Te Map Research Articles

Braid monodromy of univariate fewnomials

Let $\mathcal{C}_d\subset \mathbb{C}^{d+1}$ be the space of non-singular, univariate polynomials of degree $d$. The Vi\`{e}te map $\mathscr{V} : \mathcal{C}_d \rightarrow Sym_d(\mathbb{C})$ sends a polynomial to its unordered set of roots. It is a classical fact that the induced map $\mathscr{V}_*$ at the level of fundamental groups realises an isomorphism between $\pi_1(\mathcal{C}_d)$ and the Artin braid group $B_d$. For fewnomials, or equivalently for the intersection $\mathcal{C}$ of $\mathcal{C}_d$ with a collection of coordinate hyperplanes in $\mathbb{C}^{d+1}$, the image of the map $\mathscr{V} _* : \pi_1(\mathcal{C}) \rightarrow B_d$ is not known in general. In the present paper, we show that the map $\mathscr{V} _*$ is surjective provided that the support of the corresponding polynomials spans $\mathbb{Z}$ as an affine lattice. If the support spans a strict sublattice of index $b$, we show that the image of $\mathscr{V} _*$ is the expected wreath product of $\mathbb{Z}/b\mathbb{Z}$ with $B_{d/b}$. From these results, we derive an application to the computation of the braid monodromy for collections of univariate polynomials depending on a common set of parameters.

Weakened Lithosphere Beneath Greenland Inferred From Effective Elastic Thickness: A Hot Spot Effect?

AbstractThe effective elastic thickness (Te) of the lithosphere provides geophysical information about long‐term flexural strength and can be used to constrain thermorheological properties of the lithosphere. Te is typically calculated from the spectral analysis of gravity and topography data; variations in Te are, however, not well resolved in Greenland due to poor constraints on crustal structure (including crustal thickness) and complications due to ice loading. In addition, geological and geophysical constraints on the tectonic history of Greenland are sparse due to the thick ice cover. Here we use the global gravity model EIGEN‐6C4 together with a new model of the crust‐mantle boundary to obtain a high‐resolution Te map of Greenland. The distribution of Te indicates reduced strength in the lower crust and lithospheric mantle beneath southern and central Greenland, which may be due to the passage of the Iceland hot spot during the last 100 Ma. In contrast, the northern part of Greenland shows a large Te, implying mechanical coupling between crust and uppermost mantle and suggesting the existence of a cold and strong tectonic unit. In a relative sense, the distribution of Te values is consistent with estimates of lithospheric thickness based on seismic velocity models, indicating a dominantly thermal control on lithospheric structure and evolution.

Effective elastic thickness in the Central Andes. Correlation to orogenic deformation styles and lower crust high-gravity anomaly

Global studies have assessed the importance of elastic thickness (Te) on orogenic evolution, showing that the style and nature of upper crustal shortening are influenced by the inherited lithospheric strength. Thus, pioneer works have identified that the upper crustal deformation style in the easternmost sector of the Central Andes in South America are related to the elastic thickness (Te). There, the thick-skinned and pure-shear style of Santa Bárbara system was initially related to the existence of low Te values. In contrast, the thin-skinned and simple-shear style of deformation in the Subandean system involves high Te values. However, more recent Te studies in the Central Andes present conflicting results which lead to question this straightforward relation. Results from these studies show a strong dependence on the applied methodology hampering the general understanding of the lithospheric thermo-mechanical state of the Central Andes. To contribute to this issue, we perform a high-resolution Te map, using forward modeling by solving flexural equation of infinite plate model in two dimensions. To achieve this, the crust-mantle interface was calculated using a high-resolution gravity anomaly dataset which combines satellite and terrestrial data, and an average density contrast. Additionally, the gravity anomaly and the foreland basin depth in the Central Andes were best predicted by considering that lower crustal rocks fill the space deflected downward in the plate model. The obtained Te values show an inverse correlation with previous heat flow studies, and a strong spatial correlation with the styles and mechanisms of deformation in the easternmost sector of the Central Andes. In the Santa Bárbara system Te values less than 10 km predominate, whereas in the Subandean system high Te values were observed. Such high values correlate with the orogenic curvature and with an shallower gravity Moho zone, which breaks the regional trend of the Central Andes. This shallower gravity Moho is linked to a high-gravity anomaly located in the east part of the Eastern Cordillera and Subandean system. These results are also correlated with a high-velocity zone in the upper mantle previously found by receiver functions studies. This correlation could indicate changes in the properties of the lower crustal rocks that justify the shallower gravity Moho zone and explain in part the highest Te values.

