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 Analytical Model For Threshold Crossing Rates Of Concentration Fluctuations In Dispersing Plumes

A simple analytical model is developed for the meanupcrossing rate of plume concentration fluctuations assuming that thisprocess can be well approximated by a lognormal process. The resultingexpression requires only the specification of the in-plume fluctuationintensity and in-plume Taylor micro-time scale and, hence, does notexplicitly involve the joint probability density function of theconcentration and its derivative. The analytical model provides agood fit to some field measurements of the mean upcrossing rate ina dispersing plume.     

Study on uncertainty of inversion and resolution limit in the presence of noise

This study analyzed the uncertainty of inversion and the resolution limit in the presence of noise by means of statistical experiments. The exhaustive method is adopted to obtain the global optimal solution in each experiment. We found that even with small level of noise, solutions fluctuate in a large range for the thin bed. The distribution of solutions in the presence of noise is closely related to the spread of the cost function in the absence of noise. As a result, the area of a certain neighborhood around the true solution on the spread of the cost function in the absence of noise is used to evaluate the uncertainty of inversion and the resolution limit in the presence of noise. In the case that the SNR (signal-to-noise ratio) is 5 in this study, solutions focus around the true solution with a very small uncertainty only when the bed thickness is greater than the reciprocal of the double predominant frequency of the convoluting wavelet.     

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.     

Caledonian Low-Temperature Granulite-Facies Metamorphism in the West Kunlun Orogenic Belt—SHRIMP Chronological Evidence from Zircon

The West Kunlun orogenic belt is located at the conjunction of the paleo-Asian tectonic system and the Tethys tectonic system. Petrological and mineralogical studies of the Early Cambrian metamorphic surface crust in this region have shown that in case the metamorphism reached low-temperature granulate facies, the typical mineral assemblage is biotite-garnet-silimanite-K feldspar-plagioclase-quartz. The peak metamorphic temperatures are within the range of 720–740°C and the pressure is 0.6 GPa ±. Three types of metamorphic zircon have been detected in the metamorphic rocks: the complex inclusion-bearing type ; the early relic zircon inclusion-bearing type; and the inclusion-free type. SHRIMP age determination of these three types of metamorphic zircon have revealed that these zircons were formed principally during 400–460 Ma, indicating that pre-Cambrian metamorphic surface crust rocks underwent low-temperature granulite facies metamorphism during the Caledonian. In combination with the geological characteristics of this region, it is considered that when the oceanic basin was closed, there occurred intense intracontinental subduction (type A), bringing part of the Early Cambrian metamorphic basement in this region downwards to the lower crust. Meanwhile, there were accompanied with tectonic deformation at deep levels and medium- to high-grade metamorphism. This study provided important chronological and mineralogical evidence for the exploration of the evolutionary mechanism and process of the West Kunlun Early Paleozoic. Part of the results from the research project “ Research on the West Kunlun pre-Cambrian tectonic events” under the program “ Research on the important geological problems of China’ s pre-Cambrian” (No. 200113900070) sponsored by the China National Geological Surveying Bureau.     

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.     

Integration of reflection seismic and sediment grain-size data from Lake Khubsugul (Northern Mongolia): a reply to Prokopenko and Kendall

Prokopenko and Kendall (J Paleolimnol doi:, 2008) criticise the work presented in Fedotov et al. (J Paleolimnol 39:335–348, 2008), and instead propose an alternative interpretation for the grain-size evolution recorded in the KDP-01 core, retrieved from the central part of Lake Khubsugul. Their interpretation is based (i) on a seismic-stratigraphic re-interpretation of sparker seismic profile khub012 (which they copied from Fedotov et al. (EOS Trans 87:246–250, 2006)), (ii) on the presupposition that changes in lake level are the dominant control on facies distribution in Lake Khubsugul, and (iii) on the invalidation of our age-depth model. In this reply to their comment, we demonstrate that they interpreted seismic artefacts and geometries caused by changes in profile orientation as true stratigraphic features and that the lake-level reconstruction they derive from this interpretation is therefore incorrect. We also demonstrate that their grain-size predictions, which they consider to be predominantly driven by changes in lake level, are inconsistent with the measured sulphate concentration, which is a demonstrated proxy of lake level in Lake Khubsugul, and with the measured grain-size record. Finally, we point out that even if there would be a problem with the age-depth model, this problem would not affect the part of the sedimentary sequence discussed in Fedotov et al. (J Paleolimnol 39:335–348, 2008).     

Impacts of Climatic Factors on Runoff Coefficients in Source Regions of the Huanghe River

Runoff coefficients of the source regions of the Huanghe River in 1956–2000 were analyzed in this paper. In the 1990s runoff of Tangnaihai Hydrologic Station of the Huanghe River experienced a serious decrease, which had at- tracted considerable attention. Climate changes have important impact on the water resources availability. From the view of water cycling, runoff coefficients are important indexes of water resources in a particular catchment. Kalinin baseflow separation technique was improved based on the characteristics of precipitation and streamflow. After the separation of runoff coefficient (R/P), baseflow coefficient (Br/P) and direct runoff coefficient (Dr/P) were estimated. Statistic analyses were applied to assessing the impact of precipitation and temperature on runoff coefficients (including Dr/P, Br/P and R/P). The results show that in the source regions of the Huanghe River, mean annual baseflow coefficient was higher than mean annual direct runoff coefficient. Annual runoff coefficients were in direct proportion to annual pre- cipitation and in inverse proportion to annual mean temperature. The decrease of runoff coefficients in the 1990s was closely related to the decrease in precipitation and increase in temperature in the same period. Over different sub-basins of the source regions of the Huanghe River, runoff coefficients responded differently to precipitation and temperature. In the area above Jimai Hydrologic Station where annual mean temperature is –3.9oC, temperature is the main factor in- fluencing the runoff coefficients. Runoff coefficients were in inverse relation to temperature, and precipitation had nearly no impact on runoff coefficients. In subbasin between Jimai and Maqu Hydrologic Station Dr/P was mainly affected by precipitation while R/P and Br/P were both significantly influenced by precipitation and temperature. In the area be-tween Maqu and Tangnaihai hydrologic stations all the three runoff coefficients increased with the rising of annual precipitation, while direct runoff coefficient was inversely proportional to temperature. In the source regions of the Huanghe River with the increase of average annual temperature, the impacts of temperature on runoff coefficients be-come insignificant.