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Geothermics
journa l h omepa g e: www.elsev ier .com/ locate /geothermics
ubsurface temperature distribution in Germany
horsten Agemar ∗, Rüdiger Schellschmidt, Rüdiger Schulzeibniz Institute for Applied Geophysics, Germany
r t i c l e i n f o
rticle history:eceived 18 April 2011ccepted 9 July 2012vailable online 10 August 2012
eywords:eothermal resources
a b s t r a c t
Data from approximately 10,500 wells and more than 700 ground level data sets were used to developa three-dimensional (3D) estimate of the subsurface temperature distribution in Germany. The temper-ature model was realized with universal kriging, and extends from ground level to 5000 m below sealevel. Conventional two-dimensional (2D) mapping algorithms are often used to estimate subsurfacetemperature at certain depths. The major limitation of any 2D mapping is the possibility of inconsisten-cies between different depths due to the loss of information from shallower levels. A different approach
ubsurface temperatureeothermal information systemermanyriging
is used in this paper. The application of 3D-kriging in the context of subsurface temperature estima-tion is described in detail and variation of data density and quality are also discussed. Kriging employscustomized prediction parameters for an unbiased estimate of the subsurface temperature distribution.The kriging variance predicts the uncertainty of the temperature estimate and provides a local proba-bility interval of the temperature estimate.The developed temperature model is part of the GeothermalInformation System for Germany (GeotIS).
. Introduction
Although geothermal energy constitutes only a minor portionf renewable energy sources in Germany, the geothermal indus-ry in Germany has been developing rapidly since the governmentnacted the Renewable Energy Act in April 2000. The total installedlectric power generated from geothermal sources increased from.2 MW to 8 MW in the last three years (Schellschmidt et al.,010). Geothermal heat and power production in Germany reliesn reservoirs of low to moderate temperature. Temperatures above0 ◦C are considered to be sufficient for district heating purposes.eothermal power generation requires temperatures above 100 ◦C.he hottest water available for a geothermal plant in Germanys 160 ◦C and located at Landau in Rheinland-Pfalz (Rhineland-alatinate). Geothermal power plants in Germany use conversionechniques such as the Organic Rankine Cycle (ORC) or the Kalinaycle method.
The crucial parameters for geothermal energy use are produc-ion rate Q and the temperature at the wellhead Ti which dependsn temperature TA in the aquifer. In general, Ti is a function ofhe production rate Q, the reservoir temperature TA, and the pro-
uction duration �t. During long periods of production at highates, there is only a negligible difference between the wellheademperature and the reservoir temperature. This gives rise to
the following general relationship for the installed output P of ageothermal plant:
P ∝ Q · TA (1)
Therefore, knowledge of the subsurface temperature is crucialfor planning geothermal plants for heat and power produc-tion. Higher temperatures provide better yields and increase thecost-effectiveness of a geothermal site. Mapping subsurface tem-perature distribution from available measurements is an importantprerequisite for geothermal reservoir evaluations.
Prior investigations produced a limited number of maps forcertain depths using 2D-mapping algorithms like for instancea distance-weighted estimator (Schulz et al., 1992; Hurter andSchellschmidt, 2003). The major disadvantage of 2D algorithms isthe loss of information from shallower levels since the deep sub-surface is much less explored. A sequence of maps may suggestgeothermal gradients which are not consistent with our under-standing of a predominant conductive thermal regime. In practice,it is difficult to tackle inconsistent vertical temperature steps atunsampled locations.
In order to estimate the geothermal potential of a geologicalbody at any depth, it is necessary to determine the temperature atany point in a consistent 3D-temperature model. A 3D interpola-tion method suitable for developing such a model is kriging. Thereare several types of kriging, e.g. simple kriging, ordinary kriging,
indicator kriging, etc. (Deutsch and Journel, 1998). In this studywe applied universal kriging. Universal kriging makes it possibleto accommodate a trend in data which is essential for the estima-tion of subsurface temperatures. Generally, kriging estimates are
ig. 1. Regions in Germany suitable for geothermal exploitation (shaded area). Twoubsurface temperature models that have been developed are merged along a 20 kmide zone (hatched area).
eighted linear or non-linear combinations of the available data.t is the only method which allows the inclusion of measured spa-ial variability in the estimation process. Another major advantagef kriging is the calculation of the uncertainty associated with theredicted values.
In this study, the subsurface temperature model for Germanyas created as a part of the Geothermal Information System forermany (Agemar et al., 2007; Pester et al., 2010). Subsurface tem-eratures were estimated for depths ranging from ground level to000 m below sea level.
. Hydrothermal resources of Germany
Today, geothermal exploration and production for direct use inermany focus on deep aquifers in sedimentary basin and grabentructures at depths of 2–4 km. The most important regions foreothermal exploitation are the North German Basin, the Molasseasin in southern Germany, and the Upper Rhine Graben (Fig. 1).
The North German Basin is the central part of the Central Euro-ean Basin. The present-day sediment thickness ranges from 2 toore than 11 km (Maystrenko et al., 2006). Halokinetic movements
f the Zechstein halite layers are responsible for the intense andomplex deformation of Mesozoic and Cenozoic formations (Franket al., 1996). These movements are locally active up to recent timesnd the disturbance strongly influences the local conditions.
