Moho depth uncertainties in the Vening-Meinesz Moritz inverse problem of isostasy

We formulate an error propagation model based on solving the Vening Meinesz-Moritz (VMM) inverse problem of isostasy. The system of observation equations in the VMM model defines the relation between the isostatic gravity data and the Moho depth by means of a second-order Fredholm integral equation of the first kind. The corresponding error model (derived in a spectral domain) functionally relates the Moho depth errors with the commission errors of used gravity and topographic/bathymetric models. The error model also incorporates the non-isostatic bias which describes the disagreement, mainly of systematic nature, between the isostatic and seismic models. The error analysis is conducted at the study area of the Tibetan Plateau and Himalayas with the world largest crustal thickness. The Moho depth uncertainties due to errors of the currently available global gravity and topographic models are estimated to be typically up to 1–2 km, provided that the GOCE gravity gradient observables improved the medium-wavelength gravity spectra. The errors due to disregarding sedimentary basins can locally exceed ～2 km. The largest errors (which cause a systematic bias between isostatic and seismic models) are attributed to unmodeled mantle heterogeneities (including the core-mantle boundary) and other geophysical processes. These errors are mostly less than 2 km under significant orogens (Himalayas, Ural), but can reach up to ～10 km under the oceanic crust.     

The variances of tidal harmonics

Summary The variances, or squared standard errors, of estimates of tidal harmonic constants from analyses of a month or a year of tide-gauge data are analysed in terms of spectral properties of their noise continuum, modelled as exponential cuspsE ₁ superimposed on a smoothly monotonic non-tidal spectrumE ₀. Taking 5 representative stations, each with 19 years of data,E ₀ is evaluated from the inter-species noise levels, andE ₁ from the ratio of the variances from monthly and yearly analyses. It is shown that the cusps surrounding the diurnal tides are dominated byE ₀, whereas the more important semi-diurnal and higher species cusps are fitted by an exponential form forE ₁ with bandwidth of a few cycles per year. The variance ratios (monthly: yearly analyses) for diurnal harmonics are somewhat greater than the value expected for white noise, partly because of residual tidal lines in the monthly analyses which cannot be related to the major constituents. The corresponding ratios for semi-diurnal and higher species harmonics are less than the white noise value, on account of the cusps. The standard errors of yearly estimates of the larger tidal constituents may be predicted as proportional to their mean amplitude, as a very rough guide, in the approximate ratio of 11 mm/m.Zusammenfassung Die Varianzen — oder Quadrate der Standardabweichungen — der Abschätzungen von harmonischen Gezeitenkonstanten aus Analysen monatlicher bzw. jährlicher Pegelbeobachtungsreihen werden nach den spektralen Eigenschaften ihres Rauschens analysiert. Dieses wird durch exponentielle SpitzenE ₁, die einem glatten monotonen NichtgezeitenspektrumE ₀ überlagert sind, dargestellt. Anhand 19 jähriger Beobachtungsreihen von 5 repräsentativen Stationen wirdE ₀ aus dem Hintergrundrauschen ermittelt undE ₁ aus dem Verhältnis der Varianzen aus monatlichen und jährlichen Analysen. Es wird gezeigt, daß die Spitzen im Bereich der eintägigen Tiden vonE ₀ beherrscht werden, die wichtigeren Spitzen der halbtägigen Tiden und der Tiden höherer Ordnung werden dagegen durch einen exponentiellen Ausdruck fürE ₁ mit einer Bandbreite von einigen Perioden pro Jahr angenähert. Die Verhältnisse der Varianzen (aus monatlichen zu jährlichen Analysen) für eintägige Harmonische sind etwas größer als der Wert, den man für weißes Rauschen erwarten würde, zum Teil deshalb, weil bei monatlichen Analysen nicht alle Tiden den Hauptkomponenten zugeordnet werden können. Die entsprechenden Verhältnisse für halbtägige und höhere Harmonische sind wegen der Spitzen kleiner als der Wert für weißes Rauschen. Die Standardabweichungen der jährlichen Abschätzungen größerer Gezeitenkomponenten können grob als proportional zu ihrer mittleren Amplitude geschätzt werden mit einem Verhältnis von etwa 11 mm/m.

