comparison of pseudorandom binary sequence and squarewave...

Geophysical Prospecting, 2011, 59, 1114–1131 doi: 10.1111/j.1365-2478.2011.01006.x

Comparison of pseudo-random binary sequence and square-wavetransient controlled-source electromagnetic data over the Peon gasdiscovery, Norway

Anton Ziolkowski1∗, David Wright1 and Johan Mattsson2

1University of Edinburgh, School of Geosciences, Grant Institute, The King’s Buildings, West Mains Road, Edinburgh EH9 3JW, UK, and2Petroleum Geo-Services, Kronborgsgrand 23, 164 46 Kista, Sweden

Received December 2010, revision accepted July 2011

ABSTRACTWe discuss the problem of source control in controlled-source electromagnetic(CSEM) surveying and compare and contrast equal energy transient square-waveand transient pseudo-random binary sequence source signatures for the same towed-streamer electromagnetic survey line over the Peon gasfield in the Norwegian sectorof the North Sea. The received response of the transient square-wave data was 11dB greater than that of the pseudo-random binary sequence data, due to diffusiveattenuation of higher frequencies present in the more broadband pseudo-random bi-nary sequence signature. Deconvolution of the pseudo-random binary sequence datarecovers the total impulse response function, increases the signal-to-noise ratio by32.6 dB and separates most of the air wave from the earth impulse response by thecausality principle. The recovered impulse responses have more detailed informationin the frequency domain than the transient square-wave data. The pseudo-randombinary sequence data were acquired with a 10 Hz source bit rate but contain noinformation about the Peon gasfield at frequencies above 2 Hz. The bit rate couldhave been reduced to 4 Hz, increasing the signal energy below 2 Hz by 150% andthus, potentially, increasing the signal-to-noise ratio by a further 4 dB.

Because the total earth impulse response can be recovered from the broad-bandwidth pseudo-random binary sequence data, further time-domain processingmay be applied, including correlated noise removal, which can increase the signal-to-noise ratio by as much as 20 dB, and air wave removal using the causality principle.The information in the arrival time of the peak of the earth response provides the po-tential for traveltime to resistivity mapping to provide a starting model for inversion.

Key words: Acquisition, Electromagnetic, Parameter estimation, Signal processing.

INTRODUCTION

The purpose of this paper is to discuss the problem of sourcecontrol in controlled-source electromagnetic (CSEM) survey-ing. Our discussion centres on an experiment using a towed

∗E-mail: [email protected]

streamer configuration, which in itself is novel and differsfrom conventional CSEM surveying in a number of respects.We discuss these differences later but first describe conven-tional CSEM.

Conventional CSEM (Eidismo et al. 2002; Ellingsrud et al.

2002; Edwards 2005; Constable and Srnka 2007) has beenused mainly in deep water (deeper than 500 m) but in the lastfew years it has been used in shallower water (e.g., Darnet

1114 C© 2011 European Association of Geoscientists & Engineers

Comparison of data over the Peon gas discovery, Norway 1115

et al. 2010). Conventional CSEM employs a continuous sig-nal emitted by a horizontal electric dipole source towed about50 m above the sea floor and receiver nodes on the sea floor,which measure both orthogonal horizontal electric field com-ponents and three orthogonal magnetic field components. Thein-line component of the electric field is used to detect subsur-face resistors.

A variety of periodic continuous signals has been devel-oped for use in marine CSEM, including a square wave (e.g.,Amundsen, Johansen and Rosten 2004) and various wave-forms that concentrate the energy in selected frequencies (Con-stable and Cox 1996; Lu and Srnka 2005; Mittet and Schaug-Pettersen 2008; Meyer, Constable and Key 2010).

Duncan et al. (1980) used a continuous periodic pseudo-random binary sequence with an electric dipole source toobtain soundings onshore in Canada. The advantage of thepseudo-random binary sequence signal is that it containsall frequencies at equal amplitude within a desired band-width. Duncan et al. (1980) demonstrated its use over shallow(500 m) and deep (40 km) targets, by choosing appropriatebandwidth and source-receiver separations. We do not knowwhether this technique has been used offshore.

An alternative CSEM technique also uses a horizontal elec-tric dipole source and dipole electric receivers but the sourcesignal is transient: after a certain time the earth responsereaches a steady state. After steady state has been reached,the cycle may be repeated. We describe the transient approachin detail later. One type of transient response is the response

to a reversal in polarity of a DC current (e.g., Strack 1992;Edwards 1997; Wright, Ziolkowski and Hobbs 2002;Schwalenberg et al. 2005; Ziolkowski, Hobbs and Wright2007). Another type of transient response is the response toa single period of a pseudo-random binary sequence, demon-strated by Wright, Ziolkowski and Hall (2006) for land dataand by Ziolkowski et al. (2008) for marine data. For bothcases the full response is measured over the whole cycle time.Wright et al. (2006) concluded that using a pseudo-randombinary sequence for the source current signal rather than a stepin the DC current allowed data with better signal-to-noise ra-tio to be obtained in a shorter time.

