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_Journal of Structural Geology 32 (2010) 709-723_ _Contents lists available at ScienceDirect_ _Journal of Structural Geology_ _journal homepage: www.elsevier.com/locate/jsg_ _Surface interpolation within a continental flood basalt province: An example from the Palaeogene Faroe Islands Basalt Group_ _Simon R. Passey*, Thomas Varming_ _Jarfingi, Brekkutun 1, PO Box 3059, FO-110, Tórshavn, Faroe Islands_ _article info_ _Article history: Received 30 September 2009; Received in revised form 22 April 2010; Accepted 29 April 2010; Available online 5 May 2010_ _Keywords: Geographic information system Lithohorizon Spline interpolation Isopach maps Volcanostratigraphy_ _abstract_ _The Faroe Islands Basalt Group (FIBG) is a continental flood basalt province with four proven lithohorizons that have abundant spot height data. The spline interpolation method was used to construct spatial surfaces for the lithohorizons. The resultant surfaces conform to dip and strike estimates that were previously modelled by hand and confirm the methods reliability. The surfaces should be used as guides only, but can be quickly and easily updated as new information becomes available. The surfaces have been used for a variety of different tasks, for example, obtaining gross thickness estimates, producing isopach maps and constructing geological cross-sections. An additional benefit of the spatial surfaces is the ability to constrain disparate observations in a stratigraphic framework, which will be particularly important for future studies attempting to understand, for example, the temporal and spatial development of continental flood basalt volcanism. The spline interpolation method applied in this study can be equally used for other stratigraphic horizons (e.g., chemohorizon, chronohorizon, biohorizon) and in other continental flood basalt provinces (e.g., Deccan Traps, Columbia River Basalt Group)._ _© 2010 Elsevier Ltd. All rights reserved._ _1. Introduction_ _The often monotonous appearance and lack of or inaccessible exposure within continental flood basalt (CFB) provinces can make it difficult to constrain the stratigraphic position of isolated observations. This is important when samples are collected to test, for example, the effects of CFB provinces on palaeo-climate change, e.g., geochronological (palynological or radiometric) and geochemical studies (e.g., Self et al., 2006). The ability to constrain spatially extensive observations in a stratigraphic framework will also considerably improve our understanding of the evolution of CFB provinces and help develop 3D models (e.g., Jerram and Robbe, 2001; Single and Jerram, 2004)._ _In order to achieve this, a stratigraphically defined surface needs to be extrapolated beyond the extent of observations consisting of widespread spot height data. Traditionally, this would be achieved through the triangulation, also known as the three-point problem, of the spot height data and the resulting structural contours would be interpolated across and extrapolated beyond the study area. This method however, produces straight and angular lines for the structural contours that are geologically improbable and in the majority of available Geographic Information Systems (GIS), e.g., ArcGIS 9.2, the structural contours produced by triangulation (i.e., Triangulated Irregular Networks (TIN)) cannot be easily extrapolated outside the extent of the dataset._ _This study describes an alternative methodology employed in ArcGIS 9.2 to extrapolate spot height data to produce a spatial surface on a regional scale. The exposed remnant of the Palaeogene Faroe Islands Basalt Group (FIBG) on the Faroe Islands, NE Atlantic Ocean is chosen as the test area because it has four proven lithostratigraphic surfaces (lithohorizons) with abundant spot height data (Rasmussen and Noe-Nygaard, 1969, 1970; Passey and Jolley, 2009). Different spatial interpolation methods are evaluated through numerical comparison and by contrasting the modelled results to published surfaces that have been drawn by hand. This evaluation process led to the consistent application of the spline tool, part of the spatial analyst extension and the settings applied are presented. The resulting surfaces have been used for a variety of different tasks and include, for example, extracting surface elevations and estimating stratigraphic thicknesses at disparate locations. As an adjunct, the thickness variations across the islands are discussed based on the construction of cross-sections and isopach maps using the interpolated surfaces._ _2. Faroe Islands Basalt Group_ _The FIBG in the NE Atlantic Ocean has a minimum areal extent of ~120,000 km² and an exposed remnant of ~1400 km² occurs on the Faroe Islands (Passey and Jolley, 2009). Across the archipelago the FIBG has a gross stratigraphic thickness of ~6.6 km, where the basal ~3.4 km has only been proven in the Lopra-1 1A borehole (Fig. 1). The FIBG is subdivided into seven lithostratigraphic formations dominated by basalt lava flows and minor volcaniclastic (sedimentary and pyroclastic) lithologies and this study utilises the lithostratigraphy of Passey and Jolley (2009). The archipelago is made up of 18 main islands ranging in size from 0.8 to 373.5 km². The mountainous islands have an average height of 300 m above mean sea level (amsl) and expansive exposures of the geology are limited to near-vertical, inaccessible cliff sections. Inland, profiles through the stratigraphy are primarily restricted to stream sections, although thick (>10 m), tabular sheet lobes (flows that have widths significantly greater than their thicknesses) often form prominent benches that can be traced between streams and around mountainsides._ _The base of the FIBG is represented by the ~1.1 km thick Lopra Formation