The Mesozoic deposits of the North German Basin consist ofiltstones and sandstones, clays, carbonates, and evaporites. Sand-tone aquifers most suitable for the direct use of geothermal energy
re confined to the Permian and Mesozoic stratigraphic column:otliegend, Middle Bunter, Keuper, the Lias-Rhaetian Aquifer Com-lex, Dogger, and Lower Cretaceous (Katzung et al., 1992; Feldrappet al., 2008). The sediments of the Mesozoic are generally 2–3 km
ics 44 (2012) 65– 77
thick and have sunk to depths of 4 km and more in the basin cen-ter (Baldschuhn et al., 1996; Katzung et al., 1992). Locally, muchhigher thicknesses and greater depths occur as a result of tectonicmovements. In the Glückstadt Graben in Schleswig-Holstein forinstance, the Triassic sediments are 3.5–6.5 km thick (Maystrenkoet al., 2006). Salt tectonics cause great lateral depth and thick-ness variations over relatively short distances, and contribute tothe uncertainty of any structural model. Therefore, the geothermalpotential of individual aquifers varies strongly at a local scale.
The Molasse Basin in southern Germany is an asymmetrical fore-land basin of the alpine mountain belt which was filled during theuplift of the Alps (Lemcke, 1988). It extends over more than 300 kmfrom Switzerland in the southwest to Austria in the east. The basinis mainly filled by Tertiary sediments overlying Cretaceous, UpperJurassic and Triassic sediments. Eight aquifers in these sedimentarylayers are of interest for direct geothermal energy exploitation:Burdigalian sands, Aquitanian sands, Chattian sands, Baustein-Schichten, Ampfing-Sandstein, Gault/Cenoman-Sandstein, Malmand Upper Muschelkalk (Fritzer et al., 2010). The Upper Jurassickarstified limestone (Malm) is one of the most important geother-mal energy reservoirs in Central Europe due to its high productivityand presence beneath almost the whole Molasse Basin. South of theDanube, the Malm aquifer dips from north to south and reachesdepths of more than 5 km along the northern margin of the Alps.
The Upper Rhine Graben is part of a large rift system which tra-verses the north-western European plate (e.g. Villemin et al., 1986).The graben is 30–40 km wide and runs from Basel, Switzerland,to Frankfurt, Germany. The structure was formed during theTertiary about 45–60 Ma. It is interpreted as a doming of the crust-mantle boundary due to magmatic intrusions at 80–100 km depth.The stressed induced by folding and thermo-mechanical effectshave given rise to extensional tectonics with a maximum ver-tical offset of 4.8 km. Six Tertiary, Jurassic, Triassic and Permianaquifers are of interest for the exploitation of geothermal energyfor direct use: Hydrobien-Schichten, Grafenberg-Schichten, Haup-trogenstein, Upper Muschelkalk, Bunter Sandstone and RotliegendSandstone (Haenel and Staroste, 1988; Hurter and Haenel, 2002).The most promising geothermal energy reservoirs in the UpperRhine Graben are the Triassic Upper Muschelkalk and BunterSandstone (Haenel and Staroste, 1988). The base of the UpperMuschelkalk reaches depths of more than 4 km, whereas the baseof the Bunter reaches depths of more than 5 km.
Other areas, such as the Central German Uplands, may also provesuitable for geothermal exploitation. The introduction of enhancedgeothermal systems (EGS) would utilize the geothermal energyfrom deep crystalline basement rocks. The joint French-Germanproject at Soultz-sous-Forêts (Alsace) successfully demonstratesthe general feasibility of an EGS in Central Europe (Fritz and Gérard,2010).
3. Data
The Geophysics Information System (Kühne et al., 2003) wasthe most important data source for this study. It contains a largeamount of geophysical data, primarily within Germany, consist-ing of a main system and various subsystems. The geothermalsubsystem (Schulz and Werner, 1989) contains subsurface tem-perature data from 10,559 wells (Fig. 2). Equilibrium temperaturelogs and reservoir temperatures are considered to be optimal datawhich require no corrections. Because of the regular monitoringof production wells over many years, reservoir temperatures are
available in time series; the fluctuation in these temperatures ismainly less than 1 K.
Bottom-hole temperature data (BHT) are also stored in thegeothermal subsystem. These BHT values are recorded in almost all
T. Agemar et al. / Geotherm
0 50 100 150 200 250
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9
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T/ z = 20 K/km
T/ z = 30 K/km
T/ z = 40 K/km
T/ z = 80 K/kmmean value
Fig. 2. Temperature-depth profile of Germany: The circles denote the mean tem-perature values, the bars indicate the variation of the measured values (minimumand maximum temperature), and the figures give the number of boreholes at therespective depth. The plotted lines correspond to temperature gradients of 20 K/km,3
iaeBuAhttttiewotToica
3
dt1
When we assume similar drilling histories and geological settingsfor two wells located close to each other, the arithmetic mean of the
0 K/km, 40 K/km and 80 K/km.
ndustrial boreholes at the deepest point of the well immediatelyfter drilling has stopped. BHTs are frequently measured at differ-nt depths during the drilling operation, resulting in two or moreHT-values per well. The temperature field around a borehole issually disturbed by mud circulation related to the drilling process.
