Time variable Earth’s gravity field from SLR satellites

The time variable Earth’s gravity field contains information about the mass transport within the system Earth, i.e., the relationship between mass variations in the atmosphere, oceans, land hydrology, and ice sheets. For many years, satellite laser ranging (SLR) observations to geodetic satellites have provided valuable information of the low-degree coefficients of the Earth’s gravity field. Today, the Gravity Recovery and Climate Experiment (GRACE) mission is the major source of information for the time variable field of a high spatial resolution. We recover the low-degree coefficients of the time variable Earth’s gravity field using SLR observations up to nine geodetic satellites: LAGEOS-1, LAGEOS-2, Starlette, Stella, AJISAI, LARES, Larets, BLITS, and Beacon-C. We estimate monthly gravity field coefficients up to degree and order 10/10 for the time span 2003–2013 and we compare the results with the GRACE-derived gravity field coefficients. We show that not only degree-2 gravity field coefficients can be well determined from SLR, but also other coefficients up to degree 10 using the combination of short 1-day arcs for low orbiting satellites and 10-day arcs for LAGEOS-1/2. In this way, LAGEOS-1/2 allow recovering zonal terms, which are associated with long-term satellite orbit perturbations, whereas the tesseral and sectorial terms benefit most from low orbiting satellites, whose orbit modeling deficiencies are minimized due to short 1-day arcs. The amplitudes of the annual signal in the low-degree gravity field coefficients derived from SLR agree with GRACE K-band results at a level of 77 %. This implies that SLR has a great potential to fill the gap between the current GRACE and the future GRACE Follow-On mission for recovering of the seasonal variations and secular trends of the longest wavelengths in gravity field, which are associated with the large-scale mass transport in the system Earth.

CODE’s new solar radiation pressure model for GNSS orbit determination

The Empirical CODE Orbit Model (ECOM) of the Center for Orbit Determination in Europe (CODE), which was developed in the early 1990s, is widely used in the International GNSS Service (IGS) community. For a rather long time, spurious spectral lines are known to exist in geophysical parameters, in particular in the Earth Rotation Parameters (ERPs) and in the estimated geocenter coordinates, which could recently be attributed to the ECOM. These effects grew creepingly with the increasing influence of the GLONASS system in recent years in the CODE analysis, which is based on a rigorous combination of GPS and GLONASS since May 2003. In a first step we show that the problems associated with the ECOM are to the largest extent caused by the GLONASS, which was reaching full deployment by the end of 2011. GPS-only, GLONASS-only, and combined GPS/GLONASS solutions using the observations in the years 2009–2011 of a global network of 92 combined GPS/GLONASS receivers were analyzed for this purpose. In a second step we review direct solar radiation pressure (SRP) models for GNSS satellites. We demonstrate that only even-order short-period harmonic perturbations acting along the direction Sun-satellite occur for GPS and GLONASS satellites, and only odd-order perturbations acting along the direction perpendicular to both, the vector Sun-satellite and the spacecraft’s solar panel axis. Based on this insight we assess in the third step the performance of four candidate orbit models for the future ECOM. The geocenter coordinates, the ERP differences w. r. t. the IERS 08 C04 series of ERPs, the misclosures for the midnight epochs of the daily orbital arcs, and scale parameters of Helmert transformations for station coordinates serve as quality criteria. The old and updated ECOM are validated in addition with satellite laser ranging (SLR) observations and by comparing the orbits to those of the IGS and other analysis centers. Based on all tests, we present a new extended ECOM which substantially reduces the spurious signals in the geocenter coordinate z (by about a factor of 2–6), reduces the orbit misclosures at the day boundaries by about 10 %, slightly improves the consistency of the estimated ERPs with those of the IERS 08 C04 Earth rotation series, and substantially reduces the systematics in the SLR validation of the GNSS orbits.

