vanschoor_paper1

8/19/2019 vanschoor_paper1

http://slidepdf.com/reader/full/vanschoorpaper1 1/5

11th SAGA Biennial Technical Meeting and ExhibitionSwaziland, 16 - 18 September 2009, pages 259 - 263

Comparison between time- and frequency-domain inducedpolarisation parameters

M. van Schoor 1

, L.P. Marè2

and C.J.S. Fourie1

1. Council for Scientific and Industrial Research, South Africa, [email protected]; [email protected]

2. Geophysics Division, Council for Geoscience, South Africa, [email protected]

ABSTRACT

Physical properties of rock samples from exploration or mining sites are often needed to assist in the planning ofgeophysical surveys or in the interpretation of geophysical results. For example, the output from a physical property study may be used in numerical model studies aimed at assessing the applicability or performance of ageophysical technique. Physical properties are also useful for constraining model parameters during processing and

in the interpretation of field data. Electrical property data are often recorded in the time-domain, yielding resistivityand chargeability values; however, a frequency-domain, or even complex resistivity approach, may also befollowed. The latter approach, for example, would produce resistivity magnitude and phase angle outputs. It isshown that both the commonly used standard time-domain chargeability parameters and the (single-frequency)complex resistivity phase angle parameter could produce misleading estimates of the polarisable nature ofmineralised rocks and of the contrast between different rock types. It is further shown that a multi-frequency(spectral) approach can be used to avoid this pitfall; similarly, the calculation of different time-domain induced polarisation (IP) parameters, (using different definitions) may provide better insight into the polarisable nature ofrock samples than a single, arbitrary chargeability value.

Key words: Physical properties, induced polarisation, spectral IP

INTRODUCTION

Knowledge of the physical properties of rocks fromexploration or mining sites is often needed to assist inthe planning and/or interpretation of geophysicalsurveys. For example, physical property informationmay be used in numerical model studies aimed atassessing the applicability or performance of ageophysical technique, to determine optimumacquisition parameters, or to constrain model parameters during data processing and interpretation.

In electrical and induced polarisation (IP) investigationsthe physical properties of interest are the direct-current(DC) or steady-state resistivity and some parameter thatreflects the polarisation characteristics associated withthe termination of the current field. Most modern-dayDC/IP surveys are conducted with a low-frequencyalternating current waveform, which allows data to berecorded in either the time- or frequency-domain. Thelatter can be achieved using a complex resistivityapproach. In time-domain surveys the IP parameter isgenerally referred to as ‘chargeability’ and is derivedfrom the transient voltage decay curve. In the complexresistivity approach the IP information is contained in

the phase shift between the source current field andresulting voltage field.

Intuitively, one might expect the time- and frequency-domain IP parameters to be equivalent and that eitherapproach should enable the discrimination betweenrocks that have different polarisation properties.However, this misconception is a classic pitfall in theapplication of IP. One of the primary underlying reasonsfor this pitfall is the spectral behaviour of differentrocks – this is particularly true in the case of mineralised

rocks where significant frequency dispersions are oftenobserved. In this paper, a comparison of various time-and frequency-domain IP parameters is done through anumerical model study. Results of actual time- andfrequency-domain laboratory measurements onmineralised samples are also compared.

SPECTRAL BEHAVIOUR AND THECOLE-COLE MODEL

The electrical properties of many rocks, especially thosecontaining mineralisation, behave according to the well-known Cole-Cole impedance model. The Cole-Coleresistivity is complex, implying a phase shift betweenthe source and recorded fields. The Cole-Cole model is

259



Comparison between time- and frequency-domain IP parameters

described by four model parameters: the steady-stateresistivity ρ , a dimensionless chargeability m , a timeconstant τ and a frequency dependence c . Thedimensionless chargeability m is equivalent to thechargeability as defined by Seigel in 1959 (Kemna,2000); that is, the ratio of the secondary voltage divided

by the primary or steady-state voltage, derived from avoltage decay curve (Figure 1):

m = V s/V p (1)

Higher values of chargeability m would result in ahigher polarisability and also a higher phase angleresponse. The time constant τ relates to the time it takesfor the voltage signal to decay; for higher values of τ ,the phase angle peak is shifted to lower frequencies.Higher values of the frequency dependence c manifestas more distinct phase angle peaks.