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Varianzen harmonischer Gezeitenkonstanten

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Les variances des constantes harmoniques de marée

Résumé Les variances, ou carrés des écarts types, des estimations de constantes harmoniques de marée provenant d'analyses portant sur un mois ou une année de données marégraphiques sont analysées en terme de propriétés spectrales de leur continuum de bruit, modélisé comme des pics exponentielsE ₁ superposés à un spectre ne provenant pas de la marée sensiblement monotoneE ₀. Si l'on prend 5 stations représentatives, chacune comportant 19 années d'observations,E ₀ est évalué par les niveaux de bruit inter-espèces, etE ₁ par le rapport des variances provenant des analyses mensuelles et annuelles. On montre que les pics entourant les marées de type diurne sont dominés parE ₀, alors que les pics plus importants de type semidiurne et d'espèces supérieures sont bien approximés par une forme exponentielle pourE ₁ avec une largeur de bande de quelques cycles par an. Les rapports de variance (analyses mensuelles/annuelles) des harmoniques diurnes sont un peu plus grands que la valeur attendue pour le bruit blanc, partiellement à cause des composantes de marée résiduelles dans les analyses mensuelles qui ne peuvent pas être rattachées aux composantes majeures. En raison des pics, les rapports correspondants pour les harmoniques des espèces supérieures et semi-diurnes sont inférieures à la valeur du bruit blanc. Les écarts types des valeurs estimées annuelles des composantes principales de marée peuvent être définis grossièrement comme proportionnels à leur amplitude moyenne, en admettant un rapport de proportionnalité approximatif de 11 mm/m.

     

Fault slip and identification of the second fault plane in the Varzeghan earthquake doublet

An intraplate earthquake doublet, with 11-min delay between the events, devastated the city of Varzeghan in northwestern Iran on August 11, 2012. The first Mw 6.5 strike-slip earthquake, which occurred after more than 200 years of low seismicity, was followed by an Mw 6.4 oblique thrust event at an epicentral separation of about 6 km. While the first event can be associated with a distinct surface rupture, the absence of a surface fault trace and no clear aftershock signature makes it challenging to identify the fault plane of the second event. We use teleseismic body wave inversion to deduce the slip distribution in the first event. Using both P and SH waves stabilize the inversion and we further constrain the result with the surface rupture extent and the aftershock distribution. The obtained slip pattern shows two distinct slip patches with dissimilar slip directions where aftershocks avoid high-slip areas. Using the estimated slip for the first event, we calculate the induced Coulomb stress change on the nodal planes of the second event and find a preference for higher Coulomb stress on the N-S nodal plane. Assuming a simple slip model for the second event, we estimate the combined Coulomb stress changes from the two events on the focal planes of the largest aftershocks. We find that 90% of the aftershocks show increased Coulomb stress on one of their nodal planes when the N-S plane of the second event is assumed to be the correct fault plane.     

Nonlinear modeling of cyclic response of RC beam–column joints reinforced by plain bars

Experience of previous earthquakes shows that a considerable portion of buildings reinforced with plain bars sustain relatively large damages especially at the beam–column joints where the damages are mostly caused by either diagonal shear cracks or intersectional cracks caused by bar slippage. While previous works mainly focus on shear failure mode, in this study, the emphasis is placed on slip based cracks as the dominant failure mode. A systematic procedure is introduced to predict the dominant failure mode at the joint which is based on the dimensional properties, reinforcement details, and axial and shear load at the joint. In addition, a relatively simple and efficient nonlinear model is proposed to simulate pre- and post-elastic behavior of the joints which fail under bar slippage mode. In this model, beam and column components are represented by linear elastic elements, dimensions of the joint panel are defined by rigid elements, and effect of slip is taken into account by a nonlinear rotational spring at the end of the beam. The proposed method is validated by experimental results for both internal and external joints .     

Discovery of a late precambrian volcanic ring-complex at Jebel Abu Nahl,Bayouda Desert,Northern Sudan

A photogeologic study of Jebel Abu Nahl in the Bayouda Desert reveals that it is a Late Precambrian ring-complex, larger and more intricate than the three ring-complexes already known from the Northern Sudan. Like the latter, the Abu Nahl complex must have formed as a result of near-surface volcanic activities whereby extrusion of mainly acid lavas and tuffusites and the emplacement of high-level granites were accompanied by repeated subsidence of surface or near-surface blocks along arcuate ring-faults.