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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
b
National School of Surveying, Division of Sciences, University of Otago, 310 Castle Street, Box 56, Dunedin, New Zealand
GNS Science, PO Box 30368, Lower Hutt, New Zealand
a r t i c l e in f o
abstract
Article history:
Received 22 March 2010
Received in revised form
23 June 2010
Accepted 31 July 2010
Digital geological maps of New Zealand (QMAP) are combined with 9256 samples with rock density
measurements from the national rock catalogue PETLAB and supplementary geological sources to
generate a first digital density model of New Zealand. This digital density model will be used to compile a
new geoid model for New Zealand. The geological map GIS dataset contains 123 unique main rock types
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.
A mean surface rock density of 2440 kg/m3 for New Zealand is obtained from the analysis of the derived
digital density model. The lower North Island mean of 2336 kg/m3 reflects the predominance of relatively
young, weakly consolidated sedimentary rock, tephra, and ignimbrite compared to the South Island’s
2514 kg/m3 mean where igneous intrusions and metamorphosed sedimentary rocks including schist and
gneiss are more common. All of these values are significantly lower than the mean density of the upper
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.
Keywords:
Crust
Database
Density
Geological mapping
Gravimetry
Rock types
1. Introduction
The modelling of the geoid from gravimetric data requires a
detailed digital terrain model (DTM) and a subsurface rock digital
density model (DDM) to compute the topographical effects on the
gravity field quantities. In the absence of distributed rock density
data, a mean density value is often used and assumed to be constant
over the study area. The errors in geoid modelling due to neglecting
the anomalous topographical density distribution can then reach
several centimetres, especially in mountainous regions with variable geological composition. While DTMs are currently available
with a very high accuracy and resolution at global and regional
scales, DDMs are rarely available. However, recent studies indicate
that incorporating rock density models (including lakes and
glaciers) in the gravimetric geoid modelling process have potential
to improve results (see e.g., Martinec et al., 1995; Martinec, 1998;
Kühtreiber, 1998; Huang et al., 2001; Hunegnaw, 2001).
A mean density of 2670 kg/m3 is often assumed for the upper
continental crust in geological and gravity surveys, geophysical
exploration, gravimetric geoid modelling, compilation of regional
gravity maps, and other applications. Although this density value is
widely used, its origin remains partially obscure. Woollard (1966)
n
Corresponding author. Tel.: + 64 3 479 7592; fax: + 64 3 479 7586.
E-mail addresses: [email protected],
[email protected] (T. Robert).
suggested that this density was used for the first time by Hayford and
Bowie (1912). In reviewing several studies seeking a representative
mean density from various rock type formations, Hinze (2003) argued
that this value was used earlier by Hayford (1909) for gravity
reduction. Hayford (1909) referred to Harkness (1891) who averaged
five published values of surface rock density. Harkness’s (1891) value
of 2670 kg/m3 was confirmed later, for instance, by Gibb (1968) who
estimated the mean density for the surface rocks in a significant
portion of the Canadian Precambrian shield from over 2000 individual
measurements. Woollard (1962) examined more than 1000 rock
samples and estimated that the mean basement (crystalline) rock
density is about 2740 kg/m3. Subrahmanyam and Verma (1981)
determined that crystalline rocks in low-grade metamorphic terranes
in India have the mean density of 2750 kg/m3, while 2850 kg/m3 in
high-grade metamorphic terranes.
The geological composition of New Zealand’s land surface is
dominated by sedimentary rocks (Riddolls, 1987). Many of these
rocks were deposited beneath the sea adjacent to the present or past
plate boundaries and later uplifted and juxtaposed by tectonic
movement. The present Australian-Pacific plate boundary is marked
by the Alpine Fault through much of the South Island. The hard
‘‘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,
2007). Greywacke basement also forms the axial ranges of the
southern and eastern North Island (Begg and Johnston, 2000;
Mazengarb and Speden, 2000) and eastern Northland (Edbrooke
0098-3004/$ - see front matter & 2010 Elsevier Ltd. All rights reserved.