number of methods to extrapolate the undisturbed temperatureave therefore been developed based on various assumptions abouthe cooling effect of the circulating mud and the thermal behavior ofhe borehole and the surrounding rock. A review of existing correc-ion methods can be found in Hermanrud et al. (1990). The choice ofhe most appropriate correction method depends on the availabil-ty of data such as the circulation period, the elapsed time after thend of drilling, the number of subsequent measurements, and theell radii. Despite such corrections, these results still have errors
f up to ±8 to 10 K (Hermanrud et al., 1990; Förster, 2001), and areherefore much less accurate than undisturbed temperature logs.he best correction results can be obtained for BHTs if a time seriesf two or more measurements is available. In this study, depend-ng on the quality and quantity of the available data, the followingorrection methods have been applied (Schulz et al., 1992; Schulznd Schellschmidt, 1991):
.1. Cylinder source model – CSM
If three or more BHT values are available for one depth atifferent times after mud circulation stops, the thermal stabiliza-
ion method for a cylindrical borehole can be used (Leblanc et al.,982; Middleton, 1982). In this approach, it is assumed that the
ics 44 (2012) 65– 77 67
temperature of the mud when circulation stops (t = 0) is constant,and varies by a �T from the undisturbed rock temperature (URT):
URT = BHT(t) − �Te(−a2/4kt)−1 (2)
where URT is the undisturbed rock temperature (◦C); BHT is themeasured bottom hole temperature (◦C); �T is the initial temper-ature disturbance (K); a is the borehole radius (m); � is the thermaldiffusivity (m2/s); t is the time after circulation stops (s).
The URT is calculated by a fitting method varying �T and �,where � is the effective thermal diffusivity of the mud and thesurrounding rock (Schulz et al., 1992).
3.2. Continuous line source model – CLSM
If only two BHT values are available, a line source approach isderived from the negative heat transfer during the circulation timeof the mud (Horner, 1951):
URT = BHT(t) − q
4��ln
(t + s
t
)(3)
where q is the heat flow rate per length unit (W/m); � is the thermalconductivity (W/mK); s is the circulation time (s).
3.3. Instantaneous line source model – ILSM
If the circulation time can be ignored, a line source approachwith an “explosion” heat sink is used (Lachenbruch and Brewer,1959):
URT = BHT (t) − Q
4��t(4)
where Q is the heat per length unit (J/m).
3.4. Cylinder source model using estimated parameters
If only one BHT value is available, the cylinder source model (Eq.(2)) is used again. The unknown parameters – the temperature dis-turbance and the effective thermal diffusivity (Schulz et al., 1992)– have to be estimated statistically from regional databases.
We grouped the temperature data in categories of low, mediumor high reliability. Table 1 gives an overview of this classificationscheme. Category A consists of temperature measurements of highquality, such as undisturbed logs or reservoir temperatures. Dis-turbed logs and BHTs where at least the elapsed time is known,qualify for medium quality category B. For half the BHTs, no elapsedtime is available. In these cases the elapsed time has been estimatedon the basis of depth and other parameters. Since this methodcarries a high degree of uncertainty, BHTs with no elapsed timerecords make up category C. In addition to the problem of varyingaccuracy, there is also the risk of working with biased data due toovercorrection or insufficient correction. In a study on the Osebergoil field, Hermanrud et al. (1990) pointed out that some correc-tion methods (e.g., line source models) tend to underestimate trueformation temperatures which had been obtained from drill stemtests. Similar findings have been reported by Förster (2001) whocompared continuous logs and corrected BHT values in deep wellsin the eastern part of the North German Basin. She reported thatcorrected temperature values were about 8–9 K too low. In orderto track systematic errors, we compared samples of different qual-ity at close vertical and horizontal proximity to each other. For thiscomparison, we selected sample pairs with a maximum horizontalseparation of 5 km and a maximum vertical separation of 100 m.
difference between inaccurate and accurate measurements shouldresult in zero. Unfortunately, this may not be the case as can be seen
68 T. Agemar et al. / Geothermics 44 (2012) 65– 77
Table 1Categories of subsurface temperature data on the basis of record types. Highest quality ranks A, lowest quality ranks C. If more than one record type exists for one well, onlythe deepest record is considered.
3Z BHT, more than two values Cylinder source model
3651 B
2L BHT, two values Instantaneous line source model2H BHT, two values Continuous line source modelLOG-2 Disturbed log1E BHT with elapsed time and radius given Cylinder source model1ES BHT with elapsed time given
ifcmTbtaeaa
rpmfatsrd
ao2r
Fwsqqs
1ER BHT with radius given1EO BHT without any further information
n Fig. 3. Here, mean differences and mean deviations are plottedor various depth ranges. The diagram shows that measurements ofategory B and C may underestimate formation temperatures by asuch as 5 K. The degree of underestimation increases with depth.
he indicated overestimation for wells deeper than 3.5 km shoulde ignored due to the sparseness of the data. The underestima-ion of subsurface temperature might have physical reasons suchs the flow of fluid from the borehole into the formations. How-ver, the observed underestimation could be real when we take intoccount that some high quality logs were recorded preferentiallyt locations with high geothermal gradients.
Although category B and C data has been obtained from inaccu-ate measurements, and the applied correction methods may haveroduced biased results at certain depth intervals, it is not recom-ended to discard them all. Well data of category C were only used
or further processing when no data of a higher category was avail-ble within a lateral distance of 5 km. An exception was made whenhe C-type sample was at least 300 m lower than a B-type or A-typeample. Samples of category B in the vicinity of A-type values wereejected in the same way. This filtering reduces the use of low-gradeata and mitigates the small-scale variability in the result.
