Time-Domain Spectral Induced Polarization Based on Pseudo-random Sequence

MEI LI,1 WENBO WEI,1 WEIBIN LUO,1 and QINDONG XU1

Abstract—To reduce noise during electrical prospecting, we

hereby propose a new method using correlation identification

technology and conventional electrical exploration devices. A

correlation operation can be carried out with the transmitted

pseudo-random sequence and received time signal to suppress the

random noise, and the time-domain impulse response and fre-

quency response of the frequency domain of the underground

media can be obtained. At the same time, using a dual Cole–Cole

model to fit a complex resistivity spectrum, which is close to the

frequency response, we can get a variety of induced polarization

parameters and electromagnetic parameters of subsurface, which

can provide more useful information for the exploration of mineral

resources. This time domain prospecting method can effectively

improve the efficiency of the spectral induced polarization method.

In this article, we have carried out theoretical calculations and a

simulation to prove the feasibility of such a method.

Key words: Pseudo-random sequence, SIP,

correlation identification technology, MTEM.

1. Introduction

Conventional electrical prospecting is signifi-

cantly limited by noise and low efficiency. The

depletion of easily discovered mine reserves and

other raw materials has triggered a renewed interest

in alternative techniques for exploration.

In electrical prospecting, the use of a pseudo-

random signal as the transmitter signal source has

been shown to improve the signal-to- noise ratio

(SNR). As an example, the multi-transient electro-

magnetic system (MTEM) (ZIOLKOWSKI et al., 2006,

2007, 2009) has become an established commercial

system whose second and third generation equipment

has been used to generate pseudo-random sequences

instead of step signals, with significantly improved

SNR.

An MTEM system obtains the impulse responses

of the subsurface by deconvolution of the transmitted

and received signals. However, according to the

correlation identification theory, the correlation

operation of the received time sequence with a sent

pseudo-random sequence can not only remove ran-

dom noise to improve SNR, but also easily obtain the

impulse response and frequency response of under-

ground media (DUNCAN et al., 1980; QUINCY et al.,

1980; LUO and LI, 2009). They employed electro-

magnetic methods in their approach to interpret the

frequency response, whereas MTEM is based on DC

resistivity inversion by the peak of the impulse

response.

In fact, the complex resistivity spectrum of the

underground media can be deduced from its fre-

quency response (PRASAD et al., 2010; LIU, 2010), but

they did not explain how to obtain the complex

resistivity spectrum from its frequency response.

In this paper, we aim to propose a complex

resistivity method based on the pseudo-random

sequence, verify its feasibility with simulation, and

provide the theoretical basis for further development

of a newer generation of electrical prospecting

devices.

With fitting and inversion using the spectral

induced polarization method (SIP) of dual Cole–

Cole, we can obtain more parameters and improve the

accuracy of characterization of the underground

media. Therefore, this strategy can be considered as a

time-domain SIP method since a complex resistivity

spectrum of the subsurface can be obtained with a

single transmit–receive sequence.

1 China University of Geosciences (Beijing), Beijing 100083,

China. E-mail: maggieli@cugb.edu.cn

Pure Appl. Geophys.

� 2012 Springer Basel

DOI 10.1007/s00024-012-0624-z Pure and Applied Geophysics

2. The Correlation Identification of Subsurface

The correlation identification model of a subsur-

face is shown in Fig. 1. The impulse response of an

observing system composed of an electrode, wire,

grounding impedance and measuring device is

denoted as hsðtÞ, and the impulse response of the

earth system heðtÞ (LUO, 2007).

Then the relation between the input and output is

Eq. (1):

uðtÞ ¼ vðtÞ � heðtÞ � hsðtÞ þ nðtÞ: ð1Þ

A cross-correlation operation with the input

pseudo-random sequence can then be performed on

both sides of Eq. (1), which can eliminate the random

noise;

RvuðtÞ ¼ RvvðtÞ � heðtÞ � hsðtÞ: ð2Þ

After first obtaining the cross-correlation of the

input and output signal RvuðtÞ and the input signal

autocorrelation RvvðtÞ, the overall impulse response

of observing system and earth system he tð Þ � hs tð Þcan be obtained after deconvolution. Eventually, we

will be able to remove the influence of observing

system hsðtÞ and get the impulse response of sub-

surface heðtÞ by deconvolution.