This paper examines the application of the transient CSEMmethod in shallow water (less than 500 m deep) using dataobtained in 2009 with a towed source and receiver systemover the Peon gas field, Norway (Anderson and Mattsson2010). The location of the Peon field is shown in Fig. 1.The setup is illustrated in Fig. 2. Only the in-line electricfield component was measured. Compared with conventionalCSEM there are four major differences. First, there is muchmore water between the source and sea floor and betweenthe sea floor and the receiver. This has an attenuating effecton the response, which we discuss later. Second, the noiselevel in towed streamer electromagnetic (EM) is not well-known, whereas it is very well-known in conventional CSEM(e.g., Constable and Srnka 2007). Third, the towing speedis greater, about 4.5 knots compared with about 1.5 knotsfor conventional CSEM, so the survey covers the subsurface

Figure 1 Map of the northern North Sea showing the location of the Peon discovery.

C© 2011 European Association of Geoscientists & Engineers, Geophysical Prospecting, 59, 1114–1131

1116 A. Ziolkowski, D. Wright and J. Mattsson

Figure 2 The in-line towing configuration of source and receivers along the survey line.

faster, which increases efficiency but reduces the time to col-lect data and build a large signal-to-noise ratio. Fourth, inconventional CSEM the source is moving but the receivers arestationary on the sea floor, whereas in the towed configura-tion the source-receiver geometry is fixed but moves relativeto the sea floor.

These differences demand a fresh approach to the problemof source control and data analysis. We compare and con-trast source characteristics and received data for equal energytransient square-wave and transient pseudo-random binarysequence source signals.

We first define what we mean by a transient source signaland its response. We then describe the experiment and thedata. We present a detailed description of the deconvolutionof the pseudo-random binary sequence data for the impulseresponse and compare its amplitude spectrum with that de-rived from the square-wave data. We then show results forthe whole line, in the time and frequency domains. Finally,we discuss subsequent time-domain processing methods thatcan improve the quality and interpretability of multi-channeltowed streamer pseudo-random binary sequence data.

A TRANSIENT S OUR C E S I GN A L I NCONTROLLED- SOUR C E ELEC T OMA GNETIC

The expression ‘time domain electromagnetic sounding’ hasfor many years been based on the work of Kaufman and Keller(1983), who defined the transient field as the response to a stepin a current switched instantaneously into a magnetic or anelectric dipole. For the magnetic dipole the current is switchedon (p. 315) and for the electric dipole the current is switchedoff (p. 376). Edwards (1997) used the switch-on case for theelectric dipole source. Sheriff (1973) defined ‘transient’ as “(a)nonrepetitive pulse of short duration, such as a voltage pulseor a seismic pulse”. We use the word ‘transient’ in Sheriff’s

sense, both as a noun and as an adjective. In the following,we discuss this in relation to our experiment.

Let the source current be I(t) and the resultant voltage atthe receiver be V(t). Since Maxwell’s equations are linear,the response of the earth can be regarded as a causal linearfilter with impulse response g(t) that depends on the positionand direction of the injected current at the source and theposition and orientation of the receiver electrodes. These threequantities are related by the convolution

V(t) =∫ ∞

0g(τ )I(t − τ )dτ. (1)

The lower limit of the integral is zero because the earth iscausal and cannot respond before there is an input. Since theflow of current in a conducting earth is a lossy process, theimpulse response g(t) must decay to zero as t → ∞. Withinthe precision of the measurements, therefore,

g(t) = 0, for t > Tg, (2)

where Tg is a time greater than which the response is too smallto detect. That is, the earth impulse response g(t) is transient:it has a beginning and an end.

Given that g(t) is of finite duration, what is the best functionfor I(t)? This is the problem of source control. If I(t) is a stepfunction,

I(t) = H(t) =

⎧⎪⎨⎪⎩

11/20

t > 0t = 0t < 0

, (3)

equation (1) becomes

V(t) =∫ ∞

0g(τ )H(t − τ )dτ =

∫ t

0g(τ )dτ (4)

and V(t) is the integral of the impulse response, which isknown as the step response. In principle an infinite amountof time is required to measure the step response. However,if g(t) is of finite duration Tg, the step response tends to a



steady-state value after time Tg. That is, it is of finite durationand is a transient response.

In practice, step functions are not used. Very long periodsquare waves were used instead (Strack 1992; Wright et al.

2002; Schwalenberg et al. 2005; Ziolkowski et al. 2007), withthe period greater than 2Tg. In the vicinity of the polaritychange, these square waves have the behaviour of the sgn(t)function,

sgn(t) = 2H(t) − 1 =

⎧⎪⎨⎪⎩

10

−1

t > 0t = 0t < 0

, (5)

whose Fourier transform is (Bracewell 1965)

sgn( f ) = − i2π f

, (6)

with amplitude spectrum

∣∣sgn( f )∣∣ = 1

2π f. (7)

This function emphasizes the low frequencies relative tothe high frequencies. If we are interested in obtaining the re-sponse g(t), or its Fourier transform g( f ) without bias to anyparticular frequency, we should use a function whose ampli-tude spectrum is constant over the known frequency range ofinterest.