Long-term results of therapeutic local anesthesia (neural therapy) in 280 referred refractory chronic pain patients

BACKGROUND: Can the application of local anesthetics (Neural Therapy, NT) alone durably improve pain symptoms in referred patients with chronic and refractory pain? If the application of local anesthetics does lead to an improvement that far exceeds the duration of action of local anesthetics, we will postulate that a vicious circle of pain in the reflex arcs has been disrupted (hypothesis). METHODS: Case series design. We exclusively used procaine or lidocaine. The inclusion criteria were severe pain and chronic duration of more than three months, pain unresponsive to conventional medical measures, written referral from physicians or doctors of chiropractic explicitly to NT. Patients with improvement of pain who started on additional therapy during the study period for a reason other than pain were excluded in order to avoid a potential bias. Treatment success was measured after one year follow-up using the outcome measures of pain and analgesics intake. RESULTS: 280 chronic pain patients were included; the most common reason for referral was back pain. The average number of consultations per patient was 9.2 in the first year (median 8.0). After one year, in 60 patients pain was unchanged, 52 patients reported a slight improvement, 126 were considerably better, and 41 pain-free. At the same time, 74.1 % of the patients who took analgesics before starting NT needed less or no more analgesics at all. No adverse effects or complications were observed. CONCLUSIONS: The good long-term results of the targeted therapeutic local anesthesia (NT) in the most problematic group of chronic pain patients (unresponsive to all evidence based conventional treatment options) indicate that a vicious circle has been broken. The specific contribution of the intervention to these results cannot be determined. The low costs of local anesthetics, the small number of consultations needed, the reduced intake of analgesics, and the lack of adverse effects also suggest the practicality and cost-effectiveness of this kind of treatment. Controlled trials to evaluate the true effect of NT are needed.

Optimal Confidence Bands for Shape-Restricted Curves

Let Y be a stochastic process on [0,1] satisfying dY(t)=n 1/2 f(t)dt+dW(t) , where n≥1 is a given scale parameter (`sample size'), W is standard Brownian motion and f is an unknown function. Utilizing suitable multiscale tests, we construct confidence bands for f with guaranteed given coverage probability, assuming that f is isotonic or convex. These confidence bands are computationally feasible and shown to be asymptotically sharp optimal in an appropriate sense.

A generalisation of the fractional Brownian field based on non-Euclidean norms

We explore a generalisation of the L´evy fractional Brownian field on the Euclidean space based on replacing the Euclidean norm with another norm. A characterisation result for admissible norms yields a complete description of all self-similar Gaussian random fields with stationary increments. Several integral representations of the introduced random fields are derived. In a similar vein, several non-Euclidean variants of the fractional Poisson field are introduced and it is shown that they share the covariance structure with the fractional Brownian field and converge to it. The shape parameters of the Poisson and Brownian variants are related by convex geometry transforms, namely the radial pth mean body and the polar projection transforms.

Risk measures with the CxLS property

In the present contribution, we characterise law determined convex risk measures that have convex level sets at the level of distributions. By relaxing the assumptions in Weber (Math. Finance 16:419–441, 2006), we show that these risk measures can be identified with a class of generalised shortfall risk measures. As a direct consequence, we are able to extend the results in Ziegel (Math. Finance, 2014, http://onlinelibrary.wiley.com/doi/10.1111/mafi.12080/abstract) and Bellini and Bignozzi (Quant. Finance 15:725–733, 2014) on convex elicitable risk measures and confirm that expectiles are the only elicitable coherent risk measures. Further, we provide a simple characterisation of robustness for convex risk measures in terms of a weak notion of mixture continuity.

Fluid-related inclusions in Alpine high-pressure peridotite reveal trace element recycling during subduction-zone dehydration of serpentinized mantle (Cima di Gagnone, Swiss Alps).

