Journal of Applied Geophysics 96 (2013) 107–118

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Journal of Applied Geophysics

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A procedure to reduce side lobes of reflectionwavelets: A contribution tolow frequency information

Hakan Karslı a,1, Derman Dondurur b,⁎a Karadeniz Technical University, Department of Geophysics, 61080 Trabzon, Turkeyb Dokuz Eylül University, Institute of Marine Sciences and Technology, Baku Street, No: 100, Inciraltı, 35340 İzmir, Turkey

⁎ Corresponding author. Tel.: +90 232 278 5565; fax: +E-mail addresses: hkarsli@ktu.edu.tr (H. Karslı), derma

(D. Dondurur).1 Tel.: +90 462 337 2706; fax: +90 462 325 7405.

0926-9851/$ – see front matter © 2013 Elsevier B.V. All rihttp://dx.doi.org/10.1016/j.jappgeo.2013.07.002

a b s t r a c t

a r t i c l e i n f o

Article history:Received 18 April 2013Accepted 14 July 2013Available online 24 July 2013

Keywords:Low frequencyAmplitude envelopeSide lobesResolution

Side lobes of the wavelets arise from the lack of low frequency content in a reflection wavelet. They tend toincrease the time span of an individual reflection event and interfere with the other primary reflections or sidelobes. Furthermore, their trace-by-trace consistency may produce pseudo-reflections and may cause misinter-pretations of the side lobes as weak reflections.A procedure in order to improve the low frequency content of the seismic traces by suppressing the side lobeamplitudes based on the complex trace envelope is proposed. Using the average energies of the seismic traceand its envelope, the polarity table of the trace is obtained and used to correct the phase of the envelope. Theresultant trace is termed “side lobe reduced (SLR) trace”. The method can be applied to the stack or migratedseismic data by a trace-by-trace basis. The only required parameter of themethod is themoving average operatorlength which is used to calculate average energies of the input traces. In general, shorter operator lengths yieldbetter results when the dominant frequency of the input increases.Results from synthetics and real seismic data sets show that the procedure improves the low frequency componentsof the input trace and side lobes in the output SLR trace are significantly suppressed. Themethodmay be consideredas a seismic amplitude attribute, which aids the interpreter to obtain the true seismic signature of the geologicalformations by removing the side lobes of the wavelet and restoring the low frequency components if the lowerfrequencies of deeper reflections are of primary concern.

© 2013 Elsevier B.V. All rights reserved.

1. Introduction

In the conventional data processing, efforts are done generally onthe enhancement of higher frequency components of the recorded seis-mic signals. However, it is also an important task to improve or recoverthe lower frequencies during the processing workflow because theyare essential for imaging deeper targets and impedance inversion. Lowfrequency components are generally attenuated because of the receiverarrays in the field or low-cut filters in the processing center (Dondururand Karslı, 2012; Martin and Stewart, 1994;Masoomzadeh et al., 2006).Preservation of low frequency signals in the acquisition and processingof seismic data has attracted attention in recent years (Criss et al., 2005;Deping et al., 2006; Dondurur and Karslı, 2012; Soubaras et al., 2012),because the low frequency signal is not absorbed quicklywhen it travelsinto the subsurface, hence it contains information fromdeeper reflectors.Furthermore, the low frequency signals may contain additional infor-mation which can be used to study the internal reflection characteristics

90 232 278 5082.n.dondurur@deu.edu.tr

ghts reserved.

of a hydrocarbon reservoir such as the weak reflections from oil/watercontact (Ziolkowski et al., 2003).

