite that originally formed as coatings on fracture walls was gradually exhumed and uplifted and finally reached the today’s erosion surface about 2,000 m above the tunnel. However, the stilbite reaches the erosion surface as a K-rich variety as a result of interaction of the original low-K stilbite with surface water and near-surface groundwater. This leads to the conclusion that minerals once formed at depth may significantly change their composition once they reach the ground water zone on their way to the erosion surface. In the case of the stilbite, if surface outcrops would have been the only source of samples and data, the K-rich composition could have been mistaken for the composition of the mineral when it formed, which is not the case. Late-stage compositional readjustments may be difficult to discern in samples from surface outcrops. The provided data show that original mineral compositions may be adjusted by late-stage water–rock interaction in a highly selective way.