A Digital Rock Density Map of New Zealand

Computers & Geosciences ] (]]]]) ]]]–]]]

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Computers & Geosciences

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A digital rock density map of New Zealand

Tenzer Robert a,n, Sirguey Pascal a, Rattenbury Mark b, Nicolson Julia a a National School of Surveying, Division of Sciences, University of Otago, 310 Castle Street, Box 56, Dunedin, New Zealand b GNS Science, PO Box 30368, Lower Hutt, New Zealand article info abstract

Article history: Digital geological maps of New Zealand (QMAP) are combined with 9256 samples with rock density Received 22 March 2010 measurements from the national rock catalogue PETLAB and supplementary geological sources to Received in revised form generate a first digital density model of New Zealand. This digital density model will be used to compile a 23 June 2010 new geoid model for New Zealand. The geological map GIS dataset contains 123 unique main rock types Accepted 31 July 2010 spread over more than 1800 mapping units. Through these main rock types, rock densities from measurements in the PETLAB database and other sources have been assigned to geological mapping units. Keywords: A mean surface rock density of 2440 kg/m3 for New Zealand is obtained from the analysis of the derived Crust digital density model. The lower North Island mean of 2336 kg/m3 reflects the predominance of relatively Database young, weakly consolidated sedimentary rock, tephra, and ignimbrite compared to the South Island’s Density 2514 kg/m3 mean where igneous intrusions and metamorphosed sedimentary rocks including schist and Geological mapping Gravimetry gneiss are more common. All of these values are significantly lower than the mean density of the upper Rock types continental crust that is commonly adopted in geological, geophysical, and geodetic applications (2670 kg/m3) and typically attributed to the crystalline and granitic rock formations. The lighter density has implications for the calculation of the geoid surface and gravimetric reductions through New Zealand. & 2010 Elsevier Ltd. All rights reserved.

1. Introduction suggested that this density was used for the first time by Hayford and Bowie (1912). In reviewing several studies seeking a representative The modelling of the geoid from gravimetric data requires a mean density from various rock type formations, Hinze (2003) argued detailed digital terrain model (DTM) and a subsurface rock digital that this value was used earlier by Hayford (1909) for gravity density model (DDM) to compute the topographical effects on the reduction. Hayford (1909) referred to Harkness (1891) who averaged gravity field quantities. In the absence of distributed rock density five published values of surface rock density. Harkness’s (1891) value data, a mean density value is often used and assumed to be constant of 2670 kg/m3 was confirmed later, for instance, by Gibb (1968) who over the study area. The errors in geoid modelling due to neglecting estimated the mean density for the surface rocks in a significant the anomalous topographical density distribution can then reach portion of the Canadian Precambrian shield from over 2000 individual several centimetres, especially in mountainous regions with vari- measurements. Woollard (1962) examined more than 1000 rock able geological composition. While DTMs are currently available samples and estimated that the mean basement (crystalline) rock with a very high accuracy and resolution at global and regional density is about 2740 kg/m3. Subrahmanyam and Verma (1981) scales, DDMs are rarely available. However, recent studies indicate determined that crystalline rocks in low-grade metamorphic terranes that incorporating rock density models (including lakes and inIndiahavethemeandensityof2750kg/m3, while 2850 kg/m3 in glaciers) in the gravimetric geoid modelling process have potential high-grade metamorphic terranes. to improve results (see e.g., Martinec et al., 1995; Martinec, 1998; The geological composition of New Zealand’s land surface is Kuhtreiber,¨ 1998; Huang et al., 2001; Hunegnaw, 2001). dominated by sedimentary rocks (Riddolls, 1987). Many of these A mean density of 2670 kg/m3 is often assumed for the upper rocks were deposited beneath the sea adjacent to the present or past continental crust in geological and gravity surveys, geophysical plate boundaries and later uplifted and juxtaposed by tectonic exploration, gravimetric geoid modelling, compilation of regional movement. The present Australian-Pacific plate boundary is marked gravity maps, and other applications. Although this density value is by the Alpine Fault through much of the South Island. The hard widely used, its origin remains partially obscure. Woollard (1966) ‘‘greywacke’’ sandstone and mudstone of Mesozoic age form large areas of the South Island and the Southern Alps east of the Alpine Fault (Nathan et al., 2002; Rattenbury et al., 2006; Cox and Barrell,

n 2007). Greywacke basement also forms the axial ranges of the Corresponding author. Tel.: +64 3 479 7592; fax: +64 3 479 7586. E-mail addresses: [email protected], southern and eastern North Island (Begg and Johnston, 2000; [email protected] (T. Robert). Mazengarb and Speden, 2000) and eastern Northland (Edbrooke