In terms of the petrophysical meaning, the chargeabilitym is related to the concentration of conductive mineral particles. Differences in m are thus indicative ofdifferences in mineral composition. The time constant τ

is related to the spatial scale at which polarization takes place, and typically increases with increasing size ofmineralised grains (Kemna, 2000). Differences in τ arethus int(di(46 Tw T1 1 Tc 0(26e)8(NE )] Tiesu)9013 Tc rrh)-220057> Tj/T10o t 0 -hncycies. m303 8 6 8 c a1T1 1 Tfc 0105 374.84 Tw 10.0‘CHARGEABILIT.000Y w 00.0AND AMBIGUITY .2-5(l)1(ar05 -1.15ar05 -c)-1(ies. )] T



Van Schoor, Marè and Fourie

261

evaluated at a single frequency, the result would dependon the selected frequency. For example, if theevaluation is done at 0.125 Hz, the contrast between theGREEN or RED/MAGENTA sample and the ORANGEsample is approximately 3:1, but the BLUE andORANGE samples have almost identical phase

responses. At a frequency, approximately 1 decadehigher, the BLUE sample would have a 3:1 phase anglecontrast with the ORANGE sample, while the GREEN,ORANGE AND RED/MAGENTA samples would havelittle or no contrast. Discrimination between the BLUEand GREEN or BLUE and RED/MAGENTA samples iseven more critically dependent on selecting theappropriate frequency as the relative contrast of 3:1effectively changes polarity within approximately asingle decade of frequencies.

The differences in the time-domain curves can also beseen in Figure 3 and is quantified by the various derived

parameters given in Table 1. The dimensionlesschargeability m (and IP percent) values suggest a lowcontrast of approximately 2:1 between the BLUE,GREEN and RED/MAGENTA samples and theORANGE sample; note, however, how that this is onlytrue if a lower base frequency is used in the time-domain transformation. The results also indicate thatthere is almost no contrast between the BLUE, GREENand RED/MAGENTA samples. The integralchargeability M does, however, reveal a contrast ofmore than 5:1 between the GREEN andRED/MAGENTA samples, and the BLUE sample, andof approximately 3:1 between the GREEN and

ORANGE samples. Note that, in contrast to thedimensionless chargeability results, the integralchargeability values indicate that the ORANGE sampleis slightly more polarisable than the BLUE sample.When comparing with the spectral results it is clear thatthe integral chargeability underestimates the polarisablenature of the BLUE sample.

Finally, a comparison of actual laboratorymeasurements is shown in Figure 4. The original datasets were in the form of a Seigel-type IP percent valuesand spectral complex resistivity data. For the purpose ofcomparison, data was extracted for approximately thesame signal base frequency (~0.05 Hz) and also forsimilar source current levels of approximately 1-5 μ A.Here, the time-domain (TD) and frequency-domain(FD) data has been normalised to enable plotting on thesame graph. The correlation between the FD and TD

results is generally good, but notable exceptions occurfor three mineralised samples A4-A6. For these samplesthe FD normalised parameter is between five and seventimes greater than the TD parameter, while for mostother samples a near 1:1 relationship is evident. Thesamples that show this discrepancy are also the samples

that showed the most prominent dispersive behaviour.Even though the time-domain parameter does show thecontrast between the three most polarisable samples andthe other samples in the batch, the contrast that can beexploited is underestimated.

CONCLUSIONS

Comparison of the IP properties of rocks, or theexploitation of these properties for the purpose ofgeophysical discrimination should be conducted withcaution. Reliance on a specific time-domain parameteror on a single frequency measurement may result inmisleading comparisons or even the selection of sub-optimum field parameters when the objective is todiscriminate between specific rock types.

A spectral analysis is recommended and, if this is not possible, it is recommended to derive different time-domain parameters for the purpose of bettercomparisons.