Serpentinites release at sub-arc depths volatiles and several fluid-mobile trace elements found in arc magmas. Constraining element uptake in these rocks and defining the trace element composition of fluids released upon serpentinite dehydration can improve our understanding of mass transfer across subduction zones and to volcanic arcs. The eclogite-facies garnet metaperidotite and chlorite harzburgite bodies embedded in paragneiss of the subduction melange from Cima di Gagnone derive from serpentinized peridotite protoliths and are unique examples of ultramafic rocks that experienced subduction metasomatism and devolatilization. In these rocks, metamorphic olivine and garnet trap polyphase inclusions representing the fluid released during high-pressure breakdown of antigorite and chlorite. Combining major element mapping and laser-ablation ICP-MS bulk inclusion analysis, we characterize the mineral content of polyphase inclusions and quantify the fluid composition. Silicates, Cl-bearing phases, sulphides, carbonates, and oxides document post-entrapment mineral growth in the inclusions starting immediately after fluid entrapment. Compositional data reveal the presence of two different fluid types. The first (type A) records a fluid prominently enriched in fluid-mobile elements, with Cl, Cs, Pb, As, Sb concentrations up to 10(3) PM (primitive mantle), similar to 10(2) PM Tit Ba, while Rb, B, Sr, Li, U concentrations are of the order of 10(1) PM, and alkalis are similar to 2 PM. The second fluid (type B) has considerably lower fluid-mobile element enrichments, but its enrichment patterns are comparable to type A fluid. Our data reveal multistage fluid uptake in these peridotite bodies, including selective element enrichment during seafloor alteration, followed by fluid-rock interaction along with subduction metamorphism in the plate interface melange. Here, infiltration of sediment-equilibrated fluid produced significant enrichment of the serpentinites in As, Sb, B, Pb, an enriched trace element pattern that was then transferred to the fluid released at greater depth upon serpentine dehydration (type A fluid). The type B fluid hosted by garnet may record the composition of the chlorite breakdown fluid released at even greater depth. The Gagnone study-case demonstrates that serpentinized peridotites acquire water and fluid-mobile elements during ocean floor hydration and through exchange with sediment-equilibrated fluids in the early subduction stages. Subsequent antigorite devolatilization at subarc depths delivers aqueous fluids to the mantle wedge that can be prominently enriched in sediment-derived components, potentially triggering arc magmatism without the need of concomitant dehydration/melting of metasediments or altered oceanic crust.

Sharp comparison and maximum principles via horizontal normal mapping in the Heisenberg group

In this paper we solve a problem raised by Gutiérrez and Montanari about comparison principles for H−convex functions on subdomains of Heisenberg groups. Our approach is based on the notion of the sub-Riemannian horizontal normal mapping and uses degree theory for set-valued maps. The statement of the comparison principle combined with a Harnack inequality is applied to prove the Aleksandrov-type maximum principle, describing the correct boundary behavior of continuous H−convex functions vanishing at the boundary of horizontally bounded subdomains of Heisenberg groups. This result answers a question by Garofalo and Tournier. The sharpness of our results are illustrated by examples.

Focused fluid transfer through the mantle above subduction zones

Volcanic arcs above subduction zones are enriched in volatiles and fluid-mobile elements with respect to mid-oceanic ridge basalts. There is general consensus that this particular subduction zone signature is generated by fluid-induced extraction of these elements from subducted oceanic crust and its sedimentary cover. However, how these fluids are transferred through the mantle wedge to the locus of partial melting and what modification the fluids will experience is unresolved. Here we investigate the interaction of slab fluids with the mantle wedge through a series of high-pressure experiments. We explore two end-member processes of focused and porous reactive flow of hydrous slab melts through the mantle. Transfer by porous flow leads to the formation of hydrous minerals that sequester fluid-mobile elements and residual fluids characterized by trace element patterns inconsistent with typical arc lavas. In contrast, no hydrous minerals are formed in the reaction zone of experiments mimicking focused flow, and the typical trace element signature acquired during fluid extraction from the slab is preserved, indicating that this is an efficient process for element transfer through the mantle wedge.