Please cite this article as: Robert, T., et al., A digital rock density map of New Zealand. Computers and Geosciences (2010), doi:10.1016/ j.cageo.2010.07.010 2 T. Robert et al. / Computers & Geosciences ] (]]]]) ]]]–]]] and Brook, 2010). In central Otago, schist predominates at the digital surface density model for New Zealand. The input data are surface and has originated from metamorphism of the Mesozoic summarized in Section 2. The methodology is described in Section 3. greywacke sedimentary rock (Turnbull, 2000; Forsyth, 2001; A spatial analysis of rock density samples is provided in Section 4. Turnbull and Allibone, 2003; Rattenbury et al., 2010). A great propor- The final digital density model is presented and discussed in Section tion of the southern half of the North Island is formed of soft Neogene 5. The summary and conclusions are given in Section 6. rocks, particularly sandstone and mudstone (Mazengarb and Speden, 2000; Lee and Begg, 2002; Edbrooke, 2005; Townsend et al., 2008). Limestone is widespread throughout the North and 2. Input data South islands and is generally thin, although thicker formations occur south of Auckland, in the Wairarapa, northwest Nelson and The QMAP (Quarter-million MAP) database produced by GNS north Westland, north and south Canterbury and western South- Science provides national geological map coverage at 1:250,000 in land. Large volcanic areas occur in the central and northern North printed and digital form using ESRI’s ArcGIS Geographic Information Island, particularly between Taupo, Bay of Plenty and Coromandel System (GIS) software. The project began in 1994, and was completed Peninsula (Edbrooke, 2001). These deposits comprise a mixture of in 2010, a world-first production of a completely revised national lava flows and domes, lahar and volcano collapse deposits, ignim- geological map series designed and built using GIS software. The brite and tephra, and reworked volcanic sediments resulting from database is derived from numerous sources such as older published repeated volcanic activity over the last 10 million years. Smaller and unpublished geological maps, mining company reports, petroleum volcanic centres are located in Taranaki (Townsend et al., 2008), exploration reports, university theses, unpublished research reports, western Waikato to Auckland (Edbrooke, 2001, 2005), and North- and data collected from new field work. The QMAP geological maps are land (Isaac, 1996; Edbrooke and Brook, 2010). Old volcanic centres compiled at a scale of 1:50,000 and published at 1:250,000. The QMAP form Banks Peninsula (Forsyth et al., 2008)andOtagoPeninsula database contains thematic layers with rich attributes that describe (Bishop and Turnbull, 1996). Intrusive igneous rocks dominated by various features of a geological map. The most relevant for this study granite, diorite, granodiorite and tonalite, but including ultramafic are the geological unit polygons that define the extent of mapping units rocks mostly occur in Nelson, Westland, Fiordland, and Stewart (groups, formations, plutons, etc.). The units mapped are generally the Island (Rattenbury et al., 1998; Nathan et al., 2002; Turnbull and shallowest rock unit more than 5–10 m thick. Thin veneers are Allibone, 2003; Turnbull et al., 2010). Digital geological map data and commonly not depicted in preference for more substantial rock units density measurements are used in this study to generate the first underneath. Key attributes of the geological unit polygons are the main

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Fig. 1. Map of broad groups of main rock types in New Zealand generated from the digital QMAP geological map database.

Please cite this article as: Robert, T., et al., A digital rock density map of New Zealand. Computers and Geosciences (2010), doi:10.1016/ j.cageo.2010.07.010 T. Robert et al. / Computers & Geosciences ] (]]]]) ]]]–]]] 3 and subsidiary rock types, stratigraphic and map unit names, terrane thin veneers or deposits ranging up to several hundred metres thick. affiliation, age expressed in stratigraphic or absolute terms, and Other weakly consolidated deposits such as sand, mud, peat, pumice, lithological description. A map of main rock types in New Zealand tephra, and fill contribute 7% more. Sandstone and related medium- was generated from the digital QMAP database. The QMAP database grained clastic rocks (8.8%) and fine grained clastic rocks (10.7%, identifies 123 main rock types, not including areas of water (lakes) and predominantly mudstone), are more common in the North Island, as ice (glaciers and snowfields). The main rock and other fields within are mafic-intermediate volcanic rocks (3.1% including basalt, ande- geological mapping units and other layers of the QMAP database are site), and ignimbrite and tephra (4.6%). Metasedimentary rock undergoing national standardisation and reconciliation, but for the (4.1%), schist (6.7%) and felsic intrusive rocks (3.2%) such as granite moment contain many anomalies, inconsistencies and use of syno- are almost exclusively from the South Island and Stewart Island. nyms. To overcome some of these problems, the main rock types were PETLAB is the rock catalogue and geo-analytical database of New grouped into 18 broad categories. The generalised geological map of Zealand http://pet.gns.cri.nz (Mortimer, 2005). It is operated by GNS New Zealand consisting of 18 broad categories with place-names is Science in collaboration with the geology departments of New shown in Fig. 1. The only modification to the QMAP main rock source Zealand’s universities. The database contains locations, descriptions data for this study was the reassignment of approximately 60% of and analyses of rock and mineral samples collected throughout the ‘‘sandstone’’ occurrences to ‘‘greywacke’’. Greywacke is a poorly onshore and offshore New Zealand and Antarctica. Information was defined yet widely used term in New Zealand geology and for this study sourced from journal articles, theses, and open file reports. PETLAB it is assigned to the older, more lithified and weakly metamorphosed contains 157,363 sample records from which 40,588 have analytical sandstone-dominated basement terranes that form much of the data (as of June 2010). Wet density measurements compiled from Southern Alps and other axial ranges. This reassignment separates many sources (e.g., Hatherton and Leopard, 1964; Whiteford and these harder rocks from the generally softer Cenozoic sandstone rocks Lumb, 1973) cover 89 rock types collected at 9256 locations in New with consequences for the density measurement calculations. Zealand. The location map of rock density samples from the PETLAB Two main rock types form 42% of New Zealand’s surface rocks as rock catalogue is shown in Fig. 2. defined by the geological mapping units. Greywacke as discussed above, forms 20.5% and gravels form 21.4% of the land area. Gravels 3. Methodology that occur throughout New Zealand are primarily associated with past and present river beds, associated floodplains and alluvial fans, The preparation of the digital density model from the vector GIS scree and tills. They are typically weakly consolidated, occurring as map of main rock types consists of three processing steps (see the

