A six-step practical approach to semivariogram modeling

Geostatistical prediction and simulation are being increasingly used in the earth sciences and engineering to address the imperfect knowledge of attributes that fluctuate over large areas or volumes—pollutant concentration, electromagnetic fields, porosity, thickness of a geological formation. Central to the application of such techniques is the need to know the spatial continuity, knowledge that is commonly condensed in the form of covariance or semivariogram models. Their preparation is subdivided here into the following steps: (1) Data editing, (2) Exploratory data analysis, (3) Semivariogram estimation, (4) Directional investigation, (5) Simple modeling, (6) Nested modeling. I illustrate these stages practically with a real data set from a geophysical survey from Elk County, Kansas, USA. The applicability of the approach is not limited by the physical nature of the attribute of interest.     

Structure Function Analysis of Two-Scale Scalar Ramps. Part II: Ramp Characteristics and Surface Renewal Flux Estimation

Ramp features in the turbulent scalar field are associated with turbulent coherent structures, which dominate energy and mass fluxes in the atmospheric surface layer. Although finer scale ramp-like shapes embedded within larger scale ramp-like shapes can readily be perceived in turbulent scalar traces, their presence has largely been overlooked in the literature. We demonstrate the signature of more than one ramp scale in structure functions of the turbulent scalar field measured from above bare ground and two types of short plant canopies, using structure-function time lags ranging in scale from isotropic to larger than the characteristic coherent structures. Spectral analysis of structure functions was used to characterize different scales of turbulent structures. By expanding structure function analysis to include two ramp scales, we characterized the intermittency, duration, and surface renewal flux contribution of the smallest (i.e., Scale One) and the dominant (i.e., Scale Two) coherent structure scales. The frequencies of the coherent structure scales increase with mean wind shear, implying that both Scale One and Scale Two are shear-driven. The embedded Scale One turbulent structure scale is ineffectual in the surface-layer energy and mass transport process. The new method reported here for obtaining surface renewal-based scalar exchange works well over bare ground and short canopies under unstable conditions, effectively eliminating the α calibration for these conditions and forming the foundation for analysis over taller and more complex surfaces.     

Comparison of cell- and vertex-centered discretization methods for flow in a two-dimensional discrete-fracture–matrix system

Simulations of flow for a discrete-fracture model in fractured porous rocks have gradually become more practical, as a consequence of increased computer power and improved simulation and characterization techniques. Discrete-fracture models can be formulated in a lower-dimensional framework, where the fractures are modeled in a lower dimension than the matrix, or in an equi-dimensional form, where the fractures and the matrix have the same dimension.     

Biostratigraphy and depositional facies of the Cretaceous-Tertiary boundary strata in Amakusa-Shimojima,Kyushu, Western Japan

The Upper Himenoura Subgroup exposed in the island of Amakusa-Shimojima, Kyushu, Japan shows an example of the terminal Cretaceous stratigraphic record in the circum Pacific region. This sequence is a part of the Upper Cretaceous intra-arc basins of southwest Japan. Four cycles of upward coarse-graded facies are recognized. Each cycle consists of a basinal mud facies in the lower part and a tide-dominated shallow marine to brackish coarse clastic facies in the upper part. Biostratigraphic correlation chiefly based on ammonites, inocerami and trigoniids indicates that this sequence is Campanian to Maastrichtian in age. The occurrence of the above three fossils decreases upward and is terminated at the top of the sequence, being replaced by a molluscan assemblage similar to the Danian. This suggests that the sedimentation may have continued to the very end of the Cretaceous period and possibly to the beginning of the Tertiary.     

Using amphibole phenocrysts to track vapor transfer during magma crystallization and transport: An example from Mount St. Helens,Washington

In order to evaluate and further constrain models for volatile movement and vapor enrichment of magma stored at shallow levels, amphibole phenocrysts from 2004–2005 Mount St. Helens dacite were analyzed for major and selected trace elements (Li, Cu, Zn, Mn, and REE) and Li isotopes. Several recent studies have examined fluid-mobile trace element abundances in phencryst phases and melt inclusions as a means of tracking volatile movement within subvolcanic magmatic systems, and high Li contents in plagioclase phenocrysts from 1980 and 2004 Mount St. Helens dacites have been interpreted as evidence that shallow magma was fluxed by a Li-bearing vapor phase prior to eruption.     

