USGS Polar Temperature Logging System, Description and

USGS Polar Temperature Logging System,Description and Measurement Uncertainties

Techniques and Methods 2–E3

U.S. Department of the InteriorU.S. Geological Survey

Cover photograph: North Greenland Ice Core Project ice-coring site in central Greenland.(Photograph by Gary D. Clow, U.S. Geological Survey)

USGS Polar Temperature Logging System, Description and Measurement Uncertainties

By Gary D. Clow

Techniques and Methods 2–E3

U.S. Department of the Interior U.S. Geological Survey

U.S. Department of the Interior DIRK KEMPTHORNE, Secretary

U.S. Geological Survey Mark D. Myers, Director

U.S. Geological Survey, Reston, Virginia: 2008

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Suggested citation: Clow, Gary D., 2008, USGS Polar Temperature Logging System, Description and Measurement Uncertainties: U.S. Geological Survey Techniques and Methods 2 –E3, 24 p. Available online at: http://pubs.usgs.gov/tm/02e03

http://pubs.usgs.gov/tm/02e03

iii

Contents

Abstract 1

1 Introduction 1

2 System Description 22.1 PTLS Design Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22.2 Resistance (Temperature) Measurement System . . . . . . . . . . . . . . . . . . 3

2.2.1 Kelvin Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.2.2 Resistance Corrections . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.2.3 Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.2.4 Temperature Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.3 Depth-Measurement System . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.3.1 System Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.3.2 Depth Corrections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

3 Measurement Uncertainties 113.1 ITS-90 Temperature Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . 11

3.1.1 Resistance Readout Uncertainties . . . . . . . . . . . . . . . . . . . . . . 113.1.2 Kelvin Circuit Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . 123.1.3 Temperature-Sensor Calibration Uncertainties . . . . . . . . . . . . . . . 133.1.4 Combined ITS-90 Temperature Uncertainties . . . . . . . . . . . . . . . 16

3.2 Relative Temperature Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . 173.3 Depth Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183.4 Example: Proposed WAIS Divide Borehole, Antarctica . . . . . . . . . . . . . . 20

4 Summary 22

Appendix: Nomenclature 23

References 24

iv

Figures

1 Primary PTLS components . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 Kelvin resistance circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 Resistance corrections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 Raw noise, example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 Temperature-sensor design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 αT values for various probe series . . . . . . . . . . . . . . . . . . . . . . . . . 87 Temperature-sensor calibration data, example . . . . . . . . . . . . . . . . . . 88 Temperature resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 Force-dependent function F(Z), example . . . . . . . . . . . . . . . . . . . . 1010 Resistance correction uncertainties . . . . . . . . . . . . . . . . . . . . . . . . 1411 Temperature-sensor calibration uncertainties . . . . . . . . . . . . . . . . . . 1512 Damping of calibration bath’s temperature fluctuations . . . . . . . . . . . . 1613 Combined ITS-90 temperature measurement uncertainty . . . . . . . . . . . . 1714 Combined relative temperature measurement uncertainty . . . . . . . . . . . 1815 Example: Temperature uncertainties, WAIS Divide borehole . . . . . . . . . . 2016 Example: Depth uncertainties, WAIS Divide borehole . . . . . . . . . . . . . 21

Tables

1 PTLS specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

USGS Polar Temperature Logging System,Description and Measurement Uncertainties

By Gary D. Clow

Abstract

This paper provides an updated technical descrip-tion of the USGS Polar Temperature Logging System(PTLS) and a complete assessment of the measurementuncertainties. This measurement system is used to ac-quire subsurface temperature data for climate-changedetection in the polar regions and for reconstructingpast climate changes using the “borehole paleother-mometry” inverse method. Specifically designed forpolar conditions, the PTLS can measure temperaturesas low as −60 Celsius with a sensitivity ranging from0.02 to 0.19 millikelvin (mK). A modular design allowsthe PTLS to reach depths as great as 4.5 kilometerswith a skid-mounted winch unit or 650 meters witha small helicopter-transportable unit. The standarduncertainty (uT ) of the ITS-90 temperature measure-ments obtained with the current PTLS range from3.0 mK at −60 Celsius to 3.3 mK at 0 Celsius.Relative temperature measurements used for boreholepaleothermometry have a standard uncertainty (ur

T )whose upper limit ranges from 1.6 mK at −60 Cel-sius to 2.0 mK at 0 Celsius. The uncertainty of atemperature sensor’s depth during a log depends onspecific borehole conditions and the temperature nearthe winch and thus must be treated on a case-by-casebasis. However, recent experience indicates that whenlogging conditions are favorable, the 4.5-kilometer sys-tem is capable of producing depths with a standarduncertainty (uZ) on the order of 200–250 parts permillion.

1 Introduction

In 1993, the U.S. Geological Survey (USGS) begandeveloping a new borehole temperature logging systemspecifically to address emerging climate issues in thepolar regions. This system, referred to as the USGSPolar Temperature Logging System (PTLS), has two

primary functions. (1) Periodically obtain subsurfacetemperature data from arrays of polar boreholes forclimate-change detection. Monitoring data acquiredby the PTLS in northern Alaska contributes to theGlobal Climate Observing System (GCOS) throughthe Global Terrestrial Network for Permafrost (GTN–P). (2) Acquire data for the reconstruction of pastclimate changes in the polar regions using “boreholepaleothermometry.” Climate reconstructions derivedfrom borehole temperature measurements are hinderedby considerable temporal smearing due to heat dif-fusion processes. While it cannot be eliminated, theextent of the temporal averaging can be minimizedthrough optimal experimental design. Application ofBackus-Gilbert inverse methods to the paleoclimatereconstruction problem shows that our ability to re-solve past climatic events can be optimized by reducingthe uncertainty in the temperature measurements tono more than 0.1 percent of the paleoclimate signalwe are attempting to detect (Clow, 1992). In mostplaces on Earth, surface-temperature changes duringthe Holocene were on the order of ±1 K. Thus toenhance our ability to resolve past climate events ofthis magnitude, it is desirable to reduce the uncer-tainty of the borehole temperature measurements toabout 1 mK. Paleoclimate reconstruction has beenthe primary driver for the design requirements of thePTLS since its requirements are much more stringentthan those needed for detecting contemporary climatechange.

The objectives of this paper are to provide an up-dated technical description of the PTLS logging systemand an analysis of the measurement uncertainties. Thissystem and its uncertainties were originally describedby Clow and others (1996). However, the PTLS isa continually evolving system, warranting an updateddescription. In addition, calibration facilities and pro-cedures have changed significantly since 1996. Thecurrent paper provides a much more complete analysis

2 USGS Polar Temperature Logging System

of the measurement uncertainties than was possiblein Clow and others (1996). The need for such ananalysis is twofold: (1) The usefulness of scientific dataproduced by monitoring systems critically depends onthe availability of thorough uncertainty analyses. Thisis particularly true of climate-monitoring systems. (2)To reconstruct past climate changes using boreholepaleothermometry, one needs to know the uncertaintiesof the data. This requirement, shared by all geophysi-cal inverse techniques (Parker, 1994), determines thevery structure of the derived climate histories. Inconformance with ISO standards (ISO, 1993a; ISO,1993b), we use the CIPM1 approach for expressing andevaluating the measurement uncertainties of the PTLS.

2 System Description

2.1 PTLS Design Overview

A variety of system designs presently (2008) areused to measure temperatures in geophysical boreholes.Most systems use either a temperature-dependent re-sistive element (thermistor or RTD) or a piezoelec-tric crystal whose resonant frequency is temperature-sensitive for the sensing element. In the former case,the resistance of the sensing element is measured bya custom-built electronic bridge or by a commercialresistance readout. An advantage of a custom bridgeis that it can be made small enough to be included in aninstrument package located at the downhole end of thelogging cable, keeping the electronic lead lengths to thesensor relatively short. Such a package can be designedto measure several other parameters as well, such asfluid pressure and borehole inclination, and the result-ing data either stored within the instrument packageor digitally transmitted to the surface. A significantdisadvantage of this approach for precision thermom-etry is the difficulty of maintaining the calibrationof the electronic bridge while the instrument packageexperiences temperature changes of 10–30 K duringthe course of a logging experiment. The associatedcalibration drift of the bridge can produce temperaturemeasurement errors of 10 mK, or more. Application ofnew technologies may substantially reduce these errors,making high-precision downhole digital thermometerspossible in the near future. The current alternativeis to locate the resistance-measuring circuitry on thesurface. The advantages of this strategy are: (1)a high-quality commercial resistance readout can be

1International Committee for Weights and Measures.

utilized for the measuring circuitry instead of having todevelop custom miniaturized circuits, (2) the readoutcan be maintained at a constant temperature, elimi-nating temperature-related drift in the measurementcircuit, and (3) the calibration of the readout canbe periodically rechecked while measurements are inprogress. However, the long lead lengths between theresistance readout and the sensor, potentially up to10 km, make the measurements vulnerable to severalsources of instrumental error. Great care must beexercised to minimize these errors. Logging systemswith a downhole electronic bridge generally acquiretemperature measurements while lowering the sensordownhole at a constant speed (“continuous” logging).Another common technique is to acquire data with theprobe stopped at a fixed depth; repeating this processat multiple depths yields an incremental or “stop-and-go” temperature log. Systems with the resistance-measuring circuitry on the surface are sometimes lim-ited to this mode. Although incremental logging yieldsmeasurements at a limited number of depths, thesemeasurements are free of the “slip-ring” noise (seeSection 2.2) inherent to continuous temperature logsobtained with surface measurement circuitry.