The convolution and deconvolution operation can

also be transformed into multiplication and division

in the frequency domain (LUO, 2007) as below:

PvuðxÞ ¼ PvvðxÞ � HeðxÞ � HsðxÞ: ð3Þ

The correlation identification result in the vicinity

of the transmitter with the same observing system is

regarded as the impulse response of the observing

system hsðtÞ because the result near the transmitter is

affected only by the observing system and the influ-

ence of the earth system can be ignored. As a result,

HsðxÞ can be obtained after being transformed into

the frequency domain.

The frequency response of subsurface is obtained

via Eq. (4):

HeðxÞ ¼PvuðxÞ

PvvðxÞ � HsðxÞ: ð4Þ

The complex resistivity spectrum qðxÞ is com-

monly used in geophysics. It can be deduced from the

frequency response as follows:

qðxÞ ¼ K � HeðxÞ; ð5Þ

where K is the geometric factor. Then,

K ¼ 2p1

AM� 1

ANþ 1

BN�1

BM

; ð6Þ

in which AM, AN, BN and BM are the distances

between the electrodes. A and B are a pair of elec-

trodes of the transmitter, while M and N a pair of

receiver electrodes. The value of the geometric factor

depends on the relative positions of four electrodes A,

M, N, and B.

The complex resistivity spectrum can be inter-

preted geophysically using a complex resistivity

method. Usually, a single Cole–Cole model is used to

fit the complex resistivity spectrum and generate four

induced polarization (IP) parameters. However, as the

complex resistivity spectrum is affected by the elec-

tromagnetic coupling effects, the IP parameters

obtained this way are not accurate.

In contrast, fitting with dual Cole–Cole model can

not only get four IP apparent spectral parameters,

namely the zero-frequency apparent resistivity

q0, apparent chargeability m1, apparent frequency

dependence exponent c1, apparent time constants1,

and also three apparent spectral parameters related

with electromagnetic coupling, i.e., m2, c2, s2.

(PELTON, 1978).

qðxÞ ¼ q0 1� m1 1� 1

1þ ðjxs1Þc1

� �� �

� 1� m2 1� 1

1þ ðjxs2Þc2

� �� �ð7Þ

Therefore, this method can not only separate the

IP spectrum from the electromagnetic coupling

spectrum, but also obtain parameters such as residual

electromagnetic effects (REM) um=u0m and electro-

magnetic apparent resistivity qx using three

electromagnetic apparent spectral parameters, which

)(tv)(tr

)(tn

)(tu)(ths)(the

Figure 1The correlation identification model of subsurface

M. Li et al. Pure Appl. Geophys.

can significantly improve the detection accuracy (LUO

and ZHANG, 1998).

The result obtained in one measuring point are

the apparent spectral parameters, which reflect the

overall information about the subsurface between

the source and receiver electrodes. What we truly

need is the intrinsic Cole–Cole model parameters of

the target polarization body (ore, oil or gas reser-

voirs to be ascertained, etc.) and its geometric

distribution (including depth, thickness, shape and

other information). Therefore, information from

more than two measurement points is needed. The

information can be greatly enriched by multi-offsets

observations. This is illustrated in Fig. 2 (LUO,

2007). AB is the transmission electrode pair, M1 N1

is the first receiving electrode pair, N1M3 (that is,

M2 N2) the second and M3 N3 the third. Multiple

receivers arranged in the same line can simulta-

neously receive the electric responses of the

transmission dipole source, with increased offset.

The size of the offset reflects the depth of subsur-

face; therefore, the electric response of subsurface

with different depths can be obtained with a single

transmit-receive sequence.

After the joint inversion of the spectra of multiple

measuring points with multi-offsets, intrinsic spectral

parameters of the target polarization body and its

geometrical distribution can be worked out. Firstly,

the apparent spectrum of the target polarization body

is separated from surrounding rocks with conven-

tional complex resistivity inversion of each complex

resistivity spectrum (including amplitude and phase),

then the intrinsic spectral parameters and geometric

distribution are obtained from joint inversion of

apparent phase spectra of different offsets (LIU,

1998).