Wavelets can be defined by their different characteristics includingfrequency, phase, amplitude and side lobes (Lines and Treitel, 1991).While the dominant features such as frequency, phase and amplitudes,and their influences on the shape and character of the wavelets havebeen widely studied so far, the information about the effects of theirside lobes on the resolution of recorded signal is poor. Side lobe artifactsare a common problem in the interpretation and inversion of seismicdata, which are caused by inadequacy of low frequencies, leading tothe narrowing of the spectral bandwidth. It is generally consideredthat a wider amplitude spectrum ensures a higher resolution in thefinal image. Yılmaz (2001) showed that both high and low frequencycomponents are required to ensure the higher resolution, and therefore,the low frequency content is as important as the high frequency contentof the seismic data. Therefore, recovering or improving the lower fre-quency band of the amplitude spectrum may result in a significantimprovement on the quality of the seismic image of deeper targets(Dondurur and Karslı, 2012; Ziolkowski et al., 2003).

It is expected thatwavelet energy is concentrated in the centralmainlobe so that the largest trough or peak represents the real subsurfaceformed by rocks with different impedance (Junbin et al., 2007). This isa simpleway to link seismic reflection events to stratigraphic interfaces.

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However, side lobes of the wavelets also hold some energy in additionto the main lobe and may produce more or less continuous pseudo-seismic events. Their interference effects mask the genuine reflectionsor damage the correct amplitude/phase attributes of the primary reflec-tions. Therefore, seismic events are not only from real stratigraphic sur-faces, but they may also be formed by wavelet side lobes which cannotbe attributed to the geological interfaces, which sometimes complicatesthe correct interpretations (Danielsen and Karlsson, 1984).

Junbin et al. (2007) investigated the interference effects of side lobeson the primary reflections and showed that this interference may bea serious problem when identifying thin gas reservoirs. In zero-phasecase such as the output of a conventional Wiener deconvolution, wegenerally get a wavelet main lobe between two weak side lobes. Inthe cases of gas bearing thin sand bodies, the base reflections almostalways interfere with another peak reflected from the top of the reser-voir, which sometimesmake it difficult to identify such a sand reservoir(Hongliu, 2003; Hongliu and Backus, 2005; Hongliu and Hentz, 2004).The low frequencies play an important role by reducing side lobesand their interferences, improving the resolvability of thin beds (Duval,2012).

Normally, it is impossible to remove the side lobes of a waveletcompletely, but they can be considerably reduced by suitable signal pro-cessing techniques. Several differentmethods such as time variant spec-tral whitening (Yılmaz, 2001), frequency domain spectral extrapolation(Dasgupta and Nowack, 2008; Karslı, 2006, 2011; Sacchi and Ulrych,2007) and deconvolution (Oldenburg et al., 1983; Peacock and Treitel,1969; Robinson, 1967; Zala et al., 1988) have been used for this purpose.The main idea is that the side lobes of a reflection event are caused bythe lack of low frequency content as discussed in detail by Knapp(1993). Therefore, if the side lobes are suppressed without any distor-tion to the main lobes, low frequencies of the reflection events can beconsiderably improved.

In this study, a procedure to suppress the side lobes of the reflectionwavelets embedded in the seismic reflection data is suggested. The sidelobe reduction methodology is based on the seismic trace envelope

Fig. 1. Effects of lack of the low frequency content on a zero-phase band limited Klauder waveleof the wavelets. When the low frequencies are missing, amplitudes of the side lobes considera

calculated by complex trace approximation. Low frequency componentsof envelope trace, which have larger amplitudes with respect to the lowfrequencies of the input seismic trace, are used to reconstruct the lowerfrequency components. Several tests and applications are done onsynthetic and real seismic traces as well as on a high resolution marineseismic data.

2. What causes side lobes?

We consider a zero-phase Klauder wavelet (Klauder et al., 1960)which is the result of the auto-correlation of sweep signals, and it is per-fectly ideal to study the side lobes and their effects because it has largeside lobes on each side of the main lobe among the different wavelettypes. Its side lobes are also known as correlation noise, which causessome interpretative difficulties. In order to investigate the relation be-tween side lobe existence and lack of low frequency content, Klauderwavelets with three different bandwidths were calculated in the timedomain (Fig. 1). In the calculations, high frequency limits of the frequen-cy bands are kept unchanged, but the low frequency limits are progres-sively moved to higher frequencies (e.g. 1–80 Hz, 20–80 Hz and 40–80 Hz). Comparing the time and frequency domain representations ofthe obtained Klauderwavelets, it is clear that the lack of low frequenciesin the wavelet spectrum causes bursts in the side lobe amplitudes(Fig. 1b and c) and the ratio of the main lobe to the side lobes alsodecreases. These computations show that the higher amplitude sidelobes arise from the missing of low frequency content in the spectralbandwidth.

