Implementation aspects of sequential Gaussian simulation on irregular points

The increasing use of unstructured grids for reservoir modeling motivates the development of geostatistical techniques to populate them with properties such as facies proportions, porosity and permeability. Unstructured grids are often populated by upscaling high-resolution regular grid models, but the size of the regular grid becomes unreasonably large to ensure that there is sufficient resolution for small unstructured grid elements. The properties could be modeled directly on the unstructured grid, which leads to an irregular configuration of points in the three-dimensional reservoir volume. Current implementations of Gaussian simulation for geostatistics are for regular grids. This paper addresses important implementation details involved in adapting sequential Gaussian simulation to populate irregular point configurations including general storage and computation issues, generating random paths for improved long range variogram reproduction, and search strategies including the superblock search and the k-dimensional tree. An efficient algorithm for computing the variogram of very large irregular point sets is developed for model checking.     

Permian Peri‐glacial Deposits from Central Mongolia in Central Asian Orogenic Belt: A Possible Indicator of the Capitanian Cooling Event

A dropstone‐bearing, Middle Permian to Early Triassic peri‐glacial sedimentary unit was first discovered from the Khangai–Khentei Belt in Mongolia, Central Asian Orogenic Belt. The unit, Urmegtei Formation, is assumed to cover the early Carboniferous Khangai–Khentei accretionary complex, and is an upward‐fining sequence, consisting of conglomerates, sandstones, and varved sandstone and mudstone beds with granite dropstones in ascending order. The formation was cut by a felsic dike, and was deformed and metamorphosed together with the felsic dike. An undeformed porphyritic granite batholith finally cut all the deformed and metamorphosed rocks. LA‐ICP‐MS, U–Pb zircon dating has revealed the following ²⁰⁶Pb/²³⁸U weighted mean igneous ages: (i) a granite dropstone in the Urmegtei Formation is 273 ± 5 Ma (Kungurian of Early Permian); (ii) the deformed felsic dike is 247 ± 4 Ma (Olenekian of Early Triassic); and (iii) the undeformed granite batholith is 218 ± 9 Ma (Carnian of Late Triassic). From these data, the age of sedimentation of the Urmegtei Formation is constrained between the Kungurian and the Olenekian (273–247 Ma), and the age of deformation and metamorphism is constrained between the Olenekian and the Carnian (247–218 Ma). In Permian and Triassic times, the global climate was in a warming trend from the Serpukhovian (early Late Carboniferous) to the Kungurian long and severe cool mode (328–271 Ma) to the Roadian to Bajocian (Middle Jurassic) warm mode (271–168 Ma), with an interruption with the Capitanian Kamura cooling event (266–260 Ma). The dropstone‐bearing strata of the Urmegtei Formation, together with the glacier‐related deposits in the Verkhoyansk, Kolyma, and Omolon areas of northeastern Siberia (said to be of Middle to Late Permian age), must be products of the Capitanian cooling event. Although further study is needed, the dropstone‐bearing strata we found can be explained in two ways: (i) the Urmegtei Formation is an autochthonous formation indicating a short‐term expansion of land glacier to the central part of Siberia in Capitanian age; or (ii) the Urmegtei Formation was deposited in or around a limited ice‐covered continent in northeast Siberia in the Capitanian and was displaced to the present position by the Carnian.     

Kriging in the Presence of Locally Varying Anisotropy Using Non-Euclidean Distances

A stationary specification of anisotropy does not always capture the complexities of a geologic site. In this situation, the anisotropy can be varied locally. Directions of continuity and the range of the variogram can change depending on location within the domain being modeled. Kriging equations have been developed to use a local anisotropy specification within kriging neighborhoods; however, this approach does not account for variation in anisotropy within the kriging neighborhood. This paper presents an algorithm to determine the optimum path between points that results in the highest covariance in the presence of locally varying anisotropy. Using optimum paths increases covariance, results in lower estimation variance and leads to results that reflect important curvilinear structures. Although CPU intensive, the complex curvilinear structures of the kriged maps are important for process evaluation. Examples highlight the ability of this methodology to reproduce complex features that could not be generated with traditional kriging.     

