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ARTICLE IN PRESS Model

EOT-887; No. of Pages 19

Geothermics xxx (2012) xxx– xxx

Contents lists available at SciVerse ScienceDirect

Geothermics

journa l h omepa g e: www.elsev ier .com/ locate /geothermics

riging predictions of drill-hole stratigraphy and temperature data from theairakei geothermal field, New Zealand: Implications for conceptual modeling

. Sepúlvedaa,∗, M.D. Rosenbergb, J.V. Rowlandc, S.F. Simmonsd

Contact Energy Limited, Private Bag 2001, Taupo, New ZealandGNS-Science, Wairakei Research Centre, Private Bag 2000, Taupo, New ZealandIESE, University of Auckland, Private Bag 92019, Auckland, New ZealandHot Solutions Ltd, PO Box 32-125, Devonport 0744, Auckland, New Zealand

r t i c l e i n f o

rticle history:eceived 18 July 2010eceived in revised form 9 December 2011ccepted 3 January 2012vailable online xxx

eywords:airakei

eothermalemperaturetratigraphy

a b s t r a c t

Drill-hole temperature and stratigraphic datasets from the Wairakei geothermal field were used forgeostatistical predictions using Kriging. In order to adequately constrain Kriging models, anisotropy andtrends associated with temperature and stratigraphy were studied using standard variogram analysis, incombination with new regional and local structural data, revised gravity, and available geoscientific andreservoir data. This combined analysis lead to the incorporation of horizontal anisotropy (horizontal tovertical correlation ranging from 8:1 for regional stratigraphic units to 4:1 for local rhyolite bodies) inthe case of stratigraphic models and variable anisotropy in the case of temperature models. In the latter,the variable anisotropy was represented by two end members: an isotropic model (horizontal to verticalcorrelation of 1:1) representative of depths >2000 mGL, and an anisotropic model (horizontal to verticalcorrelation of 3:1) representative of depths <1000 mGL. Kriging models of temperature also incorporated

redictionriging

ndicator Krigingniversal Kriging

a vertical trend which is a combination of two end members at Wairakei: Boiling-Depth-Point Curve(convective) and linear (conductive). The Kriging models succeeded in identifying the primary geologicalcontrols on temperature distribution: major upflows largely controlled by structures at depth (>1000 mdepth) and shallow (<1000 m depth) outflows stratigraphically channelled through formation contactsand rhyolite edges. A combination of stratigraphy and faults explain local cold downflows in shallow

s of t
(750–1000 m depth) part
. Introduction

The Wairakei geothermal field, New Zealand, was the firstiquid-dominated reservoir in the world to be developed for elec-ricity generation, with production starting in 1958. At present,

airakei continues to generate electricity with an installed capac-ty of approximately 170 MWe, and it is projected to exceed the00 MWe mark by 2013. The expansion of a geothermal field invari-bly poses challenges in terms of the definition of productionnd injection drilling targets, both of which are equally importantn the current scheme of sustainable development of geothermalesources. Conceptual models of geothermal reservoirs play a cen-ral role in the definition of drilling strategies, and also dynamicallyvolve as more drill-hole data becomes available. As a result ofong-term production at Wairakei, drill-hole datasets have become

Please cite this article in press as: Sepúlveda, F., et al., Kriging predictiongeothermal field, New Zealand: Implications for conceptual modeling. Geo

ncreasingly available to assist the elaboration of geological con-eptual models and numerical simulations of exploitation effects.nalysis and interpretation of large geothermal drill-hole datasets

∗ Corresponding author. Tel.: +64 7 3761959; fax: +64 7 3748472.E-mail address: [email protected] (F. Sepúlveda).

375-6505/$ – see front matter © 2012 Elsevier Ltd. All rights reserved.oi:10.1016/j.geothermics.2012.01.002

he field.© 2012 Elsevier Ltd. All rights reserved.

can be challenging, but multidisciplinary analysis can be optimisedby use of geostatistical interpolation techniques (e.g., Fabbri, 2001;Teng and Koike, 2007). In this study, we applied Kriging to drillhole datasets of temperature and stratigraphy for geostatisticalmodelling to illustrate the utility and limitations of Kriging for pre-diction of drill-hole parameters at Wairakei, to exemplify the valueof existing geoscientific and reservoir knowledge in providing con-straints to geostatistical models, and to characterize and discusscorrelations between the subsurface temperature and stratigraphywith emphasis in the deep architecture of the field. Geostatisti-cal models are used to predict the value of an attribute in anunsampled location using attribute values known at sampled loca-tions. Statistical confidence of the predictions naturally decreasestowards peripheral or deep areas of a reservoir which tend to beless explored. In this context, Wairakei offers a unique opportu-nity to test geostatistical predictions based on cumulative drilling,geoscientific, and reservoir data.

s of drill-hole stratigraphy and temperature data from the Wairakeithermics (2012), doi:10.1016/j.geothermics.2012.01.002

2. Geology of the Wairakei geothermal field

The Wairakei geothermal field is located in the Taupo VolcanicZone (TVZ), an extensional volcanic arc that has been active during

dx.doi.org/10.1016/j.geothermics.2012.01.002


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ARTICLE IN PRESSG Model

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Fig. 1. Map of Central Taupo Volcanic Zone, showing geothermal areas as defined by resistivity data (Schlumberger surveys; 30 Ohm-m boundary from Bibby et al., 1995) withrespect to residual gravity anomalies (Bibby et al., 1995), earthquake data (period 1987–2011; 0–5 km depth; source GEONET; data filtered as in Bryan et al., 1999), calderamargins (after Wilson et al., 1995 and Gravley et al., 2007) and the TVZ rift architecture (after Rowland and Sibson, 2004). Base layer is shaded relief map (25 m Digital TerrainM areas

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odel). Map projection: New Zealand Map Grid (m). Abbreviations for geothermal

O = Rotorua; WW = Waimangu-Waiotapu; RE = Reporoa; TK = Te Kopia; OK = OraT = Wairakei-Tauhara.

he last 1.6 Ma (Fig. 1; Wilson et al., 1995; Houghton et al., 1995)n response to oblique subduction of the Pacific plate beneath theustralian Plate. The central segment of the TVZ, extending fromawerau geothermal field in the north to Lake Taupo in the south

Fig. 1), represents the most active silicic volcanic province onarth (780 km3/61 kyr), with a number of associated ignimbrite andaldera-forming eruptions, which represent more than 90% of theotal erupted magma of the TVZ (Wilson et al., 1995).

The central TVZ marks the concentration of the majority of high-emperature geothermal systems of New Zealand (Fig. 1), with

agmatism as the primary heat source. The depth of such heatource remains unconstrained at the scale of individual geother-al systems, but regional seismic and MT studies in the central

VZ identify low resistivity or seismically anomalous regions atepths of ∼5 km to >10 km, as an indication of partially molten rockSherburn et al., 2003; Heise et al., 2007). It is also worth noting inhe explored vertical range of the TVZ (<3 km depth), drilling evi-


ence of magma bodies is lacking and evidence of plutonic rocks iselatively rare (Browne et al., 1992; Milicich et al., 2011).