Two time functions with flat amplitude spectra that are usedextensively in the measurement of impulse responses are sweptfrequency sine waves, used in radar and exploration seismol-ogy in the vibroseis technique (e.g., Geyer and Levin 1989),and pseudo-random binary sequences, used for many decadesin electrical and electronic applications (Golomb 1955, 1982;Zierler 1959; Duncan et al. 1980). The instantaneous powerof a swept frequency signal is time-variant, whereas the in-stantaneous power of a pseudo-random binary sequence isconstant for its duration. For vibroseis, the implementationof pseudo-random binary sequences is difficult, because theinertia of the vibrating masses inhibits rapid reversal of thedirection of motion. However, it is not difficult to switch thedirection of the current flow in resistors, and pseudo-randombinary sequences are therefore very suitable for EM applica-tions.

A pseudo-random binary sequence is a sequence of N =2n − 1 samples that switches from one level to the other atpseudo-random multiples of some basic time interval �t; n

is known as the order of the sequence. The pseudo-random

binary sequence has an amplitude spectrum that is flat in thefrequency interval

1N�t

≤ f ≤ 12�t

. (8)

The recorded data need to be sampled at a rate that is greaterthan, or equal to 1/�t in order to obtain the full benefit ofthe source spectrum.

Using a current signal I(t) such as a single period of apseudo-random binary sequence, of time duration Ts , whichhas the full bandwidth of the impulse response g(t), equation(4) can be written as

V(t) =∫ Tg+Ts

0g(τ )I(t − τ )dτ. (9)

This is a complete convolution of finite duration Tg + Ts .The only issue remaining is to determine g(t), given I(t) andV(t).

We emphasize that I(t), of duration Ts , must have the fullbandwidth of the impulse response g(t). Because I(t) has finiteduration Ts , with a known beginning and known end, we sayit is a transient source signal. The response V(t) must be mea-sured for the minimum duration Tg + Ts , beginning at the starttime of the source signal. Because V(t) has a finite duration,with a known beginning and end, it is also a transient.

In the absence of noise it is straightforward to solve equa-tion (9) for g(t). Transforming equation (9) to the frequencydomain yields

V( f ) = g( f ) I( f ), (10)

in which V( f ), g( f ) and I( f ) are the Fourier transforms ofV(t), g(t) and I(t), respectively and the convolution becomesa multiplication. Dividing through by I( f ), which is knownfrom the measurement of the source current I(t), yields

g( f ) = V( f )

I( f )(11)

and transforming back to the time domain yields g(t), as re-quired. Note that if the source current and receiver voltageare measured with the same instruments, the effect of the in-struments will cancel out in the division of equation (11).

The recovery of g(t) by solving the convolution integralequation (9) is known as deconvolution (e.g., Robinson1967). For a pseudo-random binary sequence, |I( f )| = I, afrequency-independent constant, and the deconvolution doesnot change the frequency content of the received signal.



T H E D A T A

Peon is a shallow gas discovery field in the Norwegian sectorof the North Sea shown on the map in Fig. 1. The reservoir isabout 160 m below the sea floor in water about 380 m deep.The depth of the source and receiver were 10 m and 100m, respectively, as shown in Fig. 2 (Anderson and Mattsson2010). At a tow speed of about 4 knots it took about 90 minto obtain the data over one 11 km line.

A line over the Peon gas discovery was surveyed twice withthe towed streamer EM system, which included a 400 m elec-tric dipole source and two in-line towed electric field receivers:once with a transient square-wave current signature and againwith a transient pseudo-random binary sequence. In conven-tional CSEM surveying (Constable and Srnka 2007) the sig-nal is continuous. In this experiment, the 0.1 Hz square-wavesource signal was turned off after exactly 10 cycles (100 s) and20 s ‘listening time’ was recorded in addition to the record-ing made while the source was switched on, as described inthe previous section. This cycle was then repeated. The square

wave has its energy concentrated at the fundamental frequency0.1 Hz and at odd harmonics (0.3, 0.5 Hz, etc.).

The choice of 0.1 Hz is an unusual choice for the fundamen-tal frequency of the square wave; the traditional frequency is0.25 Hz (for example, Eidismo et al. 2002; Srnka, Carrazoneand Ephron 2006; Constable and Srnka 2007). The choiceof 0.1 Hz was based on modelling of the Peon anomaly andthe intention was to obtain the maximum number of frequen-cies in the bandwidth of the anomaly to enable the frequencyresponse to be properly resolved. The bandwidth was foundto be approximately 0–2 Hz. The traditional fundamentalfrequency of 0.25 Hz gives only four frequencies in this band-width: 0.25, 0.75, 1.25 and 1.75 Hz, whereas a fundamentalof 0.1 Hz gives ten: 0.1, 0.3, 0.5, 0.7, 0.9, 1.1, 1.3, 1.5, 1.7and 1.9 Hz. It was not practical to go lower than 0.1 Hz,because at least ten cycles were required in the 100 s window.

The benefits of pseudo-random binary sequences in signalprocessing have been well understood since the 1950s (e.g.,Golomb 1955, 1982) and pseudo-random binary sequence

Figure 3 Examples of source current and corresponding E-field measurements for the transient pseudo-random binary sequence and transientsquare-wave data, a) pseudo-random binary sequence source current; b) pseudo-random binary sequence E-field; c) square-wave source current;d) square-wave E-field.



