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.     

Point-block covariance: A general solution for the two-dimensional stationary random functions

The application of the theory of random functions to problems of ore evaluation may involve computations of the covariance between the mean value of a given block and the functional value at a given point. However, an analytical solution for such a covariance does not exist for nonspherical blocks and for commonly applied models of covariance functions. Further, because this covariance is a function of the spatial arrangements of the block and the point, it has to be evaluated numerically each time for given point—block arrangements. This paper presents a readily available general solution to this problem in the form of a series of graduated curves which, together with some geometric manipulations, may be used to compute the covariance between a pointand a two-dimensional block for all possible point—block arrangements. The availability of the graph thus eliminates the necessity of using the time-absorbing programs on computers for such computations. Finally, many of the approximations that are made in order to avoid cumbersome covariance evaluations are no longer necessary due to the ease of such computations with the help of the graph provided.     

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.     

ON THE GENERATION OF P AND S WAVE ENERGY IN CRYSTALLINE ROCKS*

A seismic source consisting of a 700 kg weight that could be dropped vertically or projected down a ramp inclined at 45° to the vertical was tested as a source of P, SV and SH waves within a crystalline rock body at Chalk River, Ontario. The seismic energy was recorded by arrays of both horizontal and vertical-component geophones at distances between 30 and 600 m from the source, which was operated over glacial overburden varying in thickness from less than a meter to a few tens of meters. Seismic energy was more efficiently generated when the overburden thickness was at least several meters. The signals identified visually as S are generally true S, though some may be the converted wave PS. The SV amplitudes are generally larger than those of P, regardless of the type of shot, while the signal frequencies are roughly 60 Hz and 90 Hz, respectively. The horizontal-component seismograms for the inclined shots showed no evidence of SH polarization, and the SH amplitudes were only rarely enhanced relative to P and SV amplitudes on changing from vertical to inclined shots. These unexpected results are attributed to the combined effect of the high velocity and density contrasts and the irregularity of the boundary between the glacial overburden and the rock body.     

Artificial light at night: implications for early life stages development in four temperate freshwater fish species

Flora and fauna have both evolved under a natural cycle of light and dark. But especially in urban areas, the night is now increasingly disturbed by artificial light. Many traits and behaviours in fish are triggered by a circadian clock, for example hatching and swim bladder inflation, which predominantly take place at dusk or night. As lighting becomes brighter and extends farther into rural areas, the distinction between day and night becomes increasingly blurred. Therefore, the loss of diurnal trigger by artificial light at night was hypothesized having deleterious effects on these traits and impact fish reproduction. To assess these effects, eggs of four native freshwater fishes, Eurasian perch Perca fluviatilis, roach Rutilus rutilus, bleak Alburnus alburnus and chub Leuciscus cephalus, were incubated under two different light conditions: a photoperiod of 14 h light:10 h darkness (LD) and continuous illumination (LL). The time to hatch and swim bladder inflation was recorded. The species showed inconsistent reactions to the light treatments. In roach and bleak, the time to 50% hatch was longer in LL, whereas continuous lighting had an accelerating effect in chub. Incubation in LL elongated the hatching period in perch and roach and, in perch, the onset of darkness seemed to trigger hatching. The swim bladder inflation was significantly promoted by continuous light in chub and bleak but was not affected in roach. In conclusion, nocturnal artificial illumination could have an effect on hatching and initial swim bladder filling by masking the day–night-change and thereby diminish the trigger effect. However, the reactions were species specific and the increase in variation indicated a lack of diurnal triggering, whilst a general deleterious effect of artificial light at night has not been identified on early life stages.     

First Data on the Isotopic Age of Zircons from Rocks of the Roseta Ultramafic Massif,Southern Margin of the São Francisco Craton (Brazil)

Doklady Earth Sciences - The results of isotope U–Pb dating of zircons from lherzolite and vein olivine orthopyroxenite composing the Roseta ultramafic massif are presented. The zircons...     

The role of prior model calibration on predictions with ensemble Kalman filter

This paper, based on a real world case study (Limmat aquifer, Switzerland), compares inverse groundwater flow models calibrated with specified numbers of monitoring head locations. These models are updated in real time with the ensemble Kalman filter (EnKF) and the prediction improvement is assessed in relation to the amount of monitoring locations used for calibration and updating. The prediction errors of the models calibrated in transient state are smaller if the amount of monitoring locations used for the calibration is larger. For highly dynamic groundwater flow systems a transient calibration is recommended as a model calibrated in steady state can lead to worse results than a noncalibrated model with a well-chosen uniform conductivity. The model predictions can be improved further with the assimilation of new measurement data from on-line sensors with the EnKF. Within all the studied models the reduction of 1-day hydraulic head prediction error (in terms of mean absolute error [MAE]) with EnKF lies between 31% (assimilation of head data from 5 locations) and 72% (assimilation of head data from 85 locations). The largest prediction improvements are expected for models that were calibrated with only a limited amount of historical information. It is worthwhile to update the model even with few monitoring locations as it seems that the error reduction with EnKF decreases exponentially with the amount of monitoring locations used. These results prove the feasibility of data assimilation with EnKF also for a real world case and show that improved predictions of groundwater levels can be obtained.