In conventional data processing, the seismic data is high-pass orband-pass filtered to attenuate the low frequency noise such as groundroll or swell noise. This procedure, however, also suppresses the ampli-tudes from deeper reflecting interfaces embedded in the low frequencycomponents. Thus, the filtering out of low frequencies produces higheramplitude side lobes in the time domain and attenuates the reflectionamplitudes from deeper reflectors.

ts for (a) 1–80 Hz, (b) 20–80 Hz, and (c) 40–80 Hz bandwidths, and (d) amplitude spectrably increase.

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3. Importance of low frequency components and their relationswiththe side lobes

It is easy for seismic interpreters to understand the need for higherfrequencies in the seismic data since they provide more detail aboutthe geology, such as thin stratigraphic features and subtle rock struc-tures. However, low frequencies are also important. Duval (2012) indi-cated that the low frequency components tend to suppress side lobes,which results in a better imaging of deeper reflectors and improvingthe resolution especially around the convergent reflections such aspinch-outs. Ideally, a seismic interpreter would like to have a seismicwavelet which presents a spike, an impulsive response which clearlydedicates the real subsurface reflectivity.

Fig. 2 shows the effect of frequency bandwidth on themain and sidelobes of a Klauderwavelet. In Fig. 2a, an increase in the higher frequencylimit (e.g. 20 to 55 Hz) sharpens thewaveletmain lobe (or central peak)as expected, but side lobes still remain. Side lobes, however, are largerand main lobe is broader when the bandwidth of wavelet is narrow(e.g. 10–20 Hz) while side lobes are narrow and main lobe is morespiky when the bandwidth of wavelet is wide (e.g. 10–55 Hz). Onthe other hand, introducing the low frequency components into thewavelet reduces the amplitudes of side lobes as shown in Fig. 2b.The main lobe to side lobe amplitude ratio is apparently larger forthe wavelet of 2–20 Hz bandwidth when compared to the waveletof 10–20 Hz. Broadening the frequency spectrum at both high- andlow-ends of the spectral band thereby produces a narrow waveletwith smaller side lobes, better representing the true seismic signa-ture of the interfaces.

Fig. 3.Workflow for SLR procedure. Theprocedure is based on the arithmetical summationand subtraction of the envelope trace to input trace (see text for details).

4. Side lobe reduction procedure

The procedure for side lobe reduction (SLR) is based on the use ofseismic trace envelopes and can be applied to a time or depth migratedtrace, aswell as stack sections. Themain idea is the correction of polarityof a reflection in the envelope trace. The basic workflow for the SLR

Fig. 2. Effect of frequency bandwidth towards the high- and low-ends of the spectrum for a zeroare gradually included from left to right in the top row, and (b) constant high frequency end, b

procedure is given in Fig. 3. An envelope trace of input X(t) is calculatedby complex seismic trace analysis as given by Taner et al. (1979). A com-plex seismic trace Z(t) is formed by considering the seismic trace X(t)

-phase Klauder wavelet. (a) Constant low frequency end, but high frequency componentsut low frequency components are gradually included from left to right in the bottom row.

