Redatuming through a salt canopy and target-oriented salt-flank imaging

R

R

apdtmmbvSamTld

c

R

L©

GEOPHYSICS, VOL. 73, NO. 3 �MAY-JUNE 2008�; P. S63–S71, 11 FIGS.10.1190/1.2890704

Dow

nloa

ded

09/1

5/13

to 1

28.8

3.63

.20.

Red

istr

ibut

ion

subj

ect t

o SE

G li

cens

e or

cop

yrig

ht; s

ee T

erm

s of

Use

at h

ttp://

libra

ry.s

eg.o

rg/

edatuming through a salt canopy and target-oriented salt-flank imaging

ongrong Lu1, Mark Willis1, Xander Campman2, Jonathan Ajo-Franklin3, and M. Nafi Toksöz1

pmvecmcoeetrTt

ABSTRACT

We describe a new shortcut strategy for imaging the sedimentsand salt edge around a salt flank through an overburden salt cano-py. We tested its performance and capabilities on 2D syntheticacoustic seismic data from a Gulf of Mexico style model. We firstredatumed surface shots, using seismic interferometry, from awalkaway vertical seismic profile survey as if the source and re-ceiver pairs had been located in the borehole at the positions ofthe receivers. This process creates effective downhole shot gath-ers by completely moving surface shots through the salt canopy,without any knowledge of overburden velocity structure. Afterredatuming, we can apply multiple passes of prestack migrationfrom the reference datum of the bore-hole. In our example, first-

sttds

l�dcepf

pe

ed 5 Noambridg

boratory

ratory,jo-frank

S63

ass migration, using only a simple vertical velocity gradientodel, reveals the outline of the salt edge. A second pass of re-

erse-time, prestack depth migration using full two-way wavequation was performed with an updated velocity model thatonsisted of the velocity gradient and salt dome. The second-passigration brings out dipping sediments abutting the salt flank be-

ause these reflectors were illuminated by energy that bouncedff the salt flank, forming prismatic reflections. In this target-ori-nted strategy, the computationally fast redatuming processliminates the need for the traditional complex process of veloci-y estimation, model building, and iterative depth migration toemove effects of the salt canopy and surrounding overburden.his might allow this strategy to be used in the field in near real

ime.

INTRODUCTION

An accurate image of reservoir sediment structures at the flank ofsalt dome is very important for computing reserves estimates androduction development planning. Imaging subsalt sediments ineep water in the Gulf of Mexico �GOM� requires seismic methodshat handle distortions caused by complex salt tectonics. There are

any variations of prestack depth-migration methods to handle seis-ic data, including Kirchhoff �Gray and May, 1994; Bevc, 1997�,

eam-based �Hill, 1990, 2001; Sun et al., 2000; Gray, 2005�, and re-erse-time �Baysal et al., 1983; Hokstad et al., 1998; Biondi andhan, 2002�. Proper handling of turning-ray energy would help im-ge salt overhang �Hale et al., 1992; Xu and Jin, 2006� and build aore accurate salt model �Siddiqui et al., 2003; Wang et al., 2006�.ypical imaging projects require multiple passes of migration, ve-

ocity analysis, and model building to handle complex salt overbur-en. One problem facing deep-GOM imaging objectives is that with

Manuscript received by the Editor 9April 2007; revised manuscript receiv1Massachusetts Institute of Technology, Earth Resources Laboratory, C

om; [email protected] Massachusetts Institute of Technology, Earth Resources La

ijswijk, the Netherlands. E-mail: [email protected] Massachusetts Institute of Technology, Earth Resources Labo

aboratory, Earth Science Division, Berkeley, California, U.S.A. E-mail: jba2008 Society of Exploration Geophysicists.All rights reserved.

urface seismic data only limited velocity resolution remains athe depths of many subsalt plays. Wang et al. �2005� describe howhe limited range of illumination angles in deep subsalt targets re-uces corresponding migration velocity analysis to nearly a post-tack level.

In addition, complex overburden, e.g., a salt canopy, decreases il-umination quality and makes velocity model building difficultGuitton et al., 2006�. Walkaway vertical seismic profile �WVSP�ata can increase frequency bandwidth, i.e., resolution, and can de-rease uncertainty by removing half the seismic raypath, which oth-rwise would have to travel back to surface receivers. However,restack depth migration of WVSP data suffers from the same needor iterative velocity model building as surface seismic data does.

In single-well imaging methods, data are acquired from a positionhysically closer to the reservoir. By locating the sources and receiv-rs in the same borehole, the seismic energy has a shorter distance to

vember 2007; published online 31 March 2008.e, Massachusetts, U.S.A. E-mail: [email protected]; mark_e_willis@hotmail.

, Cambridge, Massachusetts, U.S.A.; presently Shell International E&P,

Cambridge, Massachusetts, U.S.A.; presently Lawrence Berkeley [email protected].

tpth�faot

aebhtwh

tws11D22eptfr

pw

mdti2Mtsflwimt22

ttfitsltadrfn

flltcsrb

effidewBvzadrtsR4

ca

Fcd�s�ast

S64 Lu et al.

Dow

nloa

ded

09/1

5/13

to 1

28.8

3.63

.20.