Considering the advantages and disadvantages ofvarious system designs along with our scientific ob-jectives, the following requirements were establishedfor the Polar Temperature Logging System: the sys-tem must be modular and flexible so it can use avariety of sensors, can make measurements using ei-ther downhole or surface measurement circuitry, canbe operated in either the continuous or incrementallogging modes, and can utilize different length log-ging cables depending on borehole depth and avail-able logistics. In addition, the system must be ableto measure temperatures as low as −60C with anuncertainty of about 1 mK, reach depths comparableto the maximum thickness of the polar ice sheets (4–5 km), work in the presence of strong environmentalnoise (for example, changing electrostatic fields), andbe rugged enough to survive offloading from militarycargo aircraft. The PTLS evolved from a numberof refinements to a conventional temperature loggingsystem design, thereby avoiding the need to build aradically new system. This approach took advan-tage of the USGS’ considerable experience in bore-hole thermometry. Negative-temperature-coefficient(NTC) hermetically sealed thermistors were selectedfor the primary temperature sensors because of theirruggedness, stability, and high temperature coefficient,which helps produce a high system sensitivity. A

System Description 3

Temperature sensor

Depth counter

Resistance readout

Faraday cageLogging winch

Slip-ring connector

Precision measuring wheel

Logging cable

Computer

Figure 1. Layout of the USGS Polar Temperature Logging System when using surface measurement circuitry.

commercial resistance readout located on the surface sources of electrical noise.is normally used for the resistance-measuring circuitry. The three fundamental measurements made by theThis circuitry is suspended inside a Faraday cage main- PTLS are the sensor resistance, sensor depth, and timetained at 23 ± 0.5C for the duration of an experi- of data acquisition. For the time measurements, wement; thermal stability is provided by microprocessor- simply rely on the computer’s onboard clock. Thecontrolled etched-foil heaters. As an alternative to resistance and depth measurements are more involvedsurface measurement circuitry, a prototype downhole and are described in detail in the following sections.digital thermometer utilizing NTC thermistors has Resistance measurements are subsequently convertedbeen used with the PTLS. However, this device is still to temperature using a 4-term conversion function.in the testing phase and will not be discussed furtherhere. Other major system components include a 4-conductor logging cable mounted on a motorized winch 2.2 Resistance (Temperature)(fig. 1). Two different size winches are currently avail- Measurement Systemable: a small helicopter-transportable unit with 650 mof cable, and a much larger skid-mounted unit capable 2.2.1 Kelvin Circuitof reaching 4.5 km. A “slip-ring” assembly provides

To measure the resistance, a Kelvin (4-wire) cir-electrical continuity between the logging cable and thecuit is used in both the downhole and the surfacesurface electronics. Depth information is provided bymeasurement-circuitry configurations (fig. 2). Duringan optical encoder mounted on a calibrated measuringthis measurement, the resistance readout produces awheel. A laptop computer controls the system, bothhighly regulated current (displaying and storing the Is) that passes through themeasured resistance, depth,sensor. The resulting voltage drop (∆ ) across thetime, and logging speed. Cable tension provided by a Vprobe is detected by the readout’s high-impedancestrain-gage force transducer is displayed on a separateinputs, and the probe’s resistance calculated frommonitor. To minimize electrical noise, all componentsRs = ∆V/Is. This 4-wire measurement eliminates theare powered by DC batteries except for the wincheffect of the lead resistance ( ) along each conductormotors. The Faraday cage surrounding the resistance RL

between the resistance readout and the temperaturereadout, used in conjunction with cable shielding, helpssensor. There are, however, several sources of system-isolate the measurement circuitry from the remainingatic error that potentially require correction.


Thermistor probe

4 - Conductor logging cable

Slip-ring assembly

Resistance readout

!"

Is

HI

LO

!#

!#

!#

!#

$

%

&

'

Figure 2. Kelvin (4-wire) resistance circuit used by thePTLS when the measurement circuitry is located on thesurface. The test current Is passes through lines 1 and2 while the voltage drop across Rs is measured using thesense lines (3, 4). With downhole circuitry, an electronicbridge is connected directly to the probe.

2.2.2 Resistance Corrections

Leakage paths between the conductors of the Kelvincircuit can produce significant systematic error, par-ticularly when the probe resistance Rs is large. Suchunintended paths arise due to leakage currents passingdirectly through the conductor insulation, moistureabsorption by the insulation, or leakage due to con-taminants on the surface of the insulation or connec-tors. Leakage currents between the circuit’s sense linesor between the current-carrying lines will reduce themeasured resistance by

δRl =R2

s

Rs + Rl(1)

where Rl is the leakage resistance. Teflon is usedfor the Kelvin circuit insulation because of its highvolume resistivity (greater than 1016 Ω·m), low waterabsorption, and a surface that tends to repel manyfilms. This problem is further controlled by rigorouslycleaning the connectors and by using a sensor with alow resistance Rs. Part of our logging protocol is tomeasure the resistance Rl between each pair of con-ductors immediately before each logging experiment.If Rl is less than 10 GΩ for any pair of conductors,the log is aborted until the problem is rectified. Rl isgreater than 20 GΩ for nearly all logging experimentsconducted with the PTLS.

A capacitor is occasionally introduced between thereadout’s sense lines to perform high-frequency noisefiltering. This also delays the response of the circuit sothat the measured resistance is too low by

δRc = τ∂Rs

∂t. (2)

τ = RsC is the circuit’s natural response time whereC is the capacitance. If a filtering capacitor is used,the resistance offset δRc is controlled by keeping τsmall relative to the measurement integration time ofthe resistance readout and by using a slow loggingspeed v so that the rate of resistance change ∂Rs/∂t =v αT Rs (∂T/∂z) is also small; αT is the sensor’s tem-perature coefficient of resistance (αT ≡ R−1

s ∂Rs/∂T ).With typical logging speeds (2.5–5.5 cm·s−1) and tem-perature gradients (∂T/∂z ≤ 50 mK·m−1), the mostrapid resistance changes are on the order of 10−4Rs

per second. Without the filtering capacitor, C is de-termined by the capacitance of the logging cable (76 nFfor the 650-m “short” cables and 0.68 µF for the 4,600-m “long” cable).

As the current Is passes through the temperaturesensor, power dissipates within the probe at a rate P =I2s Rs. This warms the probe, effectively reducing its

resistance byα

= T ( 2IsRs)δRh (3)Pd

where Pd is the probe’s power dissipation constant.The best strategy for minimizing self-heating is to usea resistance readout with a small source current Is anda probe with a relatively low resistance. The sourcecurrent for the resistance readout used with the PTLSis ≤ 10 µA.

To provide modularity, the Kelvin circuit consistsof a number of components attached to one anotherusing high-quality electrical connectors (fig. 2). Differ-ent portions of the circuit operate at vastly differenttemperatures with the sensor-end of the circuit oftenbeing 30–70 K colder than the resistance readout.This situation has the potential to generate significantthermoelectric voltages (thermal EMFs) between elec-trical junctions separating dissimilar metals throughthe Seebeck effect (McGee, 1988). The sum of thethermal EMFs can be found by integrating the Seebeckcoefficient Q around the entire circuit, starting andending at the resistance readout’s HI and LO senseconnections (junctions a1 and a2),

Vemf = −∫ a2

Q(T ) dT. (4)a1

Q depends primarily on metal composition and secon-darily on temperature. If the metal compositions onthe HI side of the circuit exactly match those on theLO side, the total thermal EMF can be expressed by


Vemf = −∫ b1

a1

QA(T ) dT −∫ c1

b1

QB(T ) dT − · · ·

−b2

c2

QB(T ) dT −a2

b2

QA(T ) dT (5)

∫ ∫

where subscripts 1 and 2 refer to the HI and LO sides ofthe circuit, respectively; QA is the Seebeck coefficientfor the metal conductor between junctions a1 and b1

(and between a2 and b2), QB is the coefficient forthe metal between junctions b1 and c1, and so forth.Equation (5) can be rewritten in terms of the adjacentjunction pairs on the HI and LO sides of the circuit(for example, a1 and a2),

Vemf =∫ a1

a2

QA(T ) dT +∫ b2

b1

QA(T ) dT

+

[∫ b1

b2

QB(T ) dT +∫ c2

c1

QB(T ) dT

]+ · · · . (6)

[ ]

If the temperature difference between adjacent junc-tion pairs is small enough that the temperature de-pendence of the Seebeck coefficient can be ignored,equation (6) reduces to

Vemf = −QA(Ta2 − Ta1) + (QA − QB)(Tb2 − Tb1)

+ (QB − QC)(Tc2 − Tc1) + · · · . (7)

Thus, thermal EMFs can be controlled by mini-mizing the temperature difference between adjacentjunction pairs. Based on this analysis, we use anumber of strategies to minimize thermal EMFs inthe PTLS’ Kelvin circuit: (1) The use of dissimi-lar metals is kept to a minimum. Except for thejunctions themselves, the circuit paths consist almostentirely of copper or silver-plated copper. (2) Wherea dissimilar metal occurs on the HI side of the cir-cuit, the metal is matched with an identical metalat the corresponding location on the LO side. (3)The temperature difference between adjacent junctionpairs is minimized. This is accomplished by locatingthe junctions of an adjacent pair as close together aspossible, locating junction pairs within the thermallycontrolled Faraday cage where thermal gradients arevery small, and (or) by locating junction pairs withinhigh-conductivity metal shells where temperature gra-dients are also small. Before every experiment, theresistance readout is warmed up for at least an hourto minimize thermal EMFs within the readout itself.Considering the estimated temperature differences at

the adjacent junction pairs and the values of the See-beck coefficients, the total thermal EMF for the Kelvincircuit is estimated to be on the order of 0.5µV withthe dominant sources occurring at the slip-ring assem-bly. Current-reversal experiments with both the 650-mlogging cables and the 4,600-m cable confirm that Vemf

is typically ≤ 0.5µV. This voltage offset increases themeasured resistance by

δRe =Vemf

Is. (8)

In 2008, the simple constant-current source that thePTLS had used was changed to a reversing source.This allowed us to switch to a current-reversal tech-nique where a “resistance measurement” is found byaveraging two measurements made with currents ofopposite polarity. With this approach, the thermalEMFs produced during each polarity completely cancelout so that δRe = 0.

The first three systematic errors (δRl, δRc, δRh)can be controlled by using a sensor with a relativelysmall resistance. However, an additional constraintimposed by the resistance readout is that Rs mustbe much greater than the lead resistance RL for eachleg of the Kelvin circuit in order to make an accurateresistance measurement. At a minimum, Rs shouldbe at least 20 times RL. Other factors that helpcontrol the systematic errors are a small capacitanceC, a slow logging speed v, a small source current Is,carefully matching the composition of the wires, andkeeping the temperature difference between adjacentjunction pairs as small as possible. Despite effortsto control leakage paths, the capacitance effect, self-heating, and thermal EMFs, small systematic errorswill remain. We attempt to eliminate these errors byapplying equations (1) – (3) and (8) as corrections tothe resistance Rs recorded by the resistance readout toobtain our estimate of the temperature sensor’s trueresistance,

Rs = Rs + (δRl + δRc + δRh δRe). (9)−

Figure 3 shows the magnitude of the resistance correc-tions for the PTLS under typical operating conditions.Expressed in terms of temperature, the correctionsare generally limited to 0.1–0.2 mK. The uncertaintyof these systematic error corrections is discussed inSection 3.1.2.

2.2.3 Noise

Several sources of noise also perturb the resistancemeasurements when the measurement circuitry is lo-


101 10210!3

10!2

10!1

100

Rs (kΩ)

δR(Ω

)

δRl

δRc

δRh

σRn

Figure 3. Magnitude of the resistance correctionsδRl, δRc, δRh under typical operating conditions; δRe isessentially zero with the current PTLS design. In thisexample, the capacitance correction δRc assumes a loggingspeed of 5.5 centimeters per second, a temperature gradientof 25 millikelvins per meter, and a capacitance C such thatτ = 10 milliseconds. Equivalent temperature correctionsare given by ∆Tx = δRx/(αT Rs). Also shown is the ap-proximate standard deviation σRn of the raw noise (eq. 10)generated in the Kelvin circuit under typical conditions.

cated on the surface. These sources include electro-static coupling, electromagnetic EMFs, triboelectriceffects, and switching effects. Depending on the source,the noise generated within the circuit consists eitherof extraneous voltages V ′ or extraneous currents I ′.The resistance readout internally converts the extra-neous voltages into an apparent resistance noise, R′ =(V ′/Is), while the extraneous currents are convertedto R′ = Rs(I ′/Is). In the latter case, the apparentresistance noise increases in direct proportion to thetemperature sensor’s resistance.