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itself as its real part and considering the corresponding Y(t) as its imag-inary part, which is actually the Hilbert transform of input X(t),

Z tð Þ ¼ X tð Þ þ jY tð Þ; ð1Þ

where j = (−1)1/2. Using these real and imaginary parts, the envelopeis calculated as

R tð Þ ¼ Z tð Þj j ¼ X tð Þ2 þ Y tð Þ2h i0:5

: ð2Þ

An “envelope-added trace” (EAT) is obtained by summing envelopetrace R(t) with seismic trace X(t) and an “envelope-subtracted trace”(EST) is obtained by subtracting envelope trace from seismic trace(Fig. 3). In each case, the results are divided by a factor of 2,

EAT ¼ Rsum tð Þ ¼ X tð Þ þ R tð Þð Þ=2EST ¼ Rsub tð Þ ¼ X tð Þ−R tð Þð Þ=2:

ð3Þ

The analysis is proceeded by calculating the energies of X(t), EAT andEST traces, which are then further averaged by a moving average oper-ator to obtain the average energies of these traces (MX,MEAT andMESTtraces in Fig. 3, respectively),

MX ¼ Mtrace jð Þ ¼ 12mþ 1

Xm

k¼−m

Etrace jþ kð Þ

MEAT ¼ Msum jð Þ ¼ 12mþ 1

Xm

k¼−m

Esum jþ kð Þ

MEST ¼ Msub jð Þ ¼ 12mþ 1

Xm

k¼−m

Esub jþ kð Þ;

ð4Þ

where j = k + 1, k + 2,…,N-k, N is the number of samples in a trace,m is the half length of the moving average operator, Etrace(t) = X(t)2,

Fig. 4. Application of SLR method to a synthetic seismic trace. (a) Reflectivity series consisting(d) and (e) the amplitude spectra of the input seismic trace and its envelope, respectively, (f)average energies of the input trace (MX), envelope added trace (MEAT) and envelope subtrac(h). (n) Final energy difference trace obtained by the subtraction of (m) from (l). The traces in

Esum(t) = Rsum2 (t), and Esub(t) = Rsub

2 (t) representing the energies ofX(t), EAT and EST traces, respectively.

MEAT andMEST traces are subtracted fromMX to obtain energy dif-ference traces Dsum(t) and Dsub(t). By subtracting Dsum(t) from Dsub(t),the final energy difference trace Dfinal(t) is obtained as

Dsum tð Þ ¼ Mtrace tð Þ−Msum tð ÞDsub tð Þ ¼ Mtrace tð Þ−Msub tð ÞDfinal tð Þ ¼ Dsub tð Þ−Dsum tð Þ:

ð5Þ

Note that the amplitudes in the final trace only represent the energydifferences, not true values of polarity. For this reason, the sign functionof this trace is calculated to obtain the polarity tables. On the other hand,this process can blow up any low-level noise embedded in the data aswell. Therefore, we rather prefer to use a division of the energy differ-ence trace to the stabilized modulus of it,

Dsign tð Þ ¼ Dfinal tð Þ= Dfinal tð Þj j þ εð Þ; ð6Þ

where ε is the stability constant in the case that Dfinal(t) ≅ 0. The spikesare arisen from the side lobes in the seismic trace, and they should befiltered out since they do not represent primary reflection events. Thepolarity table is obtained by filtering the spikes from Dsign(t) trace bya median filter,

Rpol tð Þ ¼ sgn MEDIAN Dsign tð Þ� �� �

; ð7Þ

where sgn() is sign function. Eq. (7) is further multiplied by the enve-lope trace in Eq. (2) to get the “polarity corrected envelope” (PCE),

RC tð Þ ¼ R tð Þ:Rpol tð Þ: ð8Þ

of randomly spaced five spikes, (b) corresponding synthetic trace, (c) the envelope trace,envelope added trace, and (g) envelope subtracted trace. (h), (j) and (k) correspond to

ted trace (MEST), respectively. (l) Subtraction of (j) from (h), (m) subtraction of (k) from(h) to (m) are normalized for display purposes. See text for details.