doi:10.1016/j.cageo.2010.07.010
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
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and Brook, 2010). In central Otago, schist predominates at the
surface and has originated from metamorphism of the Mesozoic
greywacke sedimentary rock (Turnbull, 2000; Forsyth, 2001;
Turnbull and Allibone, 2003; Rattenbury et al., 2010). A great proportion of the southern half of the North Island is formed of soft Neogene
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
South islands and is generally thin, although thicker formations
occur south of Auckland, in the Wairarapa, northwest Nelson and
north Westland, north and south Canterbury and western Southland. Large volcanic areas occur in the central and northern North
Island, particularly between Taupo, Bay of Plenty and Coromandel
Peninsula (Edbrooke, 2001). These deposits comprise a mixture of
lava flows and domes, lahar and volcano collapse deposits, ignimbrite and tephra, and reworked volcanic sediments resulting from
repeated volcanic activity over the last 10 million years. Smaller
volcanic centres are located in Taranaki (Townsend et al., 2008),
western Waikato to Auckland (Edbrooke, 2001, 2005), and Northland (Isaac, 1996; Edbrooke and Brook, 2010). Old volcanic centres
form Banks Peninsula (Forsyth et al., 2008) and Otago Peninsula
(Bishop and Turnbull, 1996). Intrusive igneous rocks dominated by
granite, diorite, granodiorite and tonalite, but including ultramafic
rocks mostly occur in Nelson, Westland, Fiordland, and Stewart
Island (Rattenbury et al., 1998; Nathan et al., 2002; Turnbull and
Allibone, 2003; Turnbull et al., 2010). Digital geological map data and
density measurements are used in this study to generate the first
digital surface density model for New Zealand. The input data are
summarized in Section 2. The methodology is described in Section 3.
A spatial analysis of rock density samples is provided in Section 4.
The final digital density model is presented and discussed in Section
5. The summary and conclusions are given in Section 6.
2. Input data
The QMAP (Quarter-million MAP) database produced by GNS
Science provides national geological map coverage at 1:250,000 in
printed and digital form using ESRI’s ArcGIS Geographic Information
System (GIS) software. The project began in 1994, and was completed
in 2010, a world-first production of a completely revised national
geological map series designed and built using GIS software. The
database is derived from numerous sources such as older published
and unpublished geological maps, mining company reports, petroleum
exploration reports, university theses, unpublished research reports,
and data collected from new field work. The QMAP geological maps are
compiled at a scale of 1:50,000 and published at 1:250,000. The QMAP
database contains thematic layers with rich attributes that describe
various features of a geological map. The most relevant for this study
are the geological unit polygons that define the extent of mapping units
(groups, formations, plutons, etc.). The units mapped are generally the
shallowest rock unit more than 5–10 m thick. Thin veneers are
commonly not depicted in preference for more substantial rock units
underneath. Key attributes of the geological unit polygons are the main
168°E
172°E
176°E
34°S
38°S
38°S
;
42°S
42°S
46°S
46°S
168°E
172°E
176°E
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 ] (]]]]) ]]]–]]]
and subsidiary rock types, stratigraphic and map unit names, terrane
affiliation, age expressed in stratigraphic or absolute terms, and
lithological description. A map of main rock types in New Zealand
was generated from the digital QMAP database. The QMAP database
identifies 123 main rock types, not including areas of water (lakes) and
ice (glaciers and snowfields). The main rock and other fields within
geological mapping units and other layers of the QMAP database are
undergoing national standardisation and reconciliation, but for the
moment contain many anomalies, inconsistencies and use of synonyms. To overcome some of these problems, the main rock types were
grouped into 18 broad categories. The generalised geological map of
New Zealand consisting of 18 broad categories with place-names is
shown in Fig. 1. The only modification to the QMAP main rock source
data for this study was the reassignment of approximately 60% of
the ‘‘sandstone’’ occurrences to ‘‘greywacke’’. Greywacke is a poorly
defined yet widely used term in New Zealand geology and for this study
it is assigned to the older, more lithified and weakly metamorphosed
sandstone-dominated basement terranes that form much of the
Southern Alps and other axial ranges. This reassignment separates
these harder rocks from the generally softer Cenozoic sandstone rocks
with consequences for the density measurement calculations.
