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Fig. 55. Distortion of heat flow in borehole GFU-1 due to the topography (Figure 54) for different models of subsurface structure and conductivity (see text). Profile 1a corresponds to the preferred model.

It represents the same case as the 1a curve, but with the subsurface layers inclined to south. Distortion obtained in this case is 40% lower than in the previous case. This hints that in some cases topography and subsurface structure can balance the effects of each other. Cases 2a and 2b were calculated for the same conductivity models as 1a and 1b curves under the assumption that the temperature does not depend on the slope orientation, but on the altitude only. Both curves coincide and show still lower topographic disturbances than curve 1b. The above four models have taken into account effects of topography and subsurface anisotropy. Disturbances to the vertical heat flow in the isotropic medium, in other words, an effect of topography alone, are shown by curves 3 and 4, where the GST depends on the altitude or slope orientation, respectively. Significant distortion can be achieved in the case that has taken into account the slope orientation. According to Safanda (1994), the discrepancies between investigated models can be attributed to the asymmetric GST pattern on the edges of the plateau, where borehole GFU-1 is located.

Finally, curve 5 represents the kind of the model 4 where a step climatic temperature increase of 1K, which occurred 70 years ago, was added to the GST; thus, it illustrates combined effect of topography and climate change. As seen, the curvature of the profile 5 significantly differs from traditional "U-shape" that occurs due to climatic influence alone (e.g. Figures 13 and 20). All presented examples show that there is a potential to obtain erroneous GST history from inversion of the "raw" temperature-depth profiles and corroborate the necessity of the topographic correction of measured temperatures to improve the fidelity of the estimated GST reconstructions. According to Safanda (1994), curve 1a represents the most realistic model of the topographic effect in the vicinity of the Sporilov borehole (simultaneously it exhibits the largest heat flow distortion within the 20-150m range). This model was used for correction of the measured heat flow values. The magnitude of the topographic correction reached 5-8mW/m2; thus, it composed 8-13% of an undisturbed heat flow.

The above study has described the topographical perturbation to the steady-state subsurface temperature field. Some of numerical studies, as presented by Kohl (1999), considered the possible influence of topography on transient temperature signals and thus concentrated on the more real case when climatic disturbance is distorted by the topographic influence. As shown in numerous above-cited studies, the topographic disturbances appear to be most significant in some hundreds meters of the subsurface. This depth interval is strongly affected also by the climatic changes that occurred during the last 100-500 years. The investigations by Kohl (1999) have shown that in many locations topographic effects and GST signals can be mixed and inversion of such temperature logs may yield arbitrary results. In this work, the study of the role of each influence on the measured signal was performed on the basis of numerical solution of the 2-D forward heat transfer problem for synthetic sinusoidal topography with varying amplitudes and wavelengths as well as by the simulation of the real relief types and different kinds of GST history. Such detailed study has provided an estimation of the topographic disturbance for the large number of the field situations. To quantify the errors in the GST reconstructions occurring when temperature logs are used without topographic correction, the vertical temperature-depth profiles were extracted from calculated 2-D patterns. Comparison of the GST histories inverted from T-z profiles with and without correction revealed the errors occurring due to the topographic effect.

Numerical trial runs have shown that the interpretation of transient temperature profiles is very sensitive to the surface relief. Experiments with sinusoidal surfaces have revealed that the topographic effect became stronger in the case of small wavelength and/or higher altitude topography. Larger wavelengths penetrate deeper into the subsurface. The topographic influence may strongly disturb the subsurface temperature signal, and thus generally results in the erroneous GST histories. Even rather flat topographies with 20km wavelengths and 100 m amplitudes may introduce disturbances that perceptible distort the course of inverted GST. The T-z profiles measured in boreholes located at elevations tend to pronounce a GST cooling and to reduce warming, while the topographic influence at valleys gives an opposite effect. The most recent GST changes are practically unrecoverable from temperature profiles containing topographic perturbations. On the other hand, more remote and/or strong paleoclimate signals present even in the temperature profiles disturbed by rough relief and can provide correct inversion results when data are properly treated.