Surface temperatures have been approximated from 30 yearverages of air temperatures 2 m above ground. Most data was
btained from the state meteorological service of Germany (DWD,010). Additional data for neighboring countries was used to coveregions along the German border. The internet portals of the state
ig. 3. Mean difference between temperature measurements of varying accuracyithin a distance of <5 km and a depth slice of <100 m for five depth ranges. Dark
haded boxes indicate the mean difference between medium quality (B) and highuality (A) samples, light shaded boxes indicate the mean difference between lowuality (C) and high quality (A) samples. Bars indicate the mean deviation of theample pairs. The figures refer to the number of sample pairs.
3797 C
meteorological services of the Netherlands (KNMI, 2010) and theCzech Republic (CHMI, 2010) provide free access to relevant sta-tion data. Mean air temperature values in Luxembourg, France,Switzerland, Austria and Poland were retrieved from the WorldMeteorological Organization (WMO) global climate normals dataarchived by the National Climate Data Centre of the United States(NCDC, 2002). Climate normals of Danish meteorological stationshave been taken from Laursen et al. (1999). Altogether, data from675 German locations and from 37 locations in neighboring coun-tries has been compiled. The original data comprises monthlyaverages of air temperature for the years 1961–1990. The long termmean air temperature is a fairly good approximation of the soil tem-perature at a depth of about 13 m where the temperature remainsrelatively constant throughout the year (DWD, pers. comm.).
All temperature data used for subsurface temperature estimatesis indeed derived from temperature measurements. Modelingresults based on heat flow density have not been used for estimat-ing temperature.
4. Methods
This study applies 3D geostatistics for the prediction of sub-surface temperature at unsampled locations. The geostatisticalapproach generally assumes spatial continuity and does not respectvarying geological settings. Rocks and minerals have a broad rangeof thermal conductivities: for example, the thermal conductivity ofhalite is 2–3 times higher than most other minerals. Thus, a geosta-tistical prediction may not reflect the true temperature distributionwhere salt domes or salt pillows occur. In this case, local numericalmodels may provide more meaningful results. On the other hand,numerical models require detailed knowledge of subsurface ther-mal conductivity and heat flow density, information which is onlypartly available. Furthermore, convective heat transfer in porous orfractured rocks or karst formations is extremely difficult to modelbecause knowledge of subsurface fluid pathways is incomplete.Numerical models of subsurface temperature are therefore limitedto specific locations.
4.1. Kriging
Estimating subsurface temperature with 3D kriging has a num-ber of advantages over conventional mapping algorithms such asinterpolation by means of inverse distance weighting (IDW). Inkriging, a power parameter balances the weight between closeand remote measurements. Kriging does not assign a default dis-
tance power to represent distance decay of a variable. Instead,the geostatistical estimation process is based on a model of thespatial variability of a regionalized variable. This model is a math-ematical representation approximating the measured variability
othermics 44 (2012) 65– 77 69
omatoatesdmksTsktunTkfttths
mwvgn
vtddp
rntmsDbbd6
4
t−dpeTadccdo
Table 2Overview of surface temperature map specifications and kriging parameters.
Grid resolution 1000 m (kriging)100 m (terrain projection)
Coordinate system Gauss Krueger centralmeridian at 9◦E
Map dimensions 660 km × 880 kmEasting:3,267,000–3,927,000Northing:5,225,000–6,105,000
Kriging parameters:Model fit ExponentialRange 100 kmSill 0.37Nugget 0.1
Data Locations: 675
T. Agemar et al. / Ge
f the available samples and is commonly called the variogramodel. It relates variance � to distance between sample pairs h
nd describes the spatial dependence of a random field. Geostatis-icians have developed a number of model types to fit the full rangef results obtained from variogram analyses. The most commonlypplied models are the spherical model, the exponential model andhe Gaussian model. The intercept is commonly called the nuggetffect. It is attributed to small-scale random variability. Regardingubsurface temperature data, heat conduction should mitigate anyiscontinuity. Here, the nugget effect is probably due to measure-ent errors. A high nugget effect acts as a smoothing term during
riging estimation as it makes weights more similar. With growingeparation h, the � value also increases until it reaches a plateau.he separation beyond which the variogram value remains con-tant is commonly called the range, which defines the scope of theriging estimation. The plateau level is called the sill. It refers tohe variogram value reached at the range distance. Estimates ofnsampled areas are produced from weighted combinations of theeighboring samples with respect to both distance and redundancy.he individual weights are assigned on the basis of minimizing theriging variance. This ensures the most precise estimates possiblerom the available data. Since the estimates are only as good ashe model fits to the observed variogram values, it is importanthat the variogram is accurate over the whole estimation area. Ifhis second-order stationarity assumption is inappropriate, it mightelp to subdivide the data set into smaller regions within whichamples appear to be more homogeneous.
Regarding subsurface temperature, the presence of a geother-al gradient requires an adaption of the ordinary kriging scheme,hich is known as ‘universal kriging’ or ‘kriging with a trend’. Uni-
ersal kriging can calculate a trend automatically and producesood local estimates even when the estimate is extrapolated fromeighboring sample values.
Some data sets exhibit a non-normal distribution of samplealues. The kriging variance and mean are related to probabilityhrough the assumptions of a Gaussian distribution. If the availableata do not satisfy the criteria of statistical normality, applying aata transformation before geostatistical operations can solve thisroblem.
Predictions for a regionalized variable have little meaning if theeliability of the estimate is not known. Geostatistical estimationot only yields values for unsampled locations but also the uncer-ainty associated with these values, a result that other prediction
ethods are unable to provide. More detailed information on geo-tatistics and the kriging procedure can be found in the book byeutsch and Journel (1998) and references therein. The method haseen used for regional or local subsurface temperature predictionsefore (Dose, 2006; Sepúlveda et al., 2012) but here it is applied toevelop a nationwide 3D temperature model covering an area of60 km × 880 km.