Red

istr

ibut

ion

subj

ect t

o SE

G li

cens

e or

cop

yrig

ht; s

ee T

erm

s of

Use

at h

ttp://

libra

ry.s

eg.o

rg/

ravel to the target and thus will have reflections with simpler ray-aths. This simplifies the complexity of the wavefield and poten-ially enhances the signal-to-noise ratio. Acoustic logging toolsave been used to image features less than 20 m from the wellboreHornby, 1989; Fortin et al., 1991; Coates et al., 2000�. More power-ul downhole sources have been used to attempt to image fartherway from the borehole �Majer et al., 1997; Daley et al., 2000�. Testsf single-well methods have shown promise but might be limited byhe power and directivity of downhole sources.

Redatuming of a WVSP data set is a relatively new concept whichttempts to mimic the single-well imaging method by moving math-matically the surface VSP sources as if they were located in theorehole with receivers. Conventional redatuming methods �Berry-ill, 1984� could be used for this process, but would require a de-ailed velocity model of the overburden �e.g., salt canopy� to back-ard-propagate the prestack data to the new datum using a Kirch-off integral formulation or finite-difference modeling algorithm.

Recent advances in seismic-interferometry theory have shownhat redatuming can be performed by using simple crosscorrelationsithout a velocity model. This new approach is a generalization of

everal related technologies: acoustic daylight imaging �Claerbout,976; Rickett and Claerbout, 1996�, time-reversed acoustics �Fink,999, 2006�, seismic interferometry �Schuster et al., 2003, 2004;erode et al., 2003; Snieder, 2004; Wapenaar, 2004; Wapenaar et al.,005�, and virtual sources �Bakulin and Calvert, 2004; Calvert et al.,004�. These techniques employ the time symmetry of the wavequation along with source-receiver reciprocity to estimate the im-ulse response between two passive receivers. This allows the reda-uming process to use the extracted impulse response �or Green’sunction� instead of a modeled response based on an iteratively de-ived velocity model.

Bakulin and Calvert �2004� and Bakulin et al. �2007� show exam-les of redatuming surface sources to receivers in a near-horizontalell just beneath the overburden. This can be an excellent way to re-

igure 1. WVSP acquisition geometry for a synthetic GOM modelomposed of a simplified vertical velocity gradient and an embed-ed overhanging salt dome �SD-I� with a second salt canopy nearbySD-II�. Yellow stars indicate locations of shots, and red triangleshow locations of receivers. Note that not all 399 shots are shownextending from �7.5 to 2.5 km laterally� and not all 161 receiversre shown �extending from 0.5 to 4.5 km in depth�. The color barhown is applicable for all figures in this article that contain a veloci-y model.

ove overburden artifacts on time-lapse seismic-imaging studies toetect changes in reservoir properties. Others have applied varia-ions of seismic-interferometric redatuming to move surface sourcesnto vertical or near-vertical wells �Hornby et al., 2006; Lu et al.,006; Willis et al., 2006; Bakulin et al., 2007; Hornby and Yu, 2007;ateeva et al., 2007�. Bakulin et al. �2007� point out that because of

he ray geometry, redatumed shot records capture reflections fromtructures located somewhat parallel to the borehole: vertical saltanks for near-vertical wells and horizontal beds for near-horizontalells. For structures perpendicular to the wellbore, reflected energy

s limited to a small area intersecting the well. Details of the mathe-atical description and discussion of seismic-interferometric reda-

uming are found in many places �Schuster et al., 2004; Snieder,004; Wapenaar, 2004; Wapenaar et al., 2005; Korneev and Bakulin,006; Lu et al., 2006; Willis et al., 2006�.

We propose a strategy to image a salt flank and its associated abut-ing sediments. It contains two parts: redatuming and migration. In aypical redatuming workflow, a WVSP data set is collected with suf-cient aperture to capture turning-ray energy from salt-flank reflec-

ions. Data then are sorted into common-receiver gathers. A succes-ion of pairwise traces from the same surface shots are crosscorre-ated �interferometry�. The resulting correlograms then are stackedo obtain the effective trace representing a downhole shot recorded atdownhole receiver. This process is repeated for all combinations ofownhole receivers to create effective shot gathers for all boreholeeceiver locations. Because this process can be automated and per-ormed quickly, it could be done in the field, during acquisition, inear real time.

In the second part of the strategy, two passes of migration are per-ormed. The first pass delineates the salt edge using a simple v�z� ve-ocity model, and the second pass reveals the sediments using a ve-ocity model that includes the salt edge picked from the first migra-ion.As with the redatuming step, the first pass of prestack migrationould be performed easily in the field, when collecting data, with aimple velocity model, and first-arrival Kirchhoff migration algo-ithm �Gray and May, 1994�. This allows aperture and data quality toe checked and used in making drilling decisions.