Projection Pursuit Multivariate Transform

Transforming complex multivariate geological data to a Gaussian distribution is an important and challenging problem in geostatistics. A variety of transforms are available for this goal, but struggle with high dimensional data sets. Projection pursuit density estimation (PPDE) is a well-established nonparametric method for estimating the joint density of multivariate data. A central component of the PPDE algorithm transforms the original data toward a multivariate Gaussian distribution. The PPDE approach is modified to map complex data to a multivariate Gaussian distribution within a geostatistical modeling context. Traditional modeling may then take place on the transformed Gaussian data, with a back-transform used to return simulated variables to their original units. This approach is referred to as the projection pursuit multivariate transform (PPMT). The PPMT shows the potential to be an effective means for modeling high dimensional and complex geologic data. The PPMT algorithm is developed before discussing considerations and limitations. A case study compares modeling results against more common techniques to demonstrate the value and place of the PPMT within geostatistics.     

U–Pb zircon age from the radiolarian‐bearing Hitoegane Formation in the Hida Gaien Belt,Japan

The dating of radiolarian biostratigraphic zones from the Silurian to Devonian is only partially understood. Dating the zircons in radiolarian‐bearing tuffaceous rocks has enabled us to ascribe practical ages to the radiolarian zones. To extend knowledge in this area, radiometric dating of magmatic zircons within the radiolarian‐bearing Hitoegane Formation, Japan, was undertaken. The Hitoegane Formation is mainly composed of alternating beds of tuffaceous sandstones, tuffaceous mudstones and felsic tuff. The felsic tuff and tuffaceous mudstone yield well‐preserved radiolarian fossils. Zircon grains showing a U–Pb laser ablation–inductively coupled plasma–mass spectrometry age of 426.6 ± 3.7 Ma were collected from four horizons of the Hitoegane Formation, which is the boundary between the Pseudospongoprunum tauversi to Futobari solidus–Zadrappolus tenuis radiolarian assemblage zones. This fact strongly suggests that the boundary of these assemblage zones is around the Ludlowian to Pridolian. The last occurrence of F. solidus is considered to be Pragian based on the reinterpretation of a U–Pb sensitive high mass‐resolution ion microprobe (SHRIMP) zircon age of 408.9 ± 7.6 Ma for a felsic tuff of the Kurosegawa belt, Southwest Japan. Thus the F. solidus–Z. tenuis assemblage can be assigned to the Ludlowian or Pridolian to Pragian. The present data also contribute to establishing overall stratigraphy of the Paleozoic rocks of the Fukuji–Hitoegane area. According to the Ordovician to Carboniferous stratigraphy in this area, Ordovician to Silurian volcanism was gradually reduced to change the sedimentary environment into a tropical lagoon in the early Devonian. And the quiet Carboniferous environment was subsequently interrupted, throwing it once more into the volcanic conditions in the Middle Permian.     

Early Paleozoic subduction initiation volcanism of the Iwatsubodani Formation,Hida Gaien belt,Southwest Japan

International Journal of Earth Sciences - In placing Japanese tectonics in an Asian context, variation in the Paleozoic geological environment is a significant issue. This paper investigates the...     

Upper Silurian and Devonian pelagic deep-water radiolarian chert from the Khangai–Khentei belt of Central Mongolia: Evidence for Middle Paleozoic subduction–accretion activity in the Central Asian Orogenic Belt

