CWP-573P

Virtual source method applied to Mars field OBC data

for time-lapse monitoring

K. Mehta†, J. Sheiman††, R. Snieder† & R. Calvert†††Center for Wave Phenomena, Department of Geophysics, Colorado School of Mines, Golden, CO 80401††Shell International E & P Inc., 3737 Bellaire Blvd, Houston, TX 77001

ABSTRACT

The virtual source method has recently been proposed to image and monitorbelow a complex and time-varying overburden. The method requires surfaceshooting recorded by subsurface receivers placed below the distorting or chang-ing part of the overburden. Redatuming the recorded response to the receiverlocations allows the reconstruction of a complete downhole survey as if thesources were also buried at the receiver locations. The ability to redatum thedata independent of the knowledge of time-varying overburden velocities makesthe virtual source method a valuable tool for time-lapse monitoring. We applythe virtual source method to the Mars field OBC data acquired in the deepwa-ter Gulf of Mexico with 120 multi-component sensors permanently placed onthe seafloor. Applying to the virtual source method, a combination of up-downwavefield separation and deconvolution of the correlation gather by the sourcepower spectrum suppresses the influences of changes in the overburden (sea wa-ter), thus strengthening the virtual source method for time-lapse monitoring.

Key words: ocean-bottom cable, monitoring, wavefield separation, deconvo-lution, source power spectrum

1 INTRODUCTION

The virtual source method (Bakulin and Calvert, 2004,2006) is a technique for imaging and monitoring be-low a complex overburden without knowledge of over-burden velocities and near-surface changes. The vir-tual source method is closely related to seismic inter-ferometry (Derode, et al., 2003; Schuster, et al., 2004;Snieder, 2004; Wapenaar, 2004; Bakulin and Calvert,2005; Wapenaar, et al., 2005; Korneev and Bakulin,2006; Snieder, et al., 2006a; Larose, et al., 2006; Cur-tis, et al., 2006). Theory states that cross-correlating therecording at a given reference receiver with the recordeddata at any other receiver for all the sources and thensumming the correlated data (correlation gather) overthe physical sources gives a signal that represents therecording by the other receiver as if the reference re-ceiver acted as a source (virtual source). Apart fromimaging below a complex overburden, the virtual sourcemethod is a useful tool for time-lapse monitoring pro-

vided that the receivers are placed permanently belowthe time-varying overburden.

Time-lapse monitoring is a powerful tool for track-ing changes in the subsurface. These changes include ge-omechanical phenomena associated with the migrationof fluids. Conventionally, the changes can be tracked byobserving the differences between data from two seis-mic surveys obtained over the surveillance period. Apartfrom changes in the subsurface caused by fluid flow, thedifference in the two seismic surveys include changes inthe overburden along with the acquisition discrepancies,which are both prominent and undesirable.

We apply the virtual source method to multi-component ocean-bottom cable (OBC) data acquiredin the years 2004 and 2005 at the Mars field in deep-water Gulf of Mexico. The Mars field data are acquiredby 120 multi-component sensors permanently placed onthe seafloor 1 km deep and air guns shooting from thesea surface (Figure 1). A total of 364 air gun shots werefired along a line from the sea surface with a region of 40missing shots because of the presence of platform above

186 K. Mehta, J. Sheiman, R. Snieder & R. Calvert

1 364

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Figure 1. Depth model showing the geometry of theMars field OBC data acquisition. 120 multi-component sen-sors (triangles) are permanently placed every 50 m on theseafloor. 364 air guns (stars), spaced every 25 m, are firedfrom the sea surface with a region of 40 missing shots, dueto the presence of the platform, above receiver 80. Waterdepth for this cartoon is 1 km, roughly the depth for theMars field.

receiver 80. The sensors are placed every 50 m and theshots are fired every 25 m.

The virtual source method is advantageous over theconventional seismic method in time-lapse monitoringat the Mars field because with virtual sources generatedat each permanently placed receiver location the virtualsource gathers obtained are independent of the variationin the overburden as well as acquisition discrepancies forthe two surveys.