Figure 4 Examples of source current signature and corresponding amplitude spectrum for a transient pseudo-random binary sequence andtransient square-wave data: a) transient pseudo-random binary sequence source current; b) amplitude spectrum of (a); c) transient square-wavesource current; d) amplitude spectrum of (c).

electric dipole sources have been used in EM for at least thirtyyears (Duncan et al. 1980). The pseudo-random binary se-quence used in this experiment was order 10 (2n − 1 sampleswith n = 10) with a bit rate of 10 samples per second, givinga duration of 102.3 s. The square-wave and pseudo-randombinary sequence signals had the same amplitude ∼800 A andabout the same length, so they had approximately equal en-ergy. Calculation of their energies using the formula (A7) inAppendix A shows less than 1% difference. The ‘shot’ inter-val for each line was 120 s, so the ‘listening time’ for eachtransient was about 18 s for the pseudo-random binary se-quence and 20 s for the square wave, although recording alsoincluded the time the source was switched on. The pseudo-random binary sequence has its energy evenly spread out overa wide bandwidth (∼0.01–5 Hz). The transmitted and re-ceived signals were measured and sampled at 120 samples persecond.

Figure 3 shows the periodic nature of the recorded datafor both data sets for the Peon line. On the left is the mea-sured source current in amps. On the right is the measured

electric field in V/m; that is, the measured dipole voltage hasbeen divided by the dipole length. The measurements of thesource current and received voltage were made with identicalrecording systems, including filters. The impulse response ofthe earth is shorter than the listening time in each transientsequence. Hence, the response on the right can be regarded asa series of complete convolutions with the source signal. Thesource signal is very repeatable. The received signal varies, thevariation being caused by variations in the earth impulse re-sponse as the vessel moves across the target as well as changesin the noise.

Figure 4 compares the pseudo-random binary sequence andsquare-wave transient source signatures and their amplitudespectra. The pseudo-random binary sequence spectrum is al-most level, while the square-wave source has a spectrum withpeaks at the fundamental frequency 0.1 Hz and odd har-monics, as expected. The peak at 0.1 Hz is greater than thepseudo-random binary sequence level by a factor of about 20.Band-pass filtering in recording renders the signatures slightlydifferent from what is expected from pure theoretical



Figure 5 Upper: time-domain transient response for square-wave(black) and pseudo-random binary sequence (red); lower: correspond-ing amplitude spectra.

calculations. The spectral differences in the source signatureshave profound consequences for what can be done with therecorded data.

Figure 5 compares the time responses and their amplitudespectra for square-wave (black) and pseudo-random binary se-quence (red) transients in the same place. Using equation (A7)from Appendix A, we calculate the ‘energy’ of the square-waveresponse in Fig. 5 as 5.37 × 10−10 V2s/m2, while the ‘energy’ ofthe pseudo-random binary sequence response is 4.23 × 10−11

V2s/m2. The ratio of these ‘energies’ is 12.7, or 11 dB. That is,the energy of the square- wave response is 11 dB greater thanthe energy of the pseudo-random binary sequence response,which is the principal reason for using a square wave. Since theinput source signals had approximately the same energy, weattribute the difference in energy at the receiver to the attenu-ation of higher frequencies, especially in the water layer. Thespectrum of the pseudo-random binary sequence response ismuch flatter than that of the square wave, as shown in Fig. 4,which exhibits the expected 1/(2n−1) amplitude decay for thefundamental frequency 0.1 Hz and its odd harmonics.

S IGNATURE DECONVOLUTION OF T HEPSEUDO-RANDOM BINARY SEQUENCED A T A

The time signal a(t) may be sampled at regular intervals �t,according to

as(t) = a(t)�t∞∑

k=−∞δ(t−k�t), (12)

(Berkhout 1973, 1974), which is a series of spikes. The delta-function δ(t) has dimensions of (time)−1, so the multiplicationby �t ensures that the digital signal has the same units as theanalogue signal. To make the notation less cumbersome, wewrite the sampled signal as at = · · · , a−2, a−1, a0, a1, a2, . . .,which usually has a finite length and starts at t = 0, for ex-ample:

at = (a0, a1, a2, . . . , an). (13)

Figure 6(a) shows one period of the sampled source sig-nal, which we denote as st, Fig. 6(b) shows the correspondingreceiver response (which is the same as the red curve in theupper plot of Fig. 5), which we denote as xt, and Fig. 6(c)shows the Wiener impulse response gt (see Appendix B) plot-ted on the same time scale. A few details of interest are asfollows. The sampling interval was dt = 1/120 s; the numberof samples in the source signal (a) was n = 12284; the num-ber of samples in the receiver response (b) was m = 14400; thenumber of samples in the filter was m − n + 1 = 2117. To sta-bilize the filter calculation 0.5 per cent white noise was added(see Appendix B).

The time series gt shown in Fig. 6(c) is the filter that bestestimates the earth impulse response in a least-squares sense.Convolution of this filter with the input signal (Fig. 6a) is

yt =n∑

k=0

gkst−k, t = 0, 1, . . . , m, (14)

and is the corresponding best estimate of the signal in the data.This is shown as the blue curve in Fig. 6(d). The differencext − yt between the measurement xt and the estimated signalyt is the best estimate of the uncorrelated noise nt. This isshown as the red curve in Fig. 6(d).