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Fig. 2. The location map of PETLAB rock density samples collected throughout New Zealand.

Please cite this article as: Robert, T., et al., A digital rock density map of New Zealand. Computers and Geosciences (2010), doi:10.1016/ j.cageo.2010.07.010 4 T. Robert et al. / Computers & Geosciences ] (]]]]) ]]]–]]]

flowchart in Fig. 3). First, the densities are assigned to the main rock clinopyroxenite totalling 0.2% of land area) could not be found types of the QMAP database. Since the main rock type applies to one and a value of 2670 kg/m3 has been adopted. or more geological mapping units, the assigned density is assumed to The mean density of the main rock types varies between 900 and represent the geological mapping units also. This results in a vector 3300 kg/m3. The lowest density is attributed to loess, which is an GIS map of main rock type densities. The digital density model is then aeolian sediment formed by the accumulation of wind-blown silt obtained from the vector map after applying the data discretisation and lesser and variable amounts of sand and clay that are loosely and aggregation procedures. cemented by calcium carbonate. It is usually homogeneous and The primary source of information used to allocate the repre- highly porous (Richthofen, 1882; Neuendorf et al., 2005). The sentative densities for 123 main rock types of the QMAP database is highest density is attributed to dunite, an igneous, plutonic rock, of the PETLAB rock catalogue. The PETLAB rock catalogue provides ultramafic composition (cf. Harvey and Tracy, 1996). Dunite 8933 rock density measurements for the 56 main rock types in the typically occurs at the base of ophiolite sequences for instance in QMAP database. The densities that had been measured for each east Nelson and west and south Otago (Rattenbury et al., 1998; sample are dry density, particle density, and wet density. The dry Turnbull, 2000; Turnbull and Allibone, 2003). density represents the rock density measured after all water is The vector map of the main rock type densities was discretised removed from the voids. The particle density is equal to the mass of on a 5 5 arc-sec equal angular grid of geographical coordinates. the dried sample divided by the total grain volume of the sample. The 5 5 arc-sec grid of the main rock type densities was then The wet density value represents the density of the rock when all aggregated into the 1 1 arc-min spatial resolution digital density voids are filled with the fluid. For in situ near subsurface values, the model using a mean operator. wet density measurement is the most appropriate. The wet density values for different rock types throughout New Zealand have been extracted from the PETLAB rock catalogue and tabulated. 4. Analysis of density data The representative value of density for each main rock type was computed by averaging over all PETLAB samples of the same rock The 9256 wet density measurements in the PETLAB database type collected throughout New Zealand. The mean rock densities were averaged to calculate a first order mean density of about and complementary statistics are shown in Table 1. As seen from 2450 kg/m3, with a standard deviation of 360 kg/m3. This value Table 1, variations in density samples taken for the same rock type incorporates some sample bias in the PETLAB dataset, for example often exceed 1000 kg/m3 and can reach 1630 kg/m3 (volcanic unconsolidated sediments such as gravel, sand, clay, and silt that breccias). This indicates the practical restrictions in allocating rock form 28% of the land area are under-represented with only 0.6% of density values objectively. The densities of the remaining 67 main the measured density data. The rock densities vary from 1130 to rock types, for which the information from the PETLAB rock 5480 kg/m3, with 90% of the values ranging between 1780 and catalogue was not found, are allocated according to available 2930 kg/m3 (see Fig. 4). The apparent bimodal distribution of the sources from the literature or by assuming similarity or synon- rock densities reflects sampling bias of dominant rock types, ymity with other rock types. The list of rock density values and the particularly greywacke/schist and generally lighter Cenozoic sedi- references to relevant sources are given in Table 2. A density of 920 mentary and volcanic rocks. and 1000 kg/m3 is attributed to ice and water, respectively. Density Density measurements for the same rock type can vary values for three rock types (broken formation, calc-silicate, substantially due to the dependence on the mineral composition and porosity. This is shown in Fig. 5 which shows the box-plots of density measurement for the 89 main rock types in the PETLAB database. Fig. 5 reveals that the main rock types with lower mean Litterature PETLAB data QMAP database density tend to exhibit a larger dispersion of the sampled density values. Less dense rocks generally correspond to less consolidated sediments such as gravel, boulders, clay, mud, silt, or sand, or volcanic deposits such as tephra and scoria. These deposits may be more prone to variable compaction resulting in a larger variance of Mean density per rock type porosity which affects the density measurements (Hatherton and Leopard, 1964). Denser rocks are typically hard igneous and metamorphosed sedimentary rocks. Assign mean density to the corresponding units for When considering only the main rock types with more than 200 each rock type samples, Fig. 5 shows relatively small dispersions in density measurements for andesite, greywacke, granite, argillite, schist, basalt, and gabbro with a standard deviation consistently lower Convert the vector-based map of density than 200 kg/m3 (Table 1). These seven rock types account for 32% of values to a grid with 5x5 arc-sec spatial the area of New Zealand according to the QMAP dataset. The sampling generalisation of the experimental mean to all corresponding areas in the QMAP dataset is justified by the consistency of their density. Aggregation of the 5x5 arc-sec grid of Among the other main rock types recorded in the PETLAB density to a 1x1 arc-min raster map using a database, tuff, ignimbrite, mudstone, rhyolite, siltstone, and sand- mean operator stone exhibit greater variance with respect to density. There is a general increase in density with age of the map unit which reflects greater compaction reducing void space but also particle density increase with growth of denser metamorphic minerals Hatherton Digital density and Leopard (1964). Variation in density can occur within rocks of model the same stratigraphic unit and is partly attributed to differential compaction from variable depth of burial. The standard deviation 3 Fig. 3. The flowchart of compiling the 1 1 arc-min digital density model from the for these rock types always exceeds 200 kg/m (cf. Table 1). vector GIS map of main rock types. Together, these six classes represent 24% of the area of New