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The final SLR trace is obtained by a simple average of the PCE andX(t) trace (Fig. 3),

XSLR tð Þ ¼ X tð Þ þ RC tð Þð Þ=2: ð9Þ

The workflow in Fig. 3 is explained in detail for a synthetic seismictrace in Figs. 4 and 5. The synthetic trace in Fig. 4b is consisted of five in-dividual reflections, obtained from the convolution of randomly spacedfive spikes in the reflectivity series in Fig. 4a and a Klauder wavelet with10–80 Hz bandwidth. The wavelet is of 400 ms time duration and hashigh-amplitude side lobes. Note that a strong interference exists be-tween the reflections at 1.28 s and 1.32 s. Of these events, only the larg-est peak and trough are from the main lobe and represent stratigraphicsurfaces, whereas the other weak peaks and troughs are from side lobesand have no geologic meaning. The polarity of each event in the syn-thetic trace is indicated by the direction of its main lobe (Fig. 4b). Theenvelope trace calculated from Eq. (2) is shown in Fig. 4c which onlyhas positive polarity wavelets. It also has a lower frequency content(Fig. 4e) when compared to the spectrum of the input seismic trace(Fig. 4d). In other words, envelope trace has larger amplitudes in lowfrequencies than those in the lower frequency bandwidth of the seismictrace. This situation allows us to reconstruct the lower frequency com-ponents of the input seismic traces.

The envelope-added (EAT) and envelope-subtracted (EST) tracesobtained from Eq. (3) are shown in Fig. 4f and g, respectively. Positive

Fig. 5. (a) The scaled polarity information of energy difference trace in Fig. 4n, (b) the polaritenvelope corrected trace Rc(t) obtained by multiplying (b) and (c). For a comparison, (e), (f)respectively. (h) and (i) show close-ups of input and output traces between 1.28 s and 1.32 s.

energy reinforces and the main lobes of negative polarity diminish inthe EAT trace, while negative energy is reinforced and the main lobesof positive polarity diminish in the EST trace. Fig. 4h, j and k showsaverage energies of X(t), EAT and EST traces, respectively. These tracesare indicated byMX,MEAT andMEST andobtained by amoving averageprocess of the trace energies over an averaging window using Eq. (4).Fig. 4l and m shows energy difference traces Dsum(t) and Dsub(t)obtained from Eq. (5), and a subtraction between the two yields Dfinal(t)trace (Fig. 4n) representing the final energy difference.

Dsign(t), the polarity information of Dfinal(t) trace obtained fromEq. (6) is shown in Fig. 5a. After filtering the spikes from this trace bya median filtering as in Eq. (7), the final polarity table is obtained(Fig. 5b). It indicates the sign of the reflection polarities along the timeor depth axis, and if it is null, then there is no reflection information.Since the envelope trace doesn't distinguish the polarities of the reflec-tions, the polarity table provides us a correction of the envelope with itscorrect polarity information. The envelope trace is multiplied by thepolarity table as given by Eq. (8) to get the polarity corrected envelopetrace (Fig. 5d). After averaging of polarity corrected envelopewith inputseismic trace by Eq. (9), the final SLR trace XSLR(t) is obtained (Fig. 5e).When comparing the XSLR(t) with the input X(t) trace in Fig. 5f, sidelobes are suppressed and five individual reflections are clearly distin-guished with their correct polarities in the XSLR(t) trace. The close-upsin Fig. 5h and i show that the interference effect between the reflectionsat 1.28 s and 1.32 s is also resolved. The output XSLR(t) trace has wider

y table Rpol(t) obtained by filtering the spikes of (a), (c) the envelope trace R(t), (d) theand (g) show final SLR and input seismic traces, and their respective amplitude spectra,

Fig. 6. Test results to determine the optimummoving average window length, nw, for SLRmethod for (a) 21 (0.02 s), (b) 51 (0.05 s), (c) 81 (0.08 s), and (d) 101 (0.1 s) points. Input andoutput wavelets and their respective amplitude spectra are shown on the top and bottom rows, respectively.

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frequency bandwidth with respect to the input trace spectrum (Fig. 5g)including the restored low frequency components.

5. Determination of the moving operator length

The only parameter that should be pre-determined for the computa-tions is the length of themoving average operator, nw (or its half-lengthm) used in Eq. (4). Several tests are performed on a Klauder wavelet todetermine the optimal moving average operator length and the resultsare compared both in time- and frequency-domains in Fig. 6. We usedawavelet having 10–55 Hz frequency bandwidth and 1.0 ms time sam-pling interval and then applied SLRprocess to thewaveletwith differentmoving average window lengths. Since a certain rule does not exist todefine the optimal window length, it can be determined by trial-and-error method.