.2. Surface temperature
The 30-year-averages of surface temperature show a distinctemperature decrease with altitude. The average gradient is about3.5 K/km in areas up to elevations of 750 m above sea level. Iteclines sharply to −5.0 K/km at higher elevations. The kriging waserformed on a grid of 1 km × 1 km resolution. The kriging param-ters derived from the variogram analysis are shown in Table 2.he altitude gradient was deducted from the data beforehand anddded back to the final kriging estimate. The necessary elevationata were extracted from the in-house digital terrain model and
oarsened to a 100 m × 100 m grid. In order to account for climatehange between 1961–1990 and 2001–2010, a location indepen-ent value of 0.9 K (DWD, 2011) was added. The statistical errorf the estimated mean surface temperatures is about ±0.8 K. The
Germany + 37 neighborcountries
Air temperature 2 m above ground Years: 1961–1990
conversion from surface temperatures to soil temperatures at adepth of 13 m was accomplished without any correction curve.Local deviations between soil temperatures and surface temper-atures generally depend on site specific conditions such as depthof groundwater, moisture content of soil, vegetation or relief of theterrain. These site specific aspects raise total error to approximately±1 K. The temperature-depth relationships in the upper 100 m ofboreholes have not been extrapolated for surface temperature esti-mates. The obtained temperatures do not match meteorologicaldata due to the variability of the local parameters. The geostatis-tical analyses and the kriging estimation of surface temperatureswere performed using Paradigm’s GOCAD software package, whichincludes the functionality of the Geostatistical Software LibraryGSLIB (Deutsch and Journel, 1998).
4.3. Subsurface temperature
The estimation of a 3D field of subsurface temperatures requiresboth surface data and subsurface data. The surface data serve asthe upper limit in the estimation process and cover Germany andadjacent areas of neighboring countries. The sample coverage ofthe subsurface is less optimal. The distribution of samples reflectsthe geographical as well as the stratigraphic interests of oil andgas exploration (Fig. 4). Most wells with temperature data are inthe North German Basin. The remaining wells are concentratedin the Thuringia Basin, the Upper Rhine Graben and the MolasseBasin in southern Germany. Subsurface temperature data for otherregions are quite scarce. Besides the variable geographical distri-bution, there is also a decline in data density with depth (Fig. 5).Another problem is the co-existence of log data and scatteredpoint data in the same data set. Log data is distributed along thewell path and would be weighted too high compared to wells ormines with few samples. Furthermore, sample locations reflectinga high geothermal gradient close to sample locations reflecting alow geothermal gradient may result in the prediction of anoma-lous vertical gradients in the 3D temperature field: in some cases,temperature may seem to decrease with depth. Clearly, such pre-dicted anomalies do not reflect the real temperature field in theregions under consideration. In order to overcome this problem, weinterpolated vertically between single sample locations or betweensubsurface measurements and surface temperature. We applieda linear temperature/depth relationship and ignored the effect ofvarying thermal conductivity.
Even after removing the geothermal gradient, the completedata set exhibits a non-normal distribution and therefore does notsatisfy the basic assumption of statistical normality. The data pro-duces an asymmetric histogram. This problem can be resolved by
70 T. Agemar et al. / Geothermics 44 (2012) 65– 77
sent s
afcu
Fq
Fig. 4. A location map of wells with temperature records. Larger symbols repre
pplying multi-Gaussian kriging. Each sample value is mappedrom its original cumulative frequency to the standard S-shapedurve corresponding to a normal distribution. The normal score val-es have a mean value of 0 and a standard variance of 1. Each sample
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all wells >500 >100 0 >1500 >200 0 >2500 >3000
Nu
mb
er
of w
ells
Depth [m]
Quality C
Quality B
Quality A
ig. 5. Number of wells with temperature records penetrating certain depths. Foruality ranking A–C see Table 1.
amples of higher accuracy. For more details on quality ranking A–C see Table 1.
value is projected from its original cumulative frequency to thestandard S-shaped curve of a Gaussian distribution. The values atunsampled locations are drawn from an inverse normal score trans-formation of the estimates developed in Gaussian data space. Thisapproach has basically two benefits. First, it simplifies the devel-opment of a useful variogram relationship, and second, it dampspeak values and thus improves the kriging estimate in areas of lowdata density. Confidence envelopes can be determined by addingthe estimated standard deviation to the estimate for the upper limit,and subtracting for the lower limit. Unfortunately, GOCAD does notallow the transformation of upper and lower limits back to originalvalues. The confidence interval must be approximated by analyz-ing the relation between depth and lateral variance for each model(north and south). The probability that the true value is either lessthan (or greater than) the predicted value is 50%. The probabilitythat the true value falls within one standard error either side of theestimated value is 68%; and the risk that it is less than the lowerlimit is 16%. Because of the non-linear transform of subsurfacetemperature data to normal score before kriging, the confidenceinterval is now also non-linear and not exactly symmetrical aboutthe estimate on the original scale. Hence, the combined statementof predicted value and confidence envelope must be treated with
care – the estimate may have less than 68% confidence.
The geostatistical analyses and the kriging estimation of sub-surface temperatures were performed using Paradigm’s GOCADsoftware package. The 3D grid of the kriging estimates is
T. Agemar et al. / Geothermics 44 (2012) 65– 77 71
FG
olKlts1ztcsr(ofi
BGIcvetawRmsmInwtvddTrsvrmeoed
Table 3Overview of 3D model specifications and kriging parameters for subsurfacetemperature.