Two main rock types form 42% of New Zealand’s surface rocks as
defined by the geological mapping units. Greywacke as discussed
above, forms 20.5% and gravels form 21.4% of the land area. Gravels
that occur throughout New Zealand are primarily associated with
past and present river beds, associated floodplains and alluvial fans,
scree and tills. They are typically weakly consolidated, occurring as
168°E
172°E
3
thin veneers or deposits ranging up to several hundred metres thick.
Other weakly consolidated deposits such as sand, mud, peat, pumice,
tephra, and fill contribute 7% more. Sandstone and related mediumgrained clastic rocks (8.8%) and fine grained clastic rocks (10.7%,
predominantly mudstone), are more common in the North Island, as
are mafic-intermediate volcanic rocks (3.1% including basalt, andesite), and ignimbrite and tephra (4.6%). Metasedimentary rock
(4.1%), schist (6.7%) and felsic intrusive rocks (3.2%) such as granite
are almost exclusively from the South Island and Stewart Island.
PETLAB is the rock catalogue and geo-analytical database of New
Zealand http://pet.gns.cri.nz (Mortimer, 2005). It is operated by GNS
Science in collaboration with the geology departments of New
Zealand’s universities. The database contains locations, descriptions
and analyses of rock and mineral samples collected throughout
onshore and offshore New Zealand and Antarctica. Information was
sourced from journal articles, theses, and open file reports. PETLAB
contains 157,363 sample records from which 40,588 have analytical
data (as of June 2010). Wet density measurements compiled from
many sources (e.g., Hatherton and Leopard, 1964; Whiteford and
Lumb, 1973) cover 89 rock types collected at 9256 locations in New
Zealand. The location map of rock density samples from the PETLAB
rock catalogue is shown in Fig. 2.
3. Methodology
The preparation of the digital density model from the vector GIS
map of main rock types consists of three processing steps (see the
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. 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
types of the QMAP database. Since the main rock type applies to one
or more geological mapping units, the assigned density is assumed to
represent the geological mapping units also. This results in a vector
GIS map of main rock type densities. The digital density model is then
obtained from the vector map after applying the data discretisation
and aggregation procedures.
The primary source of information used to allocate the representative densities for 123 main rock types of the QMAP database is
the PETLAB rock catalogue. The PETLAB rock catalogue provides
8933 rock density measurements for the 56 main rock types in the
QMAP database. The densities that had been measured for each
sample are dry density, particle density, and wet density. The dry
density represents the rock density measured after all water is
removed from the voids. The particle density is equal to the mass of
the dried sample divided by the total grain volume of the sample.
The wet density value represents the density of the rock when all
voids are filled with the fluid. For in situ near subsurface values, the
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.
The representative value of density for each main rock type was
computed by averaging over all PETLAB samples of the same rock
type collected throughout New Zealand. The mean rock densities
and complementary statistics are shown in Table 1. As seen from
Table 1, variations in density samples taken for the same rock type
often exceed 1000 kg/m3 and can reach 1630 kg/m3 (volcanic
breccias). This indicates the practical restrictions in allocating rock
density values objectively. The densities of the remaining 67 main
rock types, for which the information from the PETLAB rock
catalogue was not found, are allocated according to available
sources from the literature or by assuming similarity or synonymity with other rock types. The list of rock density values and the
references to relevant sources are given in Table 2. A density of 920
and 1000 kg/m3 is attributed to ice and water, respectively. Density
values for three rock types (broken formation, calc-silicate,
Litterature
PETLAB data
QMAP database
Mean density per rock type
Assign mean density to the corresponding units for
each rock type
Convert the vector-based map of density
values to a grid with 5x5 arc-sec spatial
sampling
Aggregation of the 5x5 arc-sec grid of
density to a 1x1 arc-min raster map using a
mean operator
Digital density
model
Fig. 3. The flowchart of compiling the 1 1 arc-min digital density model from the
vector GIS map of main rock types.
clinopyroxenite totalling 0.2% of land area) could not be found
and a value of 2670 kg/m3 has been adopted.