In section 2 we discuss the causes of non-repeatability in the overburden and reasons for usingthe virtual source method for time-lapse monitoring. Insection 3 we compare the images obtained for the years2004 and 2005 by migrating conventional seismic dataand compute their difference to illustrate the causes ofnon-repeatability in the overburden (sea water). In sec-tion 4 we compare the images obtained by migratingvirtual source data and study their differences. Section5 illustrates the improvement in repeatability by in-corporating wavefield separation in the virtual sourcemethod. Finally, we illustrate in section 6 that decon-volution of the correlation gather by the source powerspectrum suppresses the influence of variations in thesource power spectrum in the virtual source data.

2 WHY VIRTUAL SOURCE METHOD?

Time-lapse seismic monitoring is a useful tool for track-ing changes in the subsurface associated with reservoirproduction. Along with the changes in the data at thereservoir level, there are prominent undesirable changesin the overburden that mask the changes of interest inthe reservoir that one seeks to monitor. For the Marsfield, the overburden consists of sea water. The varia-tions in the overburden, therefore, include changes insea water level, sea surface roughness, and sea watertemperature and salinity. Redatuming of the data downto the receiver locations using virtual source methodmakes the survey independent of these variations in the

sea water. Other causes of non-repeatability include ac-quisition discrepancies such as variations in the sourcelocation and source power spectrum. Source power spec-trum varies not only for the two surveys but also witheach shot location.

Let A and B be two receivers. The wavefieldsrecorded by the receivers is, in the frequency domain,given by

U(rA, rS, ω) = S(ω)G(rA, rS, ω),

U(rB, rS, ω) = S(ω)G(rB, rS, ω), (1)

where S(ω) is the frequency-domain representation ofthe source wavelet, G(rA, rS, ω) is the Green’s func-tion for wave propagation from the source to receiverA, G(rB, rS, ω) is the Green’s function for wave prop-agation from the source to receiver B and rS, rA andrB are the coordinates of the source and the two re-ceivers A and B, respectively. Cross-correlation of thewavefields recorded by the two receivers A and B is, inthe frequency domain,

U(rA, rS, ω)U∗(rB, rS, ω) = |S(ω)|2G(rA, rS, ω)

G∗(rB, rS, ω), (2)

where the asterisk indicates complex conjugate. Alongwith the correlation of the Green’s functions, the rightside of eq. (2) also contains the power spectrum of thesource-time function. The cross-correlation is, therefore,independent of the phase spectrum of the source-timefunction. The power spectrum of the source pulse can beexpected to differ for different shots as well as for differ-ent surveys. In order to remove the influence of varyingsource power spectrum, we deconvolve the correlationgather by the power spectrum of the source wavelet, ifit is known with sufficient accuracy. We address this insection 6 of the paper.

3 CONVENTIONAL SEISMIC IMAGING

Mars field OBC data for the baseline survey was ac-quired October-November 2004. The repeat survey wascarried out in June 2005. We first compare the conven-tional seismic images obtained from the two surveys.Conventional seismic data refers to wavefield excited bysources on the sea surface and recorded by the perma-nently placed sensors on the seafloor. To allow compar-ison with the seismic images generated after migratingthe virtual source data, the conventional seismic dataare downward continued to the seafloor using the watervelocity and the virtual source method is not applied.We migrate the refocused conventional seismic data forthe years 2004 and 2005 separately using Kirchoff depthmigration. The depth images are then converted to timeimages (Figures 2a and 2b) using the Mars field ve-locity model generated by migration velocity analysisperformed on the conventional seismic data. The timet=0 denotes the seafloor level. The gap just below the

Virtual source method for time-lapse monitoring 187

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Figure 2. Images generated by migrating the conventionalseismic data. Figure (a) is the image for the year 2004. Figure(b) is the image for the year 2005. Figure (c) is the differenceof the two images, after time alignment, obtained on the same

grey scale as that for Figures (a) and (b). The NRMS valueis shown in the box in Figure (c).

seafloor is due to blanking applied to the image gathersin order to mute data for which the opening angle at thereflection is large, which could lead to overly stretchedshallow reflections.

Figure 2c is the difference of the two images. Thisdifference is obtained after locally time-aligning theseimages to account for any geomechanical changes in thesubsurface and to separate changes within the reservoirfrom its gross movement. The local time-alignment wasdone by correlating local windows of data both in timeand space. There were no production-related subsurfacechanges at the reservoir level (around 3.5 s) between thetwo surveys over the surveillance period. Therefore, thedifferences (Figure 2c) are mainly due to variations inthe overburden and to acquisition discrepancies. Afterbeing refocused at the seafloor, the waves propagate notonly through the subsurface (solid rays in Figure 3a),but also through the time-varying overburden (dashedrays in Figure 3a). Variations in the overburden andacquisition contribute to the prominent undesirable dif-ferences observed in Figure 2c.