It is observed from Fig. 6 that side lobes have been effectively re-duced asmoving averagewindow length increases. However, the valuesof nw = 81 and nw = 101 points produce almost the same result bothin time- and frequency-domains except for a little more increment inlow frequency components for the latter. On the other hand, becauselongerwindow lengthsmay causemore decay in high-frequency ampli-tudes, the optimal window length is determined as 81 points.

It is also observed that the amplitudes of high-frequency compo-nents in the outputweaken slightly as observed in the respective ampli-tude spectrum of the output in Fig. 6b. This is because the method usesthe envelope of input trace, which has inherently lower frequency con-tent than the input (see Fig. 4e). Nevertheless, this weakening could beignored if the low frequency information is of more priority. In addition,a proper selection of the moving average window length after severaltests both in time- and frequency-domainsmay overcome this problem.As a rule of thumb, our tests indicate that shorter window lengths

Fig. 7.Application of SLR procedure to synthetic seismograms in order to characterize lateral varRed and blue lines represent the interfaces with positive and negative reflectivity coefficienseismograms, (d) 21st trace of input seismograms (indicated by an arrow), (e) SLR output oThe same scaling factor is used in (b) and (c) for display purposes.

generally produce better results for the data sets of higher dominantfrequencies. Therefore, for high resolution seismic data sets with widerfrequency bandwidth, shorter window lengths are recommended toavoid the suppression of the higher frequency content.

6. Results

The SLRmethodwas applied to synthetic seismograms of a flat-lyinginterface model generated to characterize lateral polarity variationsalong a reflection and show the influences of wavelet side lobes onthe trace-by-trace consistency of a reflection event (Fig. 7). In the calcu-lation of synthetic seismograms, a 10–55 Hz Klauder wavelet sampledat 1.0 ms interval was used. The reflection coefficient between thetraces 41 and 81 is negative while it is positive elsewhere, in Fig. 7aand calculated synthetic seismograms are shown in Fig. 7b. Becausethe large side lobes tend to be coherent laterally along the main lobes,they could be misinterpreted as weak reflectors in detailed sequenceanalysis. This trace-by-trace continuity of the side lobes is evident inFig. 7b along the upper and bottom sides of the main reflector. TheSLR output in Fig. 7c is obtained by using 0.08 s (81 points) movingaverage window length. The side lobes at both sides of the main lobeof reflection wavelets are significantly reduced for both negative andpositive polarity wavelets in the SLR output.

Two individual traces from the input and output synthetic seis-mograms are extracted to compare the effect of SLR procedure moreclearly. Fig. 7d and e shows the input and output traces of SLR processwith a positive main lobe (trace number 21) while Fig. 7f and g illus-trates the traces with a negative main lobe (trace number 61). In theSLR outputs in Fig. 7e and g, SLR trace has smaller side lobes with gentleamplitudes with respect to the main lobe.

iation in the reflectionwavelet polarity. (a)Model used to generate synthetic seismograms.ts (R), respectively. (b) Computed synthetic seismograms, (c) SLR output of syntheticf (d), (f) 61st trace of input seismograms (indicated by an arrow), (g) SLR output of (f).

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Fig. 9. Application of SLR procedure to a real marine seismic data trace. (a) Input seismic trace, (b) SLR trace, and (c) their corresponding amplitude spectra. Main reflection peaks areevident on the SLR output trace and low frequency content of the input trace is improved (see area in the dashed ellipse).