Table 1 The statistics of 56 rock type densities from the PETLAB rock catalogue.

Rock type Mean (kg/m3) STD (kg/m3) Max (kg/m3) Min (kg/m3) Number of samples Area (%)

AMPHIBOLITE 2892 115 3100 2630 62 0.3 ANDESITE 2565 170 2990 1560 418 0.8 ARGILLITE 2691 133 3160 2000 251 0.3 BASALT 2768 162 3060 1780 340 1.7 BRECCIA 2291 295 3000 1540 118 0.3 CHERT 2564 162 2740 2240 11 o0.05 CLAY 2067 171 2450 1920 9 0.1 CLAYSTONE 2067 235 2420 1520 15 0.1 COAL 1712 461 2100 1130 5 o0.05 CONGLOMERATE 2570 159 3000 2110 118 0.9 DACITE 2402 175 2700 1940 79 0.1 DIATOMITE 1528 141 1720 1390 4 o0.05 DIORITE 2797 119 3160 2430 186 1.4 DOLERITE 2749 146 3040 2360 68 o0.05 GABBRO 2884 147 3340 2260 236 0.4 GNEISS 2812 179 3150 1830 149 0.5 GRANITE 2640 77 2940 2330 288 2.3 GRANODIORITE 2681 70 2940 2530 53 0.6 GRANULITE 2765 332 3000 2530 2 o0.05 GRAVEL 2309 266 2580 1870 9 21.4 GREENSAND 2365 168 2520 2210 4 o0.05 GREENSCHIST 2923 133 3130 2620 15 0.2 GREYWACKE 2639 100 2940 2090 469 20.5 HORNFELS 2800 143 3080 2590 22 o0.05 IGNIMBRITE 2125 247 2620 1240 916 4.6 LAMPROPHYRE 2910 177 3390 2650 15 o0.05 LAVA 2680 93 2820 2540 6 o0.05 LIGNITE 1390 204 1670 1210 6 o0.05 LIMESTONE 2484 211 3010 1890 156 o0.05 MARBLE 2716 117 3140 2510 22 o0.05 METAVOLCANIC 2955 124 3150 2760 11 o0.05 MUDSTONE 2204 301 2870 1320 734 8.1 MYLONITE 2757 91 2930 2620 11 0.1 PERIDOTITE 3093 225 3340 2340 118 o0.05 PHONOLITE 2536 70 2630 2470 5 o0.05 PUMICE 1719 310 2230 1150 29 0.1 PYROCLASTIC 1986 512 2350 1130 5 o0.05 PYROXENITE 3122 218 3330 2240 25 o0.05 QUARTZITE 2612 73 2780 2490 29 0.1 RHYOLITE 2207 225 2740 1360 704 0.5 SAND 2048 351 3220 1690 27 3.2 SANDSTONE 2463 266 3000 1510 968 8.2 SCHIST 2732 115 3100 2120 419 5.8 SERPENTINITE 2634 219 3270 2240 87 0.1 SHALE 2335 190 2730 1610 193 o0.05 SILT 1979 140 2160 1720 14 0.2 SILTSTONE 2347 283 2880 1360 471 2.0 SINTER 2510 14 2520 2500 2 o0.05 SPILITE 2863 121 3090 2500 82 0.1 SYENITE 2719 145 2860 2440 15 o0.05 TEPHRA 1637 98 1750 1580 3 o0.05 TRACHYTE 2591 182 2950 2170 31 o0.05 TUFF 2113 289 2940 1410 723 0.2 ULTRAMAFIC 3288 517 4130 2750 5 o0.05 VOLCANICS 2362 471 3090 1480 110 o0.05 VOLCANIC BRECCIA 2195 358 2950 1320 60 o0.05