The deconvolution has compressed the energy of the re-ceived response of Fig. 6(b) to the much shorter durationimpulse response of Fig. 6(c). As explained in Appendix A,this compression makes the signal stand higher relative to thenoise. Using the definition of the energy compression ratio



Figure 6 a) Measured source signature (Amp); b) measured receiver response at 2025 m offset (V/m); c) Wiener impulse response derived from(a) and (b) plotted on the same time scale; d) blue curve is the part of (b) correlated with (a), red curve is the response (b) minus the bluecurve.

derived in Appendix A, we calculate the gain in the signal-to-noise ratio to be 42.75 or 32.6 dB. This dramatic gain morethan compensates for the 11 dB deficit in the energy of thepseudo-random binary sequence response compared with thesquare-wave response.

The impulse response exhibits a large impulsive air wave att = 0, which is almost completely separated from the earth re-sponse. The earth response itself consists of a primary responseplus multiple responses generated by the reverberation be-tween the sea floor and the sea-surface, similar to water-layerreverberations in seismic data (e.g., Nordskag and Amundsen2007). The dramatic separation of the air wave from the earthimpulse response in the time domain for this shallow watercase is a result of causality: in shallow water the air wavetravels to the receiver faster than the earth response and ar-rives first; the earth response travels more slowly and arrivessecond.

FREQUENCY R ESPONSE FUNCTIONS OFPSEUDO-RANDOM BINARY SEQUENCEA N D S Q U A R E - W A V E D A T A

Figure 7 shows the impulse response and its amplitude spec-trum for the first transient of the pseudo-random binary se-quence line. Figure 8 compares the amplitude spectrum ofFig. 7, the continuous curve, with the frequency response func-tion of the first transient of the square- wave line, the blacksquares. The repeatability of the source and receiver posi-tioning enables these response functions to be compared. Thevalues denoted by the black squares in Figure 8 are obtainedby dividing the amplitude spectrum of the received responseby the amplitude of the source current at the fundamentalfrequency and the odd harmonics.

It is clear that the two frequency response functions areidentical at 0.1, 0.3, 0.5 Hz, etc. but the pseudo-randombinary sequence response also has information at other



Figure 7 a) Earth impulse response obtained by deconvolving the response at receiver 2 with the measured source signature for pop 1, u26; b)amplitude spectrum of this impulse response.

Figure 8 Solid line: amplitude spectrum of the impulse response of Fig.7; black squares: amplitude spectrum obtained by frequency domaindivision at the fundamental frequency and odd harmonics.

frequencies. The pseudo-random binary sequence data allowthe full bandwidth response function to be obtained in thetime or frequency domains. The square-wave data do not.

A D ATA LINE

The method developed above is now applied to a line ofpseudo-random binary sequence data, using the second re-ceiver at offset 2545 m from the source. Figure 9 shows therecovered impulse responses in both a wiggle plot (upper) and

in colour display (lower). The air wave is the sharp peak closeto t = 0, decaying to almost zero amplitude at about 200 ms.Anomalously high amplitudes caused by the sub-sea Peon gas-field can be seen on traces 19–48 between 200–1000 ms. Theyare easier to see on the colour display.

The anomaly can be isolated very well by subtracting trace1 from all the traces, as shown in Fig. 10. The wiggle displayclearly shows that trace 1 is now dead and the other traceshave varying amounts of noise. The air wave has disappearedcompletely; this is very clear on the wiggle display.

An interesting outcome of the Wiener approach we haveused to perform the deconvolution is the ability to separatethe signal from the noise. Fig. 11 shows the pre-deconvolutionnoise for the whole line, estimated as described above. It is pre-dominantly low frequency but is clearly without a DC compo-nent as a result of the high-pass filter in the recording system.The noise does not appear to be correlated from trace to trace,which is what we would expect from true noise. It indicatesthat the separation of the signal and noise is correct.

The frequency-domain amplitude response functions for thewhole line, 0–2 Hz are displayed in Fig. 12, where the resultsof pseudo-random binary sequence and square-wave dataare compared and, importantly, trace 1 is subtracted fromall the traces so the Peon anomaly can clearly be seen. Thepseudo-random binary sequence data (upper plot) have val-ues at 0.0 Hz and at increments of 0.07 Hz. The square-wavedata have values at 0.1 Hz and at increments of 0.2 Hz, forreasons described above. The results are comparable but thepseudo-random binary sequence data have better frequencyresolution.



Figure 9 Impulse responses for whole line; upper display: wiggle; lower display: same data in colour.

SUBSEQUENT T I ME - DOMA I N PR OC ESS INGOF PSEUDO-R A N DOM BI N A R Y SE QUENCED A T A

In this section we discuss the application of three time-domain processing methods that can be applied to the pseudo-random binary sequence data after deconvolution: the re-moval of spatially-correlated noise, especially magnetotelluric(MT) noise; the removal of the air wave; and traveltime toresistivity inversion.