The mean density of the main rock types varies between 900 and
3300 kg/m3. The lowest density is attributed to loess, which is an
aeolian sediment formed by the accumulation of wind-blown silt
and lesser and variable amounts of sand and clay that are loosely
cemented by calcium carbonate. It is usually homogeneous and
highly porous (Richthofen, 1882; Neuendorf et al., 2005). The
highest density is attributed to dunite, an igneous, plutonic rock, of
ultramafic composition (cf. Harvey and Tracy, 1996). Dunite
typically occurs at the base of ophiolite sequences for instance in
east Nelson and west and south Otago (Rattenbury et al., 1998;
Turnbull, 2000; Turnbull and Allibone, 2003).
The vector map of the main rock type densities was discretised
on a 5 5 arc-sec equal angular grid of geographical coordinates.
The 5 5 arc-sec grid of the main rock type densities was then
aggregated into the 1 1 arc-min spatial resolution digital density
model using a mean operator.
4. Analysis of density data
The 9256 wet density measurements in the PETLAB database
were averaged to calculate a first order mean density of about
2450 kg/m3, with a standard deviation of 360 kg/m3. This value
incorporates some sample bias in the PETLAB dataset, for example
unconsolidated sediments such as gravel, sand, clay, and silt that
form 28% of the land area are under-represented with only 0.6% of
the measured density data. The rock densities vary from 1130 to
5480 kg/m3, with 90% of the values ranging between 1780 and
2930 kg/m3 (see Fig. 4). The apparent bimodal distribution of the
rock densities reflects sampling bias of dominant rock types,
particularly greywacke/schist and generally lighter Cenozoic sedimentary and volcanic rocks.
Density measurements for the same rock type can vary
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
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
porosity which affects the density measurements (Hatherton and
Leopard, 1964). Denser rocks are typically hard igneous and
metamorphosed sedimentary rocks.
When considering only the main rock types with more than 200
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
than 200 kg/m3 (Table 1). These seven rock types account for 32% of
the area of New Zealand according to the QMAP dataset. The
generalisation of the experimental mean to all corresponding areas
in the QMAP dataset is justified by the consistency of their density.
Among the other main rock types recorded in the PETLAB
database, tuff, ignimbrite, mudstone, rhyolite, siltstone, and sandstone 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
and Leopard (1964). Variation in density can occur within rocks of
the same stratigraphic unit and is partly attributed to differential
compaction from variable depth of burial. The standard deviation
for these rock types always exceeds 200 kg/m3 (cf. Table 1).
Together, these six classes represent 24% of the area of New
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 ] (]]]]) ]]]–]]]
5
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
ANDESITE
ARGILLITE
BASALT
BRECCIA
CHERT
CLAY
CLAYSTONE
COAL
CONGLOMERATE
DACITE
DIATOMITE
DIORITE
DOLERITE
GABBRO
GNEISS
GRANITE
GRANODIORITE
GRANULITE
GRAVEL
GREENSAND
GREENSCHIST
GREYWACKE
HORNFELS
IGNIMBRITE
LAMPROPHYRE
LAVA
LIGNITE
LIMESTONE
MARBLE
METAVOLCANIC
MUDSTONE
MYLONITE
PERIDOTITE
PHONOLITE
PUMICE
PYROCLASTIC
PYROXENITE
QUARTZITE
RHYOLITE
SAND
SANDSTONE