The central TVZ undergoes NW-SE extension at rates on therder of 7–8 mm/yr, which is mostly accommodated by faulting

as follows (from north to south): TT = Taheke-Tikitere; RT = Rotoma; KA = Kawerau;orako; NG = Ngatamariki; BO = Broadlands-Ohaaki; MK = Mokai; RW = Rotokawa;

and tectonic subsidence (Villamor and Berryman, 2001; Nicolet al., 2006). Active structures mainly consist of NE-SW trending,high-angle normal faults, and subvertical tension cracks, whichare collectively referred to as rift structures. The spatial relation-ships between geothermal activity (as delineated by shallow lowresistvity anomalies; Bibby et al., 1995, 1998), rift and caldera struc-tures, and modern seismicity (<5 km depth) are shown in Fig. 1. A“TVZ rift boundary” is shown in Fig. 1 to indicate the extent of high-temperature geothermal activity, caldera structures (ca. <330 kaold; Wilson et al., 1995), and active rift structures and tectonicsubsidence, mainly interpreted from morpho-tectonic analysis (i.e.,surface fault scarps and tracers, and graben structures; Rowlandand Sibson, 2004). Earthquake locations (Bryan et al., 1999; Fig. 1)concentrate within the TVZ boundary confirming the potentiallyactive character of most mapped faults. However, earthquake datareveals seismic gaps and NS-trending seismicity clusters (north-ern part of TVZ; Fig. 1) not coincident with active faults. It is also


noted that geothermal locations vary from relatively seismic (e.g.,Kawerau) to relatively aseismic (e.g., Ohaaki), and from havingstrong fault correlation (e.g., Kawerau, Te Kopia; Orakei-korako) tounclear fault correlation (all others). The general observation is that


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ARTICLEEOT-887; No. of Pages 19

F. Sepúlveda et al. / Geo

ystematic spatial correlations of geothermal activity with faults,aldera boundaries and seismicity are equivocal based on availableata (Fig. 1).

Both rift and caldera structures are major components of therchitecture of the central TVZ, the distinction of which is some-imes subtle in the TVZ, due to the close control exerted by rifttructures on the inception, development, and evolution of calderasSpinks et al., 2005; Gravley et al., 2007; Seebeck et al., 2010;owland et al., 2010). Oblique structures, defined here as structuresith orientations other than NE-trending, have also been docu-ented within the central TVZ (Tienfeng and Hedenquist, 1981;cocella et al., 2003; Rowland and Sibson, 2001, 2004) and along

he northern, off-shore prolongation of the TVZ (Wright, 1992;amarche et al., 2006; Mouslopoulou et al., 2008). As discussedbove, oblique structures can also be inferred from regional seis-icity (Fig. 1).

.1. Local stratigraphy and structure

A range of stratigraphic models have been proposed forairakei (Grindley, 1965; Steiner, 1977; Healy, 1984; Wood, 1994;ood and Browne, 2000; Rosenberg et al., 2009; Bignall et al.,

010), of which the Grindley (1965) illustration was influentialor several decades. In this study, a number of re-interpretations,e-definitions, and changes in nomenclature are introduced afterosenberg et al. (2009), as a result of ongoing drilling and detailed

ithological and petrographic re-examinations of core and cuttings.This study focuses on stratigraphic units underlying Huka Falls

ormation, and accordingly, a detailed discussion of the shallowtratigraphy of the Wairakei field is beyond the scope of thisaper. For the purposes of interpolation, no distinctions were madeetween the members of Huka Falls Formation and Waiora Forma-ion as described in Table 1 (Grindley, 1965; Rosenberg et al., 2009).

Stratigraphy units of interest here include, from top to bot-om: Waiora Formation (Grindley, 1965), Whakamaru Ignimbritesknown locally as Wairakei Ignimbrite) (Wilson et al., 1986), andahorakuri Formation (Gravley et al., 2006; Table 1). A range of pre-ominantly rhyolitic effusive units occur within these stratigraphic

ayers, and these are modeled as separate entities, with the aimo highlight the heterogeneous character of the stratigraphic units.he definition of Stockyard Ignimbrite and Poihipi Rhyolites as sub-nits of Tahorakuri Formation (i.e., pre-Whakamaru Ignimbrites;able 1) has been recently established, following revision of stratig-aphy and identification of Whakamaru Ignimbrite in wells WK248,

K253 and WK259 (Bignall et al., 2010).The Whakamaru Group Ignimbrites collectively represent the

ost voluminous ignimbrite complex of the TVZ (>1500 km3

f erupted magma) and an important stratigraphic marker forhe interpretation of deep stratigraphy and fault geometry at

airakei, due to both regional extent and relatively easy recog-ition (crystal type and abundance distinct from other widespreadVZ ignimbrites; Brown et al., 1998; Saunders et al., 2010). Thealdera boundary from which these ignimbrites derive encircle the

airakei, Rotokawa, and Mokai geothermal systems (Wilson et al.,986; Houghton et al., 1995; Brown et al., 1998; Fig. 1). In spitef its regional extent, this unit is highly discontinuous across theairakei field (Rosenberg et al., 2009). Fewer than ten wells have

enetrated the entire Whakamaru Ignimbrite, revealing a variablehickness ranging from <100 m (WK248) to >1000 m (WK121). Aumber of relatively deep wells such as WK301 (eastern Wairakei,2000 m deep; Fig. 2) and WK247 (Te Mihi area; ∼2750 m deep) didot encounter Whakamaru Ignimbrites; a fact used to aid interpret

Please cite this article in press as: Sepúlveda, F., et al., Kriging predictions of drill-hole stratigraphy and temperature data from the Wairakeigeothermal field, New Zealand: Implications for conceptual modeling. Geothermics (2012), doi:10.1016/j.geothermics.2012.01.002

ocations of the deep structures.Where Whakamaru Ignimbrites are absent, the definition of the

ase of Waiora Formation is generally more uncertain. Based on itsurrent understanding, the base of the Waiora Formation occurs Ta

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ig. 2. Location map of the Wairakei Geothermal Field, as defined by the resistivity bGrindley, 1961; GNS Active Fault Database – http://data.gns.cri.nz/af/) and the bouells (from which temperature and stratigraphy data are also available) not shown

n average at ca. 600 m depth beneath the Western Bore Field, andharply deepens to the west and east, being logged at ca. 1450 mepth in well WK301 (reinjection area; Fig. 2) directly overlyingahorakuri Formation. To the east of WK301, the base of Waioraormation becomes shallower (ca. 850 m depth in wells WK305nd WK307, and ca. 600 m depth in wells WK314 and WK315;ig. 2), but is much deeper again, south-eastwards into the Tauharaeothermal field.

