Kernel Principal Component Analysis for Efficient,Differentiable Parameterization of Multipoint Geostatistics

This paper describes a novel approach for creating an efficient, general, and differentiable parameterization of large-scale non-Gaussian, non-stationary random fields (represented by multipoint geostatistics) that is capable of reproducing complex geological structures such as channels. Such parameterizations are appropriate for use with gradient-based algorithms applied to, for example, history-matching or uncertainty propagation. It is known that the standard Karhunen–Loeve (K–L) expansion, also called linear principal component analysis or PCA, can be used as a differentiable parameterization of input random fields defining the geological model. The standard K–L model is, however, limited in two respects. It requires an eigen-decomposition of the covariance matrix of the random field, which is prohibitively expensive for large models. In addition, it preserves only the two-point statistics of a random field, which is insufficient for reproducing complex structures. In this work, kernel PCA is applied to address the limitations associated with the standard K–L expansion. Although widely used in machine learning applications, it does not appear to have found any application for geological model parameterization. With kernel PCA, an eigen-decomposition of a small matrix called the kernel matrix is performed instead of the full covariance matrix. The method is much more efficient than the standard K–L procedure. Through use of higher order polynomial kernels, which implicitly define a high-dimensionality feature space, kernel PCA further enables the preservation of high-order statistics of the random field, instead of just two-point statistics as in the K–L method. The kernel PCA eigen-decomposition proceeds using a set of realizations created by geostatistical simulation (honoring two-point or multipoint statistics) rather than the analytical covariance function. We demonstrate that kernel PCA is capable of generating differentiable parameterizations that reproduce the essential features of complex geological structures represented by multipoint geostatistics. The kernel PCA representation is then applied to history match a water flooding problem. This example demonstrates that kernel PCA can be used with gradient-based history matching to provide models that match production history while maintaining multipoint geostatistics consistent with the underlying training image.     

Wave-height distributions and nonlinear effects

Theoretical distributions proposed for describing the crest-to-trough heights of linear waves are reviewed briefly. To explore the effects of nonlinearities, these are generalized to second-order waves, utilizing quasi-deterministic results on the expected shape of large waves. The efficacy of Gram–Charlier models in describing the effects of third-order nonlinearities on the distributions of wave heights, crests and troughs are examined in detail. All models and a fifth-order Stokes–Rayleigh type model recently proposed are compared with linear and nonlinear waves simulated from the JONSWAP spectrum representative of long-crested extreme seas, and also with oceanic data gathered in the North Sea. Uncertainties arising from the variability of probability estimates derived from sample populations of limited size are considered. Ultimately, the comparisons show that nonlinearities do not have any discernable effect on the crest-to-trough heights of oceanic waves. Most of the linear models considered yield similar and reasonable predictions of the observed data trends. Gram–Charlier type distributions seem neither effective nor particularly useful in describing the statistics of large wave heights or crests under oceanic conditions. However, they do surprisingly well in predicting unusually large wave heights and crests observed in some 2D wave-flume experiments and 3D numerical simulations of long-crested narrow-band random waves.     

Monazite chemistry: evidence for a prehistoric journey

The chemistry of monazite from the black sand deposits of northern Sinai beach suggests that pegmatites and granites of the Eastern Desert of Egypt are the most likely source rocks. The floods associated with the pluvial periods prevailed in Egypt during the Pleistocene were able to erode the source rocks and liberate heavy minerals including monazite. The mineral grains were moved through several wadis and tributaries to the River Nile. At the confluence sites, these heavy minerals were mixed with the Ethiopian and central African heavy mineral assemblages. The grains continued to move together downriver until being deposited in their current locations.     

