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Relationships between thermal and other petrophysical properties of rocks in Finland
Pergamon
Phys. Chem. Earth, Vol. 23, No. 3, pp. 341-349, 1998 © 1998 Elsevier Science Ltd. All rights reserved Printed in Great Britain 0079-1946/98 $19.00 + 0.00 PII: S0079-1946(98)00035-4
Relationships between Thermal and other Petrophysical Properties of Rocks in Finland I. T. K u k k o n e n I and S. P e i t o n i e m i 2
lGeological Survey of Finland, P.O. Box 96, FIN-G2151 Espoo, Finland. (E-mail: ilmo.kukkonen @ gsf.fi) 2Astrock Oy, Klovinite 6 B, FIN-02180 Espoo, Finland
Received 25 April 1997; revised 10 September 1997; accepted 8 December 1997
Abstract. Relationships between thermal conductivity, heat production rate and some other petrophysical properties (density, magnetic susceptibility, intensity of remanent magnetize'on,P-wave velocity) were investigatedempirically in about 2700 drill core samples from the Finnish precambrian bedrock. The results suggest that there are no well defined relationships between the thermal and other petrophysical properties which would generally apply in crystalline rocks. Coefficients of correlation are small ( < 0.7) and the data points scatter in the cross-correlation diagrams. Nevertheless, certain trends of variation can be observed, particularly between (1) thermal conductivity and susceptibility in paramagnetic rocks, (2) heat production rate and P-wave velocity, and (3) heat production and density. However, uncertainties in these trends do not allow reliable estimations of the thermal properties. © 1998 Elsevier Science Ltd.
required, and then the thermal properties must be estimated with indirect methods. These may be either lithological interpretation of seismic, potential field or electromagnetic data, or petrophysical relationships between a measured physical property and thermal properties. Studies of the thermal properties in the Baltic (or Fennoscandian) Shield are provided by Pinet and Jaupart (1987), Sundberg (1988), Kremenetsky et al. (1989), Kukkonen (1989, 1993), Moyseyenko and Negrov (1992) and JOeleht and Kukkonen (1997). We present a summary of petrophysical measurements on about 2700 rock samples originally collected for geothermal investigations from drill holes in Finland during 1964-1995. The samples were used for thermal conductivity measurements in heat flow studies. Practically all samples have been preserved which made it possible to extend the measurements to other petrophysical properties as well. The sampled drill holes represent different Precambrian rock types in Finland, and provide a good basis for investigating petrophysical relationships empirically. We have measured thermal conductivity, radiogenic heat production rate, bulk density, magnetic susceptibility, intensity of natural remanent magnetization (NRM) and seismic P-wave velocity of the samples. We use the data in this study for investigating whether there are general relationships between thermal and other petrophysical properties in the crystalline precambrian rocks in Finland, and whether such relationships could be utilized in indirect estimation of thermal properties.
1 Introduction Thermal conductivity and radiogenic heat production rate of rocks are the most important petrophysical parameters needed in geothermal investigations. When relevant rock samples are available, these parameters can be measured in laboratory (Beck, 1988). Alternatively, in situ measurements (Rybach, 1988; Burkhardt et al., 1995) can be performed in drill holes, and drill core data can be used for modelling of the vertical variation of parameters (Lachenbruch, 1971). In geothermal modelling of the lithosphere knowledge of the thermal properties in deeper layers of the Earth is
2 Data base: Samples and measurements
The present data set is based on measurements of drill core samples collected from 63 diamond-drilled holes in Finland. The drill hole sites represent Archaean and Early to Middle Proterozoic crystalline rocks, mostly plutonic,
Correspondence to: I.T. Kukkonen 341
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I. T. Kukkonen and S. Peltoniemi
metasedimentary, metavolcanic and two sedimentary formations. The total number of samples in this study was 2705. Determination of thermal conductivity was originally the only aim in collecting the samples. The samples cut perpendicularly from the drill cores have been 10-20 era long pieces of core, of which the thermal conductivity samples were prepared. During the years the thermal conductivity sample size has slightly varied depending on the most typical drill core diameter used in Finland. Thus thermal conductivity was usually measured from rock cylinders with a diameter between 24-42 mm and height 6-9 nun. The remaining parts of the original samples have been preserved in most cases, and they were used in this study for measuring density, magnetic properties and P-wave velocity. Petrophysical properties with anisotropic character (thermal conductivity, P-wave velocity and magnetic properties) were measured in the drill hole orientation which is vertical or subvertical in most cases and usually perpendicular to the strata. All measurements were done at the Geological Survey of Finland. Thermal conductivity was measured on watersaturated samples at normal room temperature and pressure. Conductivity measurements were done with a divided bar instrument constructed by Jarvim~ki (1968) (for details, see Kukkonen and Lindberg (1995)). Disks cut from a quartz crystal and oriented perpendicular to the optical axis are used as conductivity references in the instrument. The accuracy of measurements are monitored with known glass and quartz samples used as standards (thermal conductivities between 1.2 - 10.5 W m 1 K z) and the data are corrected for thermal contact resistances. Relative errors have been smaller than 2-4 %. Thermal conductivity was measured on 2496 samples. Radiogenic heat production rate was determined from the samples with gamma ray spectrometry using a counting time of 30 minutes. The U, Th and K concentrations were analyzed using a multichannel analyzer with 2048 channels, and radiogenic heat production was calculated as in Rybach (1973) assuming that the decay series are in equilibrium. The detection limit is about 1-2 ppm for U and Th and 0.1-0.2 % for K. Heat production rate was determined for 669 samples. Bulk density was measured by weighing the samples in air and water (Archimedes's principle) using an A&D model FX-3200 balance connected to a computer. The weighing accuracy of the balance was 0.01 g. Standard error of the repeated density measurements is lower than 5 kg m 3 or about 0.1%. Porosity produces small errors but they remain mostly below 1 % (Puranen et al., 1993). Density was measured on 2583 samples. Seismic P-wave velocity was determined from watersaturated samples at atmospheric pressure and room temperature using the sample length and P-wave velocity travel time through the sample. Travel time was determined
using two identical ultrasonic (66 kHz) P-wave transducers as transmitter and receiver. The absolute measuring errors are generally lower than 200 m s1 according to measurements of standard samples with known P-wave velocities in the range 2200-2600 m s1 . Variations in repeated measurements are lower than 5 % (Puranen et al., 1993). Only samples longer than 40 mm were selected for the measurement in order to minimize the measuring errors. P-wave velocity was measured on 751 samples. Magnetic susceptibilitywas measured with a low frequency (1025 Hz) AC-bridge apparatus which is calibrated by a ferrite ball method (Puranen and Puranen, 1977). The calibration error is smaller than 3 % based on measurements of standard materials. For weak magnetic samples ( < 1000.10 ~ SI) the measurement error is lower than 2 0 " 1 0 .6 SI, but for strong magnetic materials the results may change by more than 10 % depending on the measuring direction and sample dimensions (Puranen et al., 1993). The values reported here represent the direction of the axis the cores. Susceptibility was measured for 2587 samples. Natural remanent magnetization (NRM) was measured with an Oersted-type remanence meter. The magnetic field produced by the sample is measured in six positions under a /z-metal shielding. The standard error of repeated measurements is about 10 m A m 1. Similar to susceptibility measurements, highly magnetic samples may show variations of more than 10% (Puranen et al., 1993). NRM was measured on 2123 samples. All samples were geologically classified into a uniform lithological systematics. The original geological logs of the drill cores were used in naming the rock types for each sample. In uncertain cases macroscopic investigation was used to confirm the rock name.