3. Simulation Results

To better illustrate the effects of this protocol, we

may consider the following simulation examples:

Firstly, we will use a typical second-order system

to illustrate the parameters selection of pseudo-ran-

dom sequence and to verify the identification effects

of this method because the characteristics of a typical

second-order system are well-known. Assuming its

impulse response is h tð Þ ¼ a � ebt � sin ctð Þ, where

a = 11.547, b = -5, and c = 8.66, its cutoff fre-

quency is 2 Hz and its impulse response

approximates zero after 1 s, so the duration of its

impulse response is about 1 s. Parameters are deter-

mined according to the formula (8) and (9) (LI, 1987).

0:4431

D� fmax; ð8Þ

N ¼ 1:2� 1:5ð Þ Ts

D; ð9Þ

where D is the duration of a single bit, fmax the cut-off

frequency of the system, Ts the duration of its

impulse response, N the cycle length of the sequence.

Through calculation, bit duration D can be set at

0.02 s and the cycle length of the sequence N at 63.

In order to get a better identification effect, the bit

duration could be 0.01 s, and the sequence length 100

points.

Gaussian white noise is a common type of noise.

In Fig. 3, the red ? line is the actual impulse

response of a typical second-order system to be

identified. The green diamond curve is the identifi-

cation result after adding a Gaussian white noise

whose standard deviation is 1 V. The white solid line

is the deconvolution result with observations system

effect removed. Clearly, most random noises are

1M 1N 3N3MA B

Source Receivers

Figure 2Multi-offsets observation

Time-Domain Spectral Induced Polarization

eliminated after the correlation operation, and the

deconvolution result is closer to the actual impulse

response of the system with improved SNR from

11.35 to 43.76 dB. LabVIEW, a graphical program-

ming language, makes the simulation easy.

The Fourier transform of the resulting impulse

response is HeðxÞ. The complex resistivity spectrum

can be obtained via Eq. (5).

Then the fitting and inversion of complex resis-

tivity spectrum is illustrated with a dual Cole–Cole

model with seven parameters. The more there are

parameters, the poorer the results are. Therefore the

initial selection is critical when damped least-squares

fitting method is used. Incorrect initial value may

cause non-convergence and improper results.

Since c1 is in the range between 0.1 and 0.6, c20.9

and 1.0, m1 and m2 are in the range between 0 and

0.98 and m1\m2, any initial values in these ranges

are appropriate. The zero-frequency resistivity q0 is

the value of the low frequency asymptote of real part

or amplitude.

The initial selection of s1 and s2 is more critical.

In the high-frequency band where electromagnetic

coupling is dominant, there is a peak of the imaginary

component. The frequency of the peak corresponds to

the time constant of electromagnetic coupling effects

s2. Then estimate s1 according to s1 � s2.

Am

plitu

de6

-1

0

1

2

3

4

5

Time (s)20 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

undecon result

decon result

real impulse

Figure 3Identification results

10-2

100

102

104

106

5

10

15

20

25

Frequency

Am

plitu

de

Real amplitude and inversion amplitude

Real

Inversion

10-2

100

102

104

106

0

0.2

0.4

0.6

0.8

Frequency

Pha

se

Real phase and inversion phase

Figure 4Fitting results

M. Li et al. Pure Appl. Geophys.

Figure 4 is the fitting result of a dual Cole–Cole

model in which q0 ¼ 25, m1 ¼ 0:1, c1 ¼ 0:12,

s1 ¼ 0:1, m2 ¼ 0:67, c2 ¼ 0:95, s2 ¼ 0:003 (by

MATLAB). The set error threshold is reached only

after eight iterations. The initial selection is effective.

The above procedures described the process of

obtaining the parameters of one measuring point. In

order to obtain the intrinsic spectrum parameters of the

target polarization body and its geometric distribution,

multi-point observations are needed, preferably using a

high-density geometry sounding method, i.e. multi-

offsets observations. Then intrinsic spectrum parame-

ters of the target polarization body and its geometric

distribution can be obtained by joint inversion.

4. Discussion

In this paper, a new SIP method is proposed and

simulated based on correlation identification tech-

nology. The correlation identification method is a

universal system identification method, and can be

applied to any active source electrical prospecting

methods. Besides the complex resistivity, we can also

get DC resistivity, IP and the electromagnetic

parameters. The value of the frequency response at

the frequency close to 0 is the value of the DC

apparent resistivity of the measuring point. The

inversion of values of multiple measuring points can

be done with the DC resistivity. At high frequencies

(e.g., greater than 104 Hz), electromagnetic parame-

ters can be obtained and interpreted with the

electromagnetic method. At low frequencies, the

IP parameters can be acquired, such as percent

frequency effect (PFE), differentiation of percent

frequency effect with offset, and differentiation of

relative phase with offset, among others.