Zealand. For such classes, the generalisation of the mean value observation iAf1,...,ng and di the measured density at that position (i.e., that obtained from samples attributed to a main rock type in the (both are obtained from the PETLAB database), then the experi- PETLAB database) to all corresponding areas of the QMAP dataset mental semi-variogram is expressed as may be an oversimpliﬁcation. Nevertheless, it is believed that an 1 X average value per class, along with the spatial distribution enabled g^ðhÞ¼ 9d d 92 9 ð Þ9 i j by the combination with the QMAP dataset, remains a more suitable 2 N h ði,jÞ A NðhÞ outcome than a global mean density for the whole region. In order to investigate further the statistical structure of the where g^ðhÞ is the estimator of the semi-variogram at lag (i.e., for density samples, the latter were examined within the framework of samples obtained at an approximate distance h from each other), 2 geostatistics. In this context, the experimental semi-variogram is NðhÞ¼fði,jÞA½1,...,n : JxixjJ ¼ h7eg is the set of pairs of obser- an essential tool that permits the variance of a spatially distributed vations (i, j) that are at an approximate distance h from each other quantity to be analysed as a function of the distance between (i.e., given a certain tolerance e), and 9N(h)9 is the cardinality of the samples (Cressie, 1993). Let xi be the positional vector of set N(h). The semi-variogram indicates the degree of spatial

Please cite this article as: Robert, T., et al., A digital rock density map of New Zealand. Computers and Geosciences (2010), doi:10.1016/ j.cageo.2010.07.010 6 T. Robert et al. / Computers & Geosciences ] (]]]]) ]]]–]]]

Table 2 The representative density values of 67 main rock types allocated according to supplementary geological sources.