METHODOLOGY

We illustrate our processing strategy using a synthetic, acousticxample. We create a 2D data set representing a multilevel WVSPor the model shown in Figure 1. The model is composed of a simpli-ed GOM vertical velocity gradient, an embedded overhanging saltome �SD-I� with a salt canopy nearby �SD-II�. The velocity gradi-nt and values are taken from the EAGE/SEG salt-dome model,hich represents typical GOM velocities �Aminzadeh et al., 1997�.oth salt domes have a P-wave velocity of 4480 m/s. Backgroundelocity is described by v�z� � v0 � Kz, where v is velocity in m/s,is depth in meters, v0 is velocity of the top layer �v0 � 2200 m/s�,nd K is the velocity gradient �K � 0.4 s�1�. Six reflectors are intro-uced on top of the v�z� gradient as 15% higher velocity spikes andeflectors dip up toward the salt-dome flank. Taking the wellhead ashe origin, the walkaway line consisting of 399 shots extends at theurface from �7.5 km to �2.5 km, and the shot interval is 25 m.eceivers are placed in the borehole from a depth of 0.5 km to.5 km at 25-m intervals �a total of 161 receivers�.

This model creates four imaging challenges. First is the compli-ating effect of the salt canopy on seismic energy reaching the wellnd subsequently the salt flank. Figure 2 shows a snapshot of the

wssct

sbpfripstpfawdws

tptru

R

nedcoT2ob

cWcefeTusc�trelucl

F7

tcdscgta

a

c

FcVwtst

a

Fpilttd

Salt flank redatuming and imaging S65

Dow

nloa

ded

09/1

5/13

to 1

28.8

3.63

.20.

Red

istr

ibut

ion

subj

ect t

o SE

G li

cens

e or

cop

yrig

ht; s

ee T

erm

s of

Use

at h

ttp://

libra

ry.s

eg.o

rg/

avefield for a model �Figure 2a� without and �Figure 2c� with thealt canopy. The corresponding common-shot VSP records arehown in Figure 2b and d. It is clear that the salt canopy has dramati-ally changed the wavefront that is marching forward to illuminatehe salt flank. The redatuming process should remove this effect.

The second challenge is the diverse range of structural dips at thealt flank. The vertical salt flank is parallel to the borehole and shoulde relatively easy to image. Horizontal portions of layering are per-endicular to the wellbore and will be very difficult to image awayrom the well. This is because energy from downhole shots does noteflect back to the borehole from horizontal layers except when theyntersect the well. Third is the vertical velocity variation which im-arts strong lateral velocity variation �2.6 to 3.9 km/s� from the per-pective of the downhole shot gathers. Here a prestack depth migra-ion will handle asymmetric raypaths properly. Fourth is the updip-ing curvature of layering at the salt-dome edge. Energy reflectedrom this portion of the layer subsequently bounces off the salt edgend therefore is reflected multiple times, as shown in Figure 3a, andill not image with a one-way migration algorithm. A reverse-timeepth-migration algorithm, which uses the two-way wave equation,ill overcome this challenge by back-propagating the bounce off the

alt correctly, as shown in Figure 3b and described below.To image the salt-dome edge �SD-I� and the corresponding abut-

ing sediments and address the four challenges listed above, our pro-osed strategy consists of two parts: redatum the surface source intohe borehole and perform two passes of migration on redatumed shotecords. This two-step processing strategy is illustrated in Figure 4sing a flowchart. Next, we explain each of these parts.

edatuming

The first part applies redatuming to WVSP traces. This createsew effective shot gathers, as if the sources and receivers were locat-d in the borehole. To do this, we sort WVSP data into common-ownhole-receiver gathers. Next, we select an actual downhole re-eiver location to be an effective source location. Then, we select an-ther downhole receiver location to be an effective receiver location.wo representative common-downhole-receiver gathers at depths ofkm and 3 km are shown in Figure 5.At the lowest level, operations

n these two common-receiver gathers illustrate the basic buildinglocks of the redatuming process.

Suppose we want to estimate a recording of an effective shot lo-ated at a depth of 2 km by an effective receiver at a depth of 3 km.e use these two common-receiver gathers from the original WVSP

orresponding to the desired effective shot location �Figure 5a� andffective receiver location �Figure 5b�. Pairs of traces, one tracerom each of these two common-receiver gathers, correspond toach surface shot. Each of these pairs of traces is crosscorrelated.he horizontal axes in both common-receiver gathers shown in Fig-re 5 denote the shot offset for each trace. We start with the leftmosthot offset at �7.5 km. We extract the corresponding traces fromommon-receiver gathers at depths of 2 km �left panel� and 3 kmright panel�. Crosscorrelating these two traces gives one correlatedrace, or correlogram, shown as the leftmost trace in Figure 6a. Weepeat this operation for all shot offsets in this set of common-receiv-r gathers, which fills in the rest of the traces in Figure 6a. All corre-ograms are stacked together to produce a single trace, shown in Fig-re 6b. Positive lags �causal portion� of the single-stacked trace be-ome our estimate of the recorded trace because of an effective shotocated at 2-km depth and a receiver at 3-km depth �Wapenaar and

okkema �2006��. This trace is shown at a depth of 3 km in Figurea, which represents the complete redatumed shot record.