Ocean tide loading (OTL) displacements from global and local grids: comparisons to GPS estimates over the shelf of Brittany, France

In this paper we examine OTL displacements detected by GPS stations of a dedicated campaign and validate ocean tide models. Our area of study is the continental shelf of Brittany and Cotentin in France. Brittany is one of the few places in the world where tides provoke loading displacements of ∼10–12 cm vertically and a few cm horizontally. Ocean tide models suffer from important discrepancies in this region. Seven global and regional ocean tide models were tested: FES2004 corrected for K2, TPXO.7.0, TPXO.6.2, GOT00.2, CSR4.0, NAO.99b and the most recent regional grids of the North East Atlantic (NEA2004). These gridded amplitudes and phases of ocean tides were convolved in order to get the predicted OTL displacements using two different algorithms. Data over a period of 3.5 months of 8 GPS campaign stations located on the north coast of Brittany are used, in order to evaluate the geographical distribution of the OTL effect. We have modified and implemented new algorithms in our GPS software, GINS 7.1. GPS OTL constituents are estimated based on 1-day batch solutions. We compare the observed GPS OTL constituents of M₂, S₂, N₂ and K₁ waves with the selected ocean tide models on global and regional grids. Large phase-lag and amplitude discrepancies over 20° and 1.5 cm in the vertical direction in the semi-diurnal band of M₂ between predictions and GPS/models are detected in the Bay of Mont St-Michel. From a least squares spectral analysis of the GPS time-series, significant harmonic peaks in the integer multiples of the orbital periods of the GPS satellites are observed, indicating the existence of multipath effects in the GPS OTL constituents. The GPS OTL observations agree best with FES2004, NEA2004, GOT00.2 and CSR4.0 tide models.     

The presence, characteristics and earthquake implications of the St. Lawrence fault zone within and near Lake Ontario (Canada–USA)

Questions persist concerning the earthquake potential of the populous and industrial Lake Ontario (Canada–USA) area. Pertinent to those questions is whether the major fault zone that extends along the St. Lawrence River valley, herein named the St. Lawrence fault zone, continues upstream along the St. Lawrence River valley at least as far as Lake Ontario or terminates near Cornwall (Ontario, Canada)–Massena (NY, USA). New geological studies uncovered paleotectonic bedrock faults that are parallel to, and lie within, the projection of that northeast-oriented fault zone between Cornwall and northeastern Lake Ontario, suggesting that the fault zone continues into Lake Ontario. The aforementioned bedrock faults range from meters to tens of kilometers in length and display kinematically incompatible displacements, implying that the fault zone was periodically reactivated in the study area. Beneath Lake Ontario the Hamilton–Presqu'ile fault lines up with the St. Lawrence fault zone and projects to the southwest where it coincides with the Dundas Valley (Ontario, Canada). The Dundas Valley extends landward from beneath the western end of the lake and is marked by a vertical stratigraphic displacement across its width. The alignment of the Hamilton–Presqu'ile fault with the St. Lawrence fault zone strongly suggests that the latter crosses the entire length of Lake Ontario and continues along the Dundas Valley.The Rochester Basin, an east–northeast-trending linear trough in the southeastern corner of Lake Ontario, lies along the southern part of the St. Lawrence fault zone. Submarine dives in May 1997 revealed inclined layers of glaciolacustrine clay along two different scarps within the basin. The inclined layers strike parallel to the long dimension of the basin, and dip about 20° to the north–northwest suggesting that they are the result of rigid-body rotation consequent upon post-glacial faulting. Those post-glacial faults are growth faults as demonstrated by the consistently greater thickness, unit-by-unit, of unconsolidated sediments on the downthrown (northwest) side of the faults relative to their counterparts on the upthrown (southeast) side. Underneath the western part of Lake Ontario is a monoclinal warp that displaces the glacial and post-glacial sediments, and the underlying bedrock–sediment interface. Because of the post-glacial growth faults and the monoclinal warp the St. Lawrence fault zone is inferred to be tectonically active beneath Lake Ontario. Furthermore, within the lake it crosses at least five major faults and fault zones and coexists with other neotectonic structures. Those attributes, combined with the large earthquakes associated with the St. Lawrence fault zone well to the northeast of Lake Ontario, suggest that the seismic risk in the area surrounding and including Lake Ontario is likely much greater than previously believed.     

Singularity and Nonnormality in the Classification of Compositional Data

Geologists may want to classify compositional data and express the classification as a map. Regionalized classification is a tool that can be used for this purpose, but it incorporates discriminant analysis, which requires the computation and inversion of a covariance matrix. Covariance matrices of compositional data always will be singular (noninvertible) because of the unit-sum constraint. Fortunately, discriminant analyses can be calculated using a pseudo-inverse of the singular covariance matrix; this is done automatically by some statistical packages such as SAS. Granulometric data from the Darss Sill region of the Baltic Sea is used to explore how the pseudo-inversion procedure influences discriminant analysis results, comparing the algorithm used by SAS to the more conventional Moore–Penrose algorithm. Logratio transforms have been recommended to overcome problems associated with analysis of compositional data, including singularity. A regionalized classification of the Darss Sill data after logratio transformation is different only slightly from one based on raw granulometric data, suggesting that closure problems do not influence severely regionalized classification of compositional data.     

Observations of the compact group of galaxies Shahbazian 130

Byurakan Astrophysical Observatory and Special Astrophysical Observatory, Academy of Sciences. Translated fromAstrofizika, Vol. 35, No. 1, pp. 67–75, July–August, 1991.