Grid resolution Lateral: 2000 mvertical: 100 m
Coordinate system Gauss Krueger centralmeridian at 9◦E
Map dimensions 660 km × 880 kmEasting: 3,267,000–3,927,000Northing:5,225,000–6,105,000
Kriging parameters: North: South:Model fit Spherical SphericalRange lateral 75 km 65 km
(Clauser and Villinger, 1990; Pribnow and Clauser, 2000; Pribnowand Schellschmidt, 2000). This could also explain the high spatialvariability of subsurface temperature in the Upper Rhine Graben.The cross section in Fig. 9 shows the Mesozoic layers most relevant
0
20
40
60
80
100
120
140
0
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140
0 500 1000 1500 2000 2500 3000
ig. 6. Sample variograms and variogram models for northern and southernermany calculated for 1200 m below sea level.
rthogonal and the vertical axis is zero at sea level, not at groundevel. This has implications for kriging estimates at shallow depths.utasov (1999) described how topographic features may affect
ocal subsurface temperature. Mountains, for instance, cause aemperature increase due to additional cover. Known analyticalolutions can be used to assess the effect of changing relief (Kutasov,999 and references therein). Using a grid with ground level asero would result in an overestimate of deep subsurface tempera-ures underneath mountain ranges because the effect of additionalover diminishes with increasing depth. With the sea level surfaceet to zero, subsurface temperature predictions are of higher accu-acy, especially at depths interesting for geothermal exploration>2 km). However, at shallow depths, predictions in the vicinityf mountains tend to slightly underestimate the real temperatureeld.
In order to account for different spatial variability in the Molasseasin in southern Germany, the Upper Rhine Graben and the Northerman Basin, we performed the geostatistical analyses separately.
t turned out that the samples in northern Germany show a higherorrelation than those in southern Germany. The highest spatialariability can be found in the Upper Rhine Graben and in the east-rn Bavarian Molasse Basin. The consequence is that two subsurfaceemperature models were developed – one for northern Germanynd one for southern Germany. The models overlap in a 160 kmide zone reaching from the Rheinisches Schiefergebirge (Middlehine Highlands) to the Erzgebirge (Ore Mountains) and the esti-ates of both models are merged along a 20 km wide zone for a
mooth transition. The vertical extent of the overlap zone is small,ostly less than 1000 m, because deep wells are scarce in this area.
t is important to note that all geostatistical analyses have foundo significant anisotropy in spatial variability. Sample variogramsere calculated for lateral and vertical directions and it turned out
hat the spherical model give the best fits to the data. The lateralariograms for a slice at 1200 m below sea level for both regions areisplayed in Fig. 6. 3D-model specifications and kriging parameterserived from the variogram analysis are summarized in Table 3.he variogram model for northern Germany has a larger horizontalange value than the one for southern Germany, due to the higherample correlation in lateral directions. The sample variogram andariogram model for the vertical axis is shown in Fig. 7. The verticalange for both domains is much smaller. Abrupt changes in geother-al gradient imply shorter vertical correlation lengths. Dose (2006)
stimated a vertical range between 1100 m and 1400 m for his study
n subsurface temperatures in the Upper Rhine Graben. The differ-nce might be related to the different z-axis origin and a smallerata base.
Range vertical 2 km 2 kmSill 1.0 (normal score) 1.0 (normal score)Nugget 0.2 0.2
5. Results
We have produced a comprehensive 3D-temperature model.This is the first time a 3D subsurface temperature model for allof Germany has been accomplished. Fig. 8 shows the temperaturedistribution at four depths as examples. The reduced data den-sity at deeper levels results in expanded gaps in the temperaturemodel predominately in the Central German Uplands and in south-ern Germany. The mapped 3D temperature model ends where thenormalized kriging variance reaches 1.0 and, hence, the kriging esti-mate becomes less reliable than a simple prediction on the basis ofthe average geothermal gradient. Areas with a normalized krigingvariance above 0.8 are shaded gray.
The kriging estimate of the subsurface temperature representsthe best fit to the available data. However, 0.37% of the grid cellsshowed a reverse vertical gradient after kriging. Deep wells withlow gradients affect the temperature field underneath shallowwells close-by. This is due to the large lateral scope of the krig-ing estimator. We removed these anomalies by applying a verticalfilter to the affected grid cells.
At 2500 m below sea level, temperatures range from 59 ◦C to165 ◦C with a mean value of 93 ◦C. Many areas show tempera-tures above 100 ◦C, which is the minimum temperature for powerproduction and sufficient for district heating. Areas with temper-atures above 150 ◦C are found in the northern part of the UpperRhine Graben. These unusually high temperatures are probablylimited to areas of upwelling groundwater along fracture zones
h (m)
Fig. 7. Sample variogram and variogram model for the vertical axis.
72 T. Agemar et al. / Geothermics 44 (2012) 65– 77
F and 4U
fttWtga
GdnaaaTfgeTC
otd
ig. 8. Subsurface temperature in Germany at 2500 m (A), 3000 m (B), 3500 m (C)plands) cannot be mapped due to the lack of data.
or geothermal energy exploitation near the town of Speyer. Besideshe vertical temperature trend, there is also a temperature increaseoward the graben center which is pictured on the left side of Fig. 9.
ithin the upper 1000 m, there is a further increase in subsurfaceemperatures near the south-north trending faults at the easternraben shoulder – presumably related to groundwater upwellinglong fault planes.