SCHIST
SERPENTINITE
SHALE
SILT
SILTSTONE
SINTER
SPILITE
SYENITE
TEPHRA
TRACHYTE
TUFF
ULTRAMAFIC
VOLCANICS
VOLCANIC BRECCIA
2892
2565
2691
2768
2291
2564
2067
2067
1712
2570
2402
1528
2797
2749
2884
2812
2640
2681
2765
2309
2365
2923
2639
2800
2125
2910
2680
1390
2484
2716
2955
2204
2757
3093
2536
1719
1986
3122
2612
2207
2048
2463
2732
2634
2335
1979
2347
2510
2863
2719
1637
2591
2113
3288
2362
2195
115
170
133
162
295
162
171
235
461
159
175
141
119
146
147
179
77
70
332
266
168
133
100
143
247
177
93
204
211
117
124
301
91
225
70
310
512
218
73
225
351
266
115
219
190
140
283
14
121
145
98
182
289
517
471
358
3100
2990
3160
3060
3000
2740
2450
2420
2100
3000
2700
1720
3160
3040
3340
3150
2940
2940
3000
2580
2520
3130
2940
3080
2620
3390
2820
1670
3010
3140
3150
2870
2930
3340
2630
2230
2350
3330
2780
2740
3220
3000
3100
3270
2730
2160
2880
2520
3090
2860
1750
2950
2940
4130
3090
2950
2630
1560
2000
1780
1540
2240
1920
1520
1130
2110
1940
1390
2430
2360
2260
1830
2330
2530
2530
1870
2210
2620
2090
2590
1240
2650
2540
1210
1890
2510
2760
1320
2620
2340
2470
1150
1130
2240
2490
1360
1690
1510
2120
2240
1610
1720
1360
2500
2500
2440
1580
2170
1410
2750
1480
1320
62
418
251
340
118
11
9
15
5
118
79
4
186
68
236
149
288
53
2
9
4
15
469
22
916
15
6
6
156
22
11
734
11
118
5
29
5
25
29
704
27
968
419
87
193
14
471
2
82
15
3
31
723
5
110
60
0.3
0.8
0.3
1.7
0.3
o 0.05
0.1
0.1
o 0.05
0.9
0.1
o 0.05
1.4
o 0.05
0.4
0.5
2.3
0.6
o 0.05
21.4
o 0.05
0.2
20.5
o 0.05
4.6
o 0.05
o 0.05
o 0.05
o 0.05
o 0.05
o 0.05
8.1
0.1
o 0.05
o 0.05
0.1
o 0.05
o 0.05
0.1
0.5
3.2
8.2
5.8
0.1
o 0.05
0.2
2.0
o 0.05
0.1
o 0.05
o 0.05
o 0.05
0.2
o 0.05
o 0.05
o 0.05
Zealand. For such classes, the generalisation of the mean value
(i.e., that obtained from samples attributed to a main rock type in the
PETLAB database) to all corresponding areas of the QMAP dataset
may be an oversimplification. Nevertheless, it is believed that an
average value per class, along with the spatial distribution enabled
by the combination with the QMAP dataset, remains a more suitable
outcome than a global mean density for the whole region.
In order to investigate further the statistical structure of the
density samples, the latter were examined within the framework of
geostatistics. In this context, the experimental semi-variogram is
an essential tool that permits the variance of a spatially distributed
quantity to be analysed as a function of the distance between
samples (Cressie, 1993). Let xi be the positional vector of
observation iA f1,. . .,ng and di the measured density at that position
(both are obtained from the PETLAB database), then the experimental semi-variogram is expressed as
g^ ðhÞ ¼
X
1
2
9di dj 9
29NðhÞ9 ði,jÞ A NðhÞ
where g^ ðhÞ is the estimator of the semi-variogram at lag (i.e., for
samples obtained at an approximate distance h from each other),
NðhÞ ¼ fði,jÞ A ½1,. . .,n2 : Jxi xj J ¼ h7 eg is the set of pairs of observations (i, j) that are at an approximate distance h from each other
(i.e., given a certain tolerance e), and 9N(h)9 is the cardinality of the
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
T. Robert et al. / Computers & Geosciences ] (]]]]) ]]]–]]]
6
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
PEAT
PYROCLASTIC BREC
MUD
VITRIC TUFF
LAPILLI TUFF
CALCAREOUS MUDSTONE
CATACLASITE
LEUCOGRANITE
TILL
RHYODACITE
HORNBLENDITE
BOULDERS
DEBRIS
FILL
TURBIDITE
VOLCANIC SANDSTONE
HAWAIITE