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Similar investigations were performed on the seismograms withstrong interference effects between two reflections from two closelyspaced reflectors (Fig. 8a). Fig. 8b shows synthetic model seismogramsto investigate the side lobe interference effect. Both reflectors have thesame reflection coefficient and similar computational parameters. Thesame Klauder wavelet as in Fig. 7 is used to compute the seismograms.The reflection coefficient between the traces 41 and 81 is negativewhileit is positive elsewhere. Since the time difference between two reflec-tions in Fig. 8b is 25 ms, we observe a strong interference on the sidelobes of both reflections. The interference effect is so drastic that thereis a pseudo-reflection event with positive polarity along the negativepolarity reflections between the traces 41 and 81 in Fig. 8b. In the SLRoutput seismograms, the interference effects are resolved and the sec-tion has two reflections with correct polarity information (Fig. 8c).

The interference effect was also investigated using individual tracesfrom synthetic seismograms. Two traces from the input and output syn-thetic seismograms are extracted to investigate the output of SLR proce-dure. Fig. 8d and e shows input and output traces to SLR process withpositive main lobes (trace number 40) while Fig. 8f and g illustratesthe reflections with negative main lobes (trace number 44).

The 40th trace in Fig. 8d consists of two large positive peaks and alarge negative peak while the 44th trace in Fig. 8f consists of two largenegative peaks and a large positive peak. In the SLR outputs of the tracesin Fig. 8e and g, however, there exist two main peaks with positivepolarity for 40th trace and with negative polarity for 44th trace consis-tentwith the inputmodel. The absence of side lobe interferences revealsthe realistic seismic signature of the subsurface with true polarity attri-butes of the reflections.

Fig. 8. Application of SLR procedure to synthetic seismograms to characterize interference effecsame reflection coefficients used to generate synthetic seismograms. Red and blue lines repr(b) Computed synthetic seismograms, (c) SLR output of synthetic seismograms, (d) 40th tracinput seismograms (indicated by an arrow), (g) SLR output of (f). The same scaling factor is us

The SLR procedure is then applied to a real minimum phase marineseismic trace in Fig. 9a. The tracewas band-pass filtered (20–210 Hz) toremove the swell noise and scaled by a 500 ms AGC operator as a con-ventional processing procedure, which resulted in a total removal oflow frequencies (see the amplitude spectrum in Fig. 9c). In the SLRoutput trace, side lobes are suppressed and main reflection events arerevealed (Fig. 9b). For example, while the reflection event around ap-proximately 0.38 s and 0.42 s (indicated by arrows) on the seismictrace has both positive and negative polarity cycles, this event has onlynegative polarity on the SLR trace. Comparison of the amplitude spectraindicates that low frequency components of the input trace are alsoimproved (Fig. 9c).

Although marine seismic data generally have higher resolution andwider spectral bandwidth than onshore seismic data, they generallydo not have lower frequencies available in the frequency band becauseof a band-pass filtering in the early stages of the processing to removethe swell noise. These missed frequencies cannot be sufficiently recov-ered by conventional processes, even if the data are deconvolved towiden the frequency band. These missing lower frequencies are crucialin the geologic interpretation of the deeper subsurface and they arerequired for inversion process to get the acoustic impedance.

Fig. 10 shows an application of the SLR method to a migrated highresolution minimum phase marine seismic line. Fig. 10a shows theinput line consisted of several parallel to sub-parallel gently dippingreflections with some deeper reflection events of relatively lower fre-quency. A Generator–Injector (GI) gun was used during the data acqui-sition. The gun and streamer were towed at 3 m depth below the seasurface. Shot and group intervals were 25 m and 6.25 m, respectively.

ts on the reflection wavelet side lobes. (a) Model with two closely spaced reflectors of theesent the interfaces with positive and negative reflectivity coefficients (R), respectively.e of input seismograms (indicated by an arrow), (e) SLR output of (d), (f) 44th trace ofed in (b) and (c) for display purposes.

Fig. 10. Application of SLR procedure to a real marine seismic data. (a) Input migrated data, and (b) after SLR process. Insets show the corresponding average amplitude spectra of thesections. Same amplitude scaling factor is used for both sections.

