Ernst Schetselaar

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.

Development of a controlled vocabulary for semantic interoperability of mineral exploration geodata for mining projects

Semantic interoperability of mineral exploration geodata is a long-term concern in mining projects. Inconsistent conceptual schemas and heterogeneous professional terms among various geodata sources in a mining project often hinder their efficient use and/or reuse. Our study of a controlled vocabulary focuses on interoperability of mineral exploration geodata of different mining projects of a mining group in China. In order to achieve this purpose, a proper representation of concepts and their inter-relationships in the knowledge domain of mineral exploration for mining projects is proposed. In addition, we propose that for wider interoperability of mining project geodata the controlled vocabulary underpinning them should be interoperable with concepts in related applications in the mineral exploration domain. In developing our controlled vocabulary, we adopted/adapted national standards of geosciences taxonomies and terminologies. The organization structure of terms, coding method, metadata schema for database applications and an extensible structure of our controlled vocabulary are discussed. The controlled vocabulary we developed was then used to reconcile heterogeneous geodata and to set up integrated databases for various mining projects of the mining group. Our study shows that a properly organized controlled vocabulary not only allows for efficient reconciliation of heterogeneous geodata sources in similar or related projects, but also makes related geodata to be interoperable with extramural applications in the same knowledge domain.

3D GIS as a support for mineral discovery

ABSTRACT Exploration for deep-seated mineral deposits in mature mining camps requires integration of large and heterogeneous spatial data-sets. Traditionally, geological, geochemical, and geophysical observations are acquired, processed and analysed independently within separate spatial contexts or more commonly, for geochemical data, in non-spatial feature space. Although methodological developments are still in progress, 3D GIS (geographic information system) technologies already provide powerful tools that can be used to integrate such heterogeneous data-sets to visualize, compare, and characterize geological relationships in a more supportive interpretive environment. Importantly, this technology provides better opportunities to embed all these properties in a more robust geometric framework in which structural history and palaeogeographic setting can be taken into account. We present 3D GIS applications that aid in interpreting relationship patterns amongst faults, folds and geochemical trends. Examples from the Noranda mining region, a classic VMS mining camp, demonstrate the applicability of 3D GIS to support the discovery of new mineral resources at depth.

3D seismic imaging of the Lalor volcanogenic massive sulphide deposit, Manitoba, Canada

A three-component three-dimensional seismic data set was acquired over the Lalor volcanogenic massive sulphide deposit near Snow Lake,Manitoba, Canada, to assess the reflectivity of the ore and further validate the potential of three-dimensional reflection seismic methods for deep mineral exploration. The Lalor deposit was chosen as a test site as it provided an intact, well-characterized 25-Mt-deep ore deposit with a rich catalogue of geological and geophysical data, as well as extensive drill-core and drill-hole geophysical and geological logs. An analysis of physical rock properties from borehole logging data indicates that massive sulphides associated with the zincrich zones could produce prominent reflections,whereas acoustic impedances of zones with disseminated gold do not sufficiently differ from the impedances of the host rocks to produce reflections. The interpretation of the seismic data is constrained with a detailed three-dimensional lithofacies model constructed from the categorical kriging of 15 lithological units identified in borehole intersections. Processing of the seismic data included prestack dip-moveout and poststack time migration. Final images reveal some strong reflections associated with the zinc-rich massive sulphide zones. The most prominent reflection results from the constructive interference of thin and closely spaced massive sulphide zones and felsic–mafic volcanic rock contacts above and below the mineralization. Contacts between felsic and mafic volcanic rocks, including those that were hydrothermally altered and subsequently metamorphosed, produced prominent and continuous reflections that are used to map the main architecture of the footwall rocks. At depth, a series of continuous and conformable reflections indicate the general geometry of the volcanic sequences in the area of the three-dimensional seismic survey.