To estimate traces for the next downhole receiver offset, we keephe common-receiver gather corresponding to the effective shot lo-ation �at 2 km� and grab the common-receiver gather for the newesired effective receiver location. We then repeat the set of corre-ponding correlations as described above. By doing this for all re-eiver depth levels, we create an effective common-downhole-shotather, such as in Figure 7a. This mimics a shot gather collected byhe downhole receiver array resulting from a downhole source firingt the location that we choose to be the effective source location �at

Offset (km)Offset (km)Offset (km)Offset (km)

Dp

Dp

Dp

Dpeth

)eth

)eth

)eth

)mmmmkkkk((((

−6−6−6−6 −4−4−4−4 −2−2−2−2 0000 2222

0000

1111

2222

3333

4444

5555


Dp

Dp

Dp

Dpeth

)eth

)eth

)eth

)mmmmkkkk((((

−6−6−6−6 −4−4−4−4 −2−2−2−2 0000 2222

0000

1111

2222

3333

4444

5555

Time (s)Time (s)Time (s)Time (s)

Dp

Dp

Dp

Dpeth

)eth

)eth

)eth

)mmmmkkkk ((((

1.51.51.51.5 2222 2.52.52.52.5 3333 3.53.53.53.5

0000

1111

2222

3333

4444

5555

Time (s)Time (s)Time (s)Time (s)

Dp

Dp

Dp

Dpeth

)eth

)eth

)eth

)mmmmkkkk ((((

1.51.51.51.5 2222 2.52.52.52.5 3333 3.53.53.53.5

0000

1111

2222

3333

4444

5555

) b)

) d)

igure 2. �a� Snapshot of wavefield at time � 2 s superimposed onorresponding model without the salt canopy. �b� Common-shotSP record for the model without the salt canopy. �c� Snapshot ofavefield at time � 2 s superimposed on corresponding model with

he salt canopy. �d� Common-shot VSP record for the model with thealt canopy. Notice the large distortion in arrival times and ampli-udes caused by the salt canopy.

) b)

igure 3. �a� Cartoon showing raypaths of multiple reflections ofrismatic reflections. �b� Cartoon showing the migration process tomage prismatic reflections. The shot is forward-modeled �dashedine�. The recorded wavefield is back- propagated �solid line� usinghe full two-way wave equation which allows bounces off the salt in-erface. An image is formed when the forward shot is time-coinci-ent with the back-propagated wavefield.

2gfi

gs

n�ohct

Fm

Fis3

a

Fas

S66 Lu et al.

Dow

nloa

ded

09/1

5/13

to 1

28.8

3.63

.20.

Red

istr

ibut

ion

subj

ect t

o SE

G li

cens

e or

cop

yrig

ht; s

ee T

erm

s of

Use

at h

ttp://

libra

ry.s

eg.o

rg/

km�. For comparison, Figure 7b shows the actual common-shotather modeled with a true source at a depth of 2 km, which we de-ne as the benchmark case.Comparing Figure 7a and b, we observe similar common-shot

athers, except that our redatumed downhole shot gathers includeome spurious events �indicated by red arrows in Figure 7a�

--

-

-

igure 4. Flowchart illustrating the two parts of our proposed strateigration.

eeeemmmm iiiiT

sT

sT

sT

s()

()

()

()


Depth = 2 kmDepth = 2 kmDepth = 2 kmDepth = 2 km

−6 −4 −2 0 2−6 −4 −2 0 2−6 −4 −2 0 2−6 −4 −2 0 2

0.50.50.50.5

1111

1.51.51.51.5

2222

2.52.52.52.5

3333

3.53.53.53.5

eeeemmmmiiii T

sT

sT

sT

s()

()

()

()


Depth = 3 kmDepth = 3 kmDepth = 3 kmDepth = 3 km

−6 −4 −2 0 2−6 −4 −2 0 2−6 −4 −2 0 2−6 −4 −2 0 2

0.50.50.50.5

1111

1.51.51.51.5

2222

2.52.52.52.5

3333

3.53.53.53.5

) b)

igure 5. Common-downhole-receiver gathers at depths of �a� 2 kmnd �b� 3 km. Horizontal axes denote the offset of the correspondinghot for each trace.

ot present in the actual downhole record. Wapenaar and Fokkema2006� describes these events as ghost events created by violationsf interferometric assumptions about complete source coverage,igh-frequencyapproximations,andwavefield separation. Althoughontaminated by these spurious events, the main reflections off thearget salt flank �events which arrive after 0.75 s� are present. We

also observe in Figure 7b, the linear downgoingevent �indicated by a blue arrow� coming off thefirst arrival at a depth of 1 km at time of 0.4 s isnearly absent in the redatumed traces �Figure 7a�.This event is the downgoing specular reflectionoff the underside of the flat-laying sediment layercrossing the borehole location at a depth of 1 km.This energy is omitted because not very much ofit is excited by a surface source. An actual down-hole source creates upgoing energy which is re-flected downward when it encounters layers in-tersecting the borehole. Just as in the theory formigration, to be more correct, we should putsources �or receivers� completely surroundingthe area we wish to image. If this was possible, wecould reconstruct these downgoing reflections.�Van Manen et al. �2005� used this concept ofsources all around the model for efficient simula-tion of wave propagation�. However, because thisis not practical for field-scale surveys, we mustevaluate the effect of the limited aperture on finalresults.