Cenozoic intraplate tectonics in Central Patagonia: Record of main Andean phases in a weak upper plate

Contraction in intraplate areas is still poorly understood relative to similar deformation at plate margins. In order to contribute to its comprehension, we study the Patagonian broken foreland (PBF) in South America whose evolution remains controversial. Time constraints of tectonic events and structural characterization of this belt are limited. Also, major causes of strain location in this orogen far from the plate margin are enigmatic. To unravel tectonic events, we studied the Cenozoic sedimentary record of the central sector of the Patagonian broken foreland (San Bernardo fold and thrust belt, 44°30′S-46°S) and the Andes (Meseta de Chalia, 46°S) following an approach involving growth-strata detection, U-Pb geochronology and structural modeling. Additionally, we elaborate a high resolution analysis of the effective elastic thickness (Te) to examine the relation between intraplate contraction location and variations in lithospheric strength. The occurrence of Eocene growth-strata (~44–40Ma) suggests that contraction in the Andes and the Patagonian broken foreland was linked to the Incaic phase. Detection of synextensional deposits suggests that the broken foreland collapsed partially during Oligocene to early Miocene. During middle Miocene times, the Quechua contractional phase produced folding of Neogene volcanic rocks and olistostrome deposition at ~17Ma. Finally, the presented Te map shows that intraplate contraction related to Andean phases localized preferentially along weak lithospheric zones (Te<15km). Hence, the observed strain distribution in the PBF appears to be controlled by lateral variations in the lithospheric strength. Variations in this parameter could be related to thermo-mechanical weakening produced by intraplate rifting in Paleozoic-Mesozoic times.

The effective elastic thickness of the lithosphere in the collision zone between Arabia and Eurasia in Iran

The effective elastic thickness, Te, has been calculated in the collision zone between Arabia and Eurasia in Iran from the wavelet coherence. The wavelet coherence is calculated from Bouguer anomalies and topography data using the isotropic fan wavelet method, and gives Te values between 14.2 and 62.2km. The lower value is found in the Central Iranian Blocks and the East Iranian Belt which are bounded by several large strike-slip faults with lithospheric origin. The higher value occurs in the east of the South Caspian Sea Basin. The resulting Te map shows positive and negative correlation with shear wave velocity and surface heat flow, respectively. A comparison between the seismogenic thickness (Ts) and Te in Iran suggests that Te>Ts. Results of the load ratio in Iran indicate that in most of the study area surface loads are much more prevalent than subsurface loads, except in the Central Iranian Blocks and NW of Iran. Intermediate to low Te values in Iran were inherited from multiple rifting and orogenic activities from Late Precambrian (∼650Ma) to present day which are not only reflected in thin and warm lithosphere but also an increasing seismicity rate.

Multitaper spectral method to estimate the elastic thickness of South China: Implications for intracontinental deformation

The effective elastic thickness (Te) represents the thickness of the elastic layer or the flexural rigidity of the lithosphere, the equivalent of which can be calculated from the spectral analysis of gravity and topographic data. Studies of Te have profound influence on intracontinental deformation, and coupling of the tectonic blocks. In this paper, we use the multitaper spectral estimation method to calculate the coherence between Bouguer gravity and topography data, and to obtain the Te map of South China. Through the process of correction, we discuss the relationships of Te versus heat flow, and Te versus seismicity. The results show that Te distribution of South China is affected by three factors: the original age, which controls the basic feature; the Mesozoic evolution, which affects the Te distribution; and the neotectonic movement, which shaped the final distribution. The crust age has a positive correlation with the first-order Te distribution; thus the Yangtze Craton has a relatively higher Te (about 50 km) whereas the Te in Cathaysia block is only 10–20 km. By analysis and comparison among the tectonic models of South China, the Te distribution can be well explained using the flat-subduction model. As is typical with neotectonics, the region with a higher heat flow is related with a lower Te. The seismicity does not have a clear relationship with Te, but the strong seismicity could cause a low Te. Seismogenic layer (Ts) has a similar trend as Te in the craton, whereas in other areas the relationship is complex.