Various sources of electromagnetic noise exist in the sea.As far as active electromagnetic surveying is concerned, MTsignals are noise, in the same way that earthquake waves and

microseisms are background noise for the seismic reflectionmethod.

“Natural EM signals come from an enormous variety ofprocesses and from sources ranging from the core of the earthto distant galaxies. Within the frequency range of interest inexploration, say 0.001–104 Hz, only two source regions areimportant. These are the atmosphere and the magnetosphere.Electrical storms in the lower atmosphere are the dominantcause of fields between 1 Hz and 10 kHz, whereas below 1Hz the fields originate primarily in hydromagnetic waves inthe magnetosphere” (Vozoff 1991).

In conventional CSEM data acquisition it is recognized thatthe MT noise is correlated over large distances. De la Kethulle



Figure 10 Data of Figure 9 with trace 1 subtracted from all the traces.

de Ryhove and Maaø (2008) described the use of a remotereference node to estimate this spatially-correlated noise wellaway from the source.

Ziolkowski et al. (2010) developed a method for the re-moval of correlated electromagnetic noise for transient datathat does not require a remote reference and increases thesignal-to-noise ratio of each data set by as much as 20 dB.The elements of the process are illustrated in Fig. 13 using datacollected with a multi-channel ocean-bottom cable (OBC) re-ceiver.

Figure 13(a) shows a raw common-source gather, 250 s inlength (vertical axis), with offsets (horizontal axis) increasing

from 2200 m on the left to 7000 m on the right. The long-period noise is well correlated from trace to trace; the responseto the pseudo-random binary sequence input decays dramat-ically from near to far offsets. Figure 13(b) shows the resultof deconvolution in a 20 s window containing the impulse re-sponse: the long signal responses to the pseudo-random inputcurrent were compressed to impulse responses but the uncor-related noise remains. An estimate of the noise is obtainedby subtracting the short impulse response from the nearest250 s trace. This noise estimate is similar to the noise on theother traces. To determine the component of the noise on eachsubsequent trace that is correlated with this noise estimate, a



Figure 11 Recovered noise.

Figure 12 Peon anomaly, frequency domain. Upper figure: pseudo-random binary sequence, 0–2 Hz; lower figure square-wave, 0.1–1.9 Hz.



Figure 13 a) Common-source gather, 250 s in length (vertical axis), with offsets (horizontal axis) increasing from 2200 m on the left to 7000m on the right. b) Result of deconvolving the source gather for a measured current, showing only 20 of data: the signal has been compressed toimpulse responses but the noise remains. c) Result of subtracting estimated noise from data in (b).

Wiener filter is found for each trace that best estimates thecorrelated part – the noise – from this noise estimate. Thenoise estimated in this way on each subsequent trace is thensubtracted from the trace to reveal the impulse response, asshown in Fig. 13(c). The increase in the signal-to-noise ratiofrom Fig. 13(b) to Fig.13(c) is about 20 dB.

This method could be applied very effectively to multi-channel towed streamer data, after signature deconvolution.Clearly, it cannot be applied to the square-wave data and itis obviously very difficult to use a remote reference for towedstreamer data.

In shallow water the air wave appears as a sharp peak atthe beginning of the impulse response. We see it clearly inFig. 7. At long offsets the attenuation of the direct wave inthe shallow conducting water reduces its amplitude so muchit becomes negligible compared with the air wave and theearth response. The total response is then a sum of the airwave and the earth impulse response. At very long offsetsthe amplitude of the response through the conducting earthbecomes negligible compared with the amplitude of the airwave and only the air wave is measured. Ziolkowski andWright (2007) used a very long offset measurement to estimate



Figure 14 Part of a marine OBC transient EM gather; blue curves: total impulse responses; red curves: same data with air wave removed.

Figure 15 a) Blue curve: impulse response from Peon data (same as in Fig. 7); red curve: impulse response from 1D modelling. b) 1D model.

the air wave at shorter offsets and removed the air wave fromthe data. Fig. 14 shows the result.

The structure of the earth impulse response and the re-sult of Fig. 14 can be studied by modelling. First we com-pute a 1D synthetic response (Edwards 1997) to compare

with the impulse response of Fig. 7, at the beginning of thePeon line, away from the gasfield. Using the model shown inFig. 15(b) we calculate the response shown by the red curvein Fig. 15(a), which closely matches the impulse response re-covered from the pseudo-random binary sequence data. This



Figure 16 Decomposition of the impulse response. Black curve: totalimpulse response from 1D modelling; red curve: airwave plus airwavemultiples; green curve: total response minus airwave and airwavemultiples; blue curve: earth impulse response without water layer.

response is the total impulse response, part of which is shownin Fig. 16 as a black curve. We have omitted most of the largeair wave peak in Fig. 16 to emphasize the contributions ofthe other components of the response. Second, we computethe air wave and air wave multiples response at a very longoffset (50 km) and scale it back to a 2545 m offset using 1/r3

scaling, as described by Ziolkowski and Wright (2007); this isthe red curve in Fig. 16. Subtracting the air wave and airwavemultiples from the total response gives the earth impulse re-sponse plus multiples, shown as a green curve in Fig. 16. Theblue curve in Fig. 16 is computed with the source and receiveron the sea floor but without the water layer and with the airwave removed; so this is the land case without the air waveand contains no multiples. The green curve is what is obtainedby removing the air wave plus air wave multiples and is thesame as the red responses of Fig. 14 obtained by processingreal data. Comparing the green and blue curves, it is seen thatthe presence of multiples increases the amplitude of the earthresponse and delays the time of the peak.