Individual noise components: Electrostatic cou-pling occurs when an electrically charged object suchas the system operator, moves near the Kelvin cir-cuit, generating currents in the conductors. In polarenvironments, significant electrostatic interference canalso be caused by electric charges transferred to thesheath of the logging cable by dry, blowing snow. Elec-tromagnetic voltages (EMFs) are generated when achanging magnetic field passes through the conductiveloop represented by the Kelvin circuit, or when some

portion of the conductive loop (for example, the loggingcable) moves relative to a magnetic field. For thePTLS, nearby AC fields, winch motors, and the Earth’smagnetic field are potential sources of electromagneticvoltages. We use several strategies to mitigate thenoise generated by electrostatic coupling and electro-magnetic EMFs:

(1) Once a temperature log is initiated, the systemruns in an automated mode, allowing the systemoperator to remain an adequate distance from theKelvin circuit.

(2) The entire system is shielded from the wind andblowing snow as much as possible by operating itinside an insulated shelter. The Faraday cage andassociated electronics are always operated withina protective shelter. If the wellhead cannot alsobe located inside the shelter, the shelter is placedas close as possible to the wellhead to minimizethe amount of exposed logging cable.

(3) To minimize AC power fields, all system compo-nents are powered by DC batteries except for thewinch motors.

(4) The most sensitive portions of the Kelvin circuit,especially the resistance readout, are kept as faras possible from the winch motors.

(5) All movement around the Kelvin circuit is kept toa minimum during a temperature log.

(6) The loop area of the circuit is minimized by usingtwisted-wire cables.

(7) The resistance readout is electrically shielded in-side a Faraday cage. All the cables are also elec-trically shielded.

Given these noise-reduction strategies, the domi-nant sources of noise for the PTLS are believed to bedue to switching effects within the electromechanical“slip-ring” assembly and to the triboelectric effect.Triboelectric currents arise from charges generated be-tween the insulation and conductors of the loggingcable as it flexes over the sheave wheels that guideit into a borehole. Triboelectric currents can alsooccur when the logging cable vibrates in the wind.We manage the triboelectric currents by providing asmooth path into the borehole, logging downhole at aslow steady pace with negligible accelerations, and bykeeping the logging cable shielded from strong windsas much as possible. The slip-ring noise is controlledby using high-quality slip-rings.


The internal noise of the resistance readout alsocontributes a small amount of noise to the recordedresistances, as does the truncation error associatedwith the instrument’s finite resistance resolution ∆Rr.Combining the readout noise with that due to theextraneous voltages and currents generated within theKelvin circuit, the standard deviation of the noise inthe resistance measurements is given by

σRn =

[(a∆Rr)

2 +(

V ′

Is

)2

+(

RsI ′

Is

)2]1/2

. (10)

Although the noise varies between temperature logs,depending on circumstances, the constants in equa-tion (10) are generally on the order of a ≈ 0.33,V ′ ≈ 4 µV, and I ′ ≈ 0.14 nA for the PTLS under mostconditions. Extraneous voltages dominate the noise forprobe resistances less than 20 kΩ while extraneous cur-rents dominate when Rs > 40 kΩ (fig. 3); the readout’scontribution is relatively small at all resistances. Theraw noise described by equation (10) can be substan-tially reduced by judiciously applying the resistancereadout’s internal filters or by installing a filteringcapacitor between the circuit’s sense lines. When thesehardware noise filters are used, the noise σRn

actuallypresent in the recorded resistances is less than σRn .The remaining noise is largely removed during dataprocessing by using wavelet denoising techniques.

2.2.4 Temperature Sensors

Equations (1) – (3) show that the temperature sen-sor is an important factor in determining the character-istics of the overall measurement system. The primarysensors used with the PTLS consist of a parallel-seriesnetwork of 15 negative-temperature-coefficient (NTC)thermistors divided into three packets.2 Each packet ishermetically sealed in glass (fig. 5) to prevent changesin the oxidation state of the metal oxide thermistorsand to relieve strain where the leads are attached tothe ceramic body of the thermistors. As a result, theprobes have good long-term stability with typical driftrates of ≤ 0.025 percent per year. The packets arewired in parallel so that only one third of the resis-tance readout’s excitation current Is passes throughany given thermistor bead, minimizing the self-heatingeffect. To improve the ruggedness of the design, the

2A similar design appropriate for temperatures at midlati-tudes is described by Sass and others (1971). The midlatitudeversion has a much higher resistance than the polar model andcontains 20 thermistors divided into two packets.

0 2 4 6 8 10 12!3

!2

!1

0

1

2

3

SAMPLE NUMBER (×103)

NO

ISE

(Ω)

GISP2!D

Figure 4. Raw noise for a typical logging experiment.This record was acquired from the nonconvecting portionof the GISP2-D borehole (central Greenland) without theuse of hardware noise filters. In this example, the stan-dard deviation of the noise was σRn = 0.40Ω with sensorresistances Rs ranging from 11.9 to 12.7 kΩ.

thermistor packets are completely enclosed in a 4.0-mm-diameter stainless-steel shell, allowing the probesto withstand the pressures encountered at 7–8 kmin liquid-filled boreholes and the effects of corrosivechemicals such as n-butyl acetate (many of the deepboreholes drilled by the United States polar programsare filled with n-butyl acetate). The use of manysmall thermistor beads, glass encapsulation, and ahigh-conductivity steel shell all help to produce a highpower-dissipation constant Pd. The Pd-value for thesecustom probes is 55 mW·K−1 in circulating xyleneand is believed to be similar when logging through n-butyl acetate while the αT values range from about−0.045 K−1 at 0C to −0.065 K−1 at −60C (fig. 6).An inevitable disadvantage of this probe design is therelatively slow response time. In n-butyl acetate, themeasured time constant is about 7 seconds. Five seriesof custom probes, each with a different 0C resistance,are currently available to optimize the characteristicsof the PTLS for any given experiment.

To convert sensor resistance to temperature, we usethe 4-term calibration function

T−1 = a0 + a1(lnRs) + a2(lnRs)2 + a3(lnRs)3 (11)

where the constants ai are determined for each sensor


glass envelope

thermistor bead

stainless-steel shell

Figure 5. PTLS temperature sensor. The sensor consistsof a parallel-series network of 15 small bead thermistorsdivided into three sealed packets. Beads extend overa 10-centimeter length within the 4-millimeter-diameterstainless-steel shell. The resistance readout measures thecombined resistance of the parallel-series network.

!50 !40 !30 !20 !10 0!0.065

!0.06

!0.055

!0.05

!0.045

!0.04

T (C)

αT

(K−

1)

T02

T01

P

Figure 6. Temperature coefficient of resistance (αT ) forthe P, T01, and T02 probe series used with the PolarTemperature Logging System. These probe series have anominal resistance of 27 kΩ, 3.7 kΩ, and 2.5 kΩ at 0C,respectively.

just before every field season in our thermal calibrationfacility, and T is expressed in Kelvin. Equation (11) isan extension of the often-used 3-term Steinhart-Hartequation (Steinhart and Hart, 1968), which provesinadequate for our purposes. An F -test (for example,Bevington, 1969) demonstrates that a much better fitto our calibration data can be obtained with the 4-termfunction than with the standard Steinhart-Hart equa-tion, particularly at temperatures below 0C. Sampletemperature-calibration data and the resulting 4-termcalibration fit (eq. 11) are shown in figure 7.

8.4 8.6 8.8 9 9.2 9.4 9.6 9.8 10 10.23.6

3.8

4

4.2

4.4 x 10!3

ln(Rs)

1/T

probe: T01!01CALdate: 05APR11coefs: 1.28652374e!03

3.01794892e!04!4.41740779e!063.43578394e!07

(a)

!45 !40 !35 !30 !25 !20 !15 !10 !5 0!1

!0.5

0

0.5

1

T (C)

∆T

(mK

) ! = 0.153 (mK) (b)

Figure 7. Sample calibration data for one of the tempera-ture sensors (T01-01) along with the best 4-term Steinhart-Hart fit to the data (a). In this case, residuals from thefit to the calibration data have a standard deviation of0.153 millikelvin (b).

The temperature resolution of the Kelvin circuit,

∆Tr ≈ ∆Rr

αT Rs(12)

depends on the ratio of the smallest resistance re-solvable by the resistance readout ∆Rr to the proberesistance Rs. Thus, to achieve sub-mK sensitivity,∆Rr/Rs must be less than 5 x 10−5. For the resistancereadout currently used with the PTLS, the ∆Rr/Rs

ratio ranges from 1.0 x 10−5 (worst case) to 1.0 x 10−6

(best case). The resulting temperature resolution isless than 0.2 mK under all conditions (fig. 8). With theresistance readout used prior to 2008, ∆Tr ranged from0.1 to 1.1 mK; by judicious selection of the temperatureprobe for pre-2008 logging experiments, the resolutioncould almost always be reduced to less than 0.6 mK.

2.3 Depth-Measurement System

2.3.1 System Description

Depth information is obtained by measuring theangular rotation dθ of a precision measuring wheel lo-cated within the winch assembly (fig. 1) that is pressedtightly against the logging cable. Wheel rotation isdetected by an optical shaft encoder that transmitsquadrature waveforms to a bidirectional counter. Thecounter then converts angular rotation to distance (ordepth) using dz = (Rw+r) dθ, where r and Rw are the


!60 !50 !40 !30 !20 !10 0 100

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

T (C)

∆T

r(m

K)

P

T01

T02

Figure 8. Temperature resolution of the current PTLSwhen using the P, T01, and T02 probe series.

radii of the logging cable and measuring wheel, respec-tively. The fundamental limit of the depth resolutionis determined by the effective radius of the measuringsystem (Rw + r) and the number of quadrature pulsesoutput per revolution by the optical encoder. For the4.5-km system, this limit is 0.254 cm. An additionallimitation is imposed by the depth counter. For the 6-digit counter currently used with the PTLS, the depthresolution ∆zr is 1.0 cm over the system’s full depthrange, although it can be set to ∆zr = 0.30 cm whencollecting depth-calibration data. Before 2007, ∆zr

was 0.3 cm for boreholes less than 545 m deep and3.0 cm for deeper holes due to the limited buffer sizeof the bidirectional counter used at that time.