3 Factors influencing petrophysical properties Theoretically thermal conductivity is expected to correlate with density and specific heat as well as phonon velocity and mean free path of phonons (Sch6n, 1983). Heat production rate is much more difficult to forecast theoretically in rocks, because it is dependent on concentrations of two trace elements and one major component in rock chemistry. These are controlled by the genesis and geochemistry of the rocks, which does not necessarily result in similar concentrations in rocks with the same lithulogical name. The best known theoretical approach relating heat production rate with density and P-wave velocity was given by Rybach and Buntebarth (1982, 1984) using cation packing indexes. The investigatedpetrophysicalproperties are quite different in character, and therefore there is no obvious reason to expect well defmed unique relationships between them. Thermal conductivity is controlled by the mineral composition of the rock, but also by rock texture, rock porosity and pore
Relationships between Thermal and other Petrophysicai Properties 1. PLUTONIC ROCKS Nffi1210 1.1 granite group N=690 1.1.2 granite N=272 f.1.3 granodiorite N=270 1.1.4 tonalite N=148 1.2 repakivi N=51 1.3 syenite group N=94 1,4 alkaline and carbonate rocks N=58 1,5 gabbro N=105 1.6 diorite group N=43 1.7 anorthosite N=9 1.8 uitramafics N=118 1.9 pegmatite N=42 2. DYKES N=29 2.1 dykes N=28 21.1 mineral dykes N=8 2.1.2 diabase N=19 2.1.3 porphyry N=I 2.3 kimbedite N=I 3. VOLCANIC ROCKS N=163 3.8 lava N=19 3.9 pyroclastic rocks N=10 3.10 tuffite N=24 3.13 mafic volcanic rock N=37 3.14 uitremafic volcanic rock N034 3.15 volcanic breccia N=I
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filling fluids as well as ambient temperature and pressure (Clauser and Huenges, 1995). Heat production rate is a function of the U, Th and K concentrations as well as rock density. Bulk density is determined by the densities of the rock forming minerals, rock porosity and pore filling fluids. In unweathered crystalline rock samples porosity is mostly below 0.5 % and does not influence bulk density significantly. Seismic P-wave velocity is mainly controlled by the mineral composition but also by rock texture and anisotropic properties of minerals. M icrocracks and fractures of either technical or natural origin may further modify the P-wave velocity values of drill core samples (Vemik and Nur, 1992; Popp and Kern, 1994). Magnetic susceptibility is dependent on the content of ferrimagnetic minerals (magnetite, pyrrhotite, hematite) which are usually accessory minerals in rocks, but in paramagenetic rocks ( < 1000.10 "6 SI) susceptibility is mainly influenced by the relative proportions of the main rock forming minerals which are either paramagnetic or diamagnetic. Intensity of NRM is equally controlled by the content of ferrimagnetic minerals
but particularly by the magnetic domain sizes. NRM may be also influenced by the sampling techniques, such as magnetization produced by the rotating magnetic steel parts of the diamond drill bit. However, such components are presumably magnetically soft and small. Most of the investigated properties are also dependent on ambient temperature and pressure. Due to the several factors involved, we can expect a lot of variation in cross-correlations between different properties. However, the general compositional variations between rock types suggest that petrophysical trends should exist. 4 Thermal conductivity and heat production rate as a function of rock type Means and standard deviations are presented for thermal conductivity and heat production rate in different rock types in Figs. 1 and 2. In most rock types the mean thermal conductivity is between 2-4 W m -t K+'. The mean value of all measurements (N = 2496) is 3.24 + 1.00 W m~ K-L Standard deviation of thermal conductivity is about 0.5 - 1.0 W m" K" in different rock types, but the ranges of variation
I. T. Kukkonen and S. Peltoniemi
344
(Kukkonen, 1989). Standard deviations of heat production rate are usually 0.5 - 1.5 # W m 3, which actually means a considerable variation within rock types. Highest values of heat production rate were obtained for rapakivi granites and the lowest for various ultrabasic and metamorphic ultrabasic rocks. As expected, increasing basicity decreases heat production rate.
1.2 rapakivi N=44 1.3 syenite group N=53 1.5 gabbro N=22 1.6 diodte group N=24 1.7 anorthosite N=6 1.8 ultramafics N=94 1.9 pegmatite N=5 ~ 2. DYKES N=7 2.1.1 mineral dykes N=5 2.1.3 porphyry N=2 ~ 3. VOLCANIC ROCKS N=162 3.8 lava N=17 3.9 pyroclastic rocks N=10 ~ i 3.10 tuffite N=21 3.13 marie volcanic rock N=37 3.14 ultramafic volcanic rock N=29 4. SEDIMENTARY ROCKS N=21 5. METAMORPHIC ROCKS N=188 ~
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5 Cross-correlation diagrams
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cover several W m ~ K ~. In plutonic rocks thermal conductivity increases from mafic to felsic rocks, but ultramafie rocks have mean thermal conductivity comparable to granitoids. Highest ranges of variation were observed in various metamorphic rocks, mainly due to variable concentrations of high conductivity minerals, such as graphite in metasediments. The means and ranges of variation of different rock types overlap each other, which, in general, prevents identifying unambiguosly the rock type with thermal conductivity measurements alone. The results for average thermal conductivity of different rock types are similar to values measured in the Swedish pan (Sundberg, 1988), but higher than those measured in the Russian pan of the Fennoseandian Shield (Moyseyenko and Negrov, 1992). When thermal conductivities are compared with measurements in other areas of the world (~erm~ and Rybach, 1982) our averages are found to be slightly higher. This may be due to differences in applied rock classifications or genuine differences in rock properties between different areas of the shield and other areas. The mean values of heat production rate are lower than 1.5 # W m 3 for most of the rock types (Fig. 2). The average value of all measurements (N = 669) is 1.42 -I- 2.02 #W m3. This is lower than the mean value (1.86 + 0.77 #W m3) determined for Finland by glacial till geochemistry
In the following cross-correlation plots are presented and discussed for different data pairs. The number of samples included in the plots varies depending on the available measurements for each property pair. The highest numbers were reached in data sets correlating thermal conductivity, density and magnetic properties, whereas the smallest numbers are encountered in P-wave velocity and heat production rate. This is due to larger sample volume required in P-wave velocity and heat production rate measurements which could not be met in all cases. Nevertheless, the numbers of data points range from more than 300 to about 2700, which is certainly sufficient to reveal systematic relationships between different properties if they exist. Thermal properties themselves are not correlated, which is indicated by the low coefficient of correlation (r = 0.17, Fig.3). The data points are scattered without any particular indications of trends between the properties. Thermal conductivity and density show no numerical correlation (r = -0.03), but the graph (Fig. 4) reveals a trend of decreasing density with increasing thermal conductivity. This can be explained by the variation of quartz content in
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Relationships between Thermal and other Petrophysical Properties
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FIE. $. P-wave velocity versus thermal conductivity,N = 721, r ffi 0.11. Symbolsas in Fig. 3.
1~. 7. NRM versusthermalconductivity,N = 1984. r = -0.06. Symbols as in Fig. 3.
rocks. Increasing quartz content increases thermal conductivity but decreases density. The observed trend is in a disagreement with the theoretical concept of thermal condoctivity correlating positively with demity (Seh6n, 1983). It can be attributed to the numerous factors contributing simultaneously to thermal conductivity in a large collection of different rock types.
Thermal conductivity and P-wave velocity are not numerically correlated (r = -0.11, Fig. 5). Theoretically thermal conductivity is proportional to specific heat, density, propagation velocity of phonons and the seismic velocity (Seh6n, 1983). Seismic velocities of minerals correlate positively with thermal conductivity, and therefore an increasing trend can be expected in rocks. Actually, this
346
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Fig. 8. Heatproductionrate versusdensity.N = 669, r = -0.68. Symbols as in Fig. 3.