REFERENCES

Duckworth, K., and Calvert, H., 1995, An examination of therelationship between time-domain integral chargeability andthe Cole-Cole impedance model: Geophysics, 60, 1249-1252.

Groom, R. W., and Alvarez, C., 2002, 3D EM Modelling -Application of the Localised non-linear approximator to nearsurface applications: paper presented at SAGEEP.

Habashy, T. M., Groom, R.W., and Spies, B.R., 1993, Beyondthe Born and Rytov Approximations: A Nonlinear Approachto Electromagnetic Scattering: Journal of GeophysicalResearch, 98.

Kemna, A., 2000, Tomographic Inversion of ComplexResistivity - Theory and Application: Ph.D., Ruhr University

Bochum, Germany.



Comparison between time- and frequency-domain IP parameters

Sample: BLUE GREEN ORANGE RED MAGENTA m 0.282 0.327 0.174 0.244 0.333

IP percent(IP%)

28.2 32.7 17.4 24.4 33.3

M (Newmont) 0.024 0.125 0.04 0.134 0.21

M (Newmont)In msec

15.3 81.1 25.7 87.1 136.5

Phase (mrad)@0.125 Hz

-30.7 -92.3 -28.3 -87.9 -87.9

Phase (mrad)@ 1 Hz

-90.5 -55.6 -27.5 -30.5 -30.5

Table 1: Comparison of IP parameters derived for the four Cole-Cole models described in the study. Note thatthe MAGENTA sample has the same Cole-Cole model parameters as the RED sample, but the time-domainparameters were derived for a lower current wave base frequency of 0.05 Hz, compared to 0.125 Hz (RED).

v o

l t a g e

+ VS

time0

+ VP

Figure 1: Earth voltage response associated with a typical DC current source.

Figure 2: A generalised square current waveform was used in the frequency- to time-domain transformation. Ashort linear ramp of 1 ms and a base frequency of 0.125 Hz was used.

262



Van Schoor, Marè and Fourie

263

-100

-90

-80

-70

-60

-50-40

-30

-20

-10

0

0.01 0.1 1 10 100

Frequency (Hz)

P h a s e a n g

l e ( m r a

d )

5 00 , 0 .7 5, 0 .2 5, 0 .1 5 00 , 0 .7 5, 0 .2 5, 1 .0 5 00 , 0 .2 5, 0 .2 5, 1 .0 5 00 , 0 .7 5, 0 .2 5, 3 .0

"BLUE"

0

0.2

0.4

0.6

0.8

1

1.2

0 0.5 1 1.5 2

Time (s)

V o

l t a g e

( V )

500, 0.75, 0.25, 0.1

"GREEN"

0

0.2

0.4

0.6

0.8

1

1.2

0 0.5 1 1.5

Time (s)

V o

l t a g e

( V )

2

500, 0.75, 0.25, 1.0

"ORANGE"

0

0.2

0.4

0.6

0.8

1

1.2

0 0.5 1 1.5

Time (s)

V o

l t a g e

( V )

2

500, 0.25, 0.25, 1.0

"RED/MAGENTA"(500, 0.75, 0.25, 3.0)

0

0.2

0.4

0.6

0.8

1

1.2

0 0.5 1 1.5

Time (s)

V o l

t a g e

( V )

2

0.125 Hz 0.05 Hz

Figure 3: Spectral (top) and equivalent time-domain plots for four different Cole-Cole models. The values in thelegends of the first three graphs represent , c, m and , respectively. In the fourth graph, the Cole-Coleparameters are shown below the graph title, while the model was derived for two different base frequencies.

Comparison of TD and FD IP properties for real samples

1

2

3

4

5

6

7

8

9

0.0001 0.001 0.01 0.1

Normalised IP parameter

S a m p

l e n u m

b e r s

( A 1 - A

9 )

TD FD (0.05 Hz)

Figure 4: Comparison of time-domain (TD) and frequency-domain (FD) laboratory measurements on actualsamples.

Documents

vanschoor_paper1