Major conclusion of this work was that it is useful (in some field cases indispensable) to evaluate the site-specific effects before performing the GST inversion. On the basis of the multiple simulations Kohl (1999) has worked out optimal strategy for the topographic correction. Suggested procedure includes the 3-D numerical simulation of the synthetic steady-state temperature field for the local topographic conditions/subsurface structure and subtracting this effect from the measured temperature-depth profile. Results by Kohl (1999) have shown that in most field cases correction is successful and transient surface temperature changes can be accurately extracted even for the rough Alpine environments.

Another approach to treat terrain "noise" in the borehole data was applied in the works by Pollack et al. (1996) and Beltrami et al. (1997) who performed simultaneous inversion of ensembles of borehole logs or alternative approach of averaging the individual inversion results. The authors have shown that for the suite of boreholes from the regions with differing topographic settings, the GST averaging and/or simultaneous inversion of the multiple temperature logs yield closely identical results. Calculations by Kohl (1999) have corroborated the conclusion that if statistically sufficient number of boreholes is considered, reliable GST histories can be inferred without application of a topographic and/or other terrain correction for individual boreholes, because for locations with significantly varying surface shape/cover, the magnitudes of arising disturbances can adjust themselves. However, no general rule can be applied.

2.7 Non-Conductive Heat Transfer Effect on the GST Reconstruction (Groundwater Flow Effects)

Similarly to the topography effect the groundwater flow is an important kind of the representational errors arising from the fact that all forward and/or inverse methods of the GST reconstruction are based on the assumption of the exclusive heat conduction (no advection)13 in a one-dimensional, vertically heterogeneous medium (for details see previous section). Conduction theory is an ideal approach for the description of heat transfer in consolidated rock bodies with no significant fluid movement. Natural situations are

13Advection represents transport of some conserved scalar quantity in a vector field, when the mass moves to a region where this quantity has a different value. Meteorologists deal with the advection of variables like temperature or moisture in the atmosphere caused by movement of air by the wind (e.g. the change in temperature when a warm air moves to cold region). Hydrologists are interested in the advection of heat or pollutants by a fluid movement. Generally, any substance/variable can be advected, in a similar way, by any fluid.

Fig. 56. Typical geologic cross-section of the subsurface in the vicinity of the borehole.

far more complex. Typical geologic cross-section of the subsurface in the vicinity of the borehole is presented in Figure 56. The departures of the real field situation from an ideal homogeneous layered approach may be caused by the lateral heterogeneity in thermal conductivity (see Section 2.4.2) and other physical properties, topography of the upper boundary, temporal changes in the surface (snow, ice, and vegetation cover; Section 2.6) as well as the convective disturbances to temperatures that can occur due to water flow of two types - within the fluid-filled borehole and regional water flow. The small diameter of most of the boreholes relative to their length prevents the occurrence of any intra-hole convection strong enough to disturb the thermal regime significantly (Jessop, 1990). On the contrary, regional water flow effect represents one of the most common and serious obstacles for the GST reconstructions.

Groundwater is water located beneath the ground surface in soil pore spaces and in the fractures of the geologic formations. The depth at which soil pore spaces become saturated with water is known as the water table. An aquifer is an underground layer of the water-containing permeable rock. It can also represent less consolidated materials (gravel, sand, etc.) from which groundwater can be extracted using a water well. An example of the regional groundwater flow system is presented in Figure 57. Groundwater is recharged from and/or discharged to the surface naturally. Natural discharge may occur at springs and seeps; it can result in wetlands and waterlogged areas. It should be described by at least 2-D physical models. Such modeling can be easily performed by forward calculations, while present-day GST reconstruction techniques are developed for the 1-D situation and thus cannot capture effects of topography and/or groundwater flow in principle. As shown by Kane et al. (2001), an assumption of pure conductive heat transfer through the medium is justified only for subsurfaces with negligible vertical groundwater flow. Otherwise advective component of the heat transfer associated with subsurface fluid movements is capable of producing the curvature in a temperature-depth profile that can be easily confused with the transient climatic effect.

