Application of saddlepoint approximation in reliability analysis of dynamic systems

The application of the saddlepoint approximation to reliability analysis of dynamic systems is investigated. The failure event in reliability problems is formulated as the exceedance of a single performance variable over a prescribed threshold level. The saddlepoint approximation technique provides a choice to estimate the cumulative distribution function (CDF) of the performance variable. The failure probability is obtained as the value of the complement CDF at a specif ied threshold. The method requires computing the saddlepoint from a simple algebraic equation that depends on the cumulant generating function (CGF) of the performance variable. A method for calculating the saddlepoint using random samples of the performance variable is presented. The applicable region of the saddlepoint approximation is discussed in detail. A 10-story shear building model with white noise excitation illustrates the accuracy and effi ciency of the proposed methodology.     

Lateral continuity of basement seismic reflections in 15 Ma ultrafast-spreading crust at ODP Site 1256

The Ocean Drilling Program (ODP) initiated drilling at Site 1256D in the Guatemala Basin, about 1,000 km off the East Pacific Rise to penetrate plutonic rocks, anticipated to be relatively shallow in this region, formed at an ultra-fast spreading rate. IODP Expedition E312 successfully drilled into gabbros at ~1,150 m in basement. Multi-channel seismic traces show weak laterally coherent sub-basement reflections at borehole depths. Synthetic reflectivity seismograms were computed using a Ricker wavelet and impedance profiles from borehole sonic logs. These seismograms show significant sub-basement amplitude peaks. A zero-offset vertical seismic profile, shot on E312, was processed to investigate the authenticity of these reflections and their relationship to borehole geology. A dual scheme of the median filtering and F–K dip filtering was used. Tests with synthetic seismograms indicate the approach is effective at reasonable SNR levels. Downgoing energy is clearly identified but negligible upgoing energy is visible over random noise. These results indicate that lava flows and igneous contacts in upper ocean crust have significant topography on lateral scales less than the Fresnel Zone (~300 m) due to igneous and tectonic processes.     

An inter-comparison of tidal solutions computed with a range of unstructured grid models of the Irish and Celtic Sea Regions

Three finite element codes, namely TELEMAC, ADCIRC and QUODDY, are used to compute the spatial distributions of the M₂, M₄ and M₆ components of the tide in the sea region off the west coast of Britain. This region is chosen because there is an accurate topographic dataset in the area and detailed open boundary M₂ tidal forcing for driving the model. In addition, accurate solutions (based upon comparisons with extensive observations) using uniform grid finite difference models forced with these open boundary data exist for comparison purposes. By using boundary forcing, bottom topography and bottom drag coefficients identical to those used in an earlier finite difference model, there is no danger of comparing finite element solutions for “untuned unoptimised solutions” with those from a “tuned optimised solution”. In addition, by placing the open boundary in all finite element calculations at the same location as that used in a previous finite difference model and using the same M₂ tidal boundary forcing and water depths, a like with like comparison of solutions derived with the various finite element models was possible. In addition, this open boundary was well removed from the shallow water region, namely the eastern Irish Sea where the higher harmonics were generated. Since these are not included in the open boundary, forcing their generation was determined by physical processes within the models. Consequently, an inter-comparison of these higher harmonics generated by the various finite element codes gives some indication of the degree of variability in the solution particularly in coastal regions from one finite element model to another. Initial calculations using high-resolution near-shore topography in the eastern Irish Sea and including “wetting and drying” showed that M₂ tidal amplitudes and phases in the region computed with TELEMAC were in good agreement with observations. The ADCIRC code gave amplitudes about 30 cm lower and phases about 8° higher. For the M₄ tide, in the eastern Irish Sea amplitudes computed with TELEMAC were about 4 cm higher than ADCIRC on average, with phase differences of order 5°. For the M₆ component, amplitudes and phases showed significant small-scale variability in the eastern Irish Sea, and no clear bias between the models could be found. Although setting a minimum water depth of 5 m in the near-shore region, hence removing wetting and drying, reduced the small-scale variability in the models, the differences in M₂ and M₄ tide between models remained. For M₆, a significant reduction in variability occurred in the eastern Irish Sea when a minimum 5-m water depth was specified. In this case, TELEMAC gave amplitudes that were 1 cm higher and phases 30° lower than ADCIRC on average. For QUODDY in the eastern Irish Sea, average M₂ tidal amplitudes were about 10 cm higher and phase 8° higher than those computed with TELEMAC. For M₄, amplitudes were approximately 2 cm higher with phases of order 15° higher in the northern part of the region and 15° lower in the southern part. For M₆ in the north of the region, amplitudes were 2 cm higher and about 2 cm lower in the south. Very rapid M₆ tidal-phase changes occurred in the near-shore regions. The lessons learned from this model inter-comparison study are summarised in the final section of the paper. In addition, the problems of performing a detailed model–model inter-comparison are discussed, as are the enormous difficulties of conducting a true model skill assessment that would require detailed measurements of tidal boundary forcing, near-shore topography and precise knowledge of bed types and bed forms. Such data are at present not available.     