Rock type Area (%) Density (kg/m3) Source and comment

LOESS 0.2 900 Johnson and Lorenz (2000) PEAT 0.7 1040 Schon (1996) PYROCLASTIC BREC o0.05 1600 Hall et al. (1999) MUD 1.3 1910 Clark (1966) VITRIC TUFF o0.05 2113 The adopted density the same as for Tuff LAPILLI TUFF o0.05 2113 The adopted density the same as for Tuff CALCAREOUS MUDSTONE o0.05 2200 The adopted density the same as for Mudstone CATACLASITE o0.05 2291 The adopted density the same as for Breccia LEUCOGRANITE o0.05 2291 Annen and Scaillet (2006) TILL 0.1 2310 Balco and Stone (2003) RHYODACITE o0.05 2350 Hildreth et al. (2004) HORNBLENDITE o0.05 2370 Clark (1966) BOULDERS 0.1 2400 Nott (2003) DEBRIS 0.9 2400 The adopted density the same as for boulders FILL o0.05 2400 The adopted density the same as for boulders TURBIDITE 0.5 2410 Average density of Sandstone and siltstone VOLCANIC SANDSTONE 0.2 2460 The adopted density the same as for sandstone HAWAIITE 0.3 2470 Carmichael (1982) ALGAL LIMESTONE o0.05 2480 The adopted density the same as for limestone COQUINA o0.05 2480 The adopted density the same as for limestone MICRITE o0.05 2480 The adopted density the same as for limestone SHELL BEDS o0.05 2482 The adopted density the same as for limestone (2484) KERATOPHYRE o0.05 2500 Morrow and Lockner (2001) PORPHYRY o0.05 2550 Andrew (1995) SCORIA o0.05 2550 Tamari et al. (2005) METACHERT o0.05 2560 The adopted density the same as for Chert PELITE o0.05 2560 Pettijohn (1975) ANDESITE AGGLOMERATE o0.05 2570 The same as Andesite and Conglomerate ANDESITE CONGLOMERATE o0.05 2570 The same as Andesite and Conglomerate METACONGLOMERATE o0.05 2570 The adopted density the same as for Conglomerate VOLCANIC CONGLOMERATE o0.05 2570 The adopted density the same as for Conglomerate MONZODIORITE 0.1 2580 Llambias et al. (1977) SYENOGRANITE o0.05 2610 Gaal et al. (1981) ANDESITE LAVA o0.05 2630 Hildreth et al. (2004) ORTHOGNEISS 0.1 2630 Giacomini et al. (2009) PSAMMITE 0.2 2639 The adopted density the same as for Greywacke TRONDHJEMITE o0.05 2640 Carmichael (1982) MELANGE 0.5 2660 Kimura et al. (2001) BASALTIC ANDESITE o0.05 2670 Average density of Basalt and Andesite BROKEN FORMATION 0.2 2670 No information found CALC-SILICATE o0.05 2670 No information found CLINOPYROXENITE o0.05 2670 No information found SEMISCHIST 0.8 2686 Average density of Schist and Greywacke BIOSPARITE o0.05 2690 Allaby (1999) MONZOGRANITE o0.05 2690 Oliveira et al. (2008) DIORITIC ORTHOGNEISS 0.1 2700 Pechinig et al. (2005) GABBROIC ORTHOGNEISS o0.05 2700 Pechinig et al. (2005) GRANITOID o0.05 2700 Rao et al. (2008) METASANDSTONE 2.0 2700 Carmichael (1982) OLIVINE BASALT o0.05 2700 Arrnienti et al. (1991) PARAGNEISS 0.2 2700 Samalikova (1983) TRAVERTINE o0.05 2710 Russell and Pellant (1981) GREYSCHIST 0.9 2730 The adopted density the same as for Schist PHYLLONITE o0.05 2740 Wibberley and McCaig (2000) METAPELITE 1.1 2750 Dyda (1994) QUARTZ MONZODIORITE o0.05 2770 Clark (1966) METAPSAMMITE o0.05 2800 Clark (1966) TONALITE 0.2 2800 Nettleton et al. (1969) QUARTZ DIORITE 0.1 2810 Clark (1966) ANORTHOSITE o0.05 2810 Clark (1966) MIGMATITE o0.05 2812 The adopted density the same as for Gneiss GABBRONORITE o0.05 2970 Vankova and Kropacek (1974) LIMBURGITE o0.05 2970 Vankova and Kropacek (1974) NORITE o0.05 2980 Clark (1966) OLIVINE NEPHELINITE o0.05 3150 Martinkova et al. (2000) HARZBURGITE 0.1 3200 Araﬁn et al. (2008) DUNITE o0.05 3300 Bullen (1966)

dependence in the samples. Thus, a flat semi-variogram typically Alternatively, the variogram is typically a monotonically increasing indicates that the field of measurements obeys a stationary random function of the lag. It generally reaches an upper limit (called the process (i.e., there is no spatial correlation between samples). sill) when the lag distance tends to infinity. The range of the

Fig. 4. The histogram of 9256 wet density samples from the PETLAB rock catalogue.

Fig. 5. Box-plots of density measurements for 89 main rock types in the PETLAB database. variogram corresponds to the lag distance at which the sill is nearly The experimental semi-variograms for the main rock types with reached indicating that the sampled ﬁeld dissipates into random- more than 200 samples available in the PETLAB database were ness. Within the range, the ﬁeld of observations can be interpreted computed and are shown in Fig. 6. Together they account for 56% of as having some degree of spatial correlation. the surface of New Zealand according to the QMAP dataset. All the

Please cite this article as: Robert, T., et al., A digital rock density map of New Zealand. Computers and Geosciences (2010), doi:10.1016/ j.cageo.2010.07.010 8 T. Robert et al. / Computers & Geosciences ] (]]]]) ]]]–]]]

Fig. 6. The experimental semi-variograms of density samples for 13 main rock types with more than 200 individual measurements in the PETLAB database. The horizontal error bars indicate 71 standard deviation of the lag distance between samples (i.e., accounting for the tolerance). The vertical error bars indicate 71 standard error of the variogram estimate.

other classes sampled in the PETLAB database except for gravels and experimental semi-variograms. In particular, the number of pairs sand account individually for less than 1.5% of the area and hence were of points generally decreases as the lag distance increases. This not analysed. affects the reliability of the experimental semi-variogram and its The sample size and the spatial distribution of density interpretation at long lag distances. The ﬂuctuations of g^ðhÞcan be measurement sometimes complicate the interpretation of the the result of a lack and/or clustering of data samples affecting the

