Chapter 2

Techniques Used for Estimating the Temperature of the Earth's Interior

Abstract

In this chapter we consider different approaches used presently for the estimation of the earth's temperature depending on the available data and prior information: extrapolation of the temperature heat flow gradient, solution of the heat flow equation, indirect temperature estimations using mineral, hydrochemical, isotopic and gas geothermometers. Close relations between the electrical conductivity and temperature values (tabulated or expressed as empirical formulas valid under specific conditions or attributed to some geographical area) enable, in principle, to reconstruct the temperature profiles from the laboratory studies of rock samples collected in the study area. In the absence of these data, the temperature profiles could be revealed from the electromagnetic sounding results expressed as the electrical conductivity (or resistivity) models. In the latter case a guess on the electrical conductance mechanism and appropriate activation energy are required. However, this problem could be partly overcome by solving the appropriate optimization task.

Keywords

temperature model indirect geothermometer heat flow magnetovariational sounding electrical resistivity

Chapter Outline

2.1 Temperature Models Based on the Boreholes' Logs and the Heat Flow Data 37

2.2 Temperature Estimations Using Indirect Geothermometers 39

2.2.1 Mineral Geothermometers 40

2.2.2 Hydrochemical Geothermometers 40

2.2.3 Gas Geothermometers 41

2.2.4 Isotopic Geothermometers 41

2.2.5 Geothermometers Based on the Seismicity Bounds 41

2.3 Interplay Between the electromagnetic sounding Data, Rock Physics, and Prior Geological Information 42

2.4 Technique for the Deep Temperature Model Building Using the Global Magnetovariational Sounding Data and Guess About the Conductance Mechanisms 45

2.4.1 Analysis of the Mantle Temperature Models 45

2.4.2 An Updated Formula for Deep Electrical Conductivity 48

2.4.3 The Temperature Model of the Mantle 49

2.5 Conclusions 51

References 51

Estimation of deep temperatures is one of the key factors in both the study of the geothermal processes in the earth's interior (see Clauser (2009) and references therein) and in solving of different tasks of applied geothermics (see Eppelbaum et al. (2014) and references therein). In this chapter we will briefly outline the approaches used to this end and finally demonstrate an example of building of the temperature model of the mantle from the magnetovariational data.

2.1. Temperature models based on the boreholes' logs and the heat flow data

Actual data about the measured temperatures are limited to the borehole depths amounting in most cases to 1-2 km. So, in order to get an idea of spatial temperature distribution in the studied area it is necessary to carry out interpolation/extrapolation of temperature logs measured usually in nonevenly distributed and often not numerous wells, which often results in considerable errors. Pribnow and Hamza (2000) have estimated the vertical temperature distribution in the Soultz-sous-Forêts (France) geothermal area by lateral averaging of the temperature well logs from all boreholes located in the band of 20 km width from each side of the considered profile (see Figure 7.2 from the Chapter 7). As it was shown by Spichak (2006), temperature interpolation using the geostatistical tools and artificial neural network-based techniques may decrease the relative temperature interpolation errors up to 27-30% and 12-15%, accordingly (see also Chapter 3). Temperature values beneath the boreholes are often estimated using linear extrapolation of the temperature gradients determined from the heat flow data (Foulger, 1995; Björnsson, 2008) (Figure 2.1). However, this approach is implicitly based on the assumptions that the lithosphere is homogeneous and the heat transfer mechanism is conductive, which rarely takes place in the geothermal areas and may lead to erroneous temperature estimations at given depths (see in this connection also Section 8.5.1 in the Chapter 8). Figure 2.1 Linear temperature gradient extrapolation below the well logs (after Foulger, 1995). To cope with the lack of the temperature data, indirect measurements such as the surface heat flow Qs can be used to model the subsurface temperature according to equation (2.1) for 1-D heat conduction (Limberger and van Wees, 2013):

(z)=-A2kz2+Qs+Ahkz+T0,

(2.1) where the temperature at depth T(z) is related to the layer thickness h, its thermal conductivity k (supposed to be known constant), the radiogenic heat production A and the surface temperature T0. Following this approach Limberger and van Wees synthesized the 3-D temperature model for the Europe (Figure 2.2) from 1-D profiles (2.1), with horizontal resolution of 10 × 10 km based on the two-layered model reduced from the European crust model (Tesauro et al., 2008) and heat flow data (Artemieva, 2006). Figure 2.2 Depth slices taken from the 3-D temperature model at depths 5 km (a) and 10 km (b) (after Limberger and van Wees, 2013). Solution of the heat flow equation in 2-D or 3-D statements is based on an assumption about steady state of the heat flows at lateral boundaries of the modeling domain and on prior knowledge of the heat flow (temperature) at the upper and lower boundaries of the area (Podgornykh et al., 2001; Ollinger et al., 2010). This approach may, however, fail at active margins or in areas where a significant fluid migration is suspected. In such zones the thermal field is obviously non-steady-state, and the calculation based on a stationary model may lead to significant errors. Methods for estimating the temperatures allowing for geological processes in time permit, in principle, construction of more adequate models (see, for instance Alexidze et al. (1993)). However, this approach requires knowledge on the physical nature of the processes and the geological conditions (lithology, absolute age of the formations, start date and duration of volcanism in a geological past, and so on). Lack of necessary geological and geophysical data makes such a geothermal modeling difficult.

2.2. Temperature estimations using indirect geothermometers

Global studies of hydrothermal processes showed that specific properties of the underground fluid composition are closely related with the geothermal conditions of their formation. Therefore, studying of these properties provides indirect information about the thermal state of the interior that complements the results of direct thermometry and serves as a basis for forecasting the deep geothermal conditions in scantily explored regions. Established experimentally is a temperature dependency of the composition of some characteristic hydrothermal components. Using empirical or semiempirical formulas, one can estimate the "base depth" temperature from the known amount or proportion of these components in areas of surface manifestations of thermal activity. To this end indirect geothermometers are usually used. Below we briefly discuss them following (Spichak and Zakharova, 2012).

2.2.1. Mineral Geothermometers

Stability of the alteration minerals' assemblages in different temperature ranges is used for indirect temperature estimation at depth. An empirical relationship between formation temperature and the occurrence of specific alteration minerals is used to determine a proper depth for the production casing. This method offers currently the best estimation of aquifer production temperature that can be made during drilling. Therefore, aquifers that are too cold for production can be excluded from the production part of a well based on the absence or presence of certain index minerals. Mixed-layer clay geothermometers have proved useful in the study of many geothermal systems around the world (see, for instance, Harvey and Browne (1991) and references therein). The earliest investigations were based on the dioctahedral smectite to illite transformation, but it was subsequently extended to other transformations such as trioctahedral smectite to chlorite. More recently, numerous other mixed-layer structures that may have significance as sensitive indicators of changes in temperature have been recognized. Mixed-layer clay geothermometers have proved most effective in sediments or tuff sequences but may not give correct results in fracture-dominated geothermal reservoirs, since incomplete water-rock interaction away from major flow paths may invalidate their use.

2.2.2. Hydrochemical...