The pre-volcanic basement, which is mostly made up of Meso-oic greywacke in the central TVZ (Wood et al., 2001; Mortimer,004), has not been intersected by drill-holes in Wairakei yet,nd the deepest wells drilled in the Te Mihi and reinjection areasWK247; WK317; Fig. 2) indicate the basement there is at least.9 km below surface. In the eastern side of Tauhara, well TH17

ntersected greywacke basement at a depth of ca. 2000 m. This isonsistent with similar drilling findings from other eastern fieldse.g., Rotokawa, Ohaaki, Kawerau), and validates the general cor-elation of high residual gravity anomaly values and relativelyhallow greywacke basement, to the east of the TVZ (Fig. 1).


The predominance of NE-trending (and subordinate WNW-rending) surface fault expressions at the Wairakei Field matcheshe broader tectonic grain of the Taupo Volcanic Zone and is con-istent with NW-SE directed widening of the central TVZ (Grindley,

ry (5 Ohm-m inner boundary; Risk, 1984), showing geothermal wells, surface faultses of the temperature and stratigraphy models presented in this study. Abandoned

1961; Rowland and Sibson, 2001; Fig. 2). Interpreted drill-hole data(e.g. stratigraphic offsets) and structural imaging via acoustic logs(e.g. McLean and McNamara, 2011) show active faults are domi-nantly NE-striking, normal and dip steeply (60–80◦). Earthquakehypocentres in the central TVZ (including the Wairakei area) plotas deep as 6–9 km where the brittle-ductile transition is inferredto occur (Bryan et al., 1999; Sherburn et al., 2003; Bannister et al.,2004; Harrison and White, 2004). Faulting is therefore likely to beactive through the entire depth extent of the Wairakei-Geothermalsystem.

3. Data and methods

In this study, geostatistical models of temperature and stratig-raphy were computed using the Kriging technique (e.g., Olea,1999). Temperature predictions were obtained by use of ordi-nary Kriging (referred to as Kriging) and universal Kriging,and stratigraphy predictions were computed by use of indica-tor Kriging. In simple terms, Kriging and indicator Kriging are


used for spatial prediction of continuous (numeric data) andcategorical variables, respectively. All Kriging algorithms wereimplemented in mathematical modeling software package MAT-LAB (http://www.mathworks.com). A detailed description of the


http://data.gns.cri.nz/af/

http://www.mathworks.com/



F. Sepúlveda et al. / Geothermics xxx (2012) xxx– xxx 5

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ig. 3. Temperature data, including drill-hole temperature and thermal manifestatealand Map Grid.

riging algorithms is beyond the scope of this paper, but generalverview is provided in Section 3.2. For more details on the Kriginglgorithms, as implemented here, readers can refer to Olea (1999)nd Deutsch and Journel (1992).

The following steps were undertaken as part of geostatisti-al modeling: drill-hole data validation, exploratory data analysisanisotropy and trends), analysis of geoscience/reservoir informa-ion to assist interpretation of anisotropy and trends, and spatialrediction.

.1. Drill-hole data validation

Temperature and stratigraphy drill-hole data used in this studynclude more than 200 geothermal wells covering an area of

km × 7 km and a 3 km depth range (Fig. 3). For the purpose ofeostatistical modeling, vertical resolution of drill-hole tempera-ure data was standardized to 10 m (this means, datasets collectedt higher resolution were reduced in size). Horizontal resolutions comparatively poorer and constrained by well spacing (from0 m in densely drilled areas to several km in peripheral or deepreas). Measured temperatures were used as a proxy for formationemperatures. Measured temperatures can be affected by a seriesf artifacts which were minimized or eliminated when possible.xamples include lack of thermal equilibration, effects induced by


roduction, and internal flow or development of shallow steamones.

In order to minimise artifacts due to lack of thermal equilib-ium, we selected downhole temperature logs taken 28 or more

1950–present), and boundary conditions used for this study. Map projection: New

days after well completion. Worth noting is temperature logsmay potentially equilibrate over longer periods (on the order ofmonths; Horner Method; Dowdle and Cobb, 1975; Verma et al.,2006).

Measured temperatures can be affected by extraction (e.g., asan indirect effect of pressure drawdown, or cooling due to infieldinjection). Bixley et al. (2009) documented a temperature changeup to 15 ◦C in the production areas of Wairakei as a result offluid extraction, the bulk of which took place during the period1960–1970. Accordingly, post-1970, temperature logs were prefer-entially selected to minimize artifacts due to temperature changeswith time.

The effects of internal flow or development of shallow steamzones were assessed on a well-by-well basis and removed whereidentified. Discussion on how to recognize these artifacts is beyondthe scope of this paper, but readers can refer to Grant and Bixley(2011) for guidelines.

The following boundary conditions (Fig. 3) were used to con-strain Kriging models:

• Surface temperature from thermal manifestations (GNSdatabase). These data were merged into input drill-hole datasetfor Kriging predictions

• Minimum temperature of 10 ◦C, assigned at selected topographic


locations (except for areas within 250 m of thermal manifesta-tions or drill-hole data) using a coarse 500 × 500 m regular grid(Fig. 3). These data were merged into input drill-hole datasetfor Kriging predictions. This minimum temperature was also


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implemented as post-prediction correction (i.e., all values below10 ◦C were converted to 10 ◦C)Maximum temperature of 270 ◦C (Bixley et al., 2009). This wasimplemented as a post-prediction correction (i.e., all values above270◦ were converted to 270 ◦C).

It is noted that while interpreted temperatures (input for Krig-ng models) are eventually corrected for the artifacts above, therelways remains a degree of subjectivity in the interpretations.tratigraphy can similarly be subject to uncertainty, mainly becausef its subjective nature (interpretation) and also due to the dif-culties and limitations inherent to the recovery of geologicalamples during drilling. The majority of the drill-hole material usedn Wairakei for stratigraphic descriptions is cuttings (95% versus% remaining core), which is commonly intensely hydrothermallyltered, generally undated, and locally discontinuous due to blindrilling. Accordingly, many stratigraphic definitions presented herere still regarded as provisional, and Kriging models of stratigraphyresented here may be potentially subject to revision.

.2. Kriging applied to temperature

Kriging is an exact interpolator, meaning data are honoredt sample locations. Kriging also has the ability to identify andinimize screening and clustering effects (e.g., wells in a line or

lustered locally). All these properties are relevant to the study ofrill-hole datasets, which tend to be highly scattered in 3D space.

Kriging also can handle anisotropy and spatial trends inherento data. Variogram analysis, sometimes referred to as exploratoryata analysis (EDA), is an important step in geostatistical analysishere principal directions of anisotropy and the presence of a trend

an be analyzed (EDA is discussed in more detail in Section 3.3).Kriging is based on a generalized form of linear regression, which

n the case of temperature takes the form (Olea, 1999):

(Xo) =n∑

i=1

Ti�i (1)

here Ti = measured temperatures at the sample points i = 1. . .n,i = weight coefficients, and T(Xo) = prediction of temperature at the

ocation Xo = (xo, yo, zo), with �i coefficients meeting the condition:

n

i=1

�i = 1 (2)

Kriging minimizes the variance of the estimation error �2(Xo) –hich can be expressed as a function of �i coefficients. In prac-

ical terms, variance is a measure of spatial variability. From aathematical point of view, the Kriging problem is a constrained

ptimisation, this is, minimising the variance subject to a constraintcondition (2)] which is solved through the Lagrange method of

ultipliers (Olea, 1999, and references therein):

(�i, �) = �2(Xo) + 2�

(n∑

i=1

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)(3)

here L(�i,�) is the Lagrangian function and � is a Lagrange mul-iplier.