Hg. 9. Heat productionrate versus P-wave velocity,N = 211, r = 0.55. Symbolsas in Fig. 3.
relationship can be observed only in a very wide spectrum of velocities and conductivities with practically all rock types incloded (sedimentary and crystalline, see e.g. Sch6n, 1983). Our P-wave and conductivity data represent crystalline rocks with velocities mostly between 5000 and 6500 m s1 and conductivities between 2 and 4 W m 1 K 1. Our data fit well in the relationship presented by Seh6n (1983), but since high and low values of velocity and conductivity are not represented in our data there is a lack of correlation. Susceptibility shows a bimodal distribution (Fig. 6) in the thermal conductivity-susceptibilityplot. The bimodality is characteristic for susceptibility in general in crystalline rocks of Finland (Puranen, 1989; Airo, 1990). In rocks with high susceptibilitiesabove 1000.10 ~ SI there is no correlation between the properties, but a weak negative correlation (r = -0.29) can be seen in rocks with lower susceptibility ( < 1000-10~ SI). These rocks contain practically no ferrima£metic minerals, and the trend of decreasing susceptibility can be attributed to the content of paramagnetic and diamagnetic rock forming minerals. In felsic rocks paramagnetic feldspars, mica and diamagnetic quartz dominate, but in marie rocks the contribution by marie amphiboles and pyroxenes with higher paramagnetic suceptibility is stronger. As a result the magnetic susceptibilityincreases. Simultaneously, the quartz content, which significantly influences thermal conductivity, decreases, and this results in a negative correlation with susceptibility. Thermal conductivity and intensity of NRM are not correlated (r = -0.06, Fig. 7). This can be attributed to the quite different factors controlling NRM and thermal conductivity. Our data suggests that heat production rate and density are weakly correlated (r = -0.68, Fig. 8). However, heat
production rate values are scattered over two orders of magnitude with a given density value, but nevertheless a trend of decreasing heat production rate with increasing density can be seen. Our data yields a linear regression line In A = 15.3 ( + 0 . 4 ) - 5 . 5 6 ( + 0 . 2 ) d, where A is the heat production rate (#W m 3) and d is the density (10.3 kg m3). The corresponding line calculated by Rybach and Buntebarth (1984) for Precambrian rocks is In A = 2 1 . 4 - 8.15 d. A similar graph was obtained from heat production rate versus P-wave velocity. The correlation is weak (r = -0.55, Fig. 9) and the scatter of heat production rate values is considerable, but a general trend of decreasing heat production rate with increasing P-wave velocity can be observed. A linear regression line of the data was also calculated: ln A = 10.8 (5:0.5) - 1.95 (5:0.2) Vp, where A is the heat production rate (ttW m3) and Vp is the P-wave velocity (103 m s1). For comparison, the corresponding line calculated by Rybach and Buntebarth (1984) for Precambrian rocks is In A = 16.5 - 2 . 7 4 lip. Comparison of the present results with those by Rybach and Buntebarth (1984) is complicated by the difference in conditions of measuring Pwave velocities. Our data was measured under normal atmospheric pressure whereas the above regression line by Rybach and Buntebarth (1984) was based on measurements at 50 MPa. The differences between A-Vp regression lines may be partly attributed to this fact. It should also be taken into account that Rybach and Buntebarth (1982, 1984) limited the lithologieal groups only to plutonic rocks, amphibolite, homblendite and serpentinite, whereas our data contains the full spectrum of rock types in the Finnish Precambrian. However, most of our samples represent plutonic, metamorphic and metasedimentary rock types (Figs. 1 and 2) which can be considered quite normal in crystalline
Relationships between Thermal and other Petrophysical Properties bedrock. The trends observed in heat production rate versus density and heat production rate versus P-wave velocity can be attributed to the general variation of these properties between different rock types. Increasingly felsic composition usually means decreasing P-wave velocity but increasing heat production. The radioactive elements U and Th are usually responsible for about 90 % of the heat production rate. They are incompatible with the typical silicate frameworks and have a tendency of concentrating in felsic rocks during the geochemical differentiation of the lithosphere. Our P-wave velocity-heat production rate and P-wave velocity-density results yield regression lines resembling those by Rybach and Buntebarth (1984), but actually they give quite different numerical values. If used for crustal heat production estimation the regression lines give values differing by one or half order of magnitude. Using these relationships would result in considerable uncertainties in numerical estimates. 6 Discussion
The present results suggest only weak correlations between the thermal and other petrophysical properties in crystalline rocks. The lithological types cover all main rock types and their subgroups present in the Finnish Precambrian, and are thus representative at least for the upper crust and possibly for the middle crust as well. The number of samples in the diagrams is sufficient to be statistically representative of the studied relationships. The results indicate that thermal properties cannot be very accurately estimated with the aid of these relationships. The scattered nature of the relationships can be attributed to several influencing factors. Small size of the samples increases the variations due to geological heterogeneity. Such effects can be expected particularly in those properties which are controlled by the concentrations of accessory minerals or trace elements, such as magnetic susceptibility and heat production. Further, rock texture creates anisotropy effects which increase the scatter in thermal conductivity, magnetic properties, and P-wave velocity. This effect was reduced by measuring the samples always in the same direction, i.e. the drill hole orientation which cut the strata perpendicularly in most cases. A small effect is added by the samples themselves, because the different properties were not measured exactly from the same piece of rock due to different requirements for the sample shape and size in the different measuring devices. However, this factor should not be significant since all the measurements of a rock sample represent a length of drill core less than 20 era. In the data sets several different lithological types are included in the diagrams. This may further increase the scatter of data points. It could possibly be reduced if the cross-plotting would be done within limited lithological types.
347
However, this is beyond the scope of this work, and we have concentrated here on the general relationships between petrophysieal properties of rocks. If em,s~ thermal properties are to be estimated, for instance, in geothermal modelling, there is very little constraining information on rock types in the middle and lower crust, although seismic information can be utilized in such work (Rudnick and Fountain, 1995). Our data represent the Finnish Precambrian and strictly taken the results are valid only in the study area. However, there is no reason to doubt that the Finnish bedrock is petrophysically essentially different from other shields. The present results suggest that although there are numerically only very weak correlations between thermal and other petrophysical properties, many of the cross-plots indicated trends of variation which can be at least qualitatively interpreted in terms of variation of mineralogic composition and physical properties of the relevant minerals. The result is comparable to the data by Soffel et al. (1992), Huenges (1997) and Huenges et al. (1997) on the KTB pilot hole petrophysics. Using factor analysis Huenges et al. (1997) noted that the petrophysical properties (P-wave velocity, thermal conductivity, heat production and density) correlated with lithological factors. In our study the trends are disturbed by considerable scatter of data points, which seriously limits the use of such trends for data estimation. Geological heterogeneity and the sample size in the scale of centimetres are partly responsible for the variation of d~t~j If considerably larger samples in the scale of metres could be measured, smaller variations would probably be obtained in the crosscorrelation plots. Solving this scaling problem would require empirical d_at~_on the spatial auto-correlation of the investigated properties. Such data (variograms) are not available. However, assuming that the properties should be similar within lithological types, averaging over lithological rocks groups should reduce the scatter. This was tested in most of the investigated relationships, but the result was disappointing. The coefficients of correlation were sometimes even smaller in the data averaged by rock type. This indicates that averaging may rather remove information than condense it, and that lithological rock types are not represented by only one type of a parameter distribution but may include more than one population. Measurement of P-wave velocities under normal atmospheric pressure may also increase the scatter. However, the samples were measured in a water-saturated condition which considerably reduces the effects of open microfractures on velocity which are often observed in laboratory measurements of dry samples under a small pressure (0200 MPa). P-wave velocities measured on water-saturated samples provide a satisfactory estimate of the intrinsic (zero overpressure) velocity (Huenges et al., 1997). Although our results suggest weak correlations to exist between heat production rate versus density or P-wave velocity, these relationships are very scattered and heat
348
I . T . Kukkonen and S. Peltoniemi
p r o d u c t i o n rate values cover a range o f about 2 orders o f magnitude for a given value o f P-wave velocity and density. Similar spread o f data points is seen in the data set by C e r n ~ et al. (1990) and K e r n and Siegismund (1989) as well. This is obviously a characteristic feature o f crystalline rocks in general and reflects the great natural variability o f heat production rate values. The present results are not very encouraging for using heat p r o d u c t i o n rate - P-wave velocity relationships for estimating crustal heat production (cf. Fountain, 1986, 1987; Rybach and Buntebarth, 1987).