2.3.2 Depth Corrections

To account for the force-dependent strains affect-ing the depth-measuring system, a depth-calibrationfunction Cd is established for each unique loggingenvironment. This is done by moving the loggingcable downhole approximately 40 m and comparingthe distance L reported by the depth counter with thedistance L measured by a fiberglass surveying tape thathas a low temperature coefficient of thermal expansion(9.3 x 10−6 K−1); L is taken to be a measure of the

“true” distance. Cd is then defined by

Cd(Z) ≡ L(Z)˜(Z)

− 1 (13)L

where Z is the depth of the sensor-end of the cable(according to the counter) when the (L, L)-data arecollected. Depth-calibration data are acquired withthe sensor-end of the cable at multiple depths Zi span-ning as much of a borehole’s depth range as possible.Temperature changes in the measuring wheel and inthe test section of logging cable also affect the cal-ibration data. Although we attempt to maintain aconsistent temperature during the calibration period,temperature changes do sometimes occur. To removethe temperature effects, we define thermally correctedCd values by

Cd(T !w, Zi) = Cd(Twi , Zi) − Rw

RnewrTw

−(

r

Rn

)ecrTw − αfT (T !w − Twi) (14)

( )

where T !w is a reference calibration temperature andTwi is the temperature at the measuring wheel whenthe sensor-end of the cable is at Zi. The second andthird terms on the right-handside of equation (14) ac-count for changes in the effective radius of the measur-ing system due to thermal strains while the fourth termaccounts for the thermally induced longitudinal strainin the cable as it enters the relatively cold, air-filledportion of the borehole. Assuming the temperature ofthe cable is approximately Twi when passing over themeasuring wheel, the radial strains in the wheel andcable (ewrTw , ecrTw ) are both given by

exrTw =1 + β(Twi − T !w)1 + α(Twi − T !w)

− 1 (15)

√

where α and β are the linear and volumetric coeffi-cients of thermal expansion. Our measuring wheels areisotropic disks so that β = 3α. Factor Rn = m/∆θr

is the nominal radius used by the depth counter wherem is the counter’s internal multiplier and ∆θr is theencoder’s angular resolution. Parameter fT is thefraction of the temperature difference Twi − T (h) ex-perienced by the cable during a calibration test whereT (h) is the temperature at the bottom of the air-filledportion of the borehole; fT is typically about 0.3.

Once the thermally corrected Cd values have beendetermined, a least-squares fit is made to

F(Zi) = Cd(T !w, Zi) − Cd(T !w, Z!) (16)


where Z! is a reference calibration depth selected fromone of the Zi values near the middle of the depthrange; reference temperature T !w is generally taken tobe the Twi value for the calibration data acquired atZi = Z!. The depth-calibration function is then givenby the sum of the reference Cd-value and the experi-mentally determined function F(Z), which isolates theforce-dependent effects of the depth-measuring systemrelative to C !

d(Tw, Z!),

Cd(T !w, Z) = Cd(T !w, Z!) + F(Z). (17)

Figure 9 shows an example F(Z) determined fromdepth-calibration data acquired in the 1-km-deep SipleDome A borehole in West Antarctica.

200 400 600 800 1000!5

!4

!3

!2

!1

0

1

2

3

4

5 x 10!3

Z (m)

F(Z

)

Figure 9. Least-squares fit to F(Zi) values determinedfrom depth-calibration data acquired in the Siple Dome Aborehole, West Antarctica. Dashed lines indicate the un-certainty (±1σ) of the least-squares fit.

With the availability of the F(Z) and Cd(T !w, Z)functions, the total length of cable spooled into aborehole during a logging experiment can be foundby integrating the distances dz reported by the depthcounter weighted by the depth-calibration function,

Z ≈Z

o1 + Cd(T !w, Z − z) dz. (18)

∫ [ ]

Substituting from equation (17) and letting

δZF =∫ Z

oF(Z − z) dz (19)

be the correction for the force-dependent effects, thelength Z becomes

Z ≈[1 + C (T !d Zw, !)

]Z + δZF . (20)

This estimate accounts for most of the tension-inducedradial and longitudinal strains within the logging cableand mechanical strains in the logging winch. However,a number of additional corrections must be made toobtain an estimate of the true sensor depth duringa logging experiment. These include a correction forthe buoyancy of the logging tool when immersed inthe borehole fluid, for temperature changes near themeasuring wheel affecting the radius of the depth-measuring system, and for thermal strain in the cableas it moves downhole.

The correction for tool buoyancy consists of a sim-ple offset that occurs when the logging tool enters theborehole fluid:

δZbtclF =

0

K

Z < h

g (mft − ma

t )(h +∆x), Z > h(21)

K is the elastic stretch coefficient of the cable, g is thegravitational acceleration, mf

t and mat are the weights

of the logging tool in the borehole fluid and in air, h isthe depth to the air/fluid interface in the borehole, and∆x is the horizontal distance between the measuringwheel and the hole. When logging with any of ourtemperature sensors, δZbt

clF is less than the resolution ofthe depth system and can be ignored. However, othertools for which δZbt

clF may be larger (for example, sonicand optical loggers) are occasionally used with ourlogging winch, so we include the buoyancy correctionfor completeness.

The temperature of the measuring wheel during alogging experiment can be significantly different fromthe reference calibration temperature T !w. If the tem-perature of the wheel is Tw, the radial strain ewrTw

in the wheel relative to its calibration state can befound from equation (15). Since Tw may vary consid-erably during a long logging run, the correction for thethermally induced radial change of the wheel is foundthrough an integration:

δZwrT =Rw

Rn

Z

oewrTw(z) dz. (22)

( ) ∫

The corresponding thermally induced radial strain inthe cable near the measuring wheel has a negligibleeffect (< 10 parts per million [ppm]) on the estimateddepths and can be ignored.

Measurement Uncertainties 11

In polar environments, the fluid and overlying aircolumn in a borehole are typically much colder thanconditions on the surface near the logging winch. Thus,the logging cable will contract as it moves beyond themeasuring wheel and enters the borehole. By the timea section of cable reaches depth z, it will experience athermally induced longitudinal strain,

eclT (z) = α [T (z) − Tw] , (23)

relative to its length when it passed over the measuringwheel. Some of this strain is built into the depth-calibration function Cd. Subtracting this portion, thecorrection for the thermally induced longitudinal strainin the cable is

δZclT =Z

heclT (z) dz − αfT [ T (h) − T !w]Z. (24)

∫

Applying these corrections to equation (20), ourestimate of the true sensor depth during a loggingexperiment is

Z = 1 + Cd(T !w, Z!) Z + δZF + δZbtclF

+ δZwrT + δZclT . (25)

[ ]

For most situations, δZF is the largest correction andδZclT is the second largest.

3 Measurement Uncertainties

A variety of factors influence the uncertainty ofthe quantities being measured by the PTLS. For thetemperature-measurement process, the primary un-certainties include those related to the PTLS resis-tance readout, uncertainties in the corrections made forsystematic errors in the Kelvin circuit measurements(eqs. 1, 2, 3, 8), and uncertainties in the temperaturesensor calibration used to convert measured resistanceto temperature. The primary uncertainties for thedepth-measurement process are related to the depthcorrections (eqs. 19, 21, 22, 24).

This section provides an analysis of the measure-ment uncertainties following CIPM guidelines (ISO,1993b). It is assumed the resistance-measuring cir-cuitry is located on the surface since the PTLS is nor-mally operated in this mode; several of the uncertain-ties to be described are not present when using down-hole measurement circuitry, although the temperature-related drift of the circuit potentially can be quitelarge. With the CIPM approach, the components of

a measurand’s uncertainty are classified according tothe method used to evaluate them. Type A uncertaintyevaluations are based on statistical analysis of a seriesof observations while Type B evaluations are performed“by other means” using sound scientific judgment. Theinformation used in a Type B analysis may, for exam-ple, include a general knowledge or experience withan instrument or the behavior of a material, manu-facturer’s specifications, or calibration reports. Thedegree of uncertainty for each component is given interms of the standard uncertainty ui that describesthe interval within which a quantity should occur with67 percent probability. The combined standard un-certainty of a measurement is obtained by combiningthe individual Type A and Type B standard uncer-tainties using the propagation of uncertainty law (Tay-lor and Kuyatt, 1994, Appendix A). We implementthe propagation law using the “root-sum-of-squares”(RSS) method. Although some of the uncertainties tobe discussed are quite small with the current versionof the PTLS, they were in some cases substantiallylarger with previous PTLS versions and therefore arediscussed for completeness.

3.1 ITS-90 Temperature Uncertainties

3.1.1 Resistance Readout Uncertainties

The PTLS generally utilizes a commercial readoutto measure the resistance of a temperature sensorduring a logging experiment. Sources of uncertaintyrelated to the resistance readout include the uncer-tainty of the resistance standards used to calibratethe readout, nonlinearity across the resistance scales,and internal noise. Current field procedures requiretemperature logs be completed within 24 hours of thereadout’s latest calibration.

Resistance Standards. Immediately before eachlogging experiment, the resistance readout is calibratedusing 10 kΩ and 100 kΩ DC resistance standards(Fluke 742A), and a 0 Ω short. In preparation formaking measurements at the fixed calibration points,the readout and resistance standards are warmed upand then maintained at 23 ± 0.5C for at least onehour. Once acquired, the calibration data are used todetermine the coefficients in a quadratic function fc(R)which is used to correct the readout’s measurementsat other resistances. The uncertainties at the cali-bration points are found by combining the calibrationuncertainty of the standards themselves (0.5 ppm forthe 10-kΩ standard, 1.25 ppm for the 100-kΩ stan-dard) with the uncertainty associated with their long-


term drift (2.0 ppm·yr−1 for the 10-kΩ standard and3.0 ppm·yr−1 for the 100-kΩ standard). With annualrecalibration, the combined standard uncertainty ofthe resistance standards (in normalized form) is us,n ≡(us/Rs) = 2.1 ppm at 10 kΩ and 3.2 ppm at 100 kΩ.These uncertainties are propagated to other resistancesusing a function of the same form as fc(R).

A different set of resistance standards was usedprior to 2008. These standards were periodically cal-ibrated using an instrument with a standard uncer-tainty of 58 ppm. Long-term drift between calibrationsintroduced an additional 58 ppm of uncertainty, yield-ing a combined standard uncertainty for these olderstandards of us,n = 82 ppm at both 10 kΩ and 100 kΩ.

Resistance Readout’s Short-Term Uncer-tainty. The quoted short-term accuracy of the resis-tance readout currently used with the PTLS is ±0.25Ωfor Rs < 5 kΩ and ±50 ppm for 5 kΩ ≤ Rs ≤ 200 kΩ.This specification includes the nonlinearity of the read-out across the measurement range and internal noise.According to the manufacturer, the accuracy (±a)specifies the width of a rectangular (uniform) proba-bility distribution function; this PDF is taken to havea corresponding standard uncertainty of a/

√3 (Taylor

and Kuyatt, 1994). Thus the short-term standarduncertainty of the readout is ur = 0.14 Ω for Rs < 5 kΩand ur,n ≡ (ur/Rs) = 29 ppm for 5 kΩ ≤ Rs ≤ 200 kΩ.Before 2008, a different readout was used whose accu-racy included a component for the full-scale resistancevalue Rf . For this instrument the short-term standarduncertainty was ur,n = 11.6 + 5.8 (Rf/Rs) ppm.