The variance is minimised using a minimum square errorpproach, for which the following empirical estimator of the vari-nce �2(Xo) is adopted (Olea, 1999),


(h) = 12n(h)

n(h)∑i−1

[T(Xi + h) − T(Xi)]2 (4)

PRESSics xxx (2012) xxx– xxx

where �(h) is the variogram, T is temperature, h is the lag distancevector (separation between data pairs), n(h) is the number of datapairs separated by h, and Xi = (xi, yi, zi) is the location of the samplingpoint i. A graphical representation of Eq. (4) is the �(h) versus hplot, referred to as the empirical variogram (examples discussed inSection 4.1).

Temperature increases with depth in response to the prevail-ing thermal regime. In geostatistical terms, temperature is saidto be a non-stationary variable characterised by a “vertical drift”.In a conductive thermal regime, the vertical drift can be approx-imated to a linear trend, whereas convective regimes (typicallyhigh-temperature geothermal systems like Wairakei), the verticaldrift will be governed to a large extent by the boiling-depth-point(BDP) curve. The mathematical treatment of a drift in Kriging con-sists of adding a further constraint to the Lagrange optimisationproblem discussed in Eqs. (1)–(3), as follows:

L(�i, �) = �2(Xo) + 2�o

(n∑

i=1

�i − 1

)

+ 2n∑

j−1

�j

(n∑

i−1

�ifj(Xi) − fi(Xo)

)(5)

where fj is a polynomial function representing the drift (Olea, 1999).The problem in Eq. (5) is usually referred to as a universal Krigingproblem. Conceptually, Kriging models are composed by a resid-ual random function (the prediction) plus a deterministic functionfj (the drift). In conventional Kriging (Eq. (3)), the drift is constantand unknown, and in universal Kriging (Eq. (5)), the drift is variableand modeled. Universal Kriging shares all the properties of con-ventional Kriging: it is a minimum square error, exact interpolatorthat automatically corrects for clustering in the sampling, and theobservations take weights under a screen effect (Olea, 1999). In thisstudy, both Kriging and universal Kriging predictions are shown forcomparative purposes, although universal Kriging predictions areultimately adopted for prediction of temperature at Wairakei (seeSection 4.3 for details).

3.3. Kriging applied to stratigraphy

In indicator Kriging, the m available stratigraphic units of a drill-hole dataset are categorized with an arbitrary integer kj (j = 1,. . .,m).By definition, a categorical variable is assigned discrete values asopposed to continuous numeric variables (e.g. temperature). Withstratigraphic data being reduced to categories, the following binarytransformation is applied to stratigraphic data:

Ij(Xi) ={

1 if K(Xi) = Kj

0 otherwise(6)

where Ij(Xi) is the indicator transform of the stratigraphic unit j atthe sampling point Xi = (xi, yi, zi) and k(Xi) is the stratigraphic classobserved at Xi, with i = 1,. . .,n (n is the number of sampling points).Basically, Ij(Xi) = 1 where kj is known to be present, and Ij(Xi) = 0where kj is known to be absent. Note that unlike temperature,where data is available nominally at 10 m vertical resolution, strati-graphic data is of variable vertical resolution, which is determinedby the location of all stratigraphic contacts of the stratigraphyclass kj.

In the case of categorical variables (i.e., stratigraphy), a vari-ogram model IMj may be calculated (subject to data availability)


and fitted to each empirical indicator variogram of the categorieskj, j = 1,. . .,m (Eq. (1)). Such variogram models are used as a proxyfor the local probability distribution of the stratigraphic class kj.At every interpolation location Xo, the stratigraphic class with the


ING Model

G

therm

h

K

wIIX

3

oaiaia

slaLrdrtfi

tao

b

1

2

ildeT1dfi

ao



ighest probability is assigned, this is:

(Xo) =

⎧⎪⎪⎪⎪⎨⎪⎪⎪⎪⎩

k1 if IM1(Xo) = max{IM1(Xo), IM2(Xo), . . . , IMm(Xo)}k2 if IM2(Xo) = max{IM1(Xo), IM2(Xo), . . . , IMm(Xo)}

...

km if IMm(Xo) = max{IM1(Xo), IM2(Xo), . . . , IMm(Xo)}(7)

here K(Xo) is the predicted stratigraphic class at Xo. The fact thatndicator Kriging is an exact interpolator implies that a value ofj(Xo) = 1 equivalent to 100% outcome probability is assigned ato = Xi, provided Ij(Xi) = 1.

.4. Exploratory data analysis

Empirical variograms are used to quantify the average variationf an attribute (such as temperature) as a function of lag distancend direction. Changes in direction producing significant changesn the empirical variograms are generally interpreted in terms ofnisotropy. The mathematical treatment of anisotropy in Krigings beyond the scope of this paper, but readers can refer to Deutschnd Journel (1992) and Leuangthong et al. (2008) for details.

Although variogram analysis is a 3D problem and all directionshould be eventually studied, in practice, variogram directions andag intervals can be chosen selectively subject to the condition thatll relevant directions be identified and reasonably characterised,ag intervals/increments be large enough to contain a statisticallyepresentative number of pairs (the minimum statistical confi-ence is set at 100 pairs here – at least 30 pairs per lag interval isecommended by Olea, 1999), and lag intervals be small enough sohat empirical variograms capture relevant variations for variogramtting (discussed below).

In areas/directions with poor data coverage, there is usually arade-off between statistical confidence (i.e., number of data pairst each lag interval) and level of detail (i.e., number of lag intervals)f variograms.

The generalized use of variograms in geostatistics is supportedy the following empirical observations:

) Two adjacent points tend to show similar attribute valueswhereas two distant points tend to show greater variation inthese values (also known as Tobler’s Law; Tobler, 1970). From ageostatistical point of view, the correlation of two data points isproportional to the separation distance between them.

) Under stationary conditions (this is, trend or “drift” not present;see Section 4.1 for discussion on drift), the variation in theattribute values increases up to a certain critical lag dis-tance, referred to as “range”, beyond which variance reaches a“plateau” referred to as “sill”. From a statistical point of view,sampling points separated by a distance greater than the rangeare uncorrelated.

Variance is estimated empirically using available data and thent is mathematically modeled by fitting a variogram model. Theatter is a mathematical function of lag distance, sill, range andirection. Commonly used variogram models include spherical,xponential and Gaussian (Deutsch and Journel, 1992; Olea, 1999).rial and error is a common practice for variogram fitting (Olea,999). Because of point 2) above, a good variogram fit at small lagistances, and a poor fit at big lag distances is better than a moderate


t at all lag distances.The utility of variogram analysis in Kriging as to characterizing

nisotropy and spatial trends is limited by available data. Vari-grams may not be statistically representative in peripheral or deep

PRESSics xxx (2012) xxx– xxx 7

areas of a study area due to relative lack of data. In the absenceof representative variograms, available geoscientific and reservoirdata can provide bounds to geostatistical models. In this context,surface fault lineaments (both regional and local) and gravity datawere analyzed in this study to better characterize the structuralsetting of the Wairakei field, with emphasis on the implications foranisotropy analysis (see Section 4.1 for details).