Tectonics of southwestern Mexico,isotopic evidence,nuclear Central America,Late Cretaceous break up

In the paleogeographic reconstruction of Mexico and northern Central America, an ever-increasing amount of evidence shows that the entire region is a collage of suspect terranes transported from abroad, whose timing and sense of motion are now beginning to be understood. Among these, the Chortis block (nuclear Central America) and the Baja California Peninsula have been proposed as pieces of continent separated from the Pacific coast of southwestern Mexico, that have moved either southeastward by the Farallon plate or northwestward by the Kula plate. Previous studies mainly confined to the northern margin of the Chortis block, confirmed a left-lateral displacement of 130 km in Neogene time. Further studies made northwestward along the Mexican coast provided a better understanding of magmatic and metamorphic processes in the area, and suggested times of detachment increased to 30 Ma, 40 Ma, and 66 Ma. The pre-detachment westernmost position of the block has changed, depending on the model chosen, from Puerto Vallarta and beyond, to the current position. Here we show that the isotopic mineral ages from coastal granites along the coast from Puerto Vallarta, Jalisco (80 Ma) to Puerto Angel, Oaxaca (11 Ma) record systematic decrease of cooling ages from NW to SE. This pattern is interpreted to result from the progressive uplift of rocks exposed at the present-day coast in that direction, such uplift occurred in response to the development of the Middle America Trench at the newly formed continental margin when the Chortis block was sliding at an average rate of 1.5 cm/year in a sinistral sense to its present position. Our results also constrain the position of the Kula-Farallon spreading axis north of Puerto Vallarta. These observations led us to conclude that several indicators point to this time and region for the onset of strike-slip drifting of the Chortis block toward its current position. Here, we also present several view points in terms of other possilble interpretations to different tectonic, geologic and isotopic data sets published recently by different authors.     

Decay of a highly eccentric satellite

The re-entry phase of a highly eccentric satellite is discussed. Numerical simulations allowing the prediction of the exact date of re-entry of a highly eccentric satellite are exposed.It is shown that under very particular circumstances the life of the satellite can be extended by a few days. The number of final revolutions of the rapidly contracting orbit depends critically on the air density between 70 km and 100 km.Re-entry of the European scientific satellite HEOS-1 predicted for 28 October, 1975 is near such a situation.     

Über den Eisengehalt von Alumosilikaten aus Quarzknauern

Zusammenfassung Der Eisengehalt von Andalusiten und Disthenen aus Quarzknauern im Gebiet des Ötztaler—Stubaier Altkristallins wurde regional untersucht. Der Gehalt and Gesamteisen in primären Disthen liegt zwischen 0,17 und 0,22 Gew.% Fe₂O₃, während primäre Andalusite zwischen 0,26 und 1,93 Gew.% Fe₂O₃ schwanken. Dieser Unterschied in den Andalusiten wird auf ein wechselndes Angebot von Fe₂O₃ aus dem Nachbargestein der Knauern zurückgeführt.Ein Zusammenhang zwischen dem Eisengehalt der Andalusite und den verschiedenen Umwandlungsstadien Andalusit—Disthen konnte nicht nachgewiesen werden.

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On the iron content of alumosilicates in quartz nodules

Summary A determination of the regional distribution of the ironcontent of andalusites and kyanites in quartz-segregations of the Oetztal—Stubai crystalline complex gave values of 0.17–0.22% for the total iron in primary kyanite and 0.26–1.93% in andalusite. This difference is probably due to a variation in the Fe₂O₃-content in the country rocks of the quartz veins. No relationship between the iron-content in andalusite and the different stages of transformation from andalusite to kyanite could be established.

     

Ecological-geochemical assessment of the state of the Volga source of water supply to Moscow

Long-term observational data (1992?C2009) on heavy metal (Cu, Zn, Pb, Cr, Ni, V, Mo, Co, Fe, and Mn) content of different links in the Ivankovo Reservoir ecosystem are used to consider the regularities in the distribution and behavior of heavy metals in the system anthropogenic pollution sources-reservoir and its drainage area, thus enabling the assessment of the pollution level of the Volga Source of water supply to Moscow.     

The Upper Middle Rhine Valley as a risk area

The Upper Middle Rhine Valley, granted the status of a World Heritage site, is well known for its unique inner narrow valley of Quaternary age with its historical legacy of numerous medieval castles and old towns. Less known is that this has always been a risk area of floods and gravitative mass movements. Up to the recent past, mainly ice floods caused enormous damage. The inhabitants of the valley were well aware that they lived in a risk area, but they had learned to handle the flood hazard. With the demise of ice floods over the last 40 years, due to climate change and because of the additional heating of the river water by power plants, the awareness of flood hazards has been much diminished, in contrast to that of potential damage by rockfalls and landslides which were also much feared in the past, though at the local level only. Still in the people’s memory is the Kaub catastrophe of March 10, 1876, when 28 persons were killed by a landslide. Nowadays, even minor rockfalls are a major threat, as they will affect the much-used traffic lines on both banks of the river, in particular the railroads. Therefore, since 2002, on behalf of German Rail (Deutsche Bahn, DB), all problematic slopes have been protected by costly steel-ring nets, although they are an aesthetic problem by UNESCO standards. The feeling of absolute safety created among the public is only subjective, though, as planners are well aware of. Moreover, the impact of modern climate change on slope stability is nearly unknown. Therefore, it is still necessary to develop a risk map for the narrow valley, with emphasis on gravitational hazards.