Generally, groundwater effect represents one of the most common and serious obstacles for the GST reconstructions. The influence of the groundwater flow on the subsurface temperature is a consequence of a far more effective heat transfer by moving fluid (advection)

Fig. 57. Cartoon showing the regional groundwater flow system.

than by the thermal conduction in rocks. Lewis and Wang (1992), citing the field examples, warned that even very small water flows could significantly distort the temperature log and thus affect the reconstructed GST history. They gave an example that reconstructing past climate by using data from a number of boreholes in a relatively small area of Lac Dufault (Canada) revealed the onset times of the recent warming in the unrealistic range of 35-150 years ago. Wang et al. (1994) has indicated that vast amount of Canadian temperature logs was excluded from the GST reconstruction because of obvious groundwater disturbances. Using several synthetic T-z profiles as well as the field example and applying general least squares inversion techniques in the ramp/step method Kukkonen et al. (1994) have simulated a situation of "misinterpreting" the curvature of the temperature logs caused by advec-tive disturbances due to groundwater movement in terms of the GST change. Even this simple model of the 1-D effect in the homogeneous half-space with constant soaking velocity of the fluid has demonstrated that it is possible to obtain GST histories from the boreholes with hydrological disturbances, which are acceptable with respect of our knowledge of recent climatic changes, and thus clearly indicated the probable risk of misinterpretation.

In geothermics and borehole climatology hydrologic disturbances are regarded as undesirable anomalies that should be discarded or corrected. On the contrary, hydrolo-gists are interested in the analysis of the temperature anomalies themselves to determine the pattern of the groundwater movements and their rates, groundwater flow and hydraulic conductivity with coupled water flow, and heat transfer models. The principles of using geothermal measurements as a groundwater tracer were worked out in the 1960s (e.g. Stallman, 1965) and were further developed in the recent works. For the climatolo-gists' consolation it should be mentioned that, alternatively, climatic influence on the temperature profiles was often mistakenly interpreted by hydrologists as a result of advective heat transport (e.g. Ferguson and Woodbury, 2005 and the references therein). Reiter (2004) has examined the effect of participation of both groundwater flow and climate change on the occurrence of the curved temperature logs using data from two boreholes located in central New Mexico and in eastern Canada. He has simulated a number of models that combined different cases of the water flow and the GST change, and has compared them with measured temperature logs. Based on the statistical analysis of the misfits, he has concluded that in many field situations observed subsurface anomalies may be explained by either groundwater flow or the GST change impact.

Because advection could mask or overwhelm climate-induced ground temperature changes, the negligible hydrological activity in the vicinity of investigated boreholes was thus of key importance for every past climate reconstruction approach until quite recently. In practice the researchers have performed screening of the geothermal data before processing and have used for climatic reconstructions only undisturbed and/or input data corrected for the hydrological disturbances. Most field examples, however, suffer from the general lack of satisfactory hydrological information. Thus, in the majority of the borehole sites the screening procedure represents not an easy task. According to Ferguson et al. (2003) and Reiter (2005), at least some of the GST reconstructions were performed without sufficient justification of the absence of groundwater flow.

In practice borehole T-z profiles were often used for opposing task, namely as a groundwater tracer to identify surface water infiltration, flow-through fractures, and flow patterns in groundwater areas (see the review paper by Anderson (2005) and the references therein). Three principal kinds of the groundwater movement in the vicinity of the boreholes are: (1) soaking through permeable formations, (2) up- or down-flow at narrow dipping fracture zones, (3) flow between two aquifers or fracture systems and movement of groundwater within drill hole, and the corresponding temperature-depth profiles. Figure 58 schematically sketches possible kinds of the groundwater movement in the three-layered subsurface. Surface temperature is T0 and undisturbed temperatures at the

Fig. 58. Principal types of groundwater movement in the vicinity of a borehole and corresponding temperature logs with characteristic hydrologie disturbances. Dashed line corresponds to an undisturbed geotherm.

boundaries of the first and second layers and the second and third layers are T1 and T2, respectively (Figure 58, top-left). The deviations from this undisturbed geotherm caused by the vertically moving water are presented in further panels. Top-center: Upward groundwater flow in the upper layer produces high subsurface temperatures. At the surface increased temperature steeply reduces to a value T0 determined by the current climate. This reduction creates curvature similar to that characteristic for the recent surface temperature cooling (see Figure 20). Top-right: Disturbance is much smaller in the case of upward water movement in the second layer, when the upper layer is impermeable and the heat transfer there realized by pure conduction. Basement temperature T2 remains unchanged and the temperature at the first-second layers boundary slightly increases, producing lower geothermal gradient in the second layer.