Recent mapping projects undertaken in Central Mongolia have revealed the widespread occurrence of radiolarian chert within a Paleozoic accretionary complex. We present the results of the first detailed tectonostratigraphic and radiolarian biostratigraphic investigations of the Gorkhi Formation in the Khangai–Khentei belt of the Central Asian Orogenic Belt.The Gorkhi Formation consists of sandstone shale, alternating sandstone and shale of turbidite affinity and chert with small amounts of siliceous shale, basalt, limestone, and clast-bearing mudstone. Radiolarian chert that is completely devoid of terrigenous clastic material is commonly associated with underlying basalt (sedimentary contact) and with conformably overlying siliceous shale and turbidite deposits. The tectonic stacking of basalt–chert and chert–turbidite successions is the most remarkable structural feature of the formation.The recovery of moderately well-preserved radiolarians and conodonts from red chert led to the recognition of four radiolarian assemblages that have a combined age range from the latest Silurian (Pridolian) to the Late Devonian (Frasnian). No age control exists for the siliceous shale, shale, and sandstone, although they are considered to be latest Devonian or slightly younger on the basis of stratigraphic relationships with underlying chert.The Gorkhi Formation has previously been interpreted as a thick sedimentary basin deposit overlying an unexposed Archean–Neoproterozoic basement; however, the stratigraphy within individual tectonic slices clearly corresponds to that of an ocean plate stratigraphy of an accretionary complex generated by the trenchward movement of an oceanic plate. From the lowermost to uppermost units, the stratigraphy comprises ocean floor basalt, pelagic deep-water radiolarian chert, hemipelagic siliceous shale, and terrigenous turbidite deposits. The biostratigraphic data obtained in the present study provide corroborating evidence for the existence of an extensive deep-water ocean that enabled the continuous sedimentation of pelagic chert over a period of nearly 50 million years. These data, together with structural data characterized by tectonic repetition of the stratigraphy, indicate that these rocks formed as an accretionary wedge along an active continental margin, possibly that of the Angara Craton. The mid-oceanic chert was probably deposited in the Northern Hemisphere portion of the Paleo–Pacific Ocean that faced the Angara Craton and the North China–Tarim blocks. Thus, we propose that subduction–accretion processes along the Paleo–Pacific rim played an important role in the accretionary growth of the active continental margin of the Angara Craton, directly influencing the evolution of the Central Asian Orogenic Belt.     

Geological setting of basaltic rocks in an accretionary complex,Khangai–Khentei Belt,Mongolia

We describe the mode of occurrence and geochemical characteristics of basalts, in the Khangai–Khentei belt in Mongolia, overlain by Middle Paleozoic radiolarian chert in an extensive accretionary complex. These basalts are greatly enriched in K, Ti, Fe, P, Rb, Ba, Th, and Nb in comparison to the composition of the mid‐ocean ridge basalts, indicative of within‐plate alkaline type. Ti/Y vs Nb/Y and MnO/TiO₂/P₂O₅ ratios of the basalts also suggest within‐plate affinities. Considering the geochemical characteristics as well as the conformable relationship with the overlying radiolarian chert, the alkaline basalts were clearly not continental but formed a pelagic oceanic island. The mode of occurrence and geochemistry of the basalts show that the alkaline basaltic volcanic activity had taken place to form an oceanic island in the Paleozoic pelagic region sufficiently far from continents to allow radiolarian ooze accumulation.     

Estimating Stable Measured Values and Detecting Anomalies in Groundwater Geochemistry Time Series Data Across the Athabasca Oil Sands Area,Canada

Regional groundwater monitoring in the Athabasca region of Alberta, Canada, provides information on groundwater quality and geochemical changes over time, including data useful for evaluating potential impacts of industrial activity such as oil sands mining and in situ operations. Data collected from over 5000 wells from the 1950s to 2014, including 161 wells from government’s monitoring network, were used to develop and apply bootstrap techniques for the detection of changes in groundwater geochemistry over time and at specific points in time. Increasing temporal anomalies were identified in Cl, TDS, B, and naphthenic acids in the McMurray formation across 2003 and 2008, while decreasing anomalies were found for SO₄. Temporal variance for 15 indicators was quantified for a smooth bootstrap approach to arrive at stable values representative of the most recent samples taken from wells in the study area. Stable values revealed sampling bias in the Devonian, Grand Rapids, Empress, Channel Beverly, and Muriel Lake formations suggesting expansion of sampling may be necessary. Although temporal anomalies were found in the McMurray formation, sampling bias was not identified. The entropy and relative magnitude of time series were evaluated to identify candidate wells for continued observations, which consist of wells with low measurements and low entropy that are near active industry lease boundaries. Temporal anomalies, stable values, and entropy were combined into type-well information to provide plots for visual inspection and interpretation. Stable values are useful for regional mapping, for detecting future changes and trends, and for identifying areas of interest warranting further investigation.

     

The Proportional Effect

Many regionalized variables encountered in geostatistical application show a proportional effect, that is, greater variability in high valued areas. The proportional effect is a consequence of the univariate distribution of the variable being considered. This presents several challenges including inference of variograms and conditional distributions. The correlogram and relative variogram were devised to mitigate challenges with variography. Other techniques such as normalization, direct simulation, and indicators provide a means to characterize conditional distributions. A review of these tools is given along with several examples to provide an explanation of the proportional effect.