Regional structural lineaments were obtained through the anal-ysis of a digital terrain model of the TVZ (25 model spatialresolution). Local structures were mapped in the vicinity of theWairakei Geothermal Field (Fig. 6). Fractures, faults, and veins wererecognized in exposures of Huka Falls Formation and superficialdeposits (Oruanui Formation and Taupo Formation). A descriptionof these formations can be found in Rosenberg et al. (2009) andWilson (2001).

In this study, residual gravity anomalies of Wairakei (Hunt,1991) were used for identification of subsurface structural trendsand further examined via gradient analysis, with sharp gravimetricvariations being used as a proxy for the delineation of subsurfacestructures.

4. Results and discussion

4.1. Anisotropy and drift analysis of temperature

Vertical and horizontal directions are regarded as the mostuseful for variogram analysis because geological controls on tem-perature are mainly represented by stratigraphy and structures,meaning principal directions of correlation are likely to be subhor-izontal and subvertical, respectively. This holds valid for a youngextensional regime like the TVZ, but it may not hold true forother geological settings. Also, temperature is affected by a ver-tical increase with depth, or vertical drift, meaning the vertical andhorizontal directions are best suited to characterise main drift anddrift-free directions, respectively. This holds valid for all geother-mal settings.

Fig. 4 shows horizontal variograms of temperature in the direc-tions EW, NE, NS, NW, and omnidirectional. It follows from thisfigure that differences in direction do not produce significantchanges among the horizontal variograms. This poses an appar-ent discrepancy between variogram analysis and surface fault data,the latter supporting a dominant NE-trending direction of correla-tion. In this context, geological and reservoir engineering evidence,including existing and new data, are briefly described below, bothon regional and local scale, which in view of the authors sup-ports complex anisotropy patterns (i.e., other than NE-trending)at Wairakei.

4.1.1. New and existing structural evidenceRose diagrams from regional oblique lineaments show system-

atic WNW- and NNW-trending populations (this study; Fig. 6).Other regional structural studies (Rowland and Sibson, 2001, 2004;Acocella et al., 2003; Rowland et al., 2010) describe the TVZ as asegmented rift, with a series of transitional zones or “accommoda-tion zones”, which may be manifested through local discontinuitiesin NE-trending fault activity, and/or seismic gaps (Fig. 1), and/oroccurrence of structures (faults and lineaments) running roughlyperpendicular to the NE-trending rift axis (Fig. 7). These studiesshow the Wairakei geothermal field may be spatially associatedwith stretched and magma-intruded crust in one such accom-modation zone (Fig. 1). At the scale of the Wairakei area, other


indicators favour the existence of oblique structures. These includerose diagrams of orientations of local fractures, faults, and veinsaround the Wairakei geothermal field (from this study) as shownin Fig. 6. Veins, which are fossil remnants of structural pathways





horizo

fafFW2

4

t

Fig. 4. Directional variograms obtained along selected

or hydrothermal fluid flow, follow not only a NE-trending, butlso a preferential EW-trending direction. Also, some documentedaults in the southern part of Wairakei trend WNW (Grindley, 1961;ig. 2), and, thermal manifestations of Lake Taupo (10 km south ofairakei) are strongly aligned in a NW direction (de Ronde et al.,

002).


.1.2. Existing and revised gravity dataIn general, sharp variations in residual gravity anomalies tend

o highlight structural discontinuities associated with density

ntal directions using temperature data from Wairakei.

changes, generally, changes in basement geometry (basementbeing denser than volcaniclastic cover), or borders of basin struc-tures (e.g., tectonic grabens, calderas) within which relativelylow-density volcanoclastic deposits accumulate. In the TVZ, neg-ative residual anomalies are commonly interpreted as indicative ofburied caldera and many geothermal systems sit within or near the


edge of such calderas, which tend to be of irregular strike (Bibbyet al., 1995; Fig. 1). Detailed gravity mapping at Wairakei (Hunt,1991; Hunt et al., 2009; Fig. 7) suggests both NE and NW-trendingdiscontinuities are present at subsurface (this study; Fig. 7B).


Please cite this article in press as: Sepúlveda, F., et al., Kriging predictions of drill-hole stratigraphy and temperature data from the Wairakeigeothermal field, New Zealand: Implications for conceptual modeling. Geothermics (2012), doi:10.1016/j.geothermics.2012.01.002




Fig. 5. (A) Ominidirectional horizontal variograms for <1000 mGL and >1000 mGL depth intervals; (B) Vertical variogram of temperature, along with synthetic BDP and linearvertical variograms.

Fig. 6. Map of structural lineaments of the TVZ. In the upper-left corner, rose diagrams show dominant directional trends of regional lineaments, with lineaments weightedby length. In the lower-right corner, rose diagrams show dominant directional trend of faults, fractures, and veins (weighted by frequency) exposed in the vicinity of theWairakei area (field data locations shown). Abbreviations of geothermal areas (red labels) as in Fig. 1.





F e of rei jectio

4

gWrras

amm

�

wsapnaAdd

rbtwm2os

meters below ground level (mGL)] and sub-vertical, open fracturesimaged through acoustic logs in wells WK404 and WK407. No clearcorrelation with stratigraphy could be established.

ig. 7. (A) Residual gravity map of Wairakei (Hunt, 1991); (B) map of first-derivativn yellow, orange and red) as proxies for subsurface structures (this study). Map pro

.1.3. Reservoir studiesThe hydrological connection between the Wairakei and Tauhara

eothermal fields, and overall NW-SE disposition of the greaterairakei-Tauhara system, supports a NW-SE connectivity of the

eservoir (Bixley et al., 2009). Reservoir modeling and simulationesults point to dominantly horizontal (i.e., stratigraphic) perme-bility at shallow depths in Wairakei, which can potentially maskhallow structural patterns (Mannington et al., 2004).

In the absence of conclusive evidence for anisotropy, horizontalnisotropy is not adopted as it represents a potential bias to Krigingodels. Accordingly, thermal variance is modelled using a cubicodel of variance of the form:

(h) =

⎧⎨⎩ Co + C ·

{7

(h

a

)2

− 354

(h

a

)3

+ 72

(h

a

)5

− 34

(h

a

)7}

h < a

Co + C h ≥ a

(8)

here h is the lag distance (m), a is the range (m), C is the sill (dimen-ionless) and Co is the nugget effect (microvariance at h → 0), with

= 6300, C = 4500 and Co = 0. The graphical representation of thesearameters is shown in Fig. 4E (omnidirectional variogram). It isoted that the NS direction (Fig. 4A) stands out with a variance wellbove the model variogram for lag distances greater than 4000 m.s discussed in Section 3.2, however, the poor fitting at large lagistances is not a concern provided good fit is achieved at small lagistances (in this instance, <4000 m).