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The sampling interval was 1 ms and the available spectral bandwidthof the input data is 12–180 Hz. The data was processed using a conven-tional processing flow including geometry loading, band-pass filtering

(12–180 Hz), AGC scaling, f-k filter, CDP sorting, velocity analysis, 21fold stack and poststack time migration. Deconvolution is not applied todata tomaintain the amplitude and frequency relations of the reflections.

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The main problem associated with the high resolution data is their rela-tively lower penetration due to the rapidly attenuated higher frequencycontent. In such cases, preserving or recovering the lower frequencies iscrucial to map the deeper reflections.

The SLR output of this section is shown in Fig. 10b. The section is fur-ther low-pass filtered with a 180 Hz cut-off frequency to remove thehigh frequency noise after SLR process and a trace mix with 5 trace isapplied to get a smoother seismic data. During SLR process, movingaverage window length is determined as 11 samples (or 10 ms) afterseveral tests. This window length seems to be small when comparedto those suggested during the synthetic tests. However, the bandwidthof the input data is relatively wide, and it is suitable to use shorter win-dow lengths for high resolution data sets. Therefore, there is no needto use longer window lengths because 10 ms provides enough lowfrequency improvement without any distortion on the high frequencycomponents. In the amplitude spectrum of SLR output, lower frequencycomponents especially lower than 10 Hz have larger amplitudes, whichcorrespond to relatively higher amplitudes in the deeper reflections,e.g. below 3.7 s. The amplitude spectrumof the output in Fig. 10b, how-ever, indicates that the higher frequency amplitudes are somewhatsuppressed by the SLR method, which corresponds to relatively loweramplitudes in the shallower reflections, e.g. above 3.1 s.

Fig. 11. Enlarged sections of the areas sho

After SLR processing, the amplitudes of the main lobes increaseresulting in a more robust polarity determination when side lobe inter-ference is an issue. This may improve the trace-by-trace consistencyof the reflections and may aid the interpreter during the reflectionpicking. Fig. 11 shows the enlarged areas of the input and SLR outputsections indicated in Fig. 10. The SLR output clearly shows that the inter-ference effects are reduced and the convergent reflections appear to bemore continuous in the output, which can provide and ensure the qual-ity of the data going into the inversion process, for optimum reflectivityresults if the deeper reflections and low frequency components are ofprimary concern.

7. Conclusions

Low frequency components of the seismic data are especially impor-tant for high resolution seismic surveys since they carry informationfrom deeper reflectors. These components are generally removed byconventional seismic data processing stages mainly by band-pass filter-ing. We propose a procedure to obtain side lobe reduced (SLR) trace inorder to improve low frequency content of the seismic traces by sup-pressing the side lobe amplitudes.

wn (a) in Fig. 10a, and (b) in Fig. 10b.

118 H. Karslı, D. Dondurur / Journal of Applied Geophysics 96 (2013) 107–118

The method can be applied to the stack or migrated seismic data bya trace-by-trace basis and only required parameter which should bepredetermined for the computations is the length of the movingaverage operator. Window lengths between 10 to 100 ms workwell on the high resolution shallow surveys. Longer operator lengths,however, may be required to obtain better results for the data withlower dominant frequencies.

The SLR method can contribute detailed mapping of facies distribu-tions and stratigraphy such as the case of thin layers in sediment de-posits. It may also contribute correlations of the key horizons with thecorresponding litho-units interpreted on log curves. It is also observedthat the method, however, causes in a slight suppression of the higherfrequency components which results in a decay in the amplitudes ofshallower reflections.

The method could be considered as a new amplitude attribute forthe seismic data, which aids the interpreter to obtain the true seismicsignature of the geological formations by removing the wavelet sidelobes, and restoring the low frequency components if the deeper reflec-tions and low frequency components are of primary concern.

Acknowledgments

We would like to thank Dokuz Eylül University, Institute of MarineScience and Technology for providing themarine seismic data. The con-ventional seismic processes on the data are performed by the ProMaxsoftware of Landmark Graphics.

Appendix A. Supplementary data

Supplementary data to this article can be found online at http://dx.doi.org/10.1016/j.jappgeo.2013.07.002.

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