We observe that only surface shot locations onthe correlogram panel �Figure 6a� with eventsshowing a zero time slope contribute to thestacked trace �Figure 6b�. Figure 8 shows a con-ceptual VSP model containing a single reflectorand two receivers. In Figure 8a, we select receiverk to be the redatumed shot location. The corre-sponding specular reflection point for receiver mon the reflector is shown as point y. Each station-ary-phase point on the correlogram panel revealsthe corresponding surface shot location �shot i�

atuming and


eeeemmmmiiiiT

sT

sT

sT

s()

()

()

()

−7 −6 −5 −4 −3 −2 −1 0 1 2−7 −6 −5 −4 −3 −2 −1 0 1 2−7 −6 −5 −4 −3 −2 −1 0 1 2−7 −6 −5 −4 −3 −2 −1 0 1 2

−2.5−2.5−2.5−2.5

−2−2−2−2

−1.5−1.5−1.5−1.5

−1−1−1−1

−0.5−0.5−0.5−0.5

0000

0.50.50.50.5

1111

1.51.51.51.5

2222

2.52.52.52.5

−2.5−2.5−2.5−2.5

−2−2−2−2

−1.5−1.5−1.5−1.5

−1−1−1−1

−0.5−0.5−0.5−0.5

0000

0.50.50.50.5

1111

1.51.51.51.5

2222

2.52.52.52.5

eeeemmmmiiiiT

sT

sT

sT

s ()

()

()

()

a) b)

igure 6. �a� Correlograms created by crosscorrelating correspond-ng traces from Figure 5a and b; �b� estimate of the recorded trace re-ulting from an effective shot located at 2-km depth and a receiver at-km depth obtained by stacking all the traces in Figure 6a.

gy: red

ftiRpoWatir

fdvopWpttc

gwradet

�aaaec

ersavaa

M

momrerTthvw

wugbsltc

lstsi

a

b

Fiac

S

a

FpsCwbectt


Dow

nloa

ded

09/1

5/13

to 1

28.8

3.63

.20.

Red

istr

ibut

ion

subj

ect t

o SE

G li

cens

e or

cop

yrig

ht; s

ee T

erm

s of

Use

at h

ttp://

libra

ry.s

eg.o

rg/

rom which the seismic ray passed through the redatumed shot loca-ion �receiver k�, then bounced off specular-reflection point y of thenterface and was captured at the borehole receiver �receiver m�.ays starting at surface shots, which do not pass through these threeoints �k, y, and m�, shown in Figure 8b, create the dipping portionsf the correlograms and do not contribute to the final stacked trace.e can see from this diagram that surface sources need to be used so

ll reflected energy from the target to be imaged comes from rayshat pass through the borehole array of receivers twice — once com-ng into the array as the illuminating energy and once coming back aseflected energy from target formations.

To obtain a complete redatumed downhole survey, we repeat thisor all possible effective downhole source locations. Note that to re-atum a surface shot to be in the borehole, we do not have to applyelocity analysis or complicated processing �such as statics, NMO,r anisotropy corrections�. In fact, no model-dependent processingarameters are required to move the surface shots into the borehole.e do not even need to know that a salt canopy complicates the ray-

aths of energy. For the acoustic case, this feature allows the reda-uming methodology to be performed in a fully automated mannerhat requires virtually no human effort except, for example, quality-ontrol edits.

The final step of the redatuming process is to prepare data for mi-ration. Redatumed shot gathers contain artifacts, described above,hich would contaminate the migration. Many of these artifacts ar-

ive before the direct arrivals. It is easy to eliminate these by simplypplying a mute which removes everything up to and including theirect arrivals on redatumed downhole shot gathers. We have not yetxplored other methods of removing artifacts which occur later inime on the records.

This redatuming methodology gives kinematically correct resultsWapenaar et al., 2005�, which is acceptable for structural imagingpplications. We investigate the acoustic case — for elastic energy,dditional steps are needed to handle the multicomponents. For ex-mple, the three components will need to be rotated into proper ori-ntation facing the salt flank. For stratigraphic and time-lapse appli-ations, more work is needed to ensure correct relative amplitudes.

The success of the redatuming step is determined by how muchnergy is reflected off reflectors near the salt flank and captured byeceivers in the borehole. Because we try to image underneath thealt overhang, this is usually possible only in a medium with a gener-lly increasing v�z� vertical velocity profile. In other geometries andelocity regimes, other solutions are possible. For example, Bakulinnd Calvert �2004� successfully capture reflection energy and im-ged horizontal reflectors using a horizontal well.

igration

The second part of our strategy is to perform two passes of depthigration. The first pass defines the salt-edge geometry, and the sec-

nd pass refines the image to capture sediments. We have experi-ented with Kirchhoff and reverse-time depth-migration algo-

ithms. For the first pass, it is possible to use either method. Howev-r, we found that the sediment images are obtainable only by using aeverse-time algorithm which employs the two-way wave equation.his is because sediments are illuminated only by prismatic reflec-

ions �Cavalca and Lailly, 2005�, which are created by energy whichas bounced off the salt and then is reflected by the sediments, andice versa. In reverse-time prestack migration, the shot and recordedavefields are extrapolated, and zero lag correlations between the

avefields form the image. To save CPU time and disk space, wesed an analytically derived traveltime table for the forward-propa-ated shot-wavefield simulation. We used the full wave equation toack-propagate redatumed field data. Using a traveltime table is rea-onable because our velocity model for the forward shot is a simple,inear v�z� gradient function. However, we will image only half ofhe prismatic reflections, those that bounce off salt first, and will notapture those that bounce off sediment first.