Combined Resistance-Readout UncertaintyuRs

. Combining the uncertainties of the resistancestandards with the short-term accuracy of the read-out, we obtain the combined standard uncertainty uRof the resistance readout measurements. With the

s

currently used resistance standards, uRsis dominated

by the short-term uncertainty of the readout itself.Thus uR = 0.14Ω for Rs < 5 kΩ. For the morecommon

s

sensor resistances (Rs ≥ 5 kΩ), the combinedstandard uncertainty is uR ,n ≡ (uR /Rs) = 29 ppm.Prior to 2008 the uncertain

s

ty of the standardss

was themajor contributor to uRs

at most resistances, leadingto combined readout uncertainties uR ,n ranging from83 to 107 ppm. Since both of the uncertain

s

ty compo-nents (us, ur) are classified as Type B, the combineduncertainty of the resistance readout is also Type B.

3.1.2 Kelvin Circuit Uncertainties

As discussed in Section 2.2, the Kelvin circuit mon-itored by the resistance readout introduces multiplesources of systematic error in the resistance measure-ments. These sources include leakage paths betweenthe circuit’s electrical conductors, capacitance effects,self-heating effects, and thermal EMFs. Althoughwe correct for the systematic errors, there are uncer-tainties associated with the corrections. In addition,electrostatic coupling, electromagnetic EMFs, tribo-electric currents, and switching effects within the slip-ring assembly all generate noise in the Kelvin circuit.This noise is largely removed during data processingby using 1D wavelet denoising techniques (Misiti andothers, 2005). However, because the noise removalprocess is imperfect, there remains an uncertainty inthe resistance measurements associated with the noise.

Leakage Paths. Applying the propagation of un-certainty law to the leakage path correction δRl (eq. 1),the standard uncertainty ul of the leakage correction isgiven by

ul =Rs

(Rs + Rl)2(Rs + 2Rl)2 u2

Rs+ R2

s u2Rl

(26)√

where uRl is the standard uncertainty of leakage resis-tance Rl. Since Rl ( Rs for all operational conditions,we can re-express the leakage-path uncertainty in thenormalized form

ul,n ≡(

ul

Rs

)= 4

(uRs

Rl

)2

+(

Rs

Rl

)2(uRl

Rl

)2

. (27)

√

The leakage resistance Rl is always ≥ 10 GΩ for thePTLS while the standard uncertainty of its determina-tion is uRl ≈ 11.5 GΩ based on the specifications ofthe measuring instrument. With such high Rl values,the second term within the square root of equation (27)exceeds the first term by about 108. Thus the standarduncertainty of the leakage correction reduces to

ul,n =Rs

Rl

uRl

Rl. (28)

( ) ( )

Capacitance Effects. The standard uncertaintyuc of the capacitance correction δRc (eq. 2) is given by

uc = τR′ uRs

Rs

2

+uC

C

2+

uR′

R′

2(29)

√( ) ( ) ( )

where R′ = ∂Rs/∂t is the rate of resistance changewhile logging downhole. The accuracy of the instru-ment used to measure the capacitance of the logging


cable, or of any filtering capacitors, establishes therelative capacitance uncertainty (uC/C). Based on themanufacturer’s specifications and a rectangular PDF,(uC/C) ) 0.0074. This term completely dominates(uRs/Rs), which is of the order 10−4 or smaller. Usinga Taylor Series expansion, the relative uncertainty ofR′ is found to be

(uR′

R′ ≈ 1√3

1m

+∆tr∆t

(30)) ( )

where ∆t is the sampling rate, ∆tr is the resolution ofthe time measurements (determined by the computer’sclock), and m is a measure of the resistance changebetween samples relative to the resolution ∆Rr of theresistance readout,

m =Ri+1 − Ri−1

2∆Rr. (31)

Our sampling rates are slow enough that ∆tr/∆t *1/m under all circumstances. Dropping negligibleterms, the standard uncertainty of the capacitancecorrection becomes

uc,n ≡(

uc

Rs

)=

C∆Rr

∆t

√13

+ m2uC

C

2. (32)

( )

Self-Heating Effects. For the self-heating correc-tion δRh (eq. 3), the associated standard uncertaintyuh is given by

uh =αT I2

s R2s

Pd

√

4(

uIs

Is

)2

+(

uRs

Rs

)2

+(

uPd

Pd

)2

. (33)

The relative uncertainty of the power dissipation con-stant (uPd/Pd) is estimated to be roughly 0.1, which isseveral orders of magnitude larger than either (uIs/Is)or (uRs/Rs). Dropping negligible terms, the uncer-tainty of the self-heating correction is

uh,n ≡(

uh

Rs

)=

αT I2s Rs

Pd

(uPd

Pd

). (34)

Thermal EMFs. The standard uncertainty ue ofthe thermal EMF correction δRe (eq. 8) is

ue =1Is

√

u2Vemf

+ V 2emf

(uIs

Is

)2

. (35)

Since the relative uncertainty of the regulated testcurrent Is is several orders smaller than that of the

thermoelectric voltages, the standard uncertainty ofthe thermal EMF correction is simply

ue,n ≡ ue

Rs=

uVemf

IsRs. (36)

( )

Prior to 2008, uVemf was estimated to be about thesame magnitude as Vemf (∼ 0.5µV). However, with thecurrent PTLS design, Vemf is essentially zero and thus,so is uVemf and ue.

Noise. Extensive tests with noisy synthetic datashow that the wavelet denoising methods used duringdata processing reduce the noise in the recorded resis-tances by a factor of 8. Thus the standard uncertaintyof the resistance measurements due to instrumentalnoise is un ≈ σRn

/8 where σRn≤ σRn (see discussion,

Section 2.2.3).Summary of Kelvin Circuit Uncertainties.

Equations 28, 32, 34, and 36 indicate the uncertainties(ul, uc, uh, ue) of the Kelvin-circuit resistance correc-tions depend on the specific conditions during a tem-perature log and thus must be treated on a case-by-case basis. Despite the need to specifically considerthe conditions for each experiment when evaluating theuncertainties, some general statements can be made.(1) Of the resistance-correction uncertainties, the un-certainty of the leakage-path correction (ul) is thelargest with the current PTLS operating under normalconditions (fig. 10). (2) Without the use of the resis-tance readout’s internal filters or a filtering capacitor,the uncertainty un due to noise is the dominant Kelvin-circuit uncertainty for sensor resistances less than 20–30 kΩ. Even with the use of hardware filters to reducethe noise uncertainty, un is generally still the dominantuncertainty at low resistances (Rs < 20 kΩ). (3) Athigh resistances (Rs > 70 kΩ), the uncertainty of theleakage-path correction (ul) is the dominant uncer-tainty. (4) All the uncertainties associated with theresistance corrections and noise are less than 0.1 mKfor sensor resistances in the range 10–170 kΩ. (5)The uncertainties (ul, uc, uh, ue) associated with theKelvin-circuit resistance corrections are all classified asType B uncertainties while the noise uncertainty un isType A.

3.1.3 Temperature-Sensor Calibration Uncer-tainties

Before every set of field experiments, the PTLStemperature sensors are calibrated on the ITS-90 tem-perature scale (Mangum and Furukawa, 1990) at theUSGS thermal calibration facility in Lakewood, Col-orado. Temperatures on the ITS-90 scale are defined


101 102

10!2

10!1

100

101

Rs (kΩ)

ux,

n(P

AR

TS

PE

RM

ILL

ION

)

uc,n

ul,n

uh,n

un,n

Figure 10. Standard uncertainties (ul, uc, uh) associatedwith the resistance corrections, displayed in normalizedform ux,n ≡ (ux/Rs), for typical operating conditions. Inthis example, the uncertainty of the capacitance correction(uc) corresponds to the case shown in figure 3 (v = 5.5 cen-timeters per second, ∂T/∂z = 25 millikelvins per meter,τ = 10 milliseconds, C = τ/Rs). The uncertainty of thethermal EMF correction (ue) is essentially zero with thecurrent PTLS design. The noise uncertainty (un) shownby the dashed line represents an upper bound for mostoperating conditions; it assumes hardware noise filters arenot used. Equivalent temperature uncertainties are givenby ux,n/αT .

in terms of a set of fixed points (melting, boiling,and triple points of pure substances), interpolatinginstruments, and equations relating the property mea-sured by each interpolating instrument to temperature.Between 13.8 K and 1,235 K, the official interpolatinginstrument is the standard platinum resistance ther-mometer (SPRT). Thus, equations describing how theresistance of a standard SPRT varies with temper-ature are embodied in the definition of the ITS-90temperature scale. To calibrate the PTLS temper-ature sensors, we use a 25.5-Ω quartz-sheath SPRTas our local standard. The probes to be calibratedare inserted into a copper equilibration block that isimmersed in a temperature-controlled fluid bath; theSPRT is positioned in the equilibration block at thesame distance from the center as the probes. Thecopper block effectively damps short-term temperaturefluctuations in the calibration bath and improves the

uniformity of the thermal field surrounding the probesand the SPRT. Once the bath stabilizes at a predeter-mined calibration point, the data-acquisition system si-multaneously acquires the SPRT reference temperatureT ! and the resistance R! of each temperature sensorbeing tested. This process is repeated across the entirecalibration range in 2-K increments with upcomingfield experiments determining the calibration limits.Total least squares is then used to find the constants(ai) in the 4-term calibration function (eq. 11) fromthe (T !, R!) calibration data. Residuals from this fittypically have standard deviations ranging from 0.20to 0.45 mK.

The uncertainty of the resulting PTLStemperature-sensor calibrations is determined bya number of factors, including: the uncertaintyof the SPRT calibration at ITS-90 fixed points,the propagation of error between those points, theaccuracy of the SPRT readout, the accuracy ofthe thermistor scanner, and the magnitude of thetemporal and spatial temperature variations within thecalibration bath. The residuals from the least-squaresfit to the calibration data do not reflect many aspectsof the total uncertainty of the temperature-sensorcalibration.

SPRT Reference Temperatures T !. The un-certainty of the SPRT reference temperature T ! isdetermined by the uncertainty of the SPRT calibra-tion and the accuracy of the instrument (readout)used to monitor the SPRT temperatures. Our quartzSPRT was most recently calibrated by Hart Scientific(American Fork, Utah) who provided expanded uncer-tainties (coverage factor k = 2) at fixed calibrationpoints between −200C and 0C. The equivalent stan-dard uncertainties are 0.5 mK at −197C, 0.2 mK at−38.8344C (triple point of mercury), and 0.1 mK at0.010C (triple point of water). Because the definitionof the ITS-90 temperature scale over this range is basedon equations describing the behavior of a standardSPRT, the calibration uncertainties between the fixedpoints are of the same order as those at the adjacentfixed points. We use error propagation curves providedby the National Institute of Standards and Technol-ogy to determine how the uncertainties at the triplepoint of mercury (TPHg) and triple point of water(TPW) propagate to other temperatures. Combiningthe propagated TPHg and TPW uncertainties, thestandard uncertainty of the SPRT calibration rangesfrom 0.27 mK at −60C to 0.10 mK at 0.01C.