7 Conclusions The present empirical data f r o m the Finnish Precambrian suggest that there are no well d e f m e d general relationships b e t w e e n thermal and other petrophysical properties o f crystalline rocks. This can be attributed to many mineralogical, physical and geochemical factors influencing the petrophysical properties and producing trends mitigating each other. Coefficients o f correlation are small (0-0.7) and the data is scattered. H o w e v e r , certain trends o f variation can be observed, particularly (1) between thermal conductivity and susceptibility in weakly magnetic rocks, (2) heat p r o d u c t i o n and P - w a v e velocity, and (3) heat production and
minerals. In: T.J. Ahrens (Editor), A Handbook of Physical Constants, Rock Physics and Phase Relations, Vol. 3. Amcricai Geophysical Union, Washington DC, p. 105-125. Fountain, D.M., 1986. Is there a relationship between seismic velocity and heat production for crustal rocks.'?Earth Planet. Sci. Lar., 79, 145-150. Fountain, D.M., 1987. The relationship between seismic velocity and heat production- a reply. Earth Planet. Sci. Left,, 83, 178-180. Huenges, E., 1997. Factors controlling the variances of seismic velocity, density, thermal conductivity and heat production of cores from the KTB pilot hole. Geophys. Res. Left. 24, 341-344, Huenges, E., Lauterjung, J., Biicker,C., Lippmann, E. and Hartmut, K., 1997. Seismic velocity, density, thermal conductivity and heat production of cores from the KTB pilot hole. Geophys. Res. Left, 23, 345-348. Jirvimllki, P., 1968. Geotermisistll mittauksista Suomessa (On geothermal measurementsin eln/and). Master's thesis, University of Helsinki, Institute of C-eophysics, 30 p. (in Finnish). JOeleht, A. and Kukknnen, I.T., 1997. Thermal properties of grannlite facies rocks in the Precambrianbasementof Estonia and Finland. Tecnonophysics (submitted). Kern, H. and Siegismund, S., 1989. A test of the relationship between seismic velocity and heat production for crustal rocks. Earth Planet. Sci. Left., 92, 89-94.
density. H o w e v e r , the uncertainties in these trends do not allow reliable estimations o f the thermal properties.
Kremcnetsky, A.A., Milanovsky, S.Yu. and Ovchinnikov, L.N., 1989. A heat generation model for continental crust based on deep drilling in the Baltic Shield. Tectonophysics, 159, 231-246.
Acknowledgement. We are grateful for L. Rybach, H. Winter and A. J6eleht for reviews and comments on the manuscript. The study was partly funded from a scholarship of the Finnish Association of Mining and Metallurgical Engineers.
Kukkonen, I., 1989. Terrestrial heat flow and radiogenic heat production in Finland, the central Baltic Shield. Tectonophysics, 164, 219-230.
References Aim, M.-L., 1990. Susceptibilities, intensities of remanence and densities of Precambrian and recent volcanic rocks: examples from Iceland and northem Fennoscandia. Geol. Surv. Finland, Rep. Investigan'on, 93, 24 p. Beck, A.E, 1988. Thermal properties. In: R. Haenel, L. Rybach and L. Stegena (Editors), Handbook of Terrestrial Heat-Flow Density Determination. Kluwer, Dordrecht, p. 87-124. Burkhardt, H., Honarmand, H. and Pribnow, D., 1995. Test measurements with a new thermal conductivity borehole tool. Tectonophysics, 244, 161165. ~err~k, V. and Rybach, L., 1982. Thermal conductivity and specific heat of minerals and rocks. In: G. Angenheister (Editor), Landolt-BOmstein: Numerical Data and Functional Relationships in Science and Technology, New Series, Group V (Geophysics and Space Research), Vol. l a (Physical Properties of Rocks). Springer, Berlin, p. 305-343, (~erm~, V., Bodri, L., Rybach, L. and Buntebarth, G., 1990. Relationships between seismic velocity and heat production: comparison of two data sets and test of validity. Earth Planet. Sci. Left., 99, 48-57. Clauser, C. and Huenges, E., 1995. Thermal conductivity of rocks and
Kukkonen, I.T., 1993. Heat flow map of northern and central parts of the Fermoscandian Shield based on geochemical surveys of heat producing elements. Tectonophysics, 225, 3-13. Kukkonen, I.T. and Lindberg, A., 1995. Thermal conductivity of rocks at the TVO investigation sites Olkiluoto, Romuvaam and Kivetty. Nuclear Waste Commission of Finnish Power Companies, Helsinki, Report YIT95-08, 29 p. Lachenbmch, A.H., 1971. Vertical gradients of heat production in the continental crest, 2. Some estimates from borehole data. J. Geophys. Res., 76, 3852-3860. Moyseyenko, U. and Negmv, O., 1992. Thermophysical properties of crystalline rocks. In: N.B. Dortman (Editor), Petrophysics, Handbook, Part L Nedra, Moscow, p. 240-253 (in Russian). Popp, T. and Kern, H., 1994. The influence of dry and water saturated cracks on seismic velocities of crustal rocks - a comparison of experimental data with theoretical model. Surv. Geophys,, 15, 443-465. Pinet, C. and Jaupart, C., 1987. The vertical distribution of radiogenic heat production in the Precambrian of Norway and Sweden: Geothermal implications. Geophys. Res. Left., 14, 260-263. Puranen, R., 1989. Susceptibilities, iron and magnetite content of Precambrian rocks in Finland. Geol. Surv. Finland, Rep. Investigation, 90, 45 p.
R e l a t i o n s h i p s b e t w e e n T h e r m a l a n d o t h e r P e t r o p h y s i c a l Properties
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Puranen, M. and Puranen, R., 1977. Apparatus for the measurement of magnetic susceptibility and its anisotropy. Geol. Sure. Finland, Rep. Investigation, 28, 46 p.
Rybach, L. and Buntebarth, 1984. The variation of heat generation, density and seismic velocity with rock type in the continental lithosphere. Tectonophysics, 103, 335-344.
Puranen, R., Sulkanen, K., Poikonen, A., Nissinen, R., Simelius, P. and Harinen, L., 1993. User's manual for a computerized petrophysics laboratory. Geol. Sure. Finland, Dep. of Geophys., Rep. QI9.1/27/93/1, 50 p. Rudnick, R.L. and Fountain, D.M., 1995. Nature and composition of the continental crast: a lower crustal perspective. Rev, Geophys., 33, 267309.
Rybach L. and Bun~ebarth, G., 1987. The relationship between seismic velocity and heat production- critical comments. Earth Planet. Sci. Left., 83, 175-177.
Rybach, L., 1973. Wlrmeproduktionsbestimmungenan Gesteinen der Schweizer Alpen. Beitr. Geol. $chweiz. Geatech, 51, 43 p. (in German). Rybach, L. 1988. Determination of heat production rate. In: R. Haenel, L. Ryba~h and L. Stegena (Editors), Handbook of Terrestrial Heat-Flow Density Determination. Kluwer, Dordrecht, pp. 125-142. Rybach, L. and Buntebarth, G., 1982. Relationships between the petrophysical properties density, seismic velocity, heat generation, and mineralogical constitution. Earth Planet. $ci. Left., 57, 367-37.
Sch6n, J., 1983. Petrophysik. Enke, Stuttgart, 405 p. (in German). Soffel, H.C., Bficker, Ch., Gebrande, H., Huenges, E., Lippman, E., Pohl, J., Ranen, A., Schult, A., Streit, K.M. and Wienand, F., 1992. Physical parameters measured on cores and cu~ngs from the pilot well (0 m 4000.1 m) of the German Continental Deep Drilling Program (KTB) in the Obeffalz area, Bavaria, Federal Republic of Germany. Sure. Geophys., 13, 1-34. Sundberg, J., 1988. Thermal properties of rocks and soils. Doctoral thesis, Chalmers University of Technology and University of GOteborg, Department of Geology. Gothenburg, 47 p. Vemik, L. and Nur, A., 1992. Petrophysical analysis of Cajon Pass scientific well: Implications for fluid flow and seismic studies in the continental crest. J. Geophys. Res., 97, 5121-5134.