For the first pass of migration, we need a smoothed migration-ve-ocity model. To image and define the salt edge from the redatumedhot position, only the target-oriented, background velocity betweenhe salt flank and the borehole is required. This does not include thealt, as shown in Figure 9a. The spatial uncertainly introduced by us-ng only a smoothed velocity field between the salt and borehole is

)

)

igure 7. Common-downhole-shot gathers obtained �a� by redatum-ng WVSPdata as if there were an effective source at a depth of 2 kmnd �b� by placing an actual source at a depth of 2 km �benchmarkase�.

hot i

Receiver k

Receiver m

Reflector

x

y

z

Receiver k

Receiver m

Shot j

Reflector

x

y

z

) b)

igure 8. Diagram showing a raypath generating a stationary-phaseoint in the correlograms. Receiver k is the location of the redatumedhot, and receiver m is the location of the redatumed receiver. �a�ontributing to the stationary-phase point is the ray from shot i,hich travels through the redatumed shot �receiver k� location,ounces off the specular reflection point y, and is captured by receiv-r m. �b� Shot j does not contribute to the stationary-phase point be-ause the redatumed source, at receiver k, is illuminating point z onhe reflector, whereas receiver m is recording energy from point x onhe reflector.

ct

rcgecbs

npfHpw

�bameTplTtt

nbrt

a

Fof�d�

a

Fw�rd�

S68 Lu et al.

Dow

nloa

ded

09/1

5/13

to 1

28.8

3.63

.20.

Red

istr

ibut

ion

subj

ect t

o SE

G li

cens

e or

cop

yrig

ht; s

ee T

erm

s of

Use

at h

ttp://

libra

ry.s

eg.o

rg/

onsiderably less significant than for the entire path from the surfaceo the salt, which would have needed the complicated salt canopy.

We applied the same reverse-time, prestack depth migration to theedatumed common-shot gathers and the actual modeled downholeommon-shot gathers �benchmark case�. Figure 9b shows the mi-rated image using redatumed data, and Figure 9c shows the migrat-d image of the benchmark case. The image from redatumed dataan recover most of the salt edge in a similar manner to the migratedenchmark results. Both images illuminate very little of the dippingediments.

Once the salt edge is delineated by the first pass of migration, weeed to update our velocity model to include the salt for the secondass of migration. In practice, we would do this by picking the inter-ace between the salt and the background from the migrated image.owever, we have not attempted to pick the salt edge from our first-ass migrations. Instead, by using the actual salt edge �Figure 10a�,e show the best result that might be possible.


hhhhttttppppeeeeDDDD))))

mmmmkkkk((((

0 1 20 1 20 1 20 1 2

0000

0.50.50.50.5

1111

1.51.51.51.5

2222

2.52.52.52.5

3333

3.53.53.53.5

4444

4.54.54.54.5

5555Offset (km)Offset (km)Offset (km)Offset (km)

hhhhttttppppeeeeD)

D)

D)

D)

mmmmkkkk ((((

0 1 20 1 20 1 20 1 2

0000

0.50.50.50.5

1111

1.51.51.51.5

2222

2.52.52.52.5

3333

3.53.53.53.5

4444

4.54.54.54.5

5555


hhhhttttppppeeeeDDDD))))

mmmmkkkk ((((

0 1 20 1 20 1 20 1 2

0000

0.50.50.50.5

1111

1.51.51.51.5

2222

2.52.52.52.5

3333

3.53.53.53.5

4444

4.54.54.54.5

5555

)

c)

b)

igure 9. �a� Velocity model used in the first pass of migration withnly the simple v�z� vertical velocity gradient; �b� migration resultsrom reverse-time prestack depth migration of the redatumed data;c� migration results from reverse-time prestack depth migration ofata created with downhole sources and receivers �benchmark case�.Velocity color bar is shown in Figure 1�.

For the second pass, we apply the reverse-time depth migrationwhich uses the two-way wave equation� to the redatumed andenchmark data. These migration results are shown in Figure 10bnd c, respectively. Because we include the salt dome in the velocityodel and use a full wave-equation algorithm, we can catch the en-

rgy that bounces off the salt flank and illuminates the sediments.hese second-pass images show very good delineation of the dip-ing sediments and the salt edge. Some new artifacts, large-wave-ength shadows in front of the salt edge, have crept into the image.hese artifacts can be reduced with further refinement of the migra-

ion algorithm or postprocessing of data with a high-pass spatial fil-er �e.g., Yoon et al., 2004; Fletcher et al., 2005; Guitton et al., 2006�.

