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. Electronic supplementary materialThe online version of this article (

A B S T R A C TA 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.

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Wireline logs and vertical seismic profile data were acquired in two boreholes intersecting the main mineralized zone at the Cu–Au New Afton porphyry deposit, Canada, with the objectives of imaging lithological contacts, fault zones that may have acted as conduits that channelled the mineralization, and alteration zones. Log data provide physical rock properties for the main lithologies and alteration zones. Calliper logs reveal many faults and caved‐in zones generally indicating rocks with low integrity at the borehole wall. The preponderance of these zones, as indicated by the logs, suggests that their response may dominate the seismic‐reflection wavefield. Outside fault zones, compressional and shear‐wave velocities exhibit significant variability due to porosity, the heterogeneity of volcanic fragmental rocks and alteration. Distributed acoustic sensing was used to acquire vertical seismic profiling data in the two boreholes surveyed with wireline logs. Straight and helically wound fibre‐optic cables housed standard fibres and a fibre engineered to increase the intensity of backscattering at the distributed acoustic sensing interrogator. Standard and engineered optical fibres placed in the two boreholes were daisy‐chained together to form two 5‐km‐long continuous fibres that were interrogated at once with two interrogators. A new generation of interrogator connected to the engineered fibres provided field data with lower noise level and higher signal‐to‐noise ratio. These data with higher signal‐to‐noise ratio from straight fibre‐optic cable were processed and used for depth imaging. Depth images benefitted from new migration weights that account for the directional sensitivity of the straight fibre‐optic cable and limit the extent of migration artefacts. Migration results show several reflectors with shallow dips to the northwest, some explained by faults intersecting the surveyed boreholes. The main sub‐vertical lithological and alteration contacts at New Afton generated downgoing reflections that were not considered in the migration.

The southern Taltson magmatic zone (south of 60°N) is a composite continental magmatic arc and collisional orogen resulting from the convergence of the Buffalo Head terrane with the Archean Churchill craton. Taltson basement (ca. 3.2–3.0 Ga and 2.4–2.14 Ga) and Rutledge River supracrustal gneisses (2.13–2.09 Ga) were intruded by voluminous I- and S-type magmatic rocks between 1.99 and 1.92 Ga. Taltson magmatic zone was deformed by three ductile shear zones: Leland Lakes, Charles Lake, and Andrew Lake, exhibiting both strike- and dip-lineated mylonitic domains. Kinematic data for shear zones are reported at microscopic, mesoscopic, and macroscopic (remotely sensed data) scale. We present field and U–Pb isotopic data (zircon and monazite) for magmatic and metamorphic rocks that constrain the timing of granulite to upper amphibolite-grade shearing in the Leland Lakes and Charles Lake (formerly Allan) shear zones to ca. 1938–1934 Ma. Foreland (easterly) vergent thrusting on the Andrew Lake shear zone is ca. 1932 Ma. Taltson shear zones were overprinted by widespread amphibolite- to greenschist-grade shearing, which is constrained by published 40Ar–39Ar and K–Ar dates on hornblende and muscovite to between ca. 1900 and 1800 Ma. We propose a crustal architecture, resembling a crustal-scale asymmetric flower structure, in which the Charles Lakes shear zone formed the fundamental shear zone of a middle to lower crustal sinistral transpression system that accommodated southward escape of crust in the upper plate of an oblique continental subduction–collision zone, with shortening partitioned into synchronous outwardly vergent thrust systems to the east and west of the main shear zone.