The accuracy of the SPRT readout is ±0.0005Ω forSPRT resistances less than 25Ω and ±20 ppm of the


reading at higher resistances. Based on the thermalresponse of SPRTs (McGee, 1988), these specifica-tions translate to a standard uncertainty ranging from2.77 mK at −60C to 2.90 mK at 0C. Combining theuncertainty of the SPRT calibration with that of theSPRT readout, we obtain the standard uncertainty uT !

of the SPRT reference temperatures. The combineduncertainty uT ! is clearly dominated by the uncer-tainty of the SPRT readout with values ranging from2.79 mK at −60C to 2.90 mK at 0C (fig. 11). Sincethe uncertainty of the SPRT calibration and the SPRTreadout are both evaluated using Type B methods, theuncertainty of the SPRT temperature measurements isalso classified as Type B.

Temperature-Sensor Resistance Measure-ments R!. The resistance of the PTLS temper-ature sensors being calibrated is monitored usingan 8-channel thermistor scanner whose accuracy is±100 ppm of the reading. Based on a uniform PDF,the corresponding standard uncertainty uR! of thescanner’s resistance measurements is 58 ppm. Ex-pressed in terms of temperature, uR! ranges from0.88 mK at −60C to 1.28 mK at 0C for the T01probe series; uR! is approximately 3 percent less forthe P probe series and 2 percent more for the T02probes (fig. 11). This is a Type B uncertainty. Aswith the SPRT readout, the thermistor scanner isoperated within the 18–28C range in order to achievefull accuracy.

Calibration Bath and High-ConductivityEquilibration Block. Other sources that affect theuncertainty of the temperature-sensor calibrations in-clude temporal and spatial variations of the thermalfield within the calibration bath. Both of these sourcescan cause temperature offsets between the probes beingcalibrated and the reference SPRT. The stability of thecalibration bath (Hart model 7060) is reported to be±2.5 mK at −60C. This figure represents an expandeduncertainty with coverage factor k = 2. Experimentsat −20C confirm this value. Thus we take the stabilityof the bath to be ±2.5 mK across the full calibrationrange; the corresponding standard uncertainty ubf ofthe bath fluctuations is 1.25 mK. Several experimentswere done to determine the nonuniformity of the ther-mal field in the central portion of the bath where thecalibrations are performed. We find that the standarduncertainty ubu of the spatial variations in this regionis 2.5 mK.

To further control the stability and uniformity ofthe thermal field experienced by the probes and SPRTduring calibration, we use a 7.62-cm-diameter, high-

!60 !50 !40 !30 !20 !10 00

0.5

1

1.5

2

2.5

3

3.5

T (C)

u(m

K)

uTc

uT !

uR!

uu uf

Figure 11. Combined standard uncertainty uTc of thePTLS temperature-sensor calibration. Also shown are thestandard uncertainties of the individual components: uT ! isthe uncertainty of the SPRT reference temperature, uR! isthe uncertainty of the temperature-sensor resistance mea-surements, uf is the uncertainty associated with temper-ature fluctuations in the calibration bath, and uu is theuncertainty due to bath nonuniformity. The three uR!

curves (dashed, solid, dash-dot) show the uncertainty ofthe resistance measurements for the P, T01, and T02 probeseries, respectively.

conductivity (copper) equilibration block within thecalibration bath. The SPRT and PTLS probes areinserted in tight-fitting holes located 2.90 cm fromthe center. Heat-transfer simulations show that ther-mal fluctuations in the bath with periods less than0.1 minute are completely damped at the positionof the probes, while those with periods of 3 minutes(where the largest bath fluctuations occur) are dampedby a factor of about 0.4 (function f , fig. 12). Thesefluctuations would not be an issue if the PTLS probesand the SPRT had identical time constants so thatthey would synchronously warm and cool in responseto the temperature fluctuations. However, the timeconstant of the SPRT (18.5 seconds) is much longerthan that of the PTLS temperature sensors (4.0 sec-onds) in this situation. Convolving the response func-tions of the SPRT and the PTLS temperature sensors(Saltus and Clow, 1994) with synthetic temperaturefluctuations shows that the maximum temperature dis-crepancy between the SPRT and the probes caused by


dissimilar time constants occurs at a period of about0.8 minute (function g, fig. 12). However, little poweroccurs at such short periods due to the damping ofthe block. Considering the joint effects of equilibrationblock damping and the dissimilar time constants, thelargest discrepancies between the recorded SPRT tem-peratures and the probe temperatures occur at periodsof 2–3.5 minutes (function f ·g, fig. 12). This coinciden-tally matches the period where the bath fluctuationshave their greatest power. The resulting standarduncertainty in temperature-sensor calibration relatedto bath fluctuations is uf = (0.16)ubf = 0.20 mK.

0 2 4 6 8 100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

PERIOD (minutes)

f

g

f · g

Figure 12. Damping of temperature fluctuations inthe calibration bath by the high-conductivity equilibra-tion block. Function f = (up/ubf ) describes the relativedamping provided by the block; ubf is the magnitude ofthe bath fluctuations while up is the magnitude of thefluctuations inside the block near the probes and SPRT.The block is essentially opaque to short-period fluctuations(< 0.1 minute) but is transparent to periods longer than30 minutes. Function g = (uf/up) shows the relativetemperature discrepancy between the SPRT and the probescaused by their dissimilar time constants. Combining theblock damping with the dissimilar time-constant effect, thestandard uncertainty of the temperature-sensor calibrationdue to bath fluctuations is uf = (f · g) ubf . The product(f · g) reaches a maximum value of 0.16 at periods of 2–3.5 minutes.

Persistent temperature gradients always exist tosome extent in calibration baths due to imperfect mix-ing of the bath fluid. Experiments with the Hart7060 bath show that the standard uncertainty of thethermal field in the vicinity of the equilibration blockis ubu = 2.5 mK. However, the field inside the block is

expected to be much more uniform. To quantify theuniformity, the resistance change of an array of ther-mistors located within the block was monitored whilethe block was rotated about its central axis; the bathwas held at a fixed temperature (to within ubf ) duringthese tests. After removing temporal fluctuations dueto bath instability, the thermal field was found to beuniform to within ±0.10 mK inside the block at thelocation of the probes. The primary uncertainty ofthis determination is associated with the noise of thethermistor scanner (roughly ±0.04 mK) as the experi-ment effectively removed uncertainties associated withthe calibration of the individual thermistors; calibra-tion, long-term drift, and nonlinearity of the thermistorscanner; and bath stability. The standard uncertaintyof the temperature-sensor calibration related to bathnonuniformity is then estimated to be uu = 0.10/

√3 =

0.06 mK. Both bath uncertainties (uf , uu) are classifiedType A.

Combined Temperature-Sensor CalibrationUncertainty uTc . Combining the uncertainty of theSPRT temperature measurements, of the thermistorscanner, and of the bath variations, the combinedstandard uncertainty uTc of the temperature-sensorcalibrations ranges from 2.93 mK at −60C to 3.18 mK0C (fig. 11). Although the thermistor scanner and thebath variations contribute to uTc , the uncertainty ofthe SPRT temperature is the dominant factor in thecombined calibration uncertainty. A small dependenceof uR! on the αT -characteristics of each probe seriesproduces about a 1 percent difference in the combineduncertainty at any given temperature; this effect issmall enough that it can be ignored. Because bothType A and Type B methods were used to evaluatethe component uncertainties, the combined calibrationuncertainty uTc is classified as Type A,B.

3.1.4 Combined ITS-90 TemperatureUncertainties

Combining the resistance-readout uncertainty(uRs

), the resistance-correction uncertainties (ul, uc,uh, ue), the uncertainty due to instrumental noise (un),and the temperature-sensor calibration uncertainty(uTc), we finally obtain the total standard uncertaintyuT of the PTLS temperature-measurement process. Inorder to express uT in terms of temperature, mostof the component uncertainties (uR, ul, uc, uh, ue, un)must be converted from resistances, where they aremore naturally defined, to temperatures. This con-version involves the αT -characteristics of the temper-


ature sensors. Thus, the total uncertainty of thetemperature-measurement process depends to some ex-tent on which probe is used during a logging experi-ment. This is particularly true at warm temperaturesdue to the degradation of the resistance readout’saccuracy at resistances less than 5 kΩ (fig. 13). Toavoid this degradation, we strive always to select aprobe whose resistance will remain above 5 kΩ for theduration of an experiment; thus the T02 probes, forexample, are used only at temperatures below −15Cwhile the P-series probes can be used up to at least0C. With this constraint, the standard uncertaintyof the temperature-measurement process ranges from3.0 mK at −60C to 3.3 mK at 0C with the currentPTLS. As shown in figure 13, the total temperature un-certainty uT is strongly dominated by the temperature-sensor calibration uncertainty uTc with the currentPTLS design. The resistance readout contributes 0.5–0.6 mK to the total while the upper limit of thenoise contribution is generally ≤ 0.25 mK. Individualresistance-correction uncertainties (ul, uc, uh, ue) areless than 0.1 mK under all normal conditions. Thecombined uncertainty uT of the ITS-90 temperaturemeasurements is a Type A,B uncertainty.

Several of the temperature uncertainty componentswere larger before 2008, especially the resistance read-out uncertainty uR , the uncertainty of the thermalEMF correction (

s

ue), and the uncertainty of the ca-pacitance correction (uc). During 1993–2007, uRs

wasabout 3 times larger (1.4–2.1 mK) than with the cur-rent system. In addition, the thermal EMF uncertaintywas comparable to the noise uncertainty un rather thanbeing zero. Although larger, uc was still less than0.03 mK and thus of little consequence. Combiningall the components, the total standard uncertainty uT

of the temperature-measurement process during 1993–2007 ranged from 3.2 mK at −60C to 3.8 mK at 0C.