We quantify the repeatability using normalized rootmean square amplitude (NRMS) of the difference of theimages for the years 2004 and 2005. The NRMS of thedifference is defined as

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Figure 3. Ray paths corresponding to (a) conventional seis-mic data and virtual source data generated by correlating thetotal wavefield at the virtual source with the total wavefieldat the receivers, (b) virtual source data generated by corre-lating the direct arrival windowed in the total wavefield atthe virtual source with the total wavefield at the receivers,(c) data generated by correlating the down-going waves atthe virtual source with the up-going waves at the receivers.Figure (d) is the cartoon of the ray paths of the multiplethat propagates through the overburden even after applyingwavefield separation to the virtual source method.

where ‘B’ represents the base survey (2004) and ‘M’ rep-resents the monitor survey (2005). The symbols ‘<>’represents the average value over the region whereNRMS is calculated. Decrease in the value of NRMSindicates improvement in the repeatability.

We calculate the NRMS for the entire seismic im-age. For the refocused conventional seismic data, theNRMS value is 0.2892. Table 1 shows the NRMS of thedifference for the conventional seismic image as well asfor the virtual source seismic images that will be dis-cussed in the following sections.

4 THE VIRTUAL SOURCE METHOD

We generate different virtual source gathers with everyreceiver as the virtual source and, instead of migratingthe refocused conventional seismic data, migrate the vir-tual source data generated for the years 2004 and 2005.For all the examples we use Kirchoff depth migrationand then convert the depth image to a time image us-ing the Mars field velocity model generated by migrationvelocity analysis on the conventional seismic data.

The simplest approach to generate a virtual sourcegather is to correlate the total wavefield at the virtualsource with the total wavefield at the receivers (Mehta,et al., 2006). The images for the years 2004 and 2005obtained by migrating virtual source data generated us-

188 K. Mehta, J. Sheiman, R. Snieder & R. Calvert

Table 1. Comparison of the normalized root mean squareamplitude (NRMS) values for different seismic images.‘Tot:tot’ refers to the virtual source data generated by cor-relating total wavefield at the virtual source with the to-tal wavefield at the receivers. ‘Dir’ refers to the direct ar-rival windowed in the total wavefield. ‘Down’ refers to thedown-going waves. ‘up’ refers to the up-going waves. ‘Down-dir’ refers to the direct arrival windowed in the down-goingwaves. ‘decon’ refers to the deconvolution of the correlationgather by the source power spectrum. The corresponding fig-ure number is mentioned in the second column.

Seismic image Figure number NRMS

Conventional seismic 2 0.2892

Tot:tot 4 0.3493

Dir:tot 5 0.3346

Down:up 6 0.2676

Down-dir:up 7 0.1770

Down:up:decon 9 0.1624

Down-dir:up:decon 10 0.1414

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Figure 4. Images generated by migrating the virtual sourcedata. Virtual source gathers are generated by correlating thetotal wavefield at the virtual source with the total wavefieldat the receivers. Figure (a) is the image for the year 2004.Figure (b) is the image for the year 2005. Figure (c) is thedifference of the two images, after time alignment, obtainedon the same grey scale as that in Figures (a) and (b). Figure(d) is the difference of the image amplified by a factor of 10,on the same grey scale as that in Figures (a) and (b). TheNRMS value is shown in the box in Figure (d).

ing this simplest approach are shown in Figures 4a and4b, respectively. Figure 4c is the difference of the twoimages after local time-alignment. In order to highlightthe features, we also show the difference image amplifiedby a factor of 10 in Figure 4d. The differences can be at-tributed to the waves propagating through the overbur-den (dashed rays in Figure 3a), which change betweenthe two years because of the variations in the overbur-den. The acquisition discrepancies associated with thechange in location of the source between the two years is,however, removed. The variation caused by differencesin the source power spectrum [eq. (2)], nevertheless, stillexists.

The NRMS of the difference for the virtual sourcedata generated by the simplest approach is 0.3493. Webelieve this value is higher than the NRMS for the con-ventional seismic image because the pre-processing ofconventional seismic data included suppression of thefree-surface multiples. In contrast, the virtual sourcedata generated using the simplest approach has the mul-tiples that propagate through the time-varying overbur-den.