The two-step processing strategy we propose in this section elimi-ates the need for many iterative steps of prestack depth migration touild the velocity model for the overburden. These steps have beeneplaced by the redatuming process, which takes about 10% of theotal computational effort for the proposed strategy.


hhhhttttppppeeee DDDD))))

mmmmkkkk ((((

0 1 20 1 20 1 20 1 2

0000

0.50.50.50.5

1111

1.51.51.51.5

2222

2.52.52.52.5

3333

3.53.53.53.5

4444

4.54.54.54.5

5555Offset (km)Offset (km)Offset (km)Offset (km)

hhhhttttppppeeeeD)

D)

D)

D)

mmmmkkkk((((

0 1 20 1 20 1 20 1 2

0000

0.50.50.50.5

1111

1.51.51.51.5

2222

2.52.52.52.5

3333

3.53.53.53.5

4444

4.54.54.54.5

5555


hhhhttttpppp eeeeD)

D)

D)

D)

mmmmkkkk((((

0 1 20 1 20 1 20 1 2

0000

0.50.50.50.5

1111

1.51.51.51.5

2222

2.52.52.52.5

3333

3.53.53.53.5

4444

4.54.54.54.5

5555

)

c)

b)

igure 10. �a� Velocity model used in the second pass of migrationhich includes the salt dome that could be defined in the first pass;

b� migration results from reverse-time prestack depth migration ofedatumed data; �c� migration results from reverse-time prestackepth migration of data created with downhole sources and receiversbenchmark case�. �Velocity color bar is shown in Figure 1�.

aboabtrasw

disamseToemhp

fiuvOddatrepsaaetg

tWavWimgedftgl

sm

iTgrhscmesi

iptm

VSP d


Dow

nloa

ded

09/1

5/13

to 1

28.8

3.63

.20.

Red

istr

ibut

ion

subj

ect t

o SE

G li

cens

e or

cop

yrig

ht; s

ee T

erm

s of

Use

at h

ttp://

libra

ry.s

eg.o

rg/

DISCUSSION

Comparing results of the first pass of migration for the benchmarknd redatumed cases �Figure 9b and c�, both image the edges of theottom half of the salt dome with about the same quality. However,n the upper half of the salt dome, undersides of the salt crenulationsre defined much better in the benchmark image �Figure 9c�. This isecause the actual downhole source has a better chance to illuminatehe underside of the salt and have receivers capture reflections. Theedatumed shot records �Figure 7a� most likely suffer from a lack ofperture in the original WVSP. The sediment events have nearly theame amount of clarity on the benchmark and redatumed images,ith the benchmark case having slightly better quality.The second pass of migration �Figure 10�, which uses the salt-

ome velocity in the migration model, shows somewhat improvedmages of the salt interface. However, the greatest improvement iseen in the sediments. Now the sediment interfaces are distinguish-ble as much as 0.75 km from the salt edge until the dip of the sedi-ents is nearly flat. At that distance, acquisition geometry does not

eem to capture reflections from horizontalvents except immediately around the borehole.hus, the redatuming step followed by two passesf reverse-time migration can capture the saltdge and dipping sediments. The reverse-timeigration can use the multipath arrivals, which

ave bounced off the salt edge, to make this im-rovement.

Instead of handpicking the outline from therst-pass migration results in this example, wesed the exact outline of the salt-dome edge in theelocity model for the second pass of migration.bviously, for field data, we would have had toigitize the edge. However, the outline of the salt-ome edge from the first pass of migration is im-ged well and would not be very different fromhe exact model. Therefore, we believe our finalesults are representative of the best that could bexpected but would not be too far from what isossible. We show that, by moving the surfacehots into the borehole and closer to the targetrea near the salt dome, higher-order migrationlgorithms, using key multiple reflections, can bemployed because artifacts induced by the uncer-ainties of the velocity model have been reducedreatly.

The issue that remains is whether a conven-ional prestack depth migration of the original

VSP data set would produce a comparable im-ge. To answer this question, we perform a re-erse-time, prestack depth migration of theVSP using the correct velocity model contain-

ng the salt canopy but with the salt dome re-oved, as shown in Figure 11a. To build this mi-

ration model for actual field data, multiple pass-s of prestack depth migration of surface seismicata and model building would need to be per-ormed to first define the top and then the base ofhe salt canopy. Figure 11b shows the WVSP mi-rated result using the correct velocities for theeft side of the model. As with the redatumed re-

Dpeth

)mk(

0

1

2

3

4

5

Dpeth

)mk(

−7 −6

0

1

2

3

4

5

a)

−7 −6

c)

Figure 11. �a�already have averse-time prepass of WVSPcould be definmigration of W

ult, the salt edge is imaged well, but sediments near the salt areissing.We next apply a second pass of depth migration to the WVSP us-

ng the correct velocity model containing the salt dome �Figure 11c�.he final migrated result is shown in Figure 11d. Comparing the mi-rated WVSP image from Figure 11d and the migrated image of theedatumed VSP from Figure 10b, overall we see that both methodsave imaged most of the salt edge very well. However, the under-ides of the crenulations on the top half of the salt dome are not verylear on either section. The WVSP image has reproduced the sedi-ent reflections all the way across the section and up to the salt edg-

s. The redatumed result captures the horizontal portion of only theediments extremely close to the borehole but obtains a reasonablemage of the dipping portion near the salt.

We have described a strategy to perform a shortcut approach tomage the sediments and salt edge around a salt flank through a com-lex overburden using a WVSP data set. Traditionally, depth migra-ion uses numerous iterations of migration, velocity estimation, and

odel building. The redatuming shortcut of WVSP data as if an ef-

Offset (km)−4 −3 −2 −1 0 1 2

Offset (km)

htpeD)

mk(0 1 2

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Offset (km)0 1 2

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

b)

Offset (km)−4 −3 −2 −1 0 1 2

d)

Dpeth

)mk(

y model used in the first pass of WVSPmigration which assumes weknowledge of the salt canopy �SD-II�; �b� migration results from re-epth migration of WVSPdata; �c� velocity model used in the second

tion which includes the salt canopy �SD-II� and salt dome �SD-I� thathe first pass; �d� migration results from reverse-time prestack depthata. �Velocity color bar is shown in Figure 1�.