ALGAL LIMESTONE
COQUINA
MICRITE
SHELL BEDS
KERATOPHYRE
PORPHYRY
SCORIA
METACHERT
PELITE
ANDESITE AGGLOMERATE
ANDESITE CONGLOMERATE
METACONGLOMERATE
VOLCANIC CONGLOMERATE
MONZODIORITE
SYENOGRANITE
ANDESITE LAVA
ORTHOGNEISS
PSAMMITE
TRONDHJEMITE
MELANGE
BASALTIC ANDESITE
BROKEN FORMATION
CALC-SILICATE
CLINOPYROXENITE
SEMISCHIST
BIOSPARITE
MONZOGRANITE
DIORITIC ORTHOGNEISS
GABBROIC ORTHOGNEISS
GRANITOID
METASANDSTONE
OLIVINE BASALT
PARAGNEISS
TRAVERTINE
GREYSCHIST
PHYLLONITE
METAPELITE
QUARTZ MONZODIORITE
METAPSAMMITE
TONALITE
QUARTZ DIORITE
ANORTHOSITE
MIGMATITE
GABBRONORITE
LIMBURGITE
NORITE
OLIVINE NEPHELINITE
HARZBURGITE
DUNITE
0.2
0.7
o 0.05
1.3
o 0.05
o 0.05
o 0.05
o 0.05
o 0.05
0.1
o 0.05
o 0.05
0.1
0.9
o 0.05
0.5
0.2
0.3
o 0.05
o 0.05
o 0.05
o 0.05
o 0.05
o 0.05
o 0.05
o 0.05
o 0.05
o 0.05
o 0.05
o 0.05
o 0.05
0.1
o 0.05
o 0.05
0.1
0.2
o 0.05
0.5
o 0.05
0.2
o 0.05
o 0.05
0.8
o 0.05
o 0.05
0.1
o 0.05
o 0.05
2.0
o 0.05
0.2
o 0.05
0.9
o 0.05
1.1
o 0.05
o 0.05
0.2
0.1
o 0.05
o 0.05
o 0.05
o 0.05
o 0.05
o 0.05
0.1
o 0.05
900
1040
1600
1910
2113
2113
2200
2291
2291
2310
2350
2370
2400
2400
2400
2410
2460
2470
2480
2480
2480
2482
2500
2550
2550
2560
2560
2570
2570
2570
2570
2580
2610
2630
2630
2639
2640
2660
2670
2670
2670
2670
2686
2690
2690
2700
2700
2700
2700
2700
2700
2710
2730
2740
2750
2770
2800
2800
2810
2810
2812
2970
2970
2980
3150
3200
3300
Johnson and Lorenz (2000)
Schon (1996)
Hall et al. (1999)
Clark (1966)
The adopted density the same as for Tuff
The adopted density the same as for Tuff
The adopted density the same as for Mudstone
The adopted density the same as for Breccia
Annen and Scaillet (2006)
Balco and Stone (2003)
Hildreth et al. (2004)
Clark (1966)
Nott (2003)
The adopted density the same as for boulders
The adopted density the same as for boulders
Average density of Sandstone and siltstone
The adopted density the same as for sandstone
Carmichael (1982)
The adopted density the same as for limestone
The adopted density the same as for limestone
The adopted density the same as for limestone
The adopted density the same as for limestone (2484)
Morrow and Lockner (2001)
Andrew (1995)
Tamari et al. (2005)
The adopted density the same as for Chert
Pettijohn (1975)
The same as Andesite and Conglomerate
The same as Andesite and Conglomerate
The adopted density the same as for Conglomerate
The adopted density the same as for Conglomerate
Llambias et al. (1977)
Gaal et al. (1981)
Hildreth et al. (2004)
Giacomini et al. (2009)
The adopted density the same as for Greywacke
Carmichael (1982)
Kimura et al. (2001)
Average density of Basalt and Andesite
No information found
No information found
No information found
Average density of Schist and Greywacke
Allaby (1999)
Oliveira et al. (2008)
Pechinig et al. (2005)
Pechinig et al. (2005)
Rao et al. (2008)
Carmichael (1982)
Arrnienti et al. (1991)
Samalikova (1983)
Russell and Pellant (1981)
The adopted density the same as for Schist
Wibberley and McCaig (2000)
Dyda (1994)
Clark (1966)
Clark (1966)
Nettleton et al. (1969)
Clark (1966)
Clark (1966)
The adopted density the same as for Gneiss
Vankova and Kropacek (1974)
Vankova and Kropacek (1974)
Clark (1966)
Martinkova et al. (2000)
Arafin et al. (2008)
Bullen (1966)
dependence in the samples. Thus, a flat semi-variogram typically
indicates that the field of measurements obeys a stationary random
process (i.e., there is no spatial correlation between samples).
