Eric de Kemp

Archaean quartz arenites in the Canadian Shield: examples from the Superior and Churchill Provinces

Abstract Units of remarkably pure Archaean quartz arenite occur in the northwestern part of the Superior Province and in the northern terrane of the Western Churchill Province (Rae Province) of the Canadian Shield. In the Superior Province, silica-cemented quartz arenites of Archaean age are well preserved in several greenstone belts. The example from the Keeyask Lake sedimentary assemblage displays tabular–planar and trough cross-beds, ripple marks, reactivation surfaces and pebble lag deposits. In spite of penetrative deformation and greenschist-grade metamorphism, primary textures are extremely well preserved, showing framework grains to be very well rounded and sorted. The succession of Keeyask Lake quartz-arenite beds is overlain by siltstones containing small-scale stratiform, domal and columnar stromatolites. A shallow-marine environment of deposition is inferred. Detrital heavy minerals include pyrite, magnetite, zircon, tourmaline, apatite, sphene and topaz. In the northern part of the Western Churchill Province (Rae Province), Archaean quartz arenites occur in northeasterly trending belts where intense structural deformation has in most places obscured or obliterated primary textures and structures. This has led to speculation that some of these units are metachert or recrystallized vein quartz, but local preservation of primary textures and structures provides clear evidence of epiclastic origin. In the example described herein, quartz arenites of the Woodburn Lake Group display sparse occurrences of trough and tabular–planar cross-beds, channels, ripple marks and pebble lag deposits. Probable environments of deposition for these quartz arenites include fluvial systems and shallow-marine shelf settings. The occurrence of unequivocal quartz-arenite clasts in beds of intercalated conglomerate provides direct evidence of at least two episodes of accumulation of almost pure quartz sand. Thin sections and polished slabs reveal frameworks of clastic quartz grains with little to no matrix (now mainly muscovite), and rare detrital grains of accessory heavy minerals, predominantly zircon and opaque iron oxides. Pyrite and other sulphides have been introduced along fractures, but some intergranular sulphide grains may be of detrital origin. The principal source for the quartz arenites in both areas must have been quartz-rich granitoid rocks. Conditions of intense chemical weathering are indicated. The widespread occurrence of extremely mature quartz arenites throughout Archaean terranes of the Canadian Shield, and in other shields of the world, are suggestive of crustal stability during early Earth history. The association of quartz arenites and ultramafic rocks, uncharacteristic of younger terranes, is now recognized in many Archaean greenstone belts of the Canadian Shield.

Three-Dimensional Modelling of Geological Surfaces Using Generalized Interpolation with Radial Basis Functions

A generalized interpolation framework using radial basis functions (RBF) is presented that implicitly models three-dimensional continuous geological surfaces from scattered multivariate structural data. Generalized interpolants can use multiple types of independent geological constraints by deriving for each, linearly independent functionals. This framework does not suffer from the limitations of previous RBF approaches developed for geological surface modelling that requires additional offset points to ensure uniqueness of the interpolant. A particularly useful application of generalized interpolants is that they allow augmenting on-contact constraints with gradient constraints as defined by strike-dip data with assigned polarity. This interpolation problem yields a linear system that is analogous in form to the previously developed potential field implicit interpolation method based on co-kriging of contact increments using parametric isotropic covariance functions. The general form of the mathematical framework presented herein allows us to further expand on solutions by: (1) including stratigraphic data from above and below the target surface as inequality constraints (2) modelling anisotropy by data-driven eigen analysis of gradient constraints and (3) incorporating additional constraints by adding linear functionals to the system, such as fold axis constraints. Case studies are presented that demonstrate the advantages and general performance of the surface modelling method in sparse data environments where the contacts that constrain geological surfaces are rarely exposed but structural and off-contact stratigraphic data can be plentiful.

Introduction to special section: Building complex and realistic geological models from sparse data

Earth scientists have always created spatial models of the subsurface. Before the dawn of computer-based modeling, earth models were simply drawn by hand on a piece of paper as cross section or plan views, sometimes utilizing the techniques of descriptive geometry. These hand-draw models are quick and easy to create; this is why we are still doing them on white boards, note books and sometimes even on napkins. They communicate ideas very well, but they are subjective and rarely constrained by data in a measurable way. As the number of observations grew with the advancement of data collections technologies, the possibility to use mathematical algorithms to do the modeling became a reality. These processes, first applied in 2D then in 3D, removed some of the subjectivity from the modeling. These processes work very well when the data density is high enough, meaning that models built with different mathematical methods are both realistic and similar one to another.

Implicitly modelled stratigraphic surfaces using generalized interpolation

Stratigraphic surfaces implicitly modelled using a generalized interpolation approach in various geological settings is presented to demonstrate its modelling capabilities and limitations. The generalized interpolation approach provides a useful mathematical framework in modelling continuous surfaces from scattered data consisting of the following geological constraints: contact locations and planar orientations. Examples are presented to show the effectiveness of the method in generating plausible representations of geological structures in sparse data environments. One of the major advantages of implicit surface modelling has long been claimed as its ability to model geometries with arbitrary topology. It is, however, demonstrated that this is in fact a disadvantage in robustly generating geologically realistic surfaces in structurally complex domains with a known topology.