Please cite this article as: Robert, T., et al., A digital rock density map of New Zealand. Computers and Geosciences (2010), doi:10.1016/ j.cageo.2010.07.010 T. Robert et al. / Computers & Geosciences ] (]]]]) ]]]–]]] 9 accuracy of the estimation. The fluctuations could also indicate an The relatively small and clustered distribution of ignimbrite samples underlying geological periodicity in the rock structure. It is believed in the North Island required g^ðhÞto be computed with smaller lag that the data available were not sufficient to interpret reliably these distances. It shows that the density of ignimbrite tends to be spatially fluctuations and only the general trends are discussed as to justify correlated for lag distances less than 10 km, while it loses all spatial the generalisation of the mean sample density from PETLAB to all dependence at larger lags. It is argued that the relatively short range of corresponding areas of QMAP. density measurements for ignimbriteandthequickdissipationin It appears that andesite, argillite, basalt, granite, greywacke, randomness are sufficient to justify the generalisation of the mean rhyolite, and schist have a relatively flat semi-variogram. In other density value of ignimbrite in the digital density map. words, density measurements for these types of rocks approach that Mudstone, sandstone, and siltstone exhibit very similar experi- of a stationary random field. The lack of spatial dependence further mental semi-variograms that reveal a substantial spatial pattern justifies that the mean density of the classes being generalised to all with a range of about 100 km. Although the large standard the corresponding areas in the QMAP. Despite its relatively large deviation of these sedimentary rock formations (cf. Table 1) was variance, rhyolite (s¼225 kg/m3) does not exhibit any obvious discussed above as a lack of consistency, the spatial analysis sheds spatial correlation. Therefore, it is argued that the mean density from new light on this interpretation in revealing a degree of spatial all rhyolite samples in PETLAB is applicable to all areas classified as consistency. Although these sedimentary rocks can exhibit highly rhyolite in QMAP. The semi-variogram of gabbro is more compli- variable densities, this variability appears to be significantly cated to interpret. The increasing trend up to 100 km lag distance reduced at close range. The variance of density steadily increases suggests a degree of spatial correlation. Large fluctuations and as samples are taken further apart up to 100 km when the field of associated uncertainties at larger lag distances may indicate that density becomes stationary random. Tuff also exhibits a marked the sill is reached and randomness prevails at lag distances greater spatial correlation with a larger lag distance of about 300 km. The than 100 km. Nevertheless, it is argued that gabbro has a standard large decrease in the value of g^ðhÞ at larger lag distance is deviation low enough (s¼147 kg/m3) to justify the use of the mean interpreted as the effect of a reduced number of pairs associated density across all areas dominated by gabbro. with the cluster distribution of samples. Clearly, the generalisation In addition to a relatively large standard deviation (i.e., of the mean density for such rock formations can be considered s4200 kg/m3), ignimbrite, mudstone, sandstone, siltstone, and tuff disputable although it is argued that it still provides a substantial exhibit experimental semi-variograms with clear spatial dependence. improvement over the use of a single value for the whole region.

168°E 172°E 176°E 34°S 34°S

38°S 38°S

42°S 42°S

46°S 46°S

168°E 172°E 176°E

Fig. 7. The digital density model for New Zealand compiled on a 1 1 arc-min geographical grid.

Please cite this article as: Robert, T., et al., A digital rock density map of New Zealand. Computers and Geosciences (2010), doi:10.1016/ j.cageo.2010.07.010 10 T. Robert et al. / Computers & Geosciences ] (]]]]) ]]]–]]]

The spatial structure of density revealed by this analysis potentially (2000–2700 kg/m3), 20–25% sandstones (2000–2700 kg/m3), and offers scope for further research towards a more adequate spatia- 10–15% carbonate rocks (2500–2900 kg/m3). With reference to lization of density measurements. Hinze (2003), the mean continental crust density, computed based on the areal proportion of both sedimentary and shield rocks, is about 2600 kg/m3. The sedimentary rock density typically 5. The digital density model increases with age due to lithification and metamorphism. Since large areas of New Zealand are capped by Cenozoic, particularly The digital density model at 1 1 arc-min spatial resolution for Quaternary, sedimentary and pyroclastic volcanic deposits, the New Zealand is shown in Fig. 7. The near subsurface rock densities mean rock density in New Zealand is more likely to be lower than vary between 900 and 3300 kg/m3. The mean rock density (without the average density of 2670 kg/m3 defined based on the mean value lakes and glaciers) was found from a spatial averaging of the for crystalline and granitic rock formations. This was confirmed 5 5 arc-sec grid data. It indicates a mean rock density of about from analysis of geological data from the QMAP database and 2440 kg/m3, with a standard deviation of 280 kg/m3. This value PETLAB rock catalogue. The mean density of PETLAB rock density compares to the mean density obtained from all samples available samples is 2450 kg/m3, and the value of 2440 kg/m3 was estimated in the PETLAB database. When accounting for glaciers and lakes from the new digital density model. The lower North Island mean (roughly 2% of the total area of New Zealand), the mean density value of 2336 kg/m3 reflects the predominance of relatively young, decreases to about 2415 kg/m3. unmetamorphosed sedimentary rock, tephra and ignimbrite. The The geographical configuration of surface rock densities South Island’s 2514 kg/m3 mean value reflects the influence of (see Fig. 6) mimics the major geological composition of New more common igneous intrusions and metamorphosed sedimen- Zealand (see Fig. 1). The locations of rock units with lowest tary rock, including schist and gneiss. The results also revealed that densities are correlated with volcanic areas of the central North the rock densities in New Zealand vary roughly between 900 and Island and with large areas of volcanic deposits in the North Island. 3200 kg/m3. The northern, southern and eastern parts of the North Island consist The DDM will be utilized in computing a new gravimetric geoid of denser sedimentary rock formations. In the South Island, large model for New Zealand. The DDM is based on unevenly distributed areas of central Otago, Fiordland, and along the Alpine Fault have surface density measurements and extrapolated to geological higher rock densities due to the dominance of schist, greywacke, mapping units based on the latter’s main rock type. Some of these and intrusive rocks. The locations of lower rock densities in the mapping units are thin, including the extensive gravel deposits that South Island correspond to the locations of sedimentary rocks of cover 21.4% of the land area. Increases in density below the surface sandstone and mudstone and unconsolidated gravel, sand are to be expected but the subsurface variation is difficult to model and mud. from geological map data alone and would require 3D modelling beyond the scope of this paper.