Phys. Chem. Earth, Vol. 23, No. 3, pp. 341-349, 1998 © 1998 Elsevier Science Ltd. All rights reserved Printed in Great Britain 0079-1946/98 $19.00 + 0.00 PII: S0079-1946(98)00035-4
Relationships between Thermal and other Petrophysical Properties of Rocks in Finland I. T. K u k k o n e n I and S. P e i t o n i e m i 2
lGeological Survey of Finland, P.O. Box 96, FIN-G2151 Espoo, Finland. (E-mail: ilmo.kukkonen @ gsf.fi) 2Astrock Oy, Klovinite 6 B, FIN-02180 Espoo, Finland
Received 25 April 1997; revised 10 September 1997; accepted 8 December 1997
Abstract. Relationships between thermal conductivity, heat production rate and some other petrophysical properties (density, magnetic susceptibility, intensity of remanent magnetize'on,P-wave velocity) were investigatedempirically in about 2700 drill core samples from the Finnish precambrian bedrock. The results suggest that there are no well defined relationships between the thermal and other petrophysical properties which would generally apply in crystalline rocks. Coefficients of correlation are small ( < 0.7) and the data points scatter in the cross-correlation diagrams. Nevertheless, certain trends of variation can be observed, particularly between (1) thermal conductivity and susceptibility in paramagnetic rocks, (2) heat production rate and P-wave velocity, and (3) heat production and density. However, uncertainties in these trends do not allow reliable estimations of the thermal properties. © 1998 Elsevier Science Ltd.
required, and then the thermal properties must be estimated with indirect methods. These may be either lithological interpretation of seismic, potential field or electromagnetic data, or petrophysical relationships between a measured physical property and thermal properties. Studies of the thermal properties in the Baltic (or Fennoscandian) Shield are provided by Pinet and Jaupart (1987), Sundberg (1988), Kremenetsky et al. (1989), Kukkonen (1989, 1993), Moyseyenko and Negrov (1992) and JOeleht and Kukkonen (1997). We present a summary of petrophysical measurements on about 2700 rock samples originally collected for geothermal investigations from drill holes in Finland during 1964-1995. The samples were used for thermal conductivity measurements in heat flow studies. Practically all samples have been preserved which made it possible to extend the measurements to other petrophysical properties as well. The sampled drill holes represent different Precambrian rock types in Finland, and provide a good basis for investigating petrophysical relationships empirically. We have measured thermal conductivity, radiogenic heat production rate, bulk density, magnetic susceptibility, intensity of natural remanent magnetization (NRM) and seismic P-wave velocity of the samples. We use the data in this study for investigating whether there are general relationships between thermal and other petrophysical properties in the crystalline precambrian rocks in Finland, and whether such relationships could be utilized in indirect estimation of thermal properties.
1 Introduction Thermal conductivity and radiogenic heat production rate of rocks are the most important petrophysical parameters needed in geothermal investigations. When relevant rock samples are available, these parameters can be measured in laboratory (Beck, 1988). Alternatively, in situ measurements (Rybach, 1988; Burkhardt et al., 1995) can be performed in drill holes, and drill core data can be used for modelling of the vertical variation of parameters (Lachenbruch, 1971). In geothermal modelling of the lithosphere knowledge of the thermal properties in deeper layers of the Earth is
2 Data base: Samples and measurements
The present data set is based on measurements of drill core samples collected from 63 diamond-drilled holes in Finland. The drill hole sites represent Archaean and Early to Middle Proterozoic crystalline rocks, mostly plutonic,
Correspondence to: I.T. Kukkonen 341
342
I. T. Kukkonen and S. Peltoniemi
metasedimentary, metavolcanic and two sedimentary formations. The total number of samples in this study was 2705. Determination of thermal conductivity was originally the only aim in collecting the samples. The samples cut perpendicularly from the drill cores have been 10-20 era long pieces of core, of which the thermal conductivity samples were prepared. During the years the thermal conductivity sample size has slightly varied depending on the most typical drill core diameter used in Finland. Thus thermal conductivity was usually measured from rock cylinders with a diameter between 24-42 mm and height 6-9 nun. The remaining parts of the original samples have been preserved in most cases, and they were used in this study for measuring density, magnetic properties and P-wave velocity. Petrophysical properties with anisotropic character (thermal conductivity, P-wave velocity and magnetic properties) were measured in the drill hole orientation which is vertical or subvertical in most cases and usually perpendicular to the strata. All measurements were done at the Geological Survey of Finland. Thermal conductivity was measured on watersaturated samples at normal room temperature and pressure. Conductivity measurements were done with a divided bar instrument constructed by Jarvim~ki (1968) (for details, see Kukkonen and Lindberg (1995)). Disks cut from a quartz crystal and oriented perpendicular to the optical axis are used as conductivity references in the instrument. The accuracy of measurements are monitored with known glass and quartz samples used as standards (thermal conductivities between 1.2 - 10.5 W m 1 K z) and the data are corrected for thermal contact resistances. Relative errors have been smaller than 2-4 %. Thermal conductivity was measured on 2496 samples. Radiogenic heat production rate was determined from the samples with gamma ray spectrometry using a counting time of 30 minutes. The U, Th and K concentrations were analyzed using a multichannel analyzer with 2048 channels, and radiogenic heat production was calculated as in Rybach (1973) assuming that the decay series are in equilibrium. The detection limit is about 1-2 ppm for U and Th and 0.1-0.2 % for K. Heat production rate was determined for 669 samples. Bulk density was measured by weighing the samples in air and water (Archimedes's principle) using an A&D model FX-3200 balance connected to a computer. The weighing accuracy of the balance was 0.01 g. Standard error of the repeated density measurements is lower than 5 kg m 3 or about 0.1%. Porosity produces small errors but they remain mostly below 1 % (Puranen et al., 1993). Density was measured on 2583 samples. Seismic P-wave velocity was determined from watersaturated samples at atmospheric pressure and room temperature using the sample length and P-wave velocity travel time through the sample. Travel time was determined
using two identical ultrasonic (66 kHz) P-wave transducers as transmitter and receiver. The absolute measuring errors are generally lower than 200 m s1 according to measurements of standard samples with known P-wave velocities in the range 2200-2600 m s1 . Variations in repeated measurements are lower than 5 % (Puranen et al., 1993). Only samples longer than 40 mm were selected for the measurement in order to minimize the measuring errors. P-wave velocity was measured on 751 samples. Magnetic susceptibilitywas measured with a low frequency (1025 Hz) AC-bridge apparatus which is calibrated by a ferrite ball method (Puranen and Puranen, 1977). The calibration error is smaller than 3 % based on measurements of standard materials. For weak magnetic samples ( < 1000.10 ~ SI) the measurement error is lower than 2 0 " 1 0 .6 SI, but for strong magnetic materials the results may change by more than 10 % depending on the measuring direction and sample dimensions (Puranen et al., 1993). The values reported here represent the direction of the axis the cores. Susceptibility was measured for 2587 samples. Natural remanent magnetization (NRM) was measured with an Oersted-type remanence meter. The magnetic field produced by the sample is measured in six positions under a /z-metal shielding. The standard error of repeated measurements is about 10 m A m 1. Similar to susceptibility measurements, highly magnetic samples may show variations of more than 10% (Puranen et al., 1993). NRM was measured on 2123 samples. All samples were geologically classified into a uniform lithological systematics. The original geological logs of the drill cores were used in naming the rock types for each sample. In uncertain cases macroscopic investigation was used to confirm the rock name.