Fig. 4 provides an estimate of the average horizontal range (cor-elation) for temperature data. Horizontal correlation is dictatedy lateral connectivity in the reservoir, which in turn is a func-ion of stratigraphic permeability. Reduction of primary porosityith increasing depth has been documented in a range of geother-


al fields, including Wairakei (e.g., Stern, 1982; Stimac et al.,004; Mannington et al., 2004), with the potential implicationf progressive reduction in stratigraphic permeability relative totructural permeability. In agreement with this hypothesis, McLean

sidual anomalies, showing areas of steep gravimetric gradient (>10 mGal/km; areasn: New Zealand Map Grid.

and McNamara (2011) noted a close correlation between feedzones interpreted from completion tests [depths greater than 2000


Fig. 8. Temperature profiles from selected outfield wells, exemplifying the presenceof a dominantly linear drift from 0 to −600 mRL.





g hori

tt0l0diTrcdaobfidp(

Fig. 9. Examples of omnidirectional indicator variograms calculated alon

In order to test changes in the horizontal correlation ofemperature with depth at Wairakei, omnidirectional horizon-al variograms were computed separately for depth intervals of–1000 mGL and 1000–3000 mGL (Fig. 5A). Note the number of

ag intervals of the 1000–3000 mGL variogram is less than that of–1000 mGL variogram. The reduction of lag intervals at greaterepths was adopted to increase statistical confidence per lag

nterval, although at the expense of loss of detail (Fig. 5A; seeable 2 for details). The emerging 1000–3000 mGL variogramemains highly “noisy” and only an indicative horizontal range ofa. 2000 m (about a third of the horizontal range used to modelata in the 0–1000 mGL depth interval) is shown in Fig. 5A, toccount for the apparent lack of correlation beyond a lag distancef 2000 m. Although the magnitude of the horizontal range thatest models data in the 1000–3000 mGL range is relatively dif-


cult to constrain with accuracy comparable to the 0–1000 mGLepth interval, the comparison of the two variograms clearlyoints to an overall reduction of horizontal correlation with depthFig. 5A).

Fig. 10. Temperature distribution at z = 0 mRL from Kriging model, assu

zontal directions using binary-reduced stratigraphy data from Wairakei.

The variogram in Eq. (8) cannot successfully model the verti-cal variogram of temperature (Fig. 5B). The continuous increaseof variance (lack of plateau or sill) that characterises this verticalvariogram is diagnostic of non-stationary variables affected by adrift. At Wairakei, the vertical drift of temperature is a mixtureof two end members: linear-conductive (dominant outfield, e.g.,Fig. 8) and boiling-depth-point (BDP) curve (dominant infield;Bixley et al., 2009). In order to incorporate the drift in UniversalKriging, a polynomial order for the function f(Xi) (as in Eq. (5))must be specified. In this study, a 3rd order polynomial of the formf(Xi) = a0 + a1z + a2z2 + a3z3 was found to adequately model the BDPcurve. The drift is handed automatically in the universal Krigingsystems of equations without the need of resorting to the estima-tion of the polynomial coefficients ai above. This means, Kriginghas the flexibility to compute a 3rd degree polynomial in the pres-


ence of a drift locally dominated by the BDP end member, and a1st degree (linear) polynomial where a conductive regime is dom-inant by selectively setting polynomial coefficients to zero (e.g.,coefficients a2 and a3 above). The general approach to successfully

ming isotropic variance. Map projection: New Zealand Map Grid.





Table 2Detail of omnidirectional, horizontal variogram for data in the 0–1000 mGL depth interval (plotted in Fig. 5A). Number of lag distances in class is used as a measure of statisticalconfidence in the lag interval. In general, the statistical confidence for each lag interval (which is proportional to the number of classes) in the 1000–3000 mGL variogramis remarkably lower (although above the 100 pair mark suggested by Olea, 1999) relative to data in the 0–1000 mGL depth interval (note: 1000–3000 mGL variogram withreduced number of lag intervals plotted in Fig. 5A not shown here).

Lag class No. Average lag distance h (m) Omnidirectional, horizontal variogram (0–1000 mGL) Omnidirectional, horizontal variogram (1000–3000 mGL)

No. of distances in class Semivariogram Value No. of distances in class Semivariogram Value

1 125 2178 100 88 4852 375 9460 274 568 2103 625 17,776 295 1083 2974 875 22,157 471 979 5125 1125 19,984 689 1470 716 1375 27,976 771 348 5117 1625 46,790 1467 420 24198 1875 67,660 1235 350 9569 2125 68,068 2012 293 1352

10 2375 113,196 2295 715 381111 2625 84,926 2685 738 547012 2875 51,425 2813 499 10,56013 3125 51,873 3320 975 687614 3375 42,420 3792 427 99415 3625 50,944 4087 696 137716 3875 73,533 4376 2948 80617 4125 103,443 3941 2889 162718 4375 96,850 4861 2808 299819 4625 96,774 4482 983 318120 4875 69,304 4345 4173 447021 5125 37,566 4564 1394 256622 5375 16,475 5790 672 692123 5625 9618 8297 759 599824 5875 16,811 3746 775 543625 6125 31,904 3857 1746 138626 6375 30,587 3546 478 420127 6625 30,408 3908 262 4195

422558794945

mc

twprtfiofsqtosrrs

(vtir

•

28 6875 10,059

29 7125 6170

30 7375 442

odel a variable drift is to set the polynomial order to fit the mostomplex known form of the drift.

The most challenging part of the universal Kriging problem ishe need to specify the variogram of the residuals (i.e., temperatureithout drift), not the variogram of the regionalized variable (tem-erature + drift). A common way to estimate the variogram of theesiduals is by modelling the drift-free direction (horizontal direc-ion in the case of temperature). In the case of temperature datarom Wairakei, it has been shown that the sill of the horizontal var-ogram is relatively constant over the entire vertical depth intervalf study (sill = 4500, Fig. 5A). A relatively safe assumption is there-ore that the range of the vertical variogram of the residuals is theame as that of the horizontal variogram. An independent, semi-uantitative verification of this assumption is made by comparinghe vertical variogram of temperature against synthetic variogramsf linear trend (45 ◦C/km) and BDP curve (Fig. 5B). This compari-on shows the vertical variogram of temperature is in the expectedange of variance for a variogram with a superimposed vertical driftepresented by a combination of the two end members hypothe-ised above.

The range of the horizontal variogram decreases with depthFig. 5A) posing some questions around the magnitude andariability (i.e., constant versus variable) of the range of the ver-ical variogram of residuals. The following geoscientific analysiss used to guide the choice of the vertical variogram of theesiduals:

Faults can be recognized from surface (surface fault traces)


through depths of ca. 2000–2500 m (acoustic logs; McLean andMcNamara, 2011) down to 6–9 km depth at the TVZ (distributionof seismicity; Bryan et al., 1999). Based on this ubiquitous pres-ence of faults in the vertical depth range under study (0–3 km),

10 18,403 31 2166 8 1088

subvertical connectivity of the reservoir (vertical range of vari-ogram of residuals along z direction) can be assumed constant.