The subsurface temperatures in the Molasse Basin in southernermany are somewhat lower than in the Upper Rhine Graben. Theeepest wells with temperature records are located in the southear the Alps. Wells with temperature records below 2 km depthre almost absent in the northern part of the Molasse Basin. Unusu-lly high temperatures are found in the shallow subsurface domainround the town of Landshut with up to 60 ◦C at a depth of 600 m.he geothermal plant at Unterhaching south of Munich benefitsrom high formation temperatures of 123 ◦C at 3.2 km depth. Loweothermal gradients are encountered near the Alps in the south-rnmost part of the Molasse Basin and in the area of the Wasserburgrough approximately 40 km east of Munich. In the area of Lakehiemsee, the geothermal gradient decreases to 25 K/km.
Further north, within the Central German Uplands, there arenly a few wells with temperature records below 3 km depth. It isherefore difficult to assess the subsurface temperature field. Theeepest temperature measurements stem from a 4444 m deep well
000 m (D) below sea level. The blanked areas (for the most part Central German
near Urach (Swabian Alb, south of Stuttgart), a 5848 m deep wellnear Neunkirchen (Saarland, northeast of Saarbrücken), a 4406 mdeep well near Uslar (Weser Hills, south of Hannover), and the wellsof the Deep Continental Crust Drilling (KTB) in the Oberpfalz (UpperPalatinate) with a maximum depth of 9101 m. The wells of theCentral German Uplands are located far apart from each other in dif-ferent geological settings. Relatively high subsurface temperaturesare found at Urach due to high geothermal gradients especially inthe first 400 m. The bottom of the borehole at 4444 m depth exhibitsa temperature of almost 168 ◦C. The other three wells show normalgradients of 26–30 K/km.
In northern Germany, subsurface temperatures at 2500 m belowsea level rarely exceed 100 ◦C. This difference is only partly due tolow terrain levels in northern Germany. At a depth of 3000 m belowsea level, subsurface temperatures range from 70 ◦C to 174 ◦C witha mean of 108 ◦C. Northern Germany’s mean subsurface tempera-ture at 3000 m below sea level is just above 100 ◦C. At 3500 m belowsea level the temperatures range from 79 ◦C to 181 ◦C, while theaverage temperature is about 122 ◦C. At 4000 m, subsurface tem-peratures range from 90 ◦C to 183 ◦C with a mean of 135 ◦C. The
estimated subsurface temperatures show smooth transitions andare considered to be a fairly good reproduction of the availablemeasurements. However, local deviations from regional patternsare only reproduced in areas of abundant data. A good example
T. Agemar et al. / Geothermics 44 (2012) 65– 77 73
Fig. 9. A cross section through the northern Upper Rhine Graben. The geological profile is from Jodocy and Stober (2009). Subsurface temperature contours are transferredfrom the 3D-subsurface temperature model.
74 T. Agemar et al. / Geothermics 44 (2012) 65– 77
Fig. 10. A cross section through the westernmost part of the North German Basin (Lower Saxony). The geological profile is generated by the NIBIS map server (LBEG, 2011)of the Geological Survey of Lower Saxony (after Baldschuhn et al., 1996). Subsurface temperature contours are transferred from the 3D-subsurface temperature model.
osWoaalictoawbie
saFwcaatsa
erTai
f a precise reconstruction of local temperature anomalies is pre-ented in Fig. 10. It shows the temperature distribution along a
NW–ESE geological cross section in north-western Lower Sax-ny. Elevated temperatures are found above the top of salt bodiesnd within deeply buried sediments between salt structures. Thereas underneath the salt bodies show reduced temperatures. Theowest geothermal gradients appear within the salt structures. Sim-lar examples of thermal anomaly patterns around salt structuresan be found in the literature (Fromme et al., 2010, and referencesherein). The temperature distribution displayed in Fig. 10 is first-rder controlled by the thermal conductivity contrast between saltnd sediments. Large salt domes and walls provide vertical path-ays of low thermal resistance for the conduction of heat in the
asin. The calculation of temperature fields around salt structuress discussed in the literature (Petersen and Lerche, 1995, and refer-nces therein).
Regarding the North German Basin, salt bodies are not respon-ible for all temperature anomalies. For instance, the positivenomaly found in the temperature records of the Friedland 1 andriedland 2 wells in Western Pomerania cannot be explained thisay. The cause is not clear but convection of deep groundwater
ould play a part. Fig. 11 shows the temperature distribution along SW–NE geological cross section in this area. Besides the positivenomaly in the middle, there is also a steep temperature decreaseowards the northern margin of the basin. This decrease in sub-urface temperature could be related to thinner sedimentary covernd the higher thermal conductivity of the basement.
The geothermal gradient generally follows a linear trend. How-ver, some well records show a significant deviation from a linear
elationship not related to mud circulation or measurement errors.he estimated geothermal gradient depends on the selected sitend (to a lesser extent) on the selected temperature and depthntervals.
Fig. 12 shows the spatial variation of the geothermal gradient�T/�z based on a 100 K increase in temperature relative to surfacetemperature. Eq. (5) describes how this gradient is calculated.
�T
�z= T0 − Tz
z − z0(5)
where Tz is the temperature at depth z (◦C) here Tz = T0 + 100 K; T0 isthe temperature at surface elevation (◦C); z is the depth (km abovesea level); z0 is the surface elevation (km above sea level).