Alternatively, the variogram is typically a monotonically increasing
function of the lag. It generally reaches an upper limit (called the
sill) when the lag distance tends to infinity. The range of 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 ] (]]]]) ]]]–]]]
7
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
reached indicating that the sampled field dissipates into randomness. Within the range, the field of observations can be interpreted
as having some degree of spatial correlation.
The experimental semi-variograms for the main rock types with
more than 200 samples available in the PETLAB database were
computed and are shown in Fig. 6. Together they account for 56% of
the surface of New Zealand according to the QMAP dataset. All the
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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 7 1 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
sand account individually for less than 1.5% of the area and hence were
not analysed.
The sample size and the spatial distribution of density
measurement sometimes complicate the interpretation of the
experimental semi-variograms. In particular, the number of pairs
of points generally decreases as the lag distance increases. This
affects the reliability of the experimental semi-variogram and its
interpretation at long lag distances. The fluctuations of g^ ðhÞcan be
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 ] (]]]]) ]]]–]]]
accuracy of the estimation. The fluctuations could also indicate an
underlying geological periodicity in the rock structure. It is believed
that the data available were not sufficient to interpret reliably these
fluctuations and only the general trends are discussed as to justify
the generalisation of the mean sample density from PETLAB to all
corresponding areas of QMAP.
It appears that andesite, argillite, basalt, granite, greywacke,
rhyolite, and schist have a relatively flat semi-variogram. In other
words, density measurements for these types of rocks approach that
of a stationary random field. The lack of spatial dependence further
justifies that the mean density of the classes being generalised to all
the corresponding areas in the QMAP. Despite its relatively large
variance, rhyolite (s ¼225 kg/m3) does not exhibit any obvious
spatial correlation. Therefore, it is argued that the mean density from
all rhyolite samples in PETLAB is applicable to all areas classified as
rhyolite in QMAP. The semi-variogram of gabbro is more complicated to interpret. The increasing trend up to 100 km lag distance
suggests a degree of spatial correlation. Large fluctuations and
associated uncertainties at larger lag distances may indicate that
the sill is reached and randomness prevails at lag distances greater
than 100 km. Nevertheless, it is argued that gabbro has a standard
deviation low enough (s ¼147 kg/m3) to justify the use of the mean
density across all areas dominated by gabbro.
In addition to a relatively large standard deviation (i.e.,
s 4200 kg/m3), ignimbrite, mudstone, sandstone, siltstone, and tuff
exhibit experimental semi-variograms with clear spatial dependence.
168°E
172°E
9
The relatively small and clustered distribution of ignimbrite samples
in the North Island required g^ ðhÞto be computed with smaller lag
distances. It shows that the density of ignimbrite tends to be spatially
correlated for lag distances less than 10 km, while it loses all spatial
dependence at larger lags. It is argued that the relatively short range of
density measurements for ignimbrite and the quick dissipation in
randomness are sufficient to justify the generalisation of the mean
density value of ignimbrite in the digital density map.
Mudstone, sandstone, and siltstone exhibit very similar experimental semi-variograms that reveal a substantial spatial pattern
with a range of about 100 km. Although the large standard
deviation of these sedimentary rock formations (cf. Table 1) was
discussed above as a lack of consistency, the spatial analysis sheds
new light on this interpretation in revealing a degree of spatial
consistency. Although these sedimentary rocks can exhibit highly
variable densities, this variability appears to be significantly
reduced at close range. The variance of density steadily increases
as samples are taken further apart up to 100 km when the field of
density becomes stationary random. Tuff also exhibits a marked
spatial correlation with a larger lag distance of about 300 km. The
large decrease in the value of g^ ðhÞ at larger lag distance is
interpreted as the effect of a reduced number of pairs associated
with the cluster distribution of samples. Clearly, the generalisation
of the mean density for such rock formations can be considered
disputable although it is argued that it still provides a substantial
improvement over the use of a single value for the whole region.
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
offers scope for further research towards a more adequate spatialization of density measurements.