−5

−5

Velocitgoodstack dmigraed in t

faaeotvttnogawasatvf

wfiotprlmptTam

ammbtWstrss

MCtmFF

A

B

B

B

B

B

B

C

C

C

C

D

D

F—

F

F

G

G

G

H

H—

H

H

H

H

K

L

L

M

M

S70 Lu et al.

Dow

nloa

ded

09/1

5/13

to 1

28.8

3.63

.20.

Red

istr

ibut

ion

subj

ect t

o SE

G li

cens

e or

cop

yrig

ht; s

ee T

erm

s of

Use

at h

ttp://

libra

ry.s

eg.o

rg/

ective single-well downhole survey had been collected, with shotsnd receivers in the borehole, allows us to ignore all velocity issuesssociated with the overburden. We have not discussed the velocity-stimation issue for the simple v�z� background velocities used inur migrations. We believe that by relocating our frame of referenceo the borehole perspective, the image uncertainty associated withelocity errors has been reduced greatly because the distance fromhe wellbore to the salt flank is typically comparatively small. Thisarget-oriented velocity structure could contain anisotropic terms ifeeded. In addition, we have not attempted to pick the salt edge fromur first-pass migrations to build the model for the second-pass mi-ration. Instead, we show the best that might be possible by using thectual salt edge. Obviously, the success of this method on field dataill depend on data quality, field-acquisition parameters including

perture and source and receiver spacing, and the actual geometry ofalt bodies.Another aspect is the extension of this method to 3D. Im-ges created from redatumed shots are contained intrinsically withinhe plane of the surface shots and receivers in the well. A 3D imageolume, therefore, can be created from a sequence of 2D imagesrom selected ranges of surface shots from a 3D VSP survey.

CONCLUSION

We have presented a strategy for imaging the flanks of a salt domehen an obscuring salt canopy is present in the immediate area. Therst step is to perform a redatuming of a WVSP data set so that webtain effective downhole shot gathers. Redatuming shots allows uso move our perspective closer to the salt flank. Then we apply twoasses of prestack depth migration. The use of a reverse-time algo-ithm, based on the two-way wave equation, for the second pass al-ows us to image the salt-dome edge and dipping sediments. The

ethod is target oriented and is at least three times faster than a com-arable imaging effort on the original WVSP data. It also eliminateshe need for iterative depth migrations of the complex overburden.he final image we obtain of the salt edge and the dipping sediments,lthough not as complete as the WVSP results, provides a shortcutethod to a useful image.As with all migration algorithms, the proposed method requires

n adequate acquisition aperture to capture the salt dome and sedi-ent reflections. The strategy we present using this redatumingethod was tested on acoustic model data.Additional work needs to

e done to extend this to elastic multicomponent data sets as well aso 3D salt-dome targets. Redatuming to the borehole reduces a 3D

VSP survey to 2D acquisition and imaging from the borehole per-pective. However, because we control which shots go into the reda-uming process, it might be possible to beam-steer the imaging di-ection and obtain some limited 3D images. The performance of thistrategy on field data will need to be tested for sensitivity to noiseources.

ACKNOWLEDGMENTS

The authors thank Rama Rao and Daniel Burns at ERL; Albenaateeva, Andrey Bakulin, and Jorge Lopez at Shell; and Arthurheng for numerous helpful discussions on this topic. We also thank

he editors and anonymous reviewers for their constructive com-ents. This work was funded by the Earth Resources Laboratoryounding Member Consortium and Air Force Laboratory Contract19628-03-C-0126.

REFERENCES

minzadeh, F., J. Brac, and T. Kunz, 1997, 3-D salt and overthrust models:SEG/EAGE 3D Modeling Series 1.

akulin, A., and R. Calvert, 2004, Virtual source: New method for imagingand 4D below complex overburden: 74th Annual International Meeting,SEG, ExpandedAbstracts, 2477–2480.

akulin, A., A. Mateeva, K. Mehta, P. Jorgensen, J. Ferrandis, I. S. Herhold,and J. Lopez, 2007, Virtual source applications to imaging and reservoirmonitoring: The Leading Edge, 26, 732–740.

aysal, E., D. D. Kosloff, and J. W. C. Sherwood, 1983, Reverse time migra-tion: Geophysics, 48, 1514–1524.

evc, D., 1997, Imaging complex structures with semirecursive Kirchhoffmigration: Geophysics, 62, 577–588.

erryhill, J., 1984, Wave-equation datuming before stack: Geophysics, 49,2064–2066.

iondi, B., and G. Shan, 2002, Prestack imaging of overturned reflections byreverse time migration: 72nd Annual International Meeting, SEG, Ex-pandedAbstracts, 1284–1287.

avalca, M., and P. Lailly, 2005, Prismatic reflections for the delineation ofsalt bodies: 75thAnnual International Meeting, SEG, ExpandedAbstracts,2550–2553.

alvert, R. W., A. Bakulin, and T. C. Jones, 2