The average geothermal gradient for the mapped area is32 K/km. This corresponds to an average depth of 3125 m for a tem-perature which is 100 K above surface temperature. This value ismore meaningful than the average of measured gradients becauseit is not affected by clustered data. Some regions show highergradients: as in south-western Germany. Other areas show lowergradients: such as the area east of Munich near the town Wasser-burg. Although research in geothermics in Germany has progressedin recent years, it is still difficult to explain regional or even localdeviations from the average geothermal gradient.
6. Discussion and conclusions
The most important prerequisites for the 3D subsurface tem-perature model are the amount and accuracy of temperaturemeasurements. Temperature estimates in areas close to nationalborders would benefit from additional well data in neighboringcountries. Sample locations outside Germany also improve our3D subsurface model. So far, well records from Belgium, France,
Switzerland, Austria and the Czech Republic have been included.The temperature model would benefit from additional boreholetemperatures to the north, to the west and to the east of the NorthGerman Basin.
T. Agemar et al. / Geothermics 44 (2012) 65– 77 75
Fig. 11. A cross section through the north-easternmost part of the North German Basin from Neubrandenburg to Usedom generated by the Geothermal Information Systemfor Germany (LIAG, 2011). The geological profile is based on borehole profiles and stratigraphic maps of Wormbs et al. (1989, 1992). Subsurface temperature contours aretransferred from the 3D-subsurface temperature model.
Fig. 12. Spatial variation of the geothermal gradient in Germany. The geothermal gradient is expressed as the �T/�z ratio where �T = 100 K and �z is the correspondingdepth below ground level.
7 otherm
pimacmikcAnre
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6 T. Agemar et al. / Ge
Kriging, like any other geostatistical estimation, cannot com-ensate for missing or false data. The rejection of less accurate data
n the vicinity of more accurate data improves the quality of the esti-ation. The filtering cascade with three quality categories is simple,
nd relatively few measurements are discarded. A more sophisti-ated approach could be to increase sample weighting according toeasurement accuracy. Delhomme (1978) illustrated how to mod-
fy the kriging estimator in order to account for non-constant butnown measurement errors. However, this requires the quantifi-ation of site-specific errors and the exclusion of systematic errors.
kriging system which handles variable measurement errors hasot yet been accomplished. In this study, the constant nugget effectefers to a combination of small-scale variability and measurementrror of the filtered data set.
Applying 3D kriging provides an additional benefit as it includeseasurements across a range of depths in the estimation process.
t extracts the maximum amount of information from the availableata. One major limitation of any 2D mapping is the possibility of
nconsistencies between different depths due to the loss of infor-ation from shallower levels. With 3D kriging, measurements from
hallower depths influence the temperature estimates within theertical variogram range. Nevertheless, it is important to createirtual logs from single measurements first because the lateral var-ogram range is much greater than the vertical variogram range.
ithout virtual logs, temperature estimates could decrease withepth locally.
Very important for optimum kriging estimates is the assumptionf second-order stationarity for the domain of interest. Regionaldjustments have been accomplished by dividing Germany into aorthern and southern sub-model and employing different krig-
ng parameters for each sub-model. Although both regions coverreas of varying geology, geostatistical analyses of smaller sub-ets (e.g. Molasse Basin, Upper Rhine Graben) showed very similarpatial structures and confirmed that the applied variograms areepresentative of the regions of interest. The determination of theertical range is more difficult, since the variogram hardly shows
plateau. Nevertheless, it is a critical parameter because it defineshe extrapolation depth. Deviations from a vertical trend may occurt any depth due to changing thermal conductivity or groundwa-er convection. Thus, the deepest temperature estimates of the 3Dubsurface model should be treated with extra care due to possibleocal effects.
A major advantage of kriging over conventional mapping algo-ithms is the prediction of the uncertainty associated with theemperature estimate. The estimated temperature would lose
uch of its meaning without considering the uncertainty. Fur-hermore, the kriging variance is a good tool to assess thepatial scope of the available data. 3D kriging resolves most ofhe limitations of conventional mapping techniques, however,ike any statistical estimation it does not take into considera-ion varying thermal conductivities or the thermal convection ofuids.
The 3D subsurface temperature model provides relevant dataor many geothermal studies and projects in Germany. The subsur-ace temperature distribution is an integral part of the Geothermalnformation System for Germany (GeotIS) and can be accessed viahe internet. It makes a substantial contribution to improving thelanning of geothermal sites in Germany. GeotIS is hosted by theeibniz Institute for Applied Geophysics and it is free of charge.he website at http://www.geotis.de is available in English and inerman and offers many interactive tools for retrieving and visual-
zing subsurface temperature estimates. It is for instance possible
o retrieve horizontal and vertical sections of the temperature field.
aps of stratigraphic formations with temperature are available for number of regions. Surface temperatures are also available for dis-lay and free download. The staff of the Leibniz Institute of Applied
ics 44 (2012) 65– 77
Geophysics will continue to update the 3D subsurface temperaturemodel and provide further technical improvements.
Acknowledgements
The development of the 3D subsurface temperature model hasbeen funded as part of the project “Set-up of an internet-baseddata center for geothermal energy use” by the Federal Ministry forthe Environment, Nature Conservation and Nuclear Safety (refer-ence code: 0327542A). We are grateful to F. Binot (LIAG) for manyhelpful suggestions and comments. This paper also benefitted fromconstructive comments and suggestions from the editors and fromthree anonymous reviewers.
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