composed of volcaniclastic lithologies, the majority of which are interpreted as hyaloclastites (Ellis et al., 2002; Waagstein, 2006; Passey and Jolley, 2009). The Lopra Formation is overlain by the ~3.25 km thick Beinisvár Formation dominated by laterally extensive, subaerial basalt sheet lobes (Passey and Bell, 2007). The upper surface of the Beinisvár Formation was eroded down to the second highest sheet lobe and marks an unconformity with the overlying <15 m thick Prestfjall Formation (Rasmussen and Noe-Nygaard, 1969, 1970). The unconformity is referred to as the Beinisvár-Prestfjall Unconformity (BPU) and is exposed on the islands to the south and northwest of the archipelago: Suðuroy, western Vágar and Tindhólmur (Fig. 1; Passey and Jolley, 2009). The Prestfjall Formation is composed of coals, claystones and sandstones deposited in swamp, lacustrine and fluvial environments (Lund, 1989; Ellis et al., 2002; Passey and Jolley, 2009). These units are locally overlain by the Hvannhagi Formation that is exceptionally up to 50 m thick and is composed of airfall tuffs and mass flow deposits (Passey and Jolley, 2009)._ _Lava flow volcanism resumed with the emplacement of the <1.4 km thick Malinstindur Formation dominated by subaerial compound lava flows tens of metres thick, which are made up of thinner flow lobes up to a few metres thick (Passey and Bell, 2007). Within the Malinstindur Formation there are however, a number of laterally extensive volcaniclastic units. One such example is the Kvávk Beds that occurs about two-thirds above the base of the Malinstindur Formation and commonly consists of a bedded volcaniclastic sandstone sequence up to 1.5 m thick (Passey and Jolley, 2009). The Kvávk Beds are generally found towards the base of a ~100 m thick interval dominated by brown weathering, aphyric to olivine-phyric compound basalt lava flows with a distinctive low-TiO₂ geochemistry (Rasmussen and Noe-Nygaard, 1969, 1970; Waagstein, 1988). The Kvávk Beds are exposed across SE Vágar, northern Streymoy and along the NW coastline of Eysturoy (Passey and Jolley, 2009)._ _The upper surface of the Malinstindur Formation is reddened due to weathering and marks a disconformity surface (Malinstindur-Sneis Unconformity (MSU)) overlain by the laterally extensive Sneis Formation (Passey and Jolley, 2009). The Sneis Formation is up to 30 m thick and is typically composed in northern areas by a sandstone and conglomerate pairing that thins to <2 m thick sandstones on Hestur and Sandoy (Passey, 2009; Passey and Jolley, 2009). The occurrence of the conglomerate-dominated Sneis Formation in the field is strikingly obvious due to the ubiquitous association with brown weathering, aphyric to olivine-phyric tabular invasive basalts which contrasts with the surrounding dominantly pale weathering, plagioclase-phyric compound basalt lava flows (Passey, 2009; Passey and Jolley, 2009). The MSU is exposed across the islands of Sandoy, Hestur, Koltur, Streymoy, Eysturoy, Kalsoy, Kunoy, Borðoy and Viðoy (Fig. 1)._ Ключевые слова: hald passey, varming journal, su?uroy, tin layer, passey, applications, jar?feingi t?rshavn, bor?oy, surface, prestfjall hvannhagi, base argir, fibg, childs, island, northern, streymoy, comparison, scale, eds scientic, thickness varies, faroe, andersen, faroe islands, society, rasmussen, core, regularised spline, atlantic, hald, province, sk?lafjar?artunnilin, group, yellow circle, isopach map, bounding area, volcano, data point, author, wa, sill, geological society, jolley bell, willmott, imber, base kv?v?k, circle, enni formation, e-se table, journal structural, interpolation surface, height, ha, highest, produce, faroe-shetland basin, spline interpolation, southern, interpolation, unconformity, kv?v?k beds, spline, varming, passey varming, bell, cfb province, elsevier, fault, kvvk beds, landsverk, beds, surface produced, jerram, volcanism, exposed, american, geological society london, argir, report, interpolated surface, minimal thickness, prestfjall formation, cross, basalt, lithohorizons, j?rgensen, model, science, thickness, spatial surface, structural contour, waagstein, volcanic pile, lava ?ows, interpolation method, regularised, malinstindur formation, sandoyar, passey jolley, red, highest point, svnoy-fugloy sill, stratigraphic framework, faeroe islands, thickness variation, southern area, jay, height data, dip, setting applied, tunnel, spot height, london, argir beds, observed, kriging, journal, saunders, spline tool, surface interpolation, lava, derivative rate, interval, inuence exerted, study, table, addition, lineament, data, rasmussen noe, islands, formation, southern streymoy, noe-nygaard passey, point, dip direction, selected interval, ne, gross, spot, isopach, estimate, modelled, default setting, area, reported dip, vertical accuracy, localised topography, true thickness, gross estimate, interpolated, mathematical geology, method, mit?, skopunarfjrur fault, t?rshavn, derivative, structural, bpu, shield volcano, noe nygaard, geological, structural geology, eds, ellis, cores, mathematical, regularized spline, stratigraphic position, strike, direction, dip measurement, interpolation area, malinstindur, thickest accumulation, h?jgaard, nygaard, geology, noe-nygaard, greeley, jar?feingi, jolley, northern area, modelled surface, dip estimate, rasmussen noe-nygaard, deep, bpu base, msu, faeroe, tested surface, surface modelled, rasmussen noe nygaard, exposed remnant, kv?v?k, derivative weighting, previous strike, lava ows, spatial, malinstindur-sneis unconformity, society london, waagstein waagstein, regional scale, bulletin, observation, beinisv?r?-prestfjall, stratigraphic, base, ?ows, transfer zone, numerical comparison, upper surface, spatial development, noe, isolated observation, eysturoy, sneis formation, map, spatial dependency, walker