6. Summary and conclusions Acknowledgments The combination of separate databases using GIS software tools based on spatial coincidence or, as in this case, common textural We thank David W. Heron from GNS Science for providing the attributes can yield useful cross-disciplinary derivative map pro- digital geology database QMAP. The QMAP geological mapping ducts that were not originally anticipated. We have integrated project and GIS database and the PETLAB database were supported geological mapping units and associated main rock type attribute by the Foundation for Research Science and Technology contract data from the national digital QMAP geological map GIS database C05X0401. We thank Dr. Nick Mortimer from GNS Science and with measured density values from the PETLAB national rock Professor Brent Hall from the University of Otago for their valuable catalogue and database, and other sources, to create a digital comments. model of surface rock densities for New Zealand at 1 1 arc-min spatial resolution. The surface geological composition of New Zealand is dominated by metamorphosed sedimentary rock References (31%, including 21% greywacke and 7% schist), unmetamorphosed sandstone and mudstone (19%), and unconsolidated sediment and Allaby, M., 1999. A Dictionary of Earth Sciences. Earth Sciences. Oxford University pyroclastic volcanic detritus (28%, including 21% gravels). Press 654 pp. Andrew, R.L., 1995. Porphyry copper–gold deposits of the Southwest Pacific. Mining The wet density measurements from the PETLAB rock catalogue Engineering 1, 33–38. and database provide definitive information about the near surface Annen, C., Scaillet, B., 2006. Thermal Evolution of Leucogranites in Extensional rock density. Rock density is dependent on the mineral composi- Faults: Implications for Miocene Denudation Rates in the Himalaya, vol. 268. Geological Society, London, pp. 309–326 (Special Publications). tion and porosity of the rock type, it potentially varies significantly Arafin, S., Singh, R.N., George, A.K., Al-Lazki, A., 2008. Thermoelastic and Thermo- even on samples that are taken within close proximity of each dynamic properties of Harzburgite—an upper mantle rock. Physics and other. Errors in rock density are inevitable with the assumption of a Chemistry of Solids 69 (7), 1766–1774. Arrnienti, P., Innocenti, F., Pareschi, M., Pompilio, M., Rocchi, S., 1991. Crystal representative density for each specific rock type and the assump- population density in not stationary volcanic systems: estimate of olivine tion that that rock type dominates the extent of the geological growth rate in basalts of Lanzarote (Canary Islands). Mineral Petrology 44, mapping unit. Nevertheless, the geographical distribution of 181–196. the surface rock densities mimics the geological composition of Balco, G., Stone, J.O., 2003. Measuring the density of rock, sand, till, etc. UW Cosmogenic Nuclide Laboratory, methods and procedures. Unpublished Report. New Zealand. Begg, J.G., Johnston, M.R., 2000. Geology of the Wellington Area, Institute of The value 2670 kg/m3 is commonly adopted as the mean Geological and Nuclear Sciences, Map, scale 1:250,000, geological map 10, 64 density of the upper continental crust. This value is typically pp. + 1 folded map. Bishop, D.G., Turnbull, I.M., 1996. Geology of the Dunedin area, Institute of assumed for the mean density of crystalline and granitic rocks. Geological and Nuclear Sciences, Map, scale 1:250,000, geological map 21, 52 The density of granitic rocks ranges from 2500 to 2800 kg/m3 with a pp. + 1 folded map. mean value of about 2670 kg/m3. The crystalline rocks represent Bullen, K.E., 1966. The bearing of dunite on sub-crustal problems. Bulletin of Volcanology 29, 307–312. roughly only 25% of the continental crust, while the remaining 75% Carmichael, R.S., 1982. Handbook of Physical Properties of Rocks., vol. I. CRC Press, is formed by sedimentary rocks consisting of about 65% of shale Florida 404 pp.

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Please cite this article as: Robert, T., et al., A digital rock density map of New Zealand. Computers and Geosciences (2010), doi:10.1016/ j.cageo.2010.07.010