3 Factors influencing petrophysical properties Theoretically thermal conductivity is expected to correlate with density and specific heat as well as phonon velocity and mean free path of phonons (Sch6n, 1983). Heat production rate is much more difficult to forecast theoretically in rocks, because it is dependent on concentrations of two trace elements and one major component in rock chemistry. These are controlled by the genesis and geochemistry of the rocks, which does not necessarily result in similar concentrations in rocks with the same lithulogical name. The best known theoretical approach relating heat production rate with density and P-wave velocity was given by Rybach and Buntebarth (1982, 1984) using cation packing indexes. The investigatedpetrophysicalproperties are quite different in character, and therefore there is no obvious reason to expect well defmed unique relationships between them. Thermal conductivity is controlled by the mineral composition of the rock, but also by rock texture, rock porosity and pore
Relationships between Thermal and other Petrophysicai Properties 1. PLUTONIC ROCKS Nffi1210 1.1 granite group N=690 1.1.2 granite N=272 f.1.3 granodiorite N=270 1.1.4 tonalite N=148 1.2 repakivi N=51 1.3 syenite group N=94 1,4 alkaline and carbonate rocks N=58 1,5 gabbro N=105 1.6 diorite group N=43 1.7 anorthosite N=9 1.8 uitramafics N=118 1.9 pegmatite N=42 2. DYKES N=29 2.1 dykes N=28 21.1 mineral dykes N=8 2.1.2 diabase N=19 2.1.3 porphyry N=I 2.3 kimbedite N=I 3. VOLCANIC ROCKS N=163 3.8 lava N=19 3.9 pyroclastic rocks N=10 3.10 tuffite N=24 3.13 mafic volcanic rock N=37 3.14 uitremafic volcanic rock N034 3.15 volcanic breccia N=I
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4.2 precipitated sediments N=9 5. METAMORPHIC ROCKS N=992 5.1 metamorphic sandstones N=17 51.1 quartzite N=6 5.1.2 arkosite N=I 1 5.2 schists N=296 5.2.1 phyllite N=24 5,2,2 mica schist N=181 5.2.4 leptite N=I 1 5,2,5 graphite schists N=80 5.3 gneissas N=375 5.3.3 quartz feldspar gneisses N=15 5.3.5 mica gneisses N=257 5.3.6 amphibole gneisses N=948 5.3.7 pyroxene gneisses Nffi9 5.4 migmatite N=46 5.6 meta-ultramafics N=116 5 7 greenschist N=13 5 3 amphibolite Nffi80 5.9 skam N=38 5.11 cataclastics N=I 1 6. ALTERED ROCKS N=11 6.1 altered rocks N=3 6.2 ores N=8
:
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filling fluids as well as ambient temperature and pressure (Clauser and Huenges, 1995). Heat production rate is a function of the U, Th and K concentrations as well as rock density. Bulk density is determined by the densities of the rock forming minerals, rock porosity and pore filling fluids. In unweathered crystalline rock samples porosity is mostly below 0.5 % and does not influence bulk density significantly. Seismic P-wave velocity is mainly controlled by the mineral composition but also by rock texture and anisotropic properties of minerals. M icrocracks and fractures of either technical or natural origin may further modify the P-wave velocity values of drill core samples (Vemik and Nur, 1992; Popp and Kern, 1994). Magnetic susceptibility is dependent on the content of ferrimagnetic minerals (magnetite, pyrrhotite, hematite) which are usually accessory minerals in rocks, but in paramagenetic rocks ( < 1000.10 "6 SI) susceptibility is mainly influenced by the relative proportions of the main rock forming minerals which are either paramagnetic or diamagnetic. Intensity of NRM is equally controlled by the content of ferrimagnetic minerals
but particularly by the magnetic domain sizes. NRM may be also influenced by the sampling techniques, such as magnetization produced by the rotating magnetic steel parts of the diamond drill bit. However, such components are presumably magnetically soft and small. Most of the investigated properties are also dependent on ambient temperature and pressure. Due to the several factors involved, we can expect a lot of variation in cross-correlations between different properties. However, the general compositional variations between rock types suggest that petrophysical trends should exist. 4 Thermal conductivity and heat production rate as a function of rock type Means and standard deviations are presented for thermal conductivity and heat production rate in different rock types in Figs. 1 and 2. In most rock types the mean thermal conductivity is between 2-4 W m -t K+'. The mean value of all measurements (N = 2496) is 3.24 + 1.00 W m~ K-L Standard deviation of thermal conductivity is about 0.5 - 1.0 W m" K" in different rock types, but the ranges of variation
I. T. Kukkonen and S. Peltoniemi
344
(Kukkonen, 1989). Standard deviations of heat production rate are usually 0.5 - 1.5 # W m 3, which actually means a considerable variation within rock types. Highest values of heat production rate were obtained for rapakivi granites and the lowest for various ultrabasic and metamorphic ultrabasic rocks. As expected, increasing basicity decreases heat production rate.
1.2 rapakivi N=44 1.3 syenite group N=53 1.5 gabbro N=22 1.6 diodte group N=24 1.7 anorthosite N=6 1.8 ultramafics N=94 1.9 pegmatite N=5 ~ 2. DYKES N=7 2.1.1 mineral dykes N=5 2.1.3 porphyry N=2 ~ 3. VOLCANIC ROCKS N=162 3.8 lava N=17 3.9 pyroclastic rocks N=10 ~ i 3.10 tuffite N=21 3.13 marie volcanic rock N=37 3.14 ultramafic volcanic rock N=29 4. SEDIMENTARY ROCKS N=21 5. METAMORPHIC ROCKS N=188 ~
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5 Cross-correlation diagrams
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cover several W m ~ K ~. In plutonic rocks thermal conductivity increases from mafic to felsic rocks, but ultramafie rocks have mean thermal conductivity comparable to granitoids. Highest ranges of variation were observed in various metamorphic rocks, mainly due to variable concentrations of high conductivity minerals, such as graphite in metasediments. The means and ranges of variation of different rock types overlap each other, which, in general, prevents identifying unambiguosly the rock type with thermal conductivity measurements alone. The results for average thermal conductivity of different rock types are similar to values measured in the Swedish pan (Sundberg, 1988), but higher than those measured in the Russian pan of the Fennoseandian Shield (Moyseyenko and Negrov, 1992). When thermal conductivities are compared with measurements in other areas of the world (~erm~ and Rybach, 1982) our averages are found to be slightly higher. This may be due to differences in applied rock classifications or genuine differences in rock properties between different areas of the shield and other areas. The mean values of heat production rate are lower than 1.5 # W m 3 for most of the rock types (Fig. 2). The average value of all measurements (N = 669) is 1.42 -I- 2.02 #W m3. This is lower than the mean value (1.86 + 0.77 #W m3) determined for Finland by glacial till geochemistry
In the following cross-correlation plots are presented and discussed for different data pairs. The number of samples included in the plots varies depending on the available measurements for each property pair. The highest numbers were reached in data sets correlating thermal conductivity, density and magnetic properties, whereas the smallest numbers are encountered in P-wave velocity and heat production rate. This is due to larger sample volume required in P-wave velocity and heat production rate measurements which could not be met in all cases. Nevertheless, the numbers of data points range from more than 300 to about 2700, which is certainly sufficient to reveal systematic relationships between different properties if they exist. Thermal properties themselves are not correlated, which is indicated by the low coefficient of correlation (r = 0.17, Fig.3). The data points are scattered without any particular indications of trends between the properties. Thermal conductivity and density show no numerical correlation (r = -0.03), but the graph (Fig. 4) reveals a trend of decreasing density with increasing thermal conductivity. This can be explained by the variation of quartz content in
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Relationships between Thermal and other Petrophysical Properties
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FIE. $. P-wave velocity versus thermal conductivity,N = 721, r ffi 0.11. Symbolsas in Fig. 3.
1~. 7. NRM versusthermalconductivity,N = 1984. r = -0.06. Symbols as in Fig. 3.
rocks. Increasing quartz content increases thermal conductivity but decreases density. The observed trend is in a disagreement with the theoretical concept of thermal condoctivity correlating positively with demity (Seh6n, 1983). It can be attributed to the numerous factors contributing simultaneously to thermal conductivity in a large collection of different rock types.
Thermal conductivity and P-wave velocity are not numerically correlated (r = -0.11, Fig. 5). Theoretically thermal conductivity is proportional to specific heat, density, propagation velocity of phonons and the seismic velocity (Seh6n, 1983). Seismic velocities of minerals correlate positively with thermal conductivity, and therefore an increasing trend can be expected in rocks. Actually, this
346
I.T. Kukkonen and S. Peltoniemi 10
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Fig. 8. Heatproductionrate versusdensity.N = 669, r = -0.68. Symbols as in Fig. 3.