Elastic thickness structure of the Andaman subduction zone: Implications for convergence of the Ninetyeast Ridge

We use the Bouguer coherence (Morlet isostatic response function) technique to compute the spatial variation of effective elastic thickness (Te) of the Andaman subduction zone. The recovered Te map resolves regional-scale features that correlate well with known surface structures of the subducting Indian plate and the overriding Burma plate. The major structure on the India plate, the Ninetyeast Ridge (NER), exhibits a weak mechanical strength, which is consistent with the expected signature of an oceanic ridge of hotspot origin. However, a markedly low strength (0<Te<3km) in that region, where the NER is close to the Andaman trench (north of 10°N), receives our main attention in this study. The subduction geometry derived from the Bouguer gravity forward modeling suggests that the NER has indented beneath the Andaman arc. We infer that the bending stresses of the viscous plate, which were reinforced within the subducting oceanic plate as a result of the partial subduction of the NER buoyant load, have reduced the lithospheric strength. The correlation, Te<Ts (seismogenic thickness) reveals that the upper crust is actively deforming beneath the frontal arc Andaman region. The occurrence of normal-fault earthquakes in the frontal arc, low Te zone, is indicative of structural heterogeneities within the subducting plate. The fact that the NER along with its buoyant root is subducting under the Andaman region is inhibiting the subduction processes, as suggested by the changes in trench line, interrupted back-arc volcanism, variation in seismicity mechanism, slow subduction, etc. The low Te and thinned crustal structure of the Andaman back-arc basin are attributed to a thermomechanically weakened lithosphere. The present study reveals that the ongoing back-arc spreading and strike-slip motion along the West Andaman Fault coupled with the ridge subduction exerts an important control on the frequency and magnitude of seismicity in the Andaman region.

A derivation of the free-free emission on the Galactic plane between ℓ= 20° and 44°

We present the derivation of the free-free emission on the Galactic plane between l=20 and 44 degrees and |b| < 4 degrees, using Radio Recombination Line (RRL) data from the HI Parkes All-Sky Survey (HIPASS). Following an upgrade on the RRL data reduction technique, which improves significantly the quality of the final RRL spectra, we have extended the analysis to three times the area covered in Alves et al. (2010). The final RRL map has an angular resolution of 14.8 arcmin and a velocity resolution of 20 km/s. A map of the electron temperature (Te) of the ionised gas is derived for the area under study using the line and continuum data from the present survey. The mean Te on the Galactic plane is 6000 K. The first direct measure of the free-free emission is obtained based on the derived Te map. Subtraction of this thermal component from the total continuum leaves the first direct measure of the synchrotron emission at 1.4 GHz. A narrow component of width 2 degrees is identified in the latitude distribution of the synchrotron emission. We present a list of HII regions and SNRs extracted from the present free-free and synchrotron maps, where we confirm the synchrotron nature of three objects: G41.12-0.21, G41.15+0.39 and G35.59-0.44. We also identify a bright (42 Jy) new double radio galaxy, J1841-0152, previously unrecognised owing to the high optical extinction in the region. The latitude distribution for the RRL-derived free-free emission shows that the WMAP Maximum Entropy Method (MEM) is too high by ~ 50 per cent, in agreement with other recent results. The extension of this study to the inner Galaxy region l=-50 to 50 degrees will allow a better overall comparison of the RRL result with WMAP.

Reappraisal of the effective elastic thickness for the sub-Andes using 3-D finite element flexural modelling, gravity and geological constraints

Estimates of effective elastic thickness (Te) for the western portion of the South American Plate using, independently, forward flexural modelling and coherence analysis, suggest different thermomechanical properties for the same continental lithosphere. We present a review of these Te estimates and carry out a critical reappraisal using a common methodology of 3-D finite element method to solve a differential equation for the bending of a thin elastic plate. The finite element flexural model incorporates lateral variations of Te and the Andes topography as the load. Three Te maps for the entire Andes were analysed: Stewart & Watts (1997), Tassara et al. (2007) and Pérez-Gussinyé (2007). The predicted flexural deformation obtained for each Te map was compared with the depth to the base of the foreland basin sequence. Likewise, the gravity effect of flexurally induced crust—mantle deformation was compared with the observed Bouguer gravity. Te estimates using forward flexural modelling by Stewart & Watts (1997) better predict the geological and gravity data for most of the Andean system, particularly in the Central Andes, where Te ranges from greater than 70 km in the sub-Andes to less than 15 km under the Andes Cordillera. The misfit between the calculated and observed foreland basin subsidence and the gravity anomaly for the Marañon basin in Peru and the Bermejo basin in Argentina, regardless of the assumed Te map, may be due to a dynamic topography component associated with the shallow subduction of the Nazca Plate beneath the Andes at these latitudes.