Geologically driven 3D modelling of physical rock properties in support of interpreting the seismic response of the Lalor volcanogenic massive sulphide deposit, Snow Lake, Manitoba, Canada

Abstract 3D lithofacies and physical rock property models were generated to interpret 3D seismic data acquired over the Lalor volcanogenic massive sulphide deposit, Manitoba, Canada. The lithofacies model revealed that strong seismic reflectivity is associated with ore–host rock and mafic–felsic lithofacies contacts, including their hydrothermally altered equivalents. Different physical rock property models were subjected to 3D seismic forward modelling using the SOFI3D finite difference code. Seismic synthetics from discrete and interpolated models in which kriging of P-wave velocity and density was conditioned by curvilinear grids conformable to the 3D-modelled geological structure showed a much better match to the seismic data in comparison with those generated by kriging in Cartesian space. Synthetics from these curvilinear grid models corroborate the origin of seismic reflectors, as qualitatively inferred from the lithofacies model. Seismic synthetics generated from physical rock property models in which physical rock properties were augmented by densely sampled secondary variables, such as FeO percentage, enhanced lateral continuity of seismic reflectivity, although these co-kriged petrophysical models were not more accurate than their kriged equivalents. The physical rock property modelling methodology was also useful for testing the utility of passive interferometric seismic surveys, as this highlighted the limitations of the discrete physical rock property model.

Resolution and uncertainty in lithospheric 3-D geological models

As three-dimensional (3-D) modelling of the subcontinental mantle lithosphere is increasingly performed with ever more data and better methods, the robustness of such models is increasingly questioned. Resolution thresholds and uncertainty within deep multidisciplinary 3-D models based on geophysical observations exist at a minimum of three levels. Seismic waves and potential field measurements have inherent limitations in resolution related to their dominant wavelengths. Formal uncertainties can be assigned to grid-search type forward or inverse models of observable parameter sets. Both of these uncertainties are typically minor when compared to resolution limitations related to the density and shape of a specific observation array used in seismological or potential field surveys. Seismic wave source distribution additionally applies in seismology. A fourth, more complex level of uncertainty relates to joint inversions of multiple data sets. Using independent seismic wave phases or combining diverse methods provides another measure of uncertainty of particular physical properties. Extremely sparse xenolith suites provide the only direct correlation of rock type with observed or modelled physical properties at depths greater than a few kilometers. Here we present one case study of the Canadian Mohorovičić (Moho) discontinuity using only two data sets. Refracted and converted seismic waves form the primary determinations of the Moho depth, gravity field modeling provide a secondary constraint on lateral variations, the slope of the Moho, between the sparse seismic estimates. Although statistically marginal, the resulting co-kriged Moho surface correlates better with surface geology and is thus deemed superior.

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.

3D STOCHASTIC GRAVITY INVERSION ON UNSTRUCTURED MESHES

The stochastic gravity inversion on unstructured meshes is presented. The unstructured meshes are used because they provide the flexibility required to closely approximate complicated geological structures. Sharp topographic relief and geological bodies of complex shapes are usually more accurately described by unstructured meshes rather than with regular grids. The forward method has a closed form solution and gives accurate results. A geostatistical method is applied to invert the gravity data.

A drill hole query algorithm for extracting lithostratigraphic contacts in support of 3D geologic modelling in crystalline basement

The identification and extraction of lithostratigraphic contacts in crystalline basement for constraining 3D geologic models is commonly hampered by the sparseness of diagnostic lithostratigraphic features and the limited availability of geophysical well log data. This paper presents a query algorithm that, instead of using geophysical well log measurements, extracts lithostratigraphic contacts by exploiting diagnostic patterns of lithology-encoded intervals, recurrent in adjacent drill holes. The query algorithm allows defining gaps in the pattern to search across unconformable, intrusive and tectonic contacts and allows combining multiple search patterns in a single query to account for lateral lithofacies variations. The performance of the query algorithm has been tested in the Precambrian Flin Flon greenstone belt (Canada) by evaluating the agreement between queried and logged lithostratigraphic contacts in 52 lithostratigraphic reference drill holes. Results show that the automated extraction of the unconformable and partly tectonized contact between metavolcanic rocks and its metasedimentary cover was relatively unambiguous and matched all the contacts previously established by visual inspection of drill core. The 100% match was nevertheless paired with 23% false positives due to mafic and felsic sills emplaced in sandstone and conglomerate, which overlap in composition and thickness with extrusive volcanic rocks. The automated extraction of the contact between a mine horizon, defined by laterally complex volcanic and volcaniclastic lithofacies variations and overlying basalt flows, matched the visually logged contacts for 83% with 27% false positives. The query algorithm supplements geological interpretation when patterns in drilled lithostratigraphic successions, suspected to be diagnostic for lithostratigraphic contacts, need to be extracted from large drill hole datasets in a systematic and time-efficient manner. The application of the query algorithm is particularly relevant for 3D modelling projects in Precambrian shield areas where unique lithostratigraphic markers are difficult to establish or are completely lacking.