• Stratigraphic permeability is variable in the vertical depth rangeunder study, being greater than vertical permeability at shal-low depths (<1000 mGL; Mannington et al., 2004). This implies,the average vertical range of the variogram of the residuals inthe vertical direction must be lower than 6300 m, which is theprevailing average horizontal correlation at depths <1000 mGL(Figs. 4E and 5A).

• Horizontal and vertical correlation of temperature is similar atdepths >2000 m. This hypothesis relies on indirect evidence fromreservoir models which produce a reasonable match of measuredtemperatures by adopting comparable horizontal and verticalpermeability towards the base of the models (Mannington et al.,2004).

The above three conditions are satisfied by adopting a range of2000 m for the vertical variogram of the residuals in the z direction.Let d(Xo) be the depth in meters of the prediction location Xo. An“anisotropy” factor p can be defined as:

p(Xo) =

⎧⎪⎪⎨⎪⎪⎩

1

2000 − d(Xo)2000

0

d(Xo) < 1000 m

d(Xo) ≥ 1000 m and d (Xo) ≤ 2000 m

d(Xo) > 2000 m

(9)


Kriging temperatures are ultimately calculated under variableanisotropy as:

T(Xo) = Tanisotropic(Xo)p(Xo) + Tisotropic(Xo)(1 − p(Xo)) (10)





Fig. 11. Kriging models of temperature for NE-trending cross section extending from points A to B, as shown in Fig. 10. (A) Isotropic thermal structure, no drift; (B) Isotropicthermal structure, drift (3rd order polynomial); (C) Anisotropic thermal structure (horizontal to vertical correlation of 3:1), no drift; (D) Anisotropic thermal structure(horizontal to vertical correlation of 3:1), drift (3rd order polynomial); (E) Temperature model using anisotropy as in (D) from 0 to 1000 mGL, isotropy as in (B) from 1000t ixing1

wavfv

4

tupvdigaumhbe

o 3000 mGL, and variable anisotropy between 1000 and 2000 mGL, computed as m000 mGL, 0 at 2000 mGL).

here Tanisotropic is the Kriging prediction of temperature for annisotropic model (vertical to horizontal correlation of 1:3) withertical drift, and, Tisotropic is the Kriging prediction of temperatureor an isotropic model (vertical to horizontal correlation of 1:1) withertical drift.

.2. Stratigraphical anisotropy

Both vertical indicator variograms and horizontal, omnidirec-ional indicator varigorams were computed for all stratigraphicnits. Based on preliminary analysis (not shown), a significant pro-ortion of indicator variograms were regarded as lacking statisticalalidity (applying criteria as in Section 3.2). Detailed, horizontalirectional analysis was not performed, partly due to the antic-

pated limitations in statistical validity, but also due to lackingeological justification. Regarding the latter, a well-established factt the TVZ and Wairakei is volcanic and sedimentary stratigraphicnits are by their origin and nature of emplacement, sheet-like in


orphology. The predominantly rhyolitic lava bodies at Wairakeiave higher aspect ratios than pyroclastic or volcaniclastic strata,ut are still more extensive laterally than vertically (Rosenbergt al., 2009).

line between (B) and (D) using anisotropy coefficient as a function of depth (1 at

Following this observation, statistically sound indicator vari-ograms were identified (examples in Fig. 9) and used to deriverepresentative horizontal ranges, which were extrapolated to otherstratigraphic units. The ratio of horizontal to vertical correlation(this is, the ratio between horizontal range axy and vertical rangeaz) was approximated using general thickness relationships. In gen-eral, horizontal to vertical correlation ratios used in this studyvaried from az/axy ratio of 1:4 (typically used for rhyolites such asKarapiti 2a; Fig. 6B) to az/axy ratio of 1:8 (typically used for regionalstratigraphic units such as Huka Falls Formation; Fig. 9A).

4.3. Spatial prediction

The interpretation of anisotropy can be supported by com-bined variogram analysis and geoscience. In practice, predictionmodels can also be used to assist interpretations of variogramsand anisotropy. In other words, “model variograms are used toconstrain Kriging models and Kriging models are used to con-


strain model variograms”. Although this may sound like a circularargument, a preliminary prediction model (e.g., horizontal mapof temperature) computed under the deliberate assumption ofisotropy is a first, necessary and practical step to pre-assess the





exten

ph

omu(HNecmatuoens

e(t

Fig. 12. Kriging models of temperature for NW-trending cross section

resence of anisotropy (specifically, directional anisotropy in theorizontal plane).

Geoscientific evidence was already revealing a complex patternf anisotropy at Wairakei (Section 4.1). Kriging temperatures at z = 0eters below sea level (approximately 450 mGL; Fig. 10), obtained

nder the assumption of isotropic horizontal variance (as in Eq.7)), provide further insight into what anisotropy patterns look like.igh temperature regions of Wairakei tend to concentrate alongE-trending (e.g., Te Mihi area) and NW-trending directions (East-rn Bore Field). Strictly speaking, temperature data at Wairakei areharacterized by two directions of maximum correlation which areutually perpendicular (at the depth of ca. 450 m). Whether it is

n isotropic thermal structure or a thermal structure with morehan one direction of correlation, these scenarios are potentiallyndistinguishable in variogram analysis (Fig. 4). Following thesebservations, the isotropic model of variance used for Kriging mod-ls of temperature is a practical approach, although it does notecessarily imply the existence of an underlying isotropic thermaltructure.


A sharp, NW-trending thermal boundary is evident to the north-ast of Wairakei, closely coinciding with the resistivity boundaryFig. 10). The close spatial correlation between thermal fea-ures from Geyser Valley (location as in Figs. 3 and 10) and the

ding from points C to D, as shown in Fig. 10. Explanations as in Fig. 11.

NW-trending boundary indicates the presence of a subvertical,peripheral leakage from the geothermal system to surface, but atthe same time a NW-trending barrier for lateral flow. The natureof the NW-trending boundary is unknown, but it is likely to put incontact permeable units (infield) and impermeable units (outfield).

Well WK401 shows a peak of 150 ◦C at ca. 400 mGL followed bya temperature inversion. This is an indication of a thermal outflowsourced from Wairakei and flowing to the south which leaks to thesurface at Karapiti thermal area (about 1 km north of WK401). It isnoted this thermal outflow is not observed in adjacent wells WK404and WK407 (immediately south-east of WK401; Figs. 3 and 10).

Figs. 11 and 12 show temperature distribution along NE- andNW-trending vertical cross sections (orientations in Fig. 10), basedon Kriging models. For comparative purposes, both Kriging (nodrift) and universal Kriging (drift) predictions are shown, for bothisotropic models, anisotropic models, and variable anisotropy (Eq.(10)) models.