Effective elastic thickness of South America and its implications for intracontinental deformation

The flexural rigidity or effective elastic thickness of the lithosphere, Te, primarily depends on its thermal gradient and composition. Consequently, maps of the lateral variability of Te in continents reflect their lithospheric structure. We present here a new Te map of South America generated using a compilation of satellite‐derived (GRACE and CHAMP missions) and terrestrial gravity data (including EGM96 and SAGP), and a multitaper Bouguer coherence technique. Our Te maps correlate remarkably well with other proxies for lithospheric structure: areas with high Te have, in general, high lithospheric mantle shear wave velocity and low heat flow and vice versa. In this paper we focus on the Te of the stable platform. We find that old cratonic nuclei (mainly Archean and Early/Middle Proterozoic) have, in general, high Te (&gt;70 km), while the younger Patagonian Phanerozoic terrane has much lower Te (20–30 km), suggesting that Te is related to terrane age as has already been noted in Europe. Within cratonic South America, Te variations are observed at regional scale: relatively lower Te occurs at sites that have been repeatedly reactivated throughout geological history as major sutures, rift zones, and sites of hot spot magmatism. Today, these low Te areas are surrounded by large cratonic nuclei. They concentrate most of the intracontinental seismicity and exhibit relatively high surface heat flow and low seismic velocity at 100 km depth. This implies that intracontinental deformation focuses within relatively thin, hot, and hence weak lithosphere, that cratonic interiors are strong enough to inhibit tectonism, and that the differences in lithospheric rigidity, structure, and composition between stable cratons and sites of intracontinental deformation are not transient, and may have been maintained, in some cases, for at least 500 m.y.

Temperature variations from Hubble Space Telescope imagery and spectroscopy of NGC 7009

We present new Hubble Space Telescope (HST)/WFPC2 imagery and STIS long-slit spectroscopy of the planetary nebula NGC 7009. The primary goal was to obtain high spatial resolution of the intrinsic line ratio [O III] 4364/5008 and thereby evaluate the electron temperature (Te) and the fractional mean-square Te variation (t 2 A ) across the nebula. The WFPC2 Te map is rather uniform; almost all values are between 9000‐11 000 K, with the higher Te values closely coinciding with the inner He ++ zone. The results indicate very small values ‐ 0.01 ‐ for t 2 throughout. Our STIS data allow an even more direct determination of Te and t 2 , albeit for a much smaller area than with WFPC2. We present results from binning the data along the slit into tiles that are 0.5-arcsec square (matching the slit width). The average [O III] temperature using 45 tiles (excluding the central star and STIS fiducial bars) is 10 139 K; t 2 is 0.0035. The measurements of Te reported here are an average along each line of sight. Therefore, despite finding remarkably low t 2, we cannot completely rule out temperature fluctuations along the line of sight as the cause of the large abundance discrepancy between heavy element abundances inferred from collisionally excited emission lines compared to those derived from recombination lines.

Preparation and Characterization of F3Te(map) and the Structure of Cl3Te(map) (map = 2-(methylamino)pyridinato)

The tellurium -nitrogen compounds Cl3Te(map) (1) and F3Te(map) (2) (map = 2-(methylamino)pyridinato), derived from N -silylated map and the corresponding tellurium (IV) halide, have been prepared and characterized. The crystal structure of 1 reveals a dimeric species with two five-coordinate Te(IV) centers that are bridged by longer Te ··· Cl contacts (356 pm average). Crystal data for 1: triclinic, a = 7.280(1), b = 9.512(1), c = 16.004(2) Å, ɑ = 96.67(1), β = 91.95(1), γ = 105.79(1)°, V = 1057(1) Å3, T = 293 K, space group P1̄, Z = 2. Final R and Rw values for 1 are 0.026 and 0.033, respectively.