5. The digital density model
The digital density model at 1 1 arc-min spatial resolution for
New Zealand is shown in Fig. 7. The near subsurface rock densities
vary between 900 and 3300 kg/m3. The mean rock density (without
lakes and glaciers) was found from a spatial averaging of the
5 5 arc-sec grid data. It indicates a mean rock density of about
2440 kg/m3, with a standard deviation of 280 kg/m3. This value
compares to the mean density obtained from all samples available
in the PETLAB database. When accounting for glaciers and lakes
(roughly 2% of the total area of New Zealand), the mean density
decreases to about 2415 kg/m3.
The geographical configuration of surface rock densities
(see Fig. 6) mimics the major geological composition of New
Zealand (see Fig. 1). The locations of rock units with lowest
densities are correlated with volcanic areas of the central North
Island and with large areas of volcanic deposits in the North Island.
The northern, southern and eastern parts of the North Island consist
of denser sedimentary rock formations. In the South Island, large
areas of central Otago, Fiordland, and along the Alpine Fault have
higher rock densities due to the dominance of schist, greywacke,
and intrusive rocks. The locations of lower rock densities in the
South Island correspond to the locations of sedimentary rocks of
sandstone and mudstone and unconsolidated gravel, sand
and mud.
(2000–2700 kg/m3), 20–25% sandstones (2000–2700 kg/m3), and
10–15% carbonate rocks (2500–2900 kg/m3). With reference to
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
increases with age due to lithification and metamorphism. Since
large areas of New Zealand are capped by Cenozoic, particularly
Quaternary, sedimentary and pyroclastic volcanic deposits, the
mean rock density in New Zealand is more likely to be lower than
the average density of 2670 kg/m3 defined based on the mean value
for crystalline and granitic rock formations. This was confirmed
from analysis of geological data from the QMAP database and
PETLAB rock catalogue. The mean density of PETLAB rock density
samples is 2450 kg/m3, and the value of 2440 kg/m3 was estimated
from the new digital density model. The lower North Island mean
value of 2336 kg/m3 reflects the predominance of relatively young,
unmetamorphosed sedimentary rock, tephra and ignimbrite. The
South Island’s 2514 kg/m3 mean value reflects the influence of
more common igneous intrusions and metamorphosed sedimentary rock, including schist and gneiss. The results also revealed that
the rock densities in New Zealand vary roughly between 900 and
3200 kg/m3.
The DDM will be utilized in computing a new gravimetric geoid
model for New Zealand. The DDM is based on unevenly distributed
surface density measurements and extrapolated to geological
mapping units based on the latter’s main rock type. Some of these
mapping units are thin, including the extensive gravel deposits that
cover 21.4% of the land area. Increases in density below the surface
are to be expected but the subsurface variation is difficult to model
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
attributes can yield useful cross-disciplinary derivative map products that were not originally anticipated. We have integrated
geological mapping units and associated main rock type attribute
data from the national digital QMAP geological map GIS database
with measured density values from the PETLAB national rock
catalogue and database, and other sources, to create a digital
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
(31%, including 21% greywacke and 7% schist), unmetamorphosed
sandstone and mudstone (19%), and unconsolidated sediment and
pyroclastic volcanic detritus (28%, including 21% gravels).
The wet density measurements from the PETLAB rock catalogue
and database provide definitive information about the near surface
rock density. Rock density is dependent on the mineral composition and porosity of the rock type, it potentially varies significantly
even on samples that are taken within close proximity of each
other. Errors in rock density are inevitable with the assumption of a
representative density for each specific rock type and the assumption that that rock type dominates the extent of the geological
mapping unit. Nevertheless, the geographical distribution of
the surface rock densities mimics the geological composition of
New Zealand.
The value 2670 kg/m3 is commonly adopted as the mean
density of the upper continental crust. This value is typically
assumed for the mean density of crystalline and granitic rocks.
The density of granitic rocks ranges from 2500 to 2800 kg/m3 with a
mean value of about 2670 kg/m3. The crystalline rocks represent
roughly only 25% of the continental crust, while the remaining 75%
is formed by sedimentary rocks consisting of about 65% of shale
We thank David W. Heron from GNS Science for providing the
digital geology database QMAP. The QMAP geological mapping
project and GIS database and the PETLAB database were supported
by the Foundation for Research Science and Technology contract
C05X0401. We thank Dr. Nick Mortimer from GNS Science and
Professor Brent Hall from the University of Otago for their valuable
comments.
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