Practical Incorporation of Multivariate Parameter Uncertainty in Geostatistical Resource Modeling

There is a need to bridge theory and practice for incorporating parameter uncertainty in geostatistical simulation modeling workflows. Simulation workflows are a standard practice in natural resource and recovery modeling, but the incorporation of multivariate parameter uncertainty into those workflows is challenging. However, the objectives can be met without considerable extra effort and programming. The sampling distributions of statistics comprise the core theoretical notion with the addition of the spatial degrees of freedom to account for the redundancy in the spatially correlated data. Prior parameter uncertainty is estimated from multivariate spatial resampling. Simulation-based transfer of prior parameter uncertainty results in posterior distributions which are updated by data conditioning and the model domain extents and configuration. The results are theoretically tractable and practical to achieve, providing realistic assessments of uncertainty by accounting for large-scale parameter uncertainty, which is often the most important component impacting a project. A simulation-based multivariate workflow demonstrates joint modeling of intrinsic shale properties and uncertainty in estimated ultimate recovery in a shale gas project. The multivariate workflow accounts for joint prior parameter uncertainty given the current well locations and results in posterior estimates on global distributions of all modeled properties. This is achieved by transferring the joint prior parameter uncertainty through conditional simulations.     

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.     

Reconstruction of cropland spatial patterns and its spatiotemporal changes over the 20th century on the Songnen Plain,Northeast China

We initially estimated the cropland area at county level using local historical documents for the Songnen Plain (SNP) in the 1910s and 1930s. We then allocated this cropland area to grid cells with a size of 1 km × 1 km, using a range of cultivation possibilities from high to low; this was based on topography and minimum distances to rivers, settlements, and traffic lines. Cropland areas for the 1950s were obtained from the Land Use Map of Northeast China, and map vectorization was performed with ArcGIS technology. Cropland areas for the 1970s, 1980s, 1990s, 2000s, and 2010s were retrieved from Landsat images. We found that the cropland areas were 4.92 × 10⁴ km² and 7.60 × 10⁴ km², accounting for 22.8% and 35.2% of the total area of the SNP in the 1910s and 1930s, respectively, which increased to 13.14 × 10⁴ km², accounting for 60.9% in the 2010s. The cropland increased at a rate of 1.18 × 10⁴ km² per decade from the 1910s to 1970s while it was merely 0.285 × 10⁴ km² per decade from the 1970s to 2010s. From the 1910s to 1930s, new cultivation mainly occurred in the central SNP while, from the 1930s to 1970s, it was mainly over the western and northern parts. This spatially explicit reconstruction could be offered as primary data for studying the effects of changes in human-induced land cover based on climate change over the last century.     

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).     

The property, age and formation environment of the palaeokarst in Qinghai-Xizang Plateau

The karst landforms distributed on the Qinghai-Xizang (Tibet) Plateau can be genetically classed with the Tertiary underground karst, which were gradually exhumed to the surface with the uplift of the plateau during Quaternary period. The relative deposits of the Tertiary palaeokarst processes, such as the residuum and speleothem, were discovered recently in the southern and southeastern fringe areas of the plateau, where has geological-currently been disintegrated by the headward erosion processes of the modern river systems. The major chemical components of the clay portion of the residuum consist mainly of SiO2C, Al2CO3 and Fe2O3. The clay minerals composition of the clay portion belongs to illite-kaolinite pattern for most of the residuum samples, and kaolinite-illite pattern for a few of the samples. It can be judged from the silicic acid index and the clay minerals composition that the formation of the residuum of the Plateau was in its initial phase. However, such a lower chemical weathering index only reflected the weathering degree in the bottom or lower parts of the lateritic weathering crust. The relatively intensive chemical weathering processes of the surface layers of the lateritic weathering crust could be logically speculated. The surface feature textures of quartz grains in the residuum were formed mainly by the chemical erosion, which revealed a long-term humid-tropical environment when the residuum and the palaeokarst formed.     

Relationships between southern Chilean varved lake sediments,precipitation and ENSO for the last 600 years

In this paper, the relationships between paleo-precipitation and the regional influence of El Nino Southern Oscillation (ENSO) in South America are assessed from a high-resolution calendar varve-thickness record. Two short laminated sediment cores (53 and 61 cm length) from Lago Puyehue (40° S) are analysed by continuous varve measurements through the last 600 years. The calendar varve years are determined by the occurrence of graded planktonic-rich layers. The annual sediment accumulation rates are reconstructed by using the standard varve-counting methods on thin sections. The 1980–2000 varve-thickness record is interpreted in terms of climate through correlation with limnological and local monthly instrumental climate databases. The comparison between the standardized varve thickness with the instrumental records reveals a strong correlation (r = 0.75, р = 0.07) between the total varve thickness and the austral autumn/winter precipitation. We argue that strong austral winter winds and precipitation are the forcing factors for the seasonal turn-over and phytoplankton increase in the lake sediments. During strong El Nino events the precipitation and the winds decrease abnormally, hence reducing the thickness of the biogenic sediments deposited after the winter turn-over. Our results show one significant regional maximum peak of winter precipitation (>900 mm) in the mid 20th century and a significant period with lower winter precipitation (<400 mm) before the 15th century, i.e., the late Medieval Warm Period. The first peak in the mid 20th century is confirmed by the regional precipitation database. The influence of ENSO cycles over the last 600 years is assessed by spectral analysis in Fagel et al. (2007). The possible influence of the regional volcanism and/or the seismic activity on the local climate record is also discussed. This is the sixth in a series of eight papers published in this special issue dedicated to the 17,900 year multi-proxy lacustrine record of Lago Puyehue, Chilean Lake District. The papers in this special issue were collected by M. De Batist, N. Fagel, M. -F. Loutre and E. Chapron.