The images generated by the virtual source data(Figure 4a) have lower frequency content than that ofthe conventional seismic images (Figure 2a). The dif-ference in frequency content is caused by the receiversand shots being placed along a line whereas the wave-propagation is three dimensional. Snieder, et al. (2006a)show that for such a geometry, the virtual source dataneed to be multiplied by a factor of

√iω (ω is the an-

gular frequency), thus restoring the true frequency con-tent. The pre-processing on the raw data involved band-limited spike deconvolution. In the virtual source data,the deconvolution of the correlation gather by the powerspectrum of the source wavelet gives a zero-phase band-limited source pulse. Due to this discrepancy, the source-time function for the virtual source data multiplied by√

iω has a different frequency content compared to thatof the conventional seismic data. The discrepancy be-tween the frequency contents of the virtual source dataand the conventional seismic data will, therefore, existeven after multiplying the virtual source data with the√

iω term. Hence, for the virtual source images that fol-lows, we don’t apply the

√iω term.

5 WAVEFIELD SEPARATION

The free-surface multiple are the response from the over-burden and hence, are undesirable. They contaminateFigures 4a and 4b because we correlate the total wave-field at the virtual source with the total wavefield at thereceivers, both of which contain those multiples. Thedominant event is a simple reflection from the sea sur-face and are mainly down-going waves. If, instead ofcorrelating the total wavefields, the down-going wavesat the virtual source are correlated with the up-goingwaves at the receivers, the free-surface multiple along

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Figure 5. Same as Figure 4, but for virtual source gathersgenerated by correlating the direct arrival windowed in thetotal wavefield at the virtual source with the total wavefieldat the receivers.

with other overburden reflections can be suppressed(Mehta, et al., 2007). Similar up-down wavefield sep-aration is done by Snieder et al. (2006b) in a differentcontext applied to structural engineering.

Before we discuss the wavefield separation into upand down-going waves, let us consider the image gener-ated by migrating the virtual source data produced bythe current practice. That approach to generating vir-tual source gather involves correlating the direct arrivalwindowed in the total wavefield at the virtual sourcewith the total wavefield at the receivers (Bakulin andCalvert, 2004). By windowing the direct arrival at thevirtual source, the virtual source is imposed to radi-ate predominantly downward thus, removing much ofthe overburden reflections but not all. The images forthe years 2004 and 2005 obtained by migrating virtualsource data, generated in that way are shown in Figures5a and 5b, respectively. The free-surface multiple stilldominates because instead of using only the up-goingwaves at the receivers, the total wavefield is used forcorrelation. Figure 5c is the difference of the images forthe years 2004 and 2005 and Figure 5d is the differenceimage amplified by a factor of 10. Even after windowingof the direct arrival the virtual source data generatedcontain waves that still propagate through the overbur-den after reflecting from the near-seafloor (dashed raysin Figure 3b).

The NRMS of the difference for the virtual sourcedata generated by the current practice is 0.3346. Simi-lar to the simplest approach, this value is higher thanthe NRMS for the conventional seismic image because

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the pre-processing of conventional seismic data includedsuppression of the multiples. In contrast, the virtualsource data generated using the current practice stillhave some multiples propagating through the time-varying overburden.

In order to make the virtual source data inde-pendent of the overburden, we follow the approach byMehta, et al., 2007, and generate virtual source gath-ers by correlating the down-going waves at the virtualsource with the up-going waves at the receivers. ForOBC data, up-down separation of the wavefield is pos-sible by dual-sensor summation (e.g., Robinson, 1999).Figure 6a and 6b are the images for the years 2004 and2005 respectively, obtained by migrating virtual sourcedata generated after wavefield separation into up- anddown-going waves. Because the free-surface multiple, af-ter reflecting from the free surface, is dominantly down-going energy, correlation of down-going waves at thevirtual source with the up-going waves at the receiverssuppresses the free-surface multiple and highlights, forexample, reservoir events at around 3.5 s. The differenceof the images (Figure 6c) for the years 2004 and 2005,amplified by 10 in Figure 6d is less noisy compared toFigures 5d and 4d.