5. Conclusion

Compared with existing technology, the technical

solution described in this paper improves prospecting

efficiency and accuracy with following methods:

1. To obtain the impulse response and frequency

response of subsurface by cross-correlation

operation of the received time signal and sent

pseudo-random sequence (including m-sequence

and the inverse repeat m sequence);

2. To remove the influence of observing system via

deconvolution;

3. To obtain the intrinsic spectral parameters and

geometric distribution by means of multi-offsets

observations;

4. To interpret the resulting frequency response

through complex resistivity method. Electromag-

netic parameters and finer probing can be acquired

by dual Cole–Cole model;

So far, we have completed the theoretical analysis

and simulation of the time-domain SIP method which

adopts correlation identification technology. The

results show that this method can effectively reduce

random noise. We are currently in the process of

developing an electrical prospecting receiver based

on the simulation results. In addition, the geophysical

interpretation of the time-domain impulse response

will be further studied.

Acknowledgments

The research reported in this paper was funded by

SinoProbe-01-01 (Experimental study of the conti-

nental standard grid of electromagnetic parameters).

Special thanks are extended to the authors who made

original contribution to the theory and application of

pseudo-random sequence in electrical prospecting,

e.g. Duncan P. M., Quincy E. A., Hobbs B.,

Ziolkowski A., Wright D., Prasad T. R. and Liu

Jingxian, etc.

REFERENCES

DUNCAN P. M., HWANG A., EDWARDS R. N., BAILEY R. C., and

GARLAND G. D. (1980), The development and applications of a

wide band electromagnetic sounding system using a pseudo-

noise source, Geophysics 45, 1276–1296.

LI BAINAN, The pseudo random signal and the correlation identifi-

cation (Science Press, Beijing 1987) (in Chinese).

LIU JINGXIAN. Study on the m-sequence correlation identification

and its application to induced polarization prospecting for the

method of suppressing noise. [MA thesis]. Beijing: China Uni-

versity of Geosciences, 2010 (in Chinese).

LIU SONG, SIP method (China University of Geosciences Press,

Wuhan 1998) (in Chinese).

Time-Domain Spectral Induced Polarization

LUO YANZHANG, and ZHANG GUIQING, Theory and application of

spectral induced polarization (Society of Exploration Geophysi-

cists 1998).

LUO WEIBIN. Study on Pseudorandom marine controlled-Source

electromagnetic sounding with multi-offsets. [PhD thesis].

Changsha: Central South University, 2007 (in Chinese).

LUO WEIBIN, and LI QINGCHUN (2009), Electromagnetic Explora-

tion Based on System Identification for Seafloor

Hydrocarbon Reservoir and Gas Hydrate, PIERS Proceedings,

1344–1348.

PRASAD TADEPALLI RAMMOHAN, RAMAYYA BOPPANA DASARADHA, RAO

YELAMANCHILI PURNACHANDRA. Process and device for measure-

ment of spectral induced polarization response using pseudo

random binary sequence (PRBS) current source. US Patent

2010/0102822 A1.

PELTON W.H., WARD S.H., HALLOF P.G. et al. (1978), Mineral

discrimination and removal of inductive coupling with multi-

frequency IP, Geophysics 43, 588–609.

QUINCY E. A., RHOADES MARK L., and STURM KIM A. (1980), Remote

Induction Sounding of Hanna Underground Coal Burn 11, Phase

1, Employing Pseudo noise Cross-Correlation Techniques,

Transactions on Geoscience and Remote Sensing, 18, 337–347.

ZIOLKOWSKI A., HOBBS B.A., and WRIGHT D. True amplitude tran-

sient electromagnetic system response measurement. WO2006/

114561_A2, 2006-11-02.

ZIOLKOWSKI A., HOBBS B.A., and WRIGHT D. (2007), Multitransient

electromagnetic demonstration survey in France, Geophysics,

72, 197–209.

ZIOLKOWSKI A. Optimization of MTEM parameters. US2009/

0230970_A1, 2009-09-17.

(Received April 30, 2012, revised November 5, 2012, accepted November 6, 2012)

M. Li et al. Pure Appl. Geophys.