The lack of a vertical drift (Figs. 11A, C, 12A and C) producesunrealistic temperature inversions at depths >2500 mGL, provid-


ing a validation for the use of a vertical drift and illustrating howinadequate geostatistical constraints can produce misleading pre-dictions. In similar lines, the most accepted conceptual model forWairakei is that Eastern Bore Field is an outflow structure sourced





Fig. 13. (A) Kriging models of stratigraphy for NE-trending cross section extending from points A to B, as shown in Fig. 10; (B) Interpreted stratigraphy and structure basedo

f2c

tE(stbIiermsso

n (A).

rom Te Mihi upflow (e.g., Bixley et al., 2009; Glover and Mroczek,009). Note the isotropic model in Fig. 12B fails to capture theonnectivity between Eastern Bore Field and Te Mihi.

Figs. 13A and 14A show Kriging models of stratigraphy forhe cross sections above (same directions as in Figs. 11 and 12).ach Kriging model is used to interpret stratigraphy and structureFigs. 13B and 14B, respectively). In this context, Kriging models oftratigraphy are not a finished product, but a guide for interpre-ation. Interpretations are primarily based on Kriging predictions,ut some assumptions are also made on the basis of gravity (Fig. 7).n particular, the large scale variations of gravity are interpretedn terms of basement depth, and these variations indicate deep-ning of the basement towards the northwest (i.e., decrease ofesidual anomalies to the northwest; Fig. 7A). Even though base-


ent is not depicted in the geological cross sections, relatively deeptratigraphic units like Waiora Formation are likely to mimic toome extent the geometry of the basement. As a result, the basef Waiora Formation is interpreted to deepen to the northwest

following the increase of negative residual anomalies (left handside of NW-trending cross section; Fig. 14B).

Figs. 13B and 14B are used to support interpretations in terms ofgeological controls on thermal discontinuities across Wairakei. Forthis purpose, Kriging models of temperature are superimposed oninterpreted geology (Figs. 15 and 16). Fig. 15 (NE-trending cross sec-tion) shows the Eastern Bore Field outflow is primarily controlledby stratigraphy, particularly, the interface between Wairakei Ign-imbrite and Waiora Formation. In this area, Waiora Valley Andesiteis also a relevant stratigraphic unit and likely to contribute tostratigraphic permeability (with permeability concentrated alongbrecciated margins). Other outflow structures are evident whichtend to follow Karapiti 2b Rhyolite and Karapiti 3 (Figs. 15 and 16).Karapiti 2b Rhyolite is a drilling target for mid-depth production


and it is interpreted that most lateral flows concentrate in the brec-ciated margins of the rhyolite. To date, it has not been conclusivelyresolved whether Karapiti 2a and 3 are different or equivalent flowunits.





F fromo

WfiptlaIwogh

Mc

ig. 14. (A) Kriging models of stratigraphy for NW-trending cross section extendingn (A).

The variations in thickness of Wairakei Ignimbrite acrossairakei, particularly at the transition from Te Mihi-Western Bore-

eld (from wells WK219 to WK212), can be explained in terms of aiecemeal caldera, as defined by Cole et al. (2005). According tohese authors, piecemeal calderas are characterized by multipleocalized collapses, leading to intra-caldera deposits of highly vari-ble thickness and irregular caldera floors. In areas where Wairakeignimbrite is completely absent (e.g., WK317 area), it is not clear

hether caldera geometry or post-Whakamaru caldera eventsbliterating Wairakei Ignimbrite are the cause of such a strati-raphic discontinuity. Whatever the case may be, Fig. 16 shows


ow puzzling deep architecture remains to be at Wairakei.Significant stratigraphic offsets occur in the vicinity of the Te

ihi upflow, which support the existence of fault zones as likelyonduits for vertical permeability (Figs. 15 and 16). Fig. 16 also

points C to D, as shown in Fig. 10; (B). Interpreted stratigraphy and structure based

portrays high temperature regions at depth in the WK317 area.Kriging models suggest a deep outflow structure which connectswith the shallower Eastern Bore Field outflow. This connection islikely to be an artifact of the Kriging predictions.

Relatively shallow (750–1000 mGL) temperatures inversionshave been found in Te Mihi, both in the WK243 area (four wellsdrilled off this pad, namely, WK243–WK246) and in WK257. Basedon Kriging predictions, temperature inversions are interpreted interms of cold inflows from steam-heated aquifers hosted at the baseof Waiora Formation, and top of rhyolites Karapiti 2b and/or Kara-piti 3, which permeate into deeper stratigraphic levels through a


combination of intra-formational permeability (dominant in theWK243 area) and faults (dominant at WK257; Fig. 16). All coldinflows are interpreted to be driven by pressure drawdown associ-ated with long-term production at Wairakei.





Fig. 15. NE-trending cross section with superposition of Kriging model of temperature (Fig. 11E) and interpreted geology (Fig. 13B).

g mod

5

tbfgcpithodtssl

Fig. 16. NW-trending cross section with superposition of Krigin

. Conclusions

In this paper multidisciplinary drill-hole datasets and cumula-ive geoscientific and reservoir knowledge from Wairaikei haveeen used to test the applicability of geostatistical techniquesor characterizing the permeability and temperature in Wairaikeieothermal reservoir. The geoscience and reservoir data provideonstraints to geostatistical models, particularly in relation to inter-retation of variograms, anisotropy and drift. The analysis has

llustrated the geothermal reservoir complexities at Wairakei inerms of temperature anisotropy, and provided a methodology toandle multiple anisotropy. Results show that kriging predictionsf temperature can realistically reflect anisotropy variations withepth from dominantly anisotropic at shallow depths (<1000 m),


o dominantly isotropic at greater depths (>3000 m). Based on geo-tatistical models, two cross sections have been presented in thistudy, which provide a new field wide understanding of the corre-ation of stratigraphy, faults, temperature, and fluid flow paths.

el of temperature (Fig. 12E) and interpreted geology (Fig. 14B).

A potential limitation of the geostatistical methods and modelspresented here is model confidence that is limited by data distri-bution. This implies interpretations carry generally low confidencein peripheral and/or deep areas, In addition, uncertainty in sourcedata (e.g., temperature artifacts; subjectivity of stratigraphic inter-pretations) is not quantifiable by Kriging.

Acknowledgements

This work was funded by VCUDF Grant No. 23278 (Universityof Auckland, New Zealand), Foundation for Research, Science andTechnology (projects PROJ-20199-GEO-GNS and UOAX0713 –University of Auckland) and Contact Energy. Thanks are extendedto Michael O’Sullivan, Angus Yeh, and Juliet Newson (Dept. of


Engineering Science, University of Auckland) for their guidancein the compilation of temperature data. We also acknowledge theNew Zealand GEONET project, and its sponsors EQC and Ministry ofScience and Innovation (formerly FRST) for providing earthquake


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8 F. Sepúlveda et al. / Geo

ata and GNS Science for providing fault (New Zealand Activeaults Database) and thermal manifestations data. Special thankslso to anonymous reviewers for their useful comments.

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