The NRMS of the difference image after up-downwavefield separation reduced to 0.2676 (Table 1). Theimproved match in results for the two years comparedto that for the simplest approach and current prac-tice supports the improvement in repeatability after up-down wavefield separation. This improvement resultsbecause the waves now are those that propagate pre-

190 K. Mehta, J. Sheiman, R. Snieder & R. Calvert

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Figure 7. Same as Figure 4, but for virtual source gathersgenerated by correlating the direct arrival windowed in thedown-going waves at the virtual source with the up-goingwaves at the receivers.

dominantly through the subsurface (solid rays in Fig-ure 3c). Wavefield separation applied to the virtualsource method has suppressed the down-going multi-ples propagating through the overburden, hence makingthe virtual source image less sensitive to overburden-related changes. The difference image still has somelow-amplitude coherent events. These events could beweaker-amplitude multiples that are down-going at thevirtual source, up-going at the receivers and yet stillhave propagated through the overburden (dashed raysin Figure 3d). These multiples cannot be suppressedeven by applying wavefield separation to the virtualsource method.

We can further reduce other sources of discrepan-cies in the time-lapse virtual source data by windowingthe direct arrival in the down-going waves at the virtualsource, instead of using all of the down-going waves. Bywindowing the direct arrival in the down-going waves,we are imposing a P-wave virtual source, hence sup-pressing the non-repeatability in the shear waves. Theimages for the years 2004 and 2005 obtained by mi-grating the resulting virtual source data are shown inFigures 7a and 7b, respectively and the differences areshown in Figures 7c and 7d. Compared to the imagesgenerated using the refocused conventional seismic data(Figures 2a and 2b), the images generated by the virtualsource data preserves all the coherent reflectors and areless noisy.

Using up-down wavefield separation and window-ing of the direct arrival at the virtual source hasreduced the NRMS of the difference image to just

0.1770 (Table 1). Although the discrepancy in the shearwaves is suppressed by windowing the direct arrival,the second-order multiples that propagate through thetime-varying overburden (dashed rays in Figure 3d) stillexist.

The improvement we have seen in the virtual sourcemethod by wavefield separation applied to the Mars fieldaccounts for the variation in the sea water level, seasurface roughness, sea water temperature, salinity andsource location. The variation in the source power spec-trum [eq. (2)], however, still exist in all of the aboveimages. We next address the correction for variation inthe source power spectrum variation.

6 SOURCE POWER SPECTRUM

VARIATION

The cross-correlation of the wavefields recorded by agiven pair of receivers [eq. (2)] contains the power spec-trum of the source pulse. To suppress the influence ofthe source power spectrum, and in particular its varia-tion, the cross-correlated data (correlation gather) mustbe deconvolved by the source power spectrum, pre-suming that it is known or can be well approximated(Derode, et al., 2003; Schuster, et al., 2004; Snieder,2004; Wapenaar, 2004; Wapenaar, et al., 2005). Typi-cally, the source pulse varies not only between the twosurveys but also among shots in a single survey. Since weuse air guns as sources, variation in the source pulse ismainly due to changes in the air bubble, assuming thatpre-processing of the two data sets attempted to equal-ize the source pulses. The equalization of the sourcepulse was done as follows. Small-offset traces were takenfrom each shot and the waves, in a time window of 400ms around the direct arrival, were aligned. The lengthof the time window was chosen to be 400 ms to includethe bubble. These aligned traces were then averaged, af-ter which designative filters were derived to turn theseresponses into band-limited delta functions. The sameprocedure was applied to both the surveys to obtain thesame desired band-limited delta function. This conven-tional pre-processing aimed to remove variations in thebubble sequence but was not sensitive enough to removethem completely.

The source power spectrum corresponds, in thetime domain, to the auto-correlation of the sourcewavelet. The auto-correlation of the source waveletpresent in the correlation gather varies from one shotto another because of changes in the residual bubblesequence. The variation of the auto-correlation of thesource pulse (for receiver 90) as a function of source lo-cation for the years 2004 and 2005 is shown in Figures 8aand 8b, respectively. Each of the two figures is the auto-correlation of the direct arrival windowed in the down-going waves at receiver 90 for all the source locations.Down-going waves are used for correlation to avoid

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Figure 8. Variation of the auto-correlation of the sourcepulse corresponding to receiver 90 as a function of sourcelocation for 2004 (a) and 2005 (b). Figure (c) is the differenceof the gathers in (a) and (b), obtained on the same grey scaleas Figures (a) and (b). Figure (d) is the difference of the self-decons (convolution of the source power spectrum and filterthat represents the inverse of the source power spectrum) for

the years 2004 and 2005, on the same grey scale as Figures(a) and (b).