Bottom: These examples illustrate an influence of the downward groundwater flow causing temperature decrease in the corresponding layers that increases with depth.

Based on the field studies, Drury et al. (1984) have suggested effective empirical method to detect water flow in boreholes that intersect a flow zone. These authors have detected principal flow types that generate characteristic signature on the temperature field similar to the one presented in Figure 58 and can be easily observed on the precise temperature-depth profiles measured at closely spaced intervals. Thus, often observable "step" profiles with low or even zero thermal gradients appear for the kind of water movement presented in the bottom- and top-right examples of Figure 58. Sharp discontinuities in a temperature-depth profiles (so-called "spike" anomalies) may reflect the in- and/or outflow of fluid and its movement within the borehole as well as groundwater flow along a fault or narrow horizontal layer. Such anomalies are usually well attributable. On the other hand, vertical groundwater flow can produce smooth curvature of a temperature log that can be undistin-guishable from climatic disturbance (see examples presented in Figure 59).

Pfister and Rybach (1995) have examined numerous temperature logs from the Marmara region (NW Turkey) characterized by frequent manifestations of anomalously high temperature gradients in the subsurface, thermal springs, and steaming grounds, and also have recommended a high-resolution temperature logging as a powerful tool to obtain information about various groundwater flow regimes. Majorowicz et al. (2006) have analyzed possible influence of the groundwater flow on the temperature logs measured in the Paskapoo Formation in the western part of the Western Canada Sedimentary Basin. This formation represents a mudstone-dominated unit with 5-15 m thick interbed-ded sand channels that can form separated aquifer units. All 11 available Paskapoo temperature logs exhibit noticeable "U-shape". However, modeling of the groundwater flow influence has shown that the downward flow in the region creates curvature in T-z profiles similar to the manifestations of recent warming. While the minimal recharge rates of ~5mm/year likely have minimal impact, the models using highest possible recharge rates of ~25mm/year have proved that the subsurface water flow can affect temperature profile and thus be responsible for at least a part of observed curvature. Reiter (2001) has worked out a method for estimation of the horizontal and vertical specific discharge components of groundwater flow from precision subsurface temperature measurements. The procedure includes plotting the vertical temperature gradient as a function of both z and T. Fitting this plane to the data can provide the coefficients for estimation of the vertical and horizontal flow components. The testing of suggested procedure with field examples from different flow zones with a great variety of possible flow characteristics has shown

TEMPERATURE, deg.C 0 2 4 6 8 10

TEMPERATURE, deg.C 0 2 4 6 8 10

Fig. 59. Schematic temperature-depth profiles showing the deviations from the undisturbed gradient caused by warming in the surficial layer and groundwater convection in the geothermal zone. Recharge (downward movement of ground water) results in concave upward profiles, while discharge (upward flow) produces convex upward profiles.

Fig. 59. Schematic temperature-depth profiles showing the deviations from the undisturbed gradient caused by warming in the surficial layer and groundwater convection in the geothermal zone. Recharge (downward movement of ground water) results in concave upward profiles, while discharge (upward flow) produces convex upward profiles.

good coincidence of obtained results with available hydrological information. On the other hand, this method takes into account hydrological disturbances alone, and thus can give misleading results, when the temperature log also contains climatic influence.

Kohl (1998) first has modeled combined effect of both climatic and hydrological disturbances. He has introduced the problem of the GST reconstruction for the temperature-depth profiles containing hydraulic disturbances by taking into account the combined effect of conductive heat diffusion and advection in a transient state by series of forward synthetic calculations. He has demonstrated that the climate signal could not be completely washed out by hydraulic advection even in the strongly advective dominated system. On the other hand, he has also emphasized that the paleoclimate reconstruction from advectively perturbed data using pure conductive approach may provide significantly distorted results even in the case of a strong climatic event.