3.2 Relative TemperatureUncertainties

Section 3.1 focused on the standard uncertainty uT

of the PTLS temperature measurements relative tothe ITS-90 absolute temperature scale. For climate-change detection, this is the appropriate measure ofuncertainty. However when reconstructing past cli-matic changes using borehole paleothermometry, weare not as concerned about uncertainties relative tointernational absolute measurement scales as we areabout the potential distortion of a temperature profileby measurement errors that could be misinterpreted

!60 !50 !40 !30 !20 !10 00

0.5

1

1.5

2

2.5

3

3.5

4

T (C)

u(m

K)

uT

uTc

uRs

unul

Figure 13. Combined standard uncertainty uT of theITS-90 temperature measurements obtained with the cur-rent PTLS when using the P, T01, and T02 probe series(dashed, solid, dash-dot lines, respectively). Also shownare the primary contributors to uT , specifically, uTc , thestandard uncertainty of the temperature-sensor calibra-tions, and uRs

, the standard uncertainty of the resistancemeasurements. The un curves represent the upper boundfor the noise uncertainty under most operating conditions;they assume the hardware noise filters are not used. Thestandard uncertainty of the resistance corrections is lessthan 0.1 millikelvin in all situations.

as being due to climate change; to date, boreholepaleothermometry generally has been used to analyzethe shape of individual temperature profiles. Thusthe offset of an entire temperature log due to miscali-bration or system drift will not affect a reconstructedclimate history and is of little importance in this con-text. For borehole paleothermometry, the appropriateuncertainties are those that describe the uncertaintyof a temperature profile’s shape, or expressed anotherway, the standard uncertainty (ur

T ) of the temperaturemeasurements from a single temperature log relativeto one another.

An assessment of the temperature uncertainties dis-cussed in Section 3.1 shows that nearly all are associ-ated with errors that potentially can distort a profile’sshape and thus should be included in the combinedstandard uncertainty ur

T of relative temperature mea-surements. However, because the long-term drift ofa high-quality instrument will not in general producean error that distorts a profile, the drift component


of a readout’s accuracy specification can be droppedwhile the nonlinearity and internal noise componentsshould be retained. With this change, the standarduncertainty ur

T of the relative temperature measure-ments produced by the PTLS ranges from 1.6 mKat −60C to 2.0 mK at 0C (fig. 14). The standarduncertainty ur

Tcof the temperature-sensor calibration

(based on instrument specifications) is still the largestcontributor, ranging from 1.6 mK at −60C to 1.8 mKat 0C. These uncertainty values are likely to be over-estimates because the dominant source of uncertaintyaffecting ur

Tcand ur

T is the SPRT readout, and it isused only over 1 percent of its range, whereas thenonlinearity specification pertains to the instrument’sentire range. Still, without tests to quantify the un-certainty over such a restricted range, we must usethe manufacturer’s stated full-range uncertainty. Atthis time we simply note that the residuals from fittingthe sensor calibration data to equation (11) typicallyhave standard deviations ranging from 0.20 to 0.45 mK,suggesting ur (and thus ur

Tc T ) may be substantiallysmaller than the values based on the SPRT readout’sfull-range nonlinearity specification. To accommodatethis possibility, we state that the “upper limit” of ur

Tranges from 1.6 mK at −60C to 2.0 mK at 0C. Aswith uT , the uncertainty ur

T of relative temperaturemeasurements is classified Type A,B. The ur

T upperlimit before 2008 was very similar to the current value,ranging from 1.6 mK at −60C to 2.1 mK at 0C.

3.3 Depth Uncertainties

It is difficult to accurately determine the depthbelow surface with any borehole logging system. Withthe PTLS, systematic depth errors arise from force-induced strains in the logging cable and winch, toolbuoyancy, temperature changes that alter the radius ofthe measuring wheel, and thermally induced longitudi-nal strains in the logging cable once it enters the rela-tively cold borehole. We attempt to correct for theseerrors (Section 2.3), although there are uncertaintiesin the corrections. Errors also potentially arise fromslippage of the cable on the measuring wheel, debris inthe wheel’s cable groove, and downhole cable hangups.Cable slippage is minimized by logging at a slow,steady pace (5.5 cm·s−1, or less). If slippage occurswith the PTLS, some of it presumably is incorporatedin the depth-calibration factor Cd; depth calibrationdata are collected at the same downward speed andtensions as utilized during a log. The boreholes welog in polar environments are invariably filled with a

!60 !50 !40 !30 !20 !10 00

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

T (C)

u(m

K)

urT

urTc

uRs

unul

Figure 14. Combined standard uncertainty urT of relative

temperature measurements and the individual uncertaintycomponents. The ur

T and urTc

curves represent upper limits.Symbols are identical to those used in figure 13.

clean, nonfreezing fluid (for example, n-butyl acetate,arctic diesel fuel, or a nonaromatic equivalent). Asa result, debris in the groove of the measuring wheelthat would alter the effective radius of the measuringsystem has generally not been an issue. Cable and (or)logging-tool hangups within a borehole do sometimesoccur. These are detected by monitoring cable tension.When hangups occur, the log is either stopped andrestarted once the tool is past the impediment or thelogging run is terminated, depending on the severityof the hangup and the objective of the experiment.In the former case, a depth offset with an unknownuncertainty may occur at the obstruction; in the lattercase, no depth error arises. When cable hangups donot occur, we are able to quantify the uncertainty uZ

of the logging sensor’s true depth Z using the root-sum-square method. Individual uncertainties contributingto uZ are as follows:

Recorded Depth Measurements. The leadingterm in our estimated true sensor depth (eq. 25) in-volves the depth recorded by the counter weighted by acalibration factor, [1+C ! ! ! !

d(T Zw, )] Z. Since Cd(Tw, Z )is simply a reference value that is always * 1, thestandard uncertainty of this term is equivalent to theuncertainty uZ of the measurements reported by thedepth counter. We establish uZ through statistical


analysis of multiple determinations of a borehole’s totaldepth according to the counter. Given the PTLS’operating environment, uZ is believed to primarilyreflect variations in cable slippage on the measuringwheel.

Force-Induced Strains. Starting with equa-tion (19), the standard uncertainty uF of the depthcorrection for force-induced strains (δZF ) is found tobe

uF =Z

ouF (Z − z) dz (37)

∫

where u (Z) is the standard uncertainty of the exper-Fimentally determined function F(Z). When F(Z) isadequately represented by a linear function, its depth-dependent uncertainty is

√√√ 2

√ 1(

√ Z − < Zi >u (Z) = σ + .F √√ n (38)

n ∑ (Zi − < Z

)

2

i >i=1

)

Here, σ is the standard deviation of the Fi data,< Zi > is the mean value of the calibration depthsZi, and n is the number of depth-calibration points(Bowker and Lieberman, 1972). More complicatedexpressions are required when F(Z) is nonlinear.

Tool Buoyancy. Applying the propagation ofuncertainty law to the tool buoyancy correction δZbt

clF(eq. 21), the standard uncertainty ubt of this correctionis

ubt = δZbtclF

[(uK

K

)2+

(u∆m

∆

)2+

( 2uh

m h +∆x

)

1

+( 2u∆x

h +∆x

) ] /2

(39)

where ∆m = mf at − mt . The fractional uncertainty

(uK/K) of the logging cable’s elastic stretch coefficientis estimated to be about 0.1. This greatly exceeds thefractional uncertainties associated with the mass differ-ence ∆m and the lengths h and ∆x. Thus, uncertaintyubt is well approximated by

ubt = Kg(mft − ma u

t ) (h +∆x)(

K . (40)K

)

Radial Strain of Measuring Wheel, Thermal.Letting φ(t) = Tw(t) − T !w, the standard uncertaintyuwT of the correction for the thermally induced radialstrain of the measuring wheel (δZwrT , eq. 22) during

a log is

uwT =(

Rw

Rn

)

u2α

(∫ Z

o

∂ewrTw

∂αdz

)2

+ u2φ

(Z

o

∂ewrTw

∂φdz

)21/2

(41)∫

where∂ewrTw

∂α= φ (1 + 3αφ)−1/2 (1 + αφ)−3/2 (42)

∂ewrTw

∂φ= α (1 + 3αφ)−1/2 (1 + αφ)−3/2. (43)

The uncertainty uα of the measuring wheel’s thermalexpansion coefficient is estimated to be of order 0.1αwhile uncertainty uφ is typically 0.1–1.0 K. With thesevalues, uα and uφ are both significant contributors touwT .

Longitudinal Strain of Logging Cable, Ther-mal. Uncertainties in the logging cable’s thermalexpansion coefficient α, the temperature differenceψ = T (z) − Tw, and parameter fT are all significantcontributors to the uncertainty ucT of the correctionfor the thermally induced length change of the cableas it descends a borehole (δZclT , eq. 24). Applying thepropagation of uncertainty law to δZclT and droppingnegligible terms, ucT is given by

ucT =

(uα

)2(∫ 2

Z2eclT dz

)+ u2

ψ [α (Z hα

− ) ]h

1/2

+ u2fT

α [ (h) − T ! 2T w ] Z ]

. (44)

For the logging cable, the fractional uncertainty (uα/α)is estimated to be 0.1; uψ ranges 0.1–1.0 K while ufT

is about 0.1.Combined Depth Uncertainty uZ . Combining

the individual uncertainties, the standard uncertaintyof a sensor’s true depth is

uZ =√

u2˜ + u2 + u2

F bt + u2wT + u2

Z cT . (45)

Ordinarily, uZ and uF are the dominant contributorsto uZ . Uncertainty components (uZ , uF ) are classifiedas Type A uncertainties, while (ubt, uwT , ucT ) areType B. The combined depth uncertainty uZ is thusType A,B. The magnitude of the individual compo-nents and of the combined uncertainty depend to alarge degree on specific borehole conditions and thetemperature near the winch.


!40 !30 !20 !10 0

0

1

2

3

T (C)

Z(k

m)

(a)

10!3 10!2 10!1

0

1

2

3

u (mK)

uc uh ul un

(b)

0 1 2 3

0

1

2

3

u (mK)

Z(k

m)

un uR uTc

uT

(c)

0 0.5 1.0 1.5 2.0

0

1

2

3

u (mK)

un uR urTc

urT

(d)

Figure 15. Temperature-measurement uncertainties for the proposed 3.5-kilometer deep WAIS Divide borehole in WestAntarctica. (a) Best-guess temperature profile at this site based on ice-flow modeling. (b) Expected resistance-correctionuncertainties (ul, uh, uc) and the noise uncertainty (un) assuming the hole is logged with the current PTLS using aT01-series probe at 5.5 centimeters per second. (c) Combined standard uncertainty (uT ) of the ITS-90 temperaturemeasurements along with the largest contributing uncertainties. (d) Combined standard uncertainty (ur

T ) of the relativetemperature measurements along with the largest contributing uncertainties. The ur

T and urTc

curves are upper limits.