any near-seafloor reflection interfering with the auto-correlation of the source pulse. The auto-correlation ofthe source pulse varies not only between the two sur-veys but also between each source location. The eventclose to ±0.35 s is attributable to the residual bub-ble sequence. Apart from the residual bubble, curvedevents are present for both causal and acausal times.These curved events correspond to the interference ofreflected and refracted waves with the direct arrival forlater times and larger offsets. Figure 8c is the differencein the auto-correlation of the source pulse for the years2004 and 2005. The difference in the main lobe (close totime t=0) is negligible, suggesting that pre-processingadequately equalized the primary source pulses. Thecurved events also appear to diminish in the difference.The event occurring around ±0.35 s, however, is thedifference in the residual bubble sequence and is pro-nounced and consistent for every source location. Thisconsistent difference could be due to the variation in thewater temperature between the two surveys; the basesurvey was carried out in October and the repeat sur-vey in June. Use of different air gun sources for thetwo surveys, different air gun pressures, different actualdepths of source arrays (both surveys used the samenominal source depths), and discrepancies in the sea

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Figure 9. Same as Figure 7 but with deconvolution of thecorrelation gather by the source power spectrum before sum-mation.

surface roughness could be other possible reasons forthe systematic variation in the residual bubble.

The imprint of varying source power spectrum onthe virtual source data can be removed by deconvolvingeach trace of the correlation gather by the power spec-trum of the corresponding source. This is equivalent toapplying a filter that represents the inverse of the sourcepower spectrum. We refer to the convolution of the fil-ter with the source power spectrum as self-decon. Fig-ure 8d is the difference of self-decons for the years 2004and 2005. Apart from the curved events representingthe interference of other events with the direct arrival,the contribution of the systematic residual bubble vari-ation is well suppressed. Hence, deconvolving the corre-lation gather by the source power spectrum suppressesthe source power spectrum variations.

Migrated images, for the years 2004 and 2005, gen-erated after applying both wavefield separation anddeconvolution of the correlation gather by the sourcepower spectrum are shown in Figures 9a and 9b, respec-tively with differences shown in Figures 9c and 9d. Thevirtual source data for these images are generated bycorrelating the down-going waves at the virtual sourcewith the up-going waves at the receivers. The corre-lation gather is then deconvolved by the source powerspectrum and summed over the physical sources. Theimprovement in the repeatability by combining up-downseparation and deconvolution of the correlation gatherwith the auto-correlation of the source-time function isevident by the decrease in the NRMS to 0.1624 (Table1).

192 K. Mehta, J. Sheiman, R. Snieder & R. Calvert

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Figure 10. Same as Figure 9 but with the direct arrivalwindowed in the down-going waves at the virtual source.

The repeatability can be further improved by com-bining up-down separation, windowing of the direct ar-rival and deconvolution. The images in Figure 10 are ob-tained by migrating the virtual source data generated bycombining up-down separation, windowing of the directarrival, and deconvolution. The NRMS, after combiningup-down separation, windowing the direct arrival anddeconvolution, reduces from 0.1624 without windowingto just 0.1414.

7 CONCLUSION

Combination of up-down separation, windowing the di-rect arrival and deconvolution with the source powerspectrum, improves the repeatability of the images cre-ated with the virtual source data. This makes the virtualsource method a useful tool for time-lapse monitoringwhere the goal is to image changes just in the subsurfacebeneath the sources and the receivers. Up-down separa-tion suppresses the first-order multiples from the time-varying overburden. Windowing the direct arrival inthe down-going waves imposes a P-wave virtual source,hence suppressing the overburden-related variations inthe shear waves. Finally, deconvolution of the correla-tion gather by the source power spectrum further sup-presses the non-repeatability caused by variation in thesource power spectrum. The progressively diminishingvalues of NRMS in the sequence of tests support ourobservation of improvement in time-lapse monitoring byapplying wavefield separation and deconvolution to thevirtual source method.

ACKNOWLEDGMENTS

We thank Shell for permission to show the Mars fieldOBC data and for the financial support through theGameChanger Program. We appreciate the critical com-ments from Ken Larner.

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