How do groundwater disturbances appear in the borehole temperature logs? Generally, two types of fluid circulation in the subsurface occur: (a) forced convection driven by a fluid pressure gradient such as topographically induced convection, and/or (b) free convection resulting from the temperature gradient and producing fluid density variation in a strata heated from below. In the first case (Figure 57), the flow never creates closed convective cells otherwise characteristic for the free convection. Induced flow driven by the gravity force is directed towards the topographic lows with the minimum hydraulic potential. The vertical velocities of fluid flow in this case are enhanced in comparison with the flow rates typical for a free convection in a flat terrain (Bodri, 1994).

The basic theory of the heat transfer as applied to the ground water problems can be formulated as follows. If the heterogeneous crust has no major fractures, it can be simulated as a porous medium; that is, replacing the existing network of fractures for flow with a continuous porous medium having effective hydraulic properties. Such "equivalent" porous medium is not capable to interpret adequately small-scale measurements; however, it can successfully be used for the large-scale modeling, when only "average" behavior is required (De Marsily, 1985). Consider an equivalent porous medium saturated with a single-phase fluid and assume that the medium remains more or less stationary for a long time. The fluid (water) is an incompressible liquid whose density depends upon temperature according to the law p = pf [1 —a(T—Tr)]. The reasons for the fluid flow are, on one hand, the pressure gradients and, on the other, the external gravity forces. The 3-D system of balance equations of mass, momentum, and energy for natural convection in a non-deformable rock matrix in Boussinesq approximation14 can be written as (Ene and Polisevski, 1987)

divv = 0, k v = —-{gradP — gpf[1 — a(T — Tr)]},

(pc)m IT + (pc)f vgradT = div(KmgradT) + (1 — 0)A

ot where t is the time, v Darcy velocity, / the dynamic viscosity of fluid, k the permeability tensor, ( the total porosity, P pressure, T temperature, Tr uniform reference temperature, a the volumetric coefficient of thermal expansion, K the thermal conductivity, (pc) volumetric heat capacity, A the radioactive heat generation, and g acceleration due to gravity. Subscripts "f" and "m" denote the fluid and the medium, respectively. The second equation represents the generalized form of the Darcy's law. This law can be simplified for incompressible fluids as v = — kpfg gradft, (38)

where h is the hydraulic head. Concerning boundary conditions, on impervious boundaries we assume that the normal component of fluid velocity will vanish. At a free surface the pressure P is equal to the atmospheric pressure at any point of the free surface. Expressed in hydraulic head it can be written as h = z. Boundary conditions for

14The Boussinesq approximation is used in the fluid dynamics and states that for buoyancy-driven flow the density differences are small and can be neglected, except where they appear in gravity terms. This approximation is quite accurate for a variety of natural flows, and makes mathematical modeling simpler.

temperature in the 1-D case remain as previously a prescribed temperature on the free surface and prescribed heat flow on the lower boundary.

Figure 59 illustrates possible disturbances to the conductive geotherm that can occur in zones of the vertical fluid flow. Calculations were performed with the 1-D analog of Eq. (37), that takes into account advective heat transport in the porous medium with thermal conductivity and volumetric heat capacity of 2.5W/mK and 2.5 X 106 J/m3K, respectively, and volumetric heat capacity of fluid 4.187 X 106J/m3K. Geothermal gradient equals 20K/km. Initial surface temperature was 0°C, and sharp temperature increase of 1°C occurred 50 years B.P. Relatively high Darcy's velocities of ± 10~8m/s were used in calculation to emphasize the effect of fluid flow. In the absence of ground water flow, subsurface temperature has curvature ("U-shape") in the surficial zone and normally follows the linear steady-state geotherm below it. Ground water flow perturbs the geother-mal gradient by infiltration of relatively cold fluid in recharge areas and upward flow of warmer fluid in discharge areas, causing concave upward profiles in recharge area and convex upward geotherms in discharge areas. Amplitude of disturbances in this case decreases with depth more slowly than for pure conductive conditions.

Figure 60 presents results of numerical trial runs with synthetic temperature logs to demonstrate the impact of hydraulic flow in the case of moderate advection in the stratum. Temperature-depth profiles were generated for the homogeneous half-space with the thermal parameters and surface history used in the example above. For the sake of simplicity the flow velocity was assumed to be steady state and constant all over the investigated depth. The noticeable advective temperature disturbances can occur for flow velocities above 10~9m/s ("moderate" convection). In case of topographically

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