Although the air wave is easy to see in the time-domainimpulse response, an enormous amount of work has beendone to tackle its removal in the frequency domain and onereviewer wanted us particularly to mention the patent of Lu,Srnka and Carazzone (2007).

An additional processing step available to transient EM datais the extraction of resistivity information from the peak timeof the earth impulse response (Edwards 1997). Wright andZiolkowski (2007) showed that for the land case an equiv-alent half-space resistivity can be calculated from the arrivaltime of the peak for each source-receiver pair and calculatingthe gradient of the traveltime gives an interval resistivity anal-

ogous to interval velocities in seismic data processing. Thereis further potential to develop the use of traveltime informa-tion from EM data and apply a data processing approach toresistivity determination.

CONCLUSIONS

We distinguish between source control, which must be per-formed in the time domain and data processing and analysisthat may be performed in the time domain, the frequencydomain, or other domains.

The energies of the two transient source signatures werealmost exactly equal: the energy of the pseudo-random bi-nary sequence transient was less than 1% greater than thatof the transient square wave. However, the received responseof the transient square wave was 11 dB greater than the re-sponse to the transient pseudo-random binary sequence in thesame place. We attribute the difference to the attenuation ofhigher frequencies especially in the water layer. This affectsthe pseudo-random binary sequence more than the squarewave: the amplitude spectrum of the pseudo-random binarysequence response is much flatter than that of the square wave,which exhibits the expected 1/(2n−1) amplitude decay for thefundamental frequency 0.1 Hz and its odd harmonics.

We have shown that the deconvolution step compressesthe received energy of the pseudo-random binary sequencedata into an impulse response, resulting in a gain in signal-to-random noise of 32.6 dB, in this particular case, handsomelycompensating for the initial advantage of the square-wavedata before deconvolution. There is a dramatic separation ofthe air wave from the earth response as a result of causality:the air wave travels faster and arrives first; the earth responsetravels slower and arrives second. The pseudo-random binarysequence data after deconvolution have more detailed infor-mation in the frequency domain than the square-wave data.There is no information about the Peon anomaly in the dataabove 2 Hz. It follows that the 10 Hz bit rate of the pseudo-random binary sequence source signature could potentiallyhave been reduced to 4 Hz, thus increasing the signal energybelow 2 Hz by 150% and providing a further 4dB boost to thesignal-to-noise ratio before deconvolution. No such option isavailable to the square-wave transient.

In addition, pseudo-random binary sequence data havethe advantage that further time-domain processing may beapplied, including correlated noise removal, which can in-crease the signal-to-noise ratio by as much as 20 dB and airwave removal. In addition, using the time of the peak of theearth impulse response function and traveltime to resistivity



mapping has the potential to provide a starting model forinversion.

ACKNOWLEDGE ME N T S

We thank Johnathan Linfoot and especially John Brittan ofPGS for many useful discussions and for comments and sug-gestions on our paper. We are very grateful to PGS for per-mission to show the data. We thank the anonymous reviewersand especially Associate Editor Alan Reid for their very help-ful comments and suggestions.

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AP PENDIX A: GA I N I N S I GN A L - N OI SERATIO BY PSEUDO- R A N DOM BI N A R YSEQUENCE DEC ON V OLUT I ON

We show how deconvolution of the pseudo-random binarysequence signal increases the signal-to-noise ratio in the timedomain by compressing the signal energy to a shorter time.But first we show that this gain is less obvious in the frequencydomain. Let the output of the receiver be

x(t) = V(t) + n(t), (A1)

where n(t) is noise, independent of the source and V(t) is thesignal

V(t) =∫ Tg+Ts

0g(τ )I(t − τ )dτ, (A2)

as defined in equation (9). Using equation (A2) in equation(A1), the Fourier transform of equation (A1) is

x( f ) = g( f ) I( f ) + n( f ), (A3)

and the signal-to-noise ratio in the frequency domain (beforedeconvolution) is

rb( f ) =

∣∣∣g( f ) I( f )∣∣∣

|n( f )| =|g( f )|

∣∣∣ I( f )∣∣∣

|n( f )| . (A4)

Dividing equation (A3) by I( f ) yields

x( f )

I( f )= g( f ) + n( f )

I( f ), (A5)

and the signal-to-noise ratio in the frequency domain (afterdeconvolution) is

ra( f ) = |g( f )|/ |n( f )|∣∣∣ I( f )

∣∣∣ = |g( f )| | I( f )||n( f )| . (A6)

In the frequency domain the signal-to-noise ratio appears tobe the same at all frequencies before and after deconvolution,so it is not obvious that there is any advantage in doing this.However, equations (A4) and (A6) only consider the ampli-tude spectrum and ignore the phase spectrum. As shown byBerkhout (1973, 1974), for example, the phase spectrum hasan extremely important role to play in the ability to detect andresolve events. The effect of the change in the phase spectrumis easily understood by considering what happens in the timedomain.