Hg. 9. Heat productionrate versus P-wave velocity,N = 211, r = 0.55. Symbolsas in Fig. 3.
relationship can be observed only in a very wide spectrum of velocities and conductivities with practically all rock types incloded (sedimentary and crystalline, see e.g. Sch6n, 1983). Our P-wave and conductivity data represent crystalline rocks with velocities mostly between 5000 and 6500 m s1 and conductivities between 2 and 4 W m 1 K 1. Our data fit well in the relationship presented by Seh6n (1983), but since high and low values of velocity and conductivity are not represented in our data there is a lack of correlation. Susceptibility shows a bimodal distribution (Fig. 6) in the thermal conductivity-susceptibilityplot. The bimodality is characteristic for susceptibility in general in crystalline rocks of Finland (Puranen, 1989; Airo, 1990). In rocks with high susceptibilitiesabove 1000.10 ~ SI there is no correlation between the properties, but a weak negative correlation (r = -0.29) can be seen in rocks with lower susceptibility ( < 1000-10~ SI). These rocks contain practically no ferrima£metic minerals, and the trend of decreasing susceptibility can be attributed to the content of paramagnetic and diamagnetic rock forming minerals. In felsic rocks paramagnetic feldspars, mica and diamagnetic quartz dominate, but in marie rocks the contribution by marie amphiboles and pyroxenes with higher paramagnetic suceptibility is stronger. As a result the magnetic susceptibilityincreases. Simultaneously, the quartz content, which significantly influences thermal conductivity, decreases, and this results in a negative correlation with susceptibility. Thermal conductivity and intensity of NRM are not correlated (r = -0.06, Fig. 7). This can be attributed to the quite different factors controlling NRM and thermal conductivity. Our data suggests that heat production rate and density are weakly correlated (r = -0.68, Fig. 8). However, heat
production rate values are scattered over two orders of magnitude with a given density value, but nevertheless a trend of decreasing heat production rate with increasing density can be seen. Our data yields a linear regression line In A = 15.3 ( + 0 . 4 ) - 5 . 5 6 ( + 0 . 2 ) d, where A is the heat production rate (#W m 3) and d is the density (10.3 kg m3). The corresponding line calculated by Rybach and Buntebarth (1984) for Precambrian rocks is In A = 2 1 . 4 - 8.15 d. A similar graph was obtained from heat production rate versus P-wave velocity. The correlation is weak (r = -0.55, Fig. 9) and the scatter of heat production rate values is considerable, but a general trend of decreasing heat production rate with increasing P-wave velocity can be observed. A linear regression line of the data was also calculated: ln A = 10.8 (5:0.5) - 1.95 (5:0.2) Vp, where A is the heat production rate (ttW m3) and Vp is the P-wave velocity (103 m s1). For comparison, the corresponding line calculated by Rybach and Buntebarth (1984) for Precambrian rocks is In A = 16.5 - 2 . 7 4 lip. Comparison of the present results with those by Rybach and Buntebarth (1984) is complicated by the difference in conditions of measuring Pwave velocities. Our data was measured under normal atmospheric pressure whereas the above regression line by Rybach and Buntebarth (1984) was based on measurements at 50 MPa. The differences between A-Vp regression lines may be partly attributed to this fact. It should also be taken into account that Rybach and Buntebarth (1982, 1984) limited the lithologieal groups only to plutonic rocks, amphibolite, homblendite and serpentinite, whereas our data contains the full spectrum of rock types in the Finnish Precambrian. However, most of our samples represent plutonic, metamorphic and metasedimentary rock types (Figs. 1 and 2) which can be considered quite normal in crystalline
Relationships between Thermal and other Petrophysical Properties bedrock. The trends observed in heat production rate versus density and heat production rate versus P-wave velocity can be attributed to the general variation of these properties between different rock types. Increasingly felsic composition usually means decreasing P-wave velocity but increasing heat production. The radioactive elements U and Th are usually responsible for about 90 % of the heat production rate. They are incompatible with the typical silicate frameworks and have a tendency of concentrating in felsic rocks during the geochemical differentiation of the lithosphere. Our P-wave velocity-heat production rate and P-wave velocity-density results yield regression lines resembling those by Rybach and Buntebarth (1984), but actually they give quite different numerical values. If used for crustal heat production estimation the regression lines give values differing by one or half order of magnitude. Using these relationships would result in considerable uncertainties in numerical estimates. 6 Discussion
The present results suggest only weak correlations between the thermal and other petrophysical properties in crystalline rocks. The lithological types cover all main rock types and their subgroups present in the Finnish Precambrian, and are thus representative at least for the upper crust and possibly for the middle crust as well. The number of samples in the diagrams is sufficient to be statistically representative of the studied relationships. The results indicate that thermal properties cannot be very accurately estimated with the aid of these relationships. The scattered nature of the relationships can be attributed to several influencing factors. Small size of the samples increases the variations due to geological heterogeneity. Such effects can be expected particularly in those properties which are controlled by the concentrations of accessory minerals or trace elements, such as magnetic susceptibility and heat production. Further, rock texture creates anisotropy effects which increase the scatter in thermal conductivity, magnetic properties, and P-wave velocity. This effect was reduced by measuring the samples always in the same direction, i.e. the drill hole orientation which cut the strata perpendicularly in most cases. A small effect is added by the samples themselves, because the different properties were not measured exactly from the same piece of rock due to different requirements for the sample shape and size in the different measuring devices. However, this factor should not be significant since all the measurements of a rock sample represent a length of drill core less than 20 era. In the data sets several different lithological types are included in the diagrams. This may further increase the scatter of data points. It could possibly be reduced if the cross-plotting would be done within limited lithological types.
347
However, this is beyond the scope of this work, and we have concentrated here on the general relationships between petrophysieal properties of rocks. If em,s~ thermal properties are to be estimated, for instance, in geothermal modelling, there is very little constraining information on rock types in the middle and lower crust, although seismic information can be utilized in such work (Rudnick and Fountain, 1995). Our data represent the Finnish Precambrian and strictly taken the results are valid only in the study area. However, there is no reason to doubt that the Finnish bedrock is petrophysically essentially different from other shields. The present results suggest that although there are numerically only very weak correlations between thermal and other petrophysical properties, many of the cross-plots indicated trends of variation which can be at least qualitatively interpreted in terms of variation of mineralogic composition and physical properties of the relevant minerals. The result is comparable to the data by Soffel et al. (1992), Huenges (1997) and Huenges et al. (1997) on the KTB pilot hole petrophysics. Using factor analysis Huenges et al. (1997) noted that the petrophysical properties (P-wave velocity, thermal conductivity, heat production and density) correlated with lithological factors. In our study the trends are disturbed by considerable scatter of data points, which seriously limits the use of such trends for data estimation. Geological heterogeneity and the sample size in the scale of centimetres are partly responsible for the variation of d~t~j If considerably larger samples in the scale of metres could be measured, smaller variations would probably be obtained in the crosscorrelation plots. Solving this scaling problem would require empirical d_at~_on the spatial auto-correlation of the investigated properties. Such data (variograms) are not available. However, assuming that the properties should be similar within lithological types, averaging over lithological rocks groups should reduce the scatter. This was tested in most of the investigated relationships, but the result was disappointing. The coefficients of correlation were sometimes even smaller in the data averaged by rock type. This indicates that averaging may rather remove information than condense it, and that lithological rock types are not represented by only one type of a parameter distribution but may include more than one population. Measurement of P-wave velocities under normal atmospheric pressure may also increase the scatter. However, the samples were measured in a water-saturated condition which considerably reduces the effects of open microfractures on velocity which are often observed in laboratory measurements of dry samples under a small pressure (0200 MPa). P-wave velocities measured on water-saturated samples provide a satisfactory estimate of the intrinsic (zero overpressure) velocity (Huenges et al., 1997). Although our results suggest weak correlations to exist between heat production rate versus density or P-wave velocity, these relationships are very scattered and heat
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I . T . Kukkonen and S. Peltoniemi
p r o d u c t i o n rate values cover a range o f about 2 orders o f magnitude for a given value o f P-wave velocity and density. Similar spread o f data points is seen in the data set by C e r n ~ et al. (1990) and K e r n and Siegismund (1989) as well. This is obviously a characteristic feature o f crystalline rocks in general and reflects the great natural variability o f heat production rate values. The present results are not very encouraging for using heat p r o d u c t i o n rate - P-wave velocity relationships for estimating crustal heat production (cf. Fountain, 1986, 1987; Rybach and Buntebarth, 1987).
