A temperature log assumed to be in equilibrium was recorded in the KTB (see figure C.2 for well location) pilot hole down to 3990 m on September 17, 1997 and analysed in Clauser [1999].
An earlier recording, dating from February 1996, was analysed in detail for thermal processes, including transient effects of paleoclimate [Clauser et al., 1997]. Shallow temperature logs in the vicinity of the KTB site have also been interpreted in terms of paleoclimatic influence [Clauser and Mareschal, 1995; Clauser, 1999]. In the light of the previous sections, the analysis of the KTB borehole is revisited and the uncertainties connected with the interpretation are discussed.
In that study the temperature data was inverted for paleoclimate in the period from 105 to 102 years before present, using 100 time steps, a thermal conductivity of 2.92 W (m K)-1, a thermal diffusivity of 10-6 m2 s-1, and a heat production rate of 1.1 µW m-3. The analysis yielded a peak-to-peak amplitude of 10 K for the temperature increase from the latest glacial stage to the Holocene.
The geological profile in the KTB pilot hole is primarily composed of two lithologies: Metaba-sites and gneisses. These can easily be separated using the Gamma-ray-log (SGR) (figure 2.16).
Thermal conductivity (figure 2.16) does not seem to vary systematically over the depth of the borehole, justifying the assumption of a homogeneous half-space. The mean thermal conduc-tivity is (2.93 ± 0.60) W(m K)−1. This value reduces to 2.82 W(m K)−1 if a temperature and pressure correction is applied to the data [Buntebarth, 1991]. Knowledge of the thermal diffu-sivity is much more uncertain. For Gneiss a range of (0.5 − 1.2) · 10−6 m2s−1 is reported, for Amphibolites a range of (0.6 − 0.8) · 10−6 m2s−1 [ ˇCermák and Rybach, 1982]. Seipold [1995]
measured a value of (0.8 ± 0.2) · 10−6m2s−1for Amphibolite samples from neighbouring sites.
Again, a correction for temperature and pressure of the value given by Seipold [1995] reduces the mean diffusivity to a value of 0.70 · 10−6 m2s−1. Heat production rate is computed from spectral and total γ-ray logs [Rybach, 1988; Bücker and Rybach, 1996], yielding values of (1.19
± 0.46) µW m-3and (1.23 ± 1.14) µW m-3. A value of 1.2 µW m-3is used in the inversion.
The next step in the analysis is the choice of the optimum regularisation parameter . Fig-ure 2.17 shows the L-curve for varying values of . The optimum choice seems to be = 0.4, the value also chosen in the study of Clauser et al. [1997]. Figure 2.18 illustrates this in more detail showing inverted time series for the different values of . The direct comparison of results is particularly helpful to analyse which features of the GST history are numerical oscillations and which ones represent actual information. At a level of = 0.4, oscillations that change the
ÑT [K km ]-1
T [°C]
SGR [API]
-6 -3
A (mean) [10 W m ] l (corrected) [W (m K) ]-1
l (mean) [W (m K) ]-1
l s± 1
-6 -3
A (SGR) [10 W m ]
A s± 1 l (core) [W (m K) ]-1
-6 2 -1
k (mean) [10 m s ]
k s± 1
-6 2 -1
k (corrected) [10 m s ]
a) b) c) d) e)
Figure 2.16: Composite log of the KTB pilot hole. a) Spectral Gamma Ray (SGR), temperature (T ), temperature gradient (∇T ). b) Generalised lithology. c) Core thermal conductivity (λ core) [Clauser et al., 1997], mean value (λ mean), standard deviation of the mean value (λ ± 1σ), thermal conductivity corrected for temperature and pressure (λ corrected). d) Heat production rate from spectral gamma ray (A SGR), mean value (A mean), standard deviation (A ± 1σ). e) Mean thermal diffusivity from cores (κ mean), corrected for PT-conditions (κ corrected), standard deviation of the core measurements (κ ± 1σ). Logging data courtesy of the KTB project management (http:
//www.icdp-online.org).
warming amplitude seem to be attenuated. A more conservative interpreter might choose an even higher value of = 0.6, but in this range of -values the main features are only changed by a few tenths of a Kelvin.
Following the choice of the damping parameter, the detrimental effect of a reduced log length will be illustrated. The maximum depth of originally 3990 m is successively truncated to lengths of 3000 m, 2000 m, and 1500 m. Figure 2.19 shows the reconstructed GST history and transient temperature perturbation in the borehole for these truncation depths. The differences in this example are similar to those analysed in section 2.4.2.
Deviations from the inversion result for the full depth of the temperature log become signifi-cant for depths of less than 3000 m. The minimum temperature of the last glacial stage increases
0 50 100 150 200 0
10 20 30 40 50 60 70 80
0.1 0.01 1 10
||m||
||G(m)−d||
Optimum ε ≈ 0.4
Figure 2.17: L-curve for the inversion of the KTB pilot hole-temperature log.
Table 2.2: Inversion results for the KTB log, truncated at successively smaller depths. The inverted parameters vary systematically with the depth of the log.
Depth T0 q0 ∇T
[m] [°C] [W m-2] [mK m-1]
4000 4.14 0.0863 29.6
3000 4.70 0.0848 29.6
2000 5.51 0.0818 28.0
1500 6.15 0.0781 26.7
and the temperature maximum in the Holocene is shifted, consistent with the discussion in sec-tion 2.4.1. Table 2.2 shows the inversion results for the steady-state GST T0, the surface heat flux density q0, and the steady-state temperature gradient ∇T . This emphasises that the system-atic variation of the GST history is accompanied by a corresponding change in the steady-state parameters. As discussed before with respect to the length of temperature logs, the heat flux density value decreases whereas the steady-state ground surface temperature T0 increases. This is consistent with inverting a step increase in ground surface temperature using a log that is too short to fully resolve the GST history. It can be expected from this data that crustal heat flux density estimates may be too low if a paleoclimatic correction is used based on insufficiently deep temperature data. In this case this amounts to 8 mW m-2, about 10 % less than the value obtained for the inversion of the full depth temperature log. The amount by which an undisturbed heat flux density value is underestimated depends on (1) the maximum depth of the temperature log used for the inversion and (2) the magnitude of the paleoclimatic variation at the site of the
102 103 104 105 106
Figure 2.18: Inverted GST histories T (t) for increasing values of the damping parameter .
borehole. While the former effect can be estimated using synthetic forward models of differing depths, as was done here, the latter influence is much harder to estimate because this requires information on the paleotemperature prior to the inversion.