3.4 Example: Proposed WAIS Divide modeling (Tom Neumann, written commun., 2006).We anticipate the fluid in the proposed borehole will beBorehole, Antarcticastably stratified (nonconvecting) within 2,000 m of thesurface once the hole is completed. Figure 15b showsTo illustrate the magnitude of the uncertainties and the uncertainty of the resistance corrections assumingthe degree to which they can vary with depth, we con- the hole is logged with the current PTLS using a T01-sider the conditions at the proposed WAIS Divide Ice series probe, the logging speed is 5.5 cm s−1, a 0.47-Core site in West Antarctica (7928′ S., 11205′ W.). ·µF filtering capacitor is used, and the hardware noiseFigure 15a shows the “best-guess” temperature profile filters are off. With a T01-series probe, the sensor resis-within the ice sheet at this location based on ice-flow


tance should range from 20.2 kΩ at the coldest temper-atures encountered (−33.9C) to 4.6 kΩ at the bottomof the hole. The standard uncertainty (ul, uh, uc, ue)of the resistance corrections are expected to be lessthan 0.011 mK at all depths while the uncertainty un

associated with electrical noise is predicted to increasefrom about 0.06 mK in the upper 2,000 m of theborehole to 0.24 mK at the bottom.

Despite the 30-K temperature change along theprofile, the combined standard uncertainty uT of theITS-90 temperature measurements has only a smalldepth dependence, varying from 3.05 mK in the upper2,000 m to 3.19 mK at the bottom (fig. 15c). Thisstems from the weak temperature dependence of thedominant term, uTc . Similarly, the combined standarduncertainty ur

T of the relative temperature measure-ments that would be used for borehole paleothermom-etry is only mildly depth-dependent (fig. 15d), rangingfrom 1.71 mK in the upper 2,000 m to 1.86 mK at thebase of the ice sheet (about 3,465 m).

Figure 16 shows the uncertainty of the temperaturesensor’s location (depth) when logging the WAIS Di-vide borehole using plausible values for various param-eters. However, it must be emphasized the true depthuncertainties for WAIS Divide temperature logs willdepend on the actual borehole conditions and param-eter values that occur during those logs. These factorswill not be known until the borehole is completed andthe hole has been logged several times. For the exampleshown in figure 16, we assume the temperature Tw(t) ofthe measuring wheel follows a diurnal cosine-function,fluctuating ±5C about a mean value of −10C, i.etypical summertime temperatures inside the drillingstructure where the logging winch will be located. Thereference calibration temperature of the wheel (T !w) istaken to be −10C, the fluid level in the borehole isset at the firn/ice transition (h = 73 m), parameterfT is 0.3, and uncertainties uφ and uψ are both 1 K.With these values, the standard uncertainty uwT of thedepth correction for the thermally induced radial strainin the measuring wheel during a log is limited to 11–12 ppm. The correction for the shortening of the cablein the cold borehole has a standard uncertainty ucT

ranging from 25 ppm near the surface to a peak valueof about 40 ppm when the sensor reaches Z ≈ 1,800 m.For a PTLS temperature sensor, the uncertainty ubt ofthe tool buoyancy correction is less than 2 ppm andcan be ignored.

To account for force-dependent effects on the depthmeasuring system, we assume in this example thatnine pairs of depth-calibration data (L, L) are col-

0 0.2 0.4 0.6 0.8

0

1

2

3

u (m)

Z(k

m)

uZ

uZ

uFucT

uwT

(a)

0 50 100 150 200 250

0

1

2

3

u/Z (ppm)

Z(k

m)

uZ

uZ

uF

ucT

uwT

(b)

Figure 16. Depth uncertainties for the proposed WAISDivide borehole as a function of sensor depth Z based onplausible values for various parameters. (uF , ucT , uwT ) arethe standard uncertainties of the primary depth correctionswhile uZ is the standard uncertainty of the measurementsreported by the depth counter. The combined standarduncertainty uZ of the sensor’s true depth ranges from 200to 250 parts per million.

lected across the range of borehole depths and thatthe standard deviation of the fit to the resulting Fi

data is σ = 3.0x10−4. This value for σ is interme-diate between that obtained in the recently logged 1-km Siple Dome A borehole (2.4x10−4) and the 3-kmGISP2-D borehole (4.1x10−4); GISP2-D was loggedbefore the PTLS winch had a level-wind system, so


Table 1. Specifications of the USGS Polar Temperature Logging System, mid-2008.

[C, degree Celsius; mK, millikelvin; m, meter; cm, centimeter; ppm, parts per million]

Temperature range −60C to +23C

Temperature resolution 0.02–0.19 mK

Depth range 0–4,500 m

Depth resolution 1.0 cm

Standard uncertainty, ITS-90 temperature measurements 3.0–3.3 mK (Type A,B)

Standard uncertainty, relative temperature measurements 1.6–2.0 mK† (Type A,B)

Standard uncertainty, depth measurements 200–250 ppm‡ (Type A,B)

† Upper limit.‡ 4.5-km winch with favorable logging conditions.

a much higher value for σ is expected from thoselogs than would occur today. With the proposed setof calibration data, the standard uncertainty uF ofthe depth correction for force-induced strains rangesfrom 200 ppm near the surface to a minimum value of130 ppm at Z ≈ 2,500 m. The greatest unknown inthe projected depth uncertainties for the WAIS Divideborehole involves the standard uncertainty uZ of themeasurements reported by the depth counter. For thefinal set of logs obtained in the Siple Dome A borehole,the uncertainty uZ was about 140 ppm. Thus, whenlogging conditions are favorable, the repeatability ofthe measurements reported by the depth counter isfairly high. In the WAIS Divide example, we use anominal value for uZ of 150 ppm. Combining theindividual uncertainty terms, the standard uncertaintyof the temperature sensor’s true depth ranges from 200to 250 ppm (fig. 16b).

4 Summary

From its origins in the early 1990s, the USGSPolar Temperature Logging System has evolved intoa reliable high-precision data-acquisition system forcold polar environments. This field-proven system hasbeen extensively used in Greenland, Antarctica, andarctic Alaska. With a temperature resolution betterthan 0.2 mK, the PTLS is capable of detecting smallsubsurface temperature changes due to fluid convectionand other phenomena. Our initial goal of reducing theuncertainty of the temperature measurements to about

1 mK has proven difficult to achieve. The standard un-certainty uT of the system’s ITS-90 temperature mea-surements is 3.0–3.3 mK. This is more than adequatefor climate-change detection and monitoring, especiallyin the Arctic where contemporary surface-temperaturechanges exceeding 1 K/decade have recently been ob-served. Relative temperature measurements used toreconstruct past climate changes with borehole pale-othermometry have a standard uncertainty ur

T whoseupper limit ranges from 1.6 to 2.0 mK. This is tanta-lizingly close to 1 mK.

The uncertainty of the temperature sensor’s loca-tion (depth) during a log depends on specific boreholeconditions and the temperature near the measuringwheel. Thus the depth uncertainty must be treatedon a case-by-case basis. However, recent experiencewith our large winch indicates that when conditionsare favorable (that is the winch is operated within ashelter, steady power is available for the winch motor,fluid in the borehole is free of debris, and so forth),the 4.5-km system can produce depths with a standarduncertainty uZ on the order of 200–250 ppm. Thesmall helicopter-transportable winches have undergonea number of design changes recently. Although thedepth-measurement system for the small winches isvery similar to the 4.5-km system, we do not yethave enough information about various parameters toquantitatively assess uZ for logs acquired with theseportable winches. The current specifications for theUSGS Polar Temperature Logging System are summa-rized in Table 1.

Appendix 23

Appendix: Nomenclature

C capacitanceCd(Tw, Z) depth calibration functioneclT strain, cable, longitudinal, thermalecrT strain, cable, radial, thermalewrT strain, measuring wheel, radial, thermalF(Z) force-dependent functiong gravitational accelerationh depth to air/fluid interface in a boreholeK elastic stretch coefficientIs source currentI ′ extraneous current (noise)Pd power-dissipation constant, thermistorQ Seebeck coefficientr radius, logging cableRl interconductor leakage resistanceRL lead resistance (Kelvin circuit)Rs temperature-sensor resistance (true)Rs temperature-sensor resistance (measured)Rn nominal radius used by depth counterRw radius, depth-measuring wheelR! sensor resistance during calibrationt timeT temperatureTw measuring wheel temperatureT !

w reference depth-calibration temperatureT ! SPRT reference temperatureubt standard uncertainty, tool buoyancy correctionuc standard uncertainty, capacitance correctionucT standard uncertainty, correction for thermal

strain (longitudinal) of logging cableue standard uncertainty, thermal EMFsuf standard uncertainty of temperature-sensor

calibration due to bath fluctuationsuF standard uncertainty, force-induced correctionsu standard uncertainty of functionF Fuh standard uncertainty, self-heating correctionul standard uncertainty, leakage correctionun standard uncertainty, instrumental noiseur standard uncertainty, resistance readoutuRs

combined standard uncertainty, resistancereadout measurements

uR! standard uncertainty, temperature-sensorresistance measurements during calibration

us standard uncertainty, resistance standardsuT combined standard uncertainty, ITS-90

temperature measurementsur

T combined standard uncertainty, relativetemperature measurements

uTc combined standard uncertainty, temperature-sensor calibration

uT ! combined standard uncertainty, SPRT referencetemperature

uu standard uncertainty of temperature-sensorcalibration due to bath nonuniformity

uwT standard uncertainty, correction for thermalstrain of depth measuring wheel

uZ combined standard uncertainty, sensor depthuZ standard uncertainty of sensor depth

(as reported by counter)v logging speedV voltageV ′ extraneous voltage (noise)Vemf thermoelectric voltage (thermal EMF)z true depth coordinatez counter depth coordinateZ sensor depth (true)Z sensor depth (reported by counter)Z! reference calibration depthα coefficient of thermal expansion, linearαT coefficient of resistance, thermistorβ coefficient of thermal expansion, volumetricδRc resistance correction, capacitanceδRe resistance correction, thermal EMFsδRh resistance correction, self-heatingδRl resistance correction, leakage∆Rr resistance resolution∆Tr temperature resolution∆t data sampling rate∆x horizontal distance between measuring wheel

and borehole∆zr depth resolutionδZbt

clF depth correction, tool buoyancy, cable,longitudinal

δZclT depth correction, cable, longitudinal, thermalδZF depth correction, force-induced strainsδZwrT depth correction, measuring wheel, radial,

thermalσRn standard deviation of resistance noiseσRn

standard deviation of recorded noiseτ circuit response time

Acknowledgments. I gratefully thank Jack Kennelly andMark Ohms for their contributions to the design of thePTLS and their exceptional skill in fabricating it. I alsothank Frank Urban for performing experiments used toquantify some of the critical measurement uncertainties,Tom Neumann for supplying the “best-guess” temperatureprofile for the proposed WAIS Divide Ice Core site (WestAntarctica), and the reviewers for their helpful comments.Funding for this work was provided by the U.S. GeologicalSurvey’s Earth Surface Dynamics Program.


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Publishing support provided by: Denver Publishing Service Center Manuscript approved for publication, July 2008 Edited by Mary A. Kidd Layout by Gary D. Clow

For more information concerning this publication, contact: Science Center Chief, USGS Rocky Mountain Geographic Science Center Box 25046, Mail Stop 516 Denver, CO 80225 (303) 202-4106

Or visit the Earth Surface Processes Team Web site at: http://esp.cr.usgs.gov/

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