7 Conclusions The present empirical data f r o m the Finnish Precambrian suggest that there are no well d e f m e d general relationships b e t w e e n thermal and other petrophysical properties o f crystalline rocks. This can be attributed to many mineralogical, physical and geochemical factors influencing the petrophysical properties and producing trends mitigating each other. Coefficients o f correlation are small (0-0.7) and the data is scattered. H o w e v e r , certain trends o f variation can be observed, particularly (1) between thermal conductivity and susceptibility in weakly magnetic rocks, (2) heat p r o d u c t i o n and P - w a v e velocity, and (3) heat production and
minerals. In: T.J. Ahrens (Editor), A Handbook of Physical Constants, Rock Physics and Phase Relations, Vol. 3. Amcricai Geophysical Union, Washington DC, p. 105-125. Fountain, D.M., 1986. Is there a relationship between seismic velocity and heat production for crustal rocks.'?Earth Planet. Sci. Lar., 79, 145-150. Fountain, D.M., 1987. The relationship between seismic velocity and heat production- a reply. Earth Planet. Sci. Left,, 83, 178-180. Huenges, E., 1997. Factors controlling the variances of seismic velocity, density, thermal conductivity and heat production of cores from the KTB pilot hole. Geophys. Res. Left. 24, 341-344, Huenges, E., Lauterjung, J., Biicker,C., Lippmann, E. and Hartmut, K., 1997. Seismic velocity, density, thermal conductivity and heat production of cores from the KTB pilot hole. Geophys. Res. Left, 23, 345-348. Jirvimllki, P., 1968. Geotermisistll mittauksista Suomessa (On geothermal measurementsin eln/and). Master's thesis, University of Helsinki, Institute of C-eophysics, 30 p. (in Finnish). JOeleht, A. and Kukknnen, I.T., 1997. Thermal properties of grannlite facies rocks in the Precambrianbasementof Estonia and Finland. Tecnonophysics (submitted). Kern, H. and Siegismund, S., 1989. A test of the relationship between seismic velocity and heat production for crustal rocks. Earth Planet. Sci. Left., 92, 89-94.
density. H o w e v e r , the uncertainties in these trends do not allow reliable estimations o f the thermal properties.
Kremcnetsky, A.A., Milanovsky, S.Yu. and Ovchinnikov, L.N., 1989. A heat generation model for continental crust based on deep drilling in the Baltic Shield. Tectonophysics, 159, 231-246.
Acknowledgement. We are grateful for L. Rybach, H. Winter and A. J6eleht for reviews and comments on the manuscript. The study was partly funded from a scholarship of the Finnish Association of Mining and Metallurgical Engineers.
Kukkonen, I., 1989. Terrestrial heat flow and radiogenic heat production in Finland, the central Baltic Shield. Tectonophysics, 164, 219-230.
References Aim, M.-L., 1990. Susceptibilities, intensities of remanence and densities of Precambrian and recent volcanic rocks: examples from Iceland and northem Fennoscandia. Geol. Surv. Finland, Rep. Investigan'on, 93, 24 p. Beck, A.E, 1988. Thermal properties. In: R. Haenel, L. Rybach and L. Stegena (Editors), Handbook of Terrestrial Heat-Flow Density Determination. Kluwer, Dordrecht, p. 87-124. Burkhardt, H., Honarmand, H. and Pribnow, D., 1995. Test measurements with a new thermal conductivity borehole tool. Tectonophysics, 244, 161165. ~err~k, V. and Rybach, L., 1982. Thermal conductivity and specific heat of minerals and rocks. In: G. Angenheister (Editor), Landolt-BOmstein: Numerical Data and Functional Relationships in Science and Technology, New Series, Group V (Geophysics and Space Research), Vol. l a (Physical Properties of Rocks). Springer, Berlin, p. 305-343, (~erm~, V., Bodri, L., Rybach, L. and Buntebarth, G., 1990. Relationships between seismic velocity and heat production: comparison of two data sets and test of validity. Earth Planet. Sci. Left., 99, 48-57. Clauser, C. and Huenges, E., 1995. Thermal conductivity of rocks and
Kukkonen, I.T., 1993. Heat flow map of northern and central parts of the Fermoscandian Shield based on geochemical surveys of heat producing elements. Tectonophysics, 225, 3-13. Kukkonen, I.T. and Lindberg, A., 1995. Thermal conductivity of rocks at the TVO investigation sites Olkiluoto, Romuvaam and Kivetty. Nuclear Waste Commission of Finnish Power Companies, Helsinki, Report YIT95-08, 29 p. Lachenbmch, A.H., 1971. Vertical gradients of heat production in the continental crest, 2. Some estimates from borehole data. J. Geophys. Res., 76, 3852-3860. Moyseyenko, U. and Negmv, O., 1992. Thermophysical properties of crystalline rocks. In: N.B. Dortman (Editor), Petrophysics, Handbook, Part L Nedra, Moscow, p. 240-253 (in Russian). Popp, T. and Kern, H., 1994. The influence of dry and water saturated cracks on seismic velocities of crustal rocks - a comparison of experimental data with theoretical model. Surv. Geophys,, 15, 443-465. Pinet, C. and Jaupart, C., 1987. The vertical distribution of radiogenic heat production in the Precambrian of Norway and Sweden: Geothermal implications. Geophys. Res. Left., 14, 260-263. Puranen, R., 1989. Susceptibilities, iron and magnetite content of Precambrian rocks in Finland. Geol. Surv. Finland, Rep. Investigation, 90, 45 p.
R e l a t i o n s h i p s b e t w e e n T h e r m a l a n d o t h e r P e t r o p h y s i c a l Properties
349
Puranen, M. and Puranen, R., 1977. Apparatus for the measurement of magnetic susceptibility and its anisotropy. Geol. Sure. Finland, Rep. Investigation, 28, 46 p.
Rybach, L. and Buntebarth, 1984. The variation of heat generation, density and seismic velocity with rock type in the continental lithosphere. Tectonophysics, 103, 335-344.
Puranen, R., Sulkanen, K., Poikonen, A., Nissinen, R., Simelius, P. and Harinen, L., 1993. User's manual for a computerized petrophysics laboratory. Geol. Sure. Finland, Dep. of Geophys., Rep. QI9.1/27/93/1, 50 p. Rudnick, R.L. and Fountain, D.M., 1995. Nature and composition of the continental crast: a lower crustal perspective. Rev, Geophys., 33, 267309.
Rybach L. and Bun~ebarth, G., 1987. The relationship between seismic velocity and heat production- critical comments. Earth Planet. Sci. Left., 83, 175-177.
Rybach, L., 1973. Wlrmeproduktionsbestimmungenan Gesteinen der Schweizer Alpen. Beitr. Geol. $chweiz. Geatech, 51, 43 p. (in German). Rybach, L. 1988. Determination of heat production rate. In: R. Haenel, L. Ryba~h and L. Stegena (Editors), Handbook of Terrestrial Heat-Flow Density Determination. Kluwer, Dordrecht, pp. 125-142. Rybach, L. and Buntebarth, G., 1982. Relationships between the petrophysical properties density, seismic velocity, heat generation, and mineralogical constitution. Earth Planet. $ci. Left., 57, 367-37.
Sch6n, J., 1983. Petrophysik. Enke, Stuttgart, 405 p. (in German). Soffel, H.C., Bficker, Ch., Gebrande, H., Huenges, E., Lippman, E., Pohl, J., Ranen, A., Schult, A., Streit, K.M. and Wienand, F., 1992. Physical parameters measured on cores and cu~ngs from the pilot well (0 m 4000.1 m) of the German Continental Deep Drilling Program (KTB) in the Obeffalz area, Bavaria, Federal Republic of Germany. Sure. Geophys., 13, 1-34. Sundberg, J., 1988. Thermal properties of rocks and soils. Doctoral thesis, Chalmers University of Technology and University of GOteborg, Department of Geology. Gothenburg, 47 p. Vemik, L. and Nur, A., 1992. Petrophysical analysis of Cajon Pass scientific well: Implications for fluid flow and seismic studies in the continental crest. J. Geophys. Res., 97, 5121-5134.