Before deconvolution the signal is Vt with duration (Tg +Ts); after deconvolution the signal is the response gt with du-ration (Tg). Deconvolution of the pseudo-random binary se-quence compresses the signal in time, without changing thesignal-to-noise ratio in the frequency domain. If the noise israndom and stationary before deconvolution, it is also randomand stationary after deconvolution for the pseudo-random bi-nary sequence, because its amplitude spectrum is flat and thecompression of the signal energy to a shorter time windowsimply makes the signal stand higher relative to the noise. Wenow quantify this effect.

First, following Robinson (1967), we define the energy of asignal s(t) of duration T as

Es =∫ T

0|s(t)|2 dt. (A7)

Now consider a pseudo-random binary sequence of ordern, with N = 2n − 1 samples, switching between +1 and –1at pseudo-random multiples of a basic time interval �t. Itsenergy is

EPRBS = �tN∑1

12 = N�t. (A8)

If this energy is now concentrated into a single sample ofduration �t, it must have amplitude

√N. Thus deconvolution

of the pseudo-random binary sequence with itself gives anamplitude gain of

√N, or

Gain = 20 log10(√

N) = 10 log10 (N) dB. (A9)

The amplitude spectrum of a pseudo-random binary se-quence of N samples is virtually the same as the amplitudespectrum of a single sample of amplitude

√N, followed by

(N − 1) zeros but the phase spectra are different.



We can arrive at the result of equation (A9) using a moregeneral formulation. First define the centre of energy tc of asignal s(t), such that∫ T

0|s(t)|2 (t − tc)dt = 0. (A10)

That is, the moment of signal energy before t = tc is equaland opposite to the moment of signal energy after t = tc. Now,using an idea from Berkhout (1973, 1974), we define thelength of signal s(t) as

Ls =∫ T

0 |s(t)|2 |t − tc| dt

Es. (A11)

Normalizing by the signal energy in equation (A11) givesLs the same dimensions as t (in this case time) and permits acomparison of the lengths of signals with different dimensions.The pseudo-random binary sequence signal has its energy uni-formly distributed and centred at time N�t/2; its length is

LPRBS = 2∫ N�t/2

0 tdt

N�t= (N�t/2)2

N�t= N�t

4, (A12)

whereas the impulse of amplitude√

N and duration �t, withthe same energy as the pseudo-random binary sequence, hascentre of energy at time �t/2 and length

LIMP = 2∫ �t/2

0 Ntdt

N�t= N (�t/2)2

N�t= �t

4. (A13)

The temporal compression ratio of the energy for this ex-ample is

LPRBS/LIMP = N, (A14)

and the gain in the signal-to-random noise ratio as a result ofthis compression is 10 log10(N)dB.

APPENDIX B: THE W IENER FILTER

The discrete sampled receiver response xt is the convolutionof the source signal st with the impulse response of the earthgt plus noise nt:

xt = st ∗ gt + nt (B1)

The noise is what would be measured if there were no signaland is uncorrelated with the signal. The presence of noisecomplicates the deconvolution problem.

Wiener (1949) solved the problem of finding gt from equa-tion (B1), given xt and st. He proposed the calculation of afilter gt = g0, g1, . . . , gn that best approximates gt. The con-volution of the input signal st with gt is

yt =n∑

k=0

gkst−k. (B2)

The sum of the squares of the differences between the trueresponse xt and the convolution yt is

I =∑

t

(xt − yt)2. (B3)

Minimization of I is achieved by differentiating I with re-spect to each of the filter coefficients gt and setting the resultto zero. This yields a set of equations, known as the ‘normalequations’, which may be written in matrix form as:⎡⎢⎢⎢⎢⎣

φss(0) φss(1) · · · φss(n)φss(1) φss(0) · · · φss(n − 1)

...... · · ·

...φss(n) φss(n − 1) · · · φss(0)

⎤⎥⎥⎥⎥⎦

⎡⎢⎢⎢⎢⎣

g0

g1

...gn

⎤⎥⎥⎥⎥⎦ =

⎡⎢⎢⎢⎢⎣

φxs(0)φxs(1)

...φxs(n)

⎤⎥⎥⎥⎥⎦ , (B4)

where the autocorrelation of st is defined as

φss(τ ) =∑

t

stst−τ , (B5)

and the cross-correlation of xt with st is defined as

φxs(τ ) =∑

t

xtst−τ . (B6)

Levinson (1947) exploited the Toeplitz symmetry of thesquare matrix in equation (B4) to find a recursive solution thatrequires n2 arithmetic operations for its inversion comparedwith n3 operations using conventional methods.

To stabilize the inversion it is normally necessary to add asmall constant to the leading diagonal. This is usually doneby multiplying φss(0) by a factor slightly greater than one;typically the factor is expressed as

1 + w

100, (A7)

indicating that it is equivalent to adding w per cent whitenoise to the input signal st. For a pure pseudo-random binarysequence this stabilization is unnecessary.


comparison of pseudorandom binary sequence and squarewave...

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