Integration of remote sensing data with the field and laboratory investigation for lithological mapping of granitic phases: Kadabora pluton, Eastern Desert, Egypt

In the current study, an integration of Enhanced Thematic Mapper Plus (ETM+), field, and laboratory data have been used for lithological mapping of different granitic phases in the Kadabora area, Eastern Desert, Egypt. Application of enhancement techniques, including a new proposed band ratio combination (ratio 5/3, 3/1, 7/5 in RGB, respectively) and supervised classification images are used in discriminating different granitic phases in the Kadabora pluton from each other and from their environs. The data have been proved with the help of field and geochemical investigations. The results revealed that: (1) the Kadabora granitic pluton could be distinguished into three phases that recognized by field and laboratory investigation including granodiorite (phase I), monzogranite (phase II), and syeno-alkali feldspar granite (phase III). These phases are arranged according to their relative ages while the country rocks include ophiolitic mélange and metagabbro–diorite complex. It is also confirmed that the granitic pluton is invaded by dyke swarms which is trending in N–S direction. Geochemically, results show that the granodiorite is calc-alkaline, I-type and formed under subduction tectonic regime. Monzogranite falls within the alkaline and highly fractionated calc-alkaline granites, whereas syeno-alkali feldspar granite extends into proper alkaline granitoids field. Monzogranite and syeno-alkali feldspar granite belong to the A₂-subtype granite. This A₂-subtype granite was probably formed in an extensional regime, subsequent to subduction which can lead to tensional break-up of the crust (i.e., post-collisional, post-orogenic granites). The monzogranite and the syeno-alkali feldspar granite were probably formed by partial melting of relatively anhydrous lower crust source and/or tonalite to granodiorite is viable alternative to the granulite source.     

Tonian–Ediacaran Tectonometamorphic History of the Sa’al Complex, Sinai (Egypt): Implications for the Tectonostratigraphic Framework of the Northern Arabian–Nubian Shield

The Sa''al Metamorphic Complex (SMC; southern Sinai) encompasses the oldest arc rocks in the Arabian–Nubian Shield, comprising two non-consanguineous metavolcanic successions (the Agramiya Group and the Post-Ra''ayan Formation) separated by the metasediments of the Ra''ayan Formation. It experienced three distinct deformational events (D1–D3) and two low-medium grade regional metamorphic events (M1–M2). The Agramiya Group and the Ra''ayan Formation experienced all tectonometamorphic events (D1–D3 and M1–M2), whereas the Post-Ra''ayan volcanic rocks were only affected by the D3 and M2 events. D1 is an extensional event and is connected to the late Rodinia break-up (~Tonian; 900–870 Ma). The M1 metamorphism variably affected the older Agramiya Group, the rhyolitic tuffs experiencing lower to upper greenschist facies conditions and the basic and intermediate volcanic rocks undergoing amphibolite facies metamorphism. The Ra''ayan Formation metasediments experienced upper greenschist to amphibolite facies metamorphism. The upper greenschist facies M2 affected the youngest Post-Ra''ayan volcanic rocks and other stratigraphic successions. The compressive D2 and D3 events were coeval with the accretion of dismembered terranes in the assembly of Gondwana. D2 can be linked to the Tonian–Cryogenian arc-arc assembly (~880–760 Ma; in Elat and Sinai), whereas D3 and the accompanying M2 is constrained to 622–600 Ma (Ediacaran).     

Climatology of dust storm frequency and its association with temperature and precipitation patterns over Pakistan

Natural Hazards - Diversified topography and uneven distribution of both temperature and precipitation contribute to formation of suitable synoptic conditions for incidents of dust storm (DS). This...     

Tectonic and Anthropogenic Characteristics of the November 15, 2019 Micro Earthquakes Sequence,Kuwait

Geotectonics - On November 15, 2019, a sequence of small/micro earthquakes struck specific area near an oil production field in the northern part of the State of Kuwait. Generally, the phenomenon...     

Modeling of the radial and transverse components of the albedo function

In this work, we shall confine ourselves to solve analytically the integrals called , for the two components of albedo radiation pressure on an Earth’s satellite. When the Earth’s albedo is variable, as far as we know, this case has not been dealt with analytically. We shall solve these two integrals when the satellite’ horizon is illuminated and when the sun lies on the equator. This approach will facilitate the evaluation of the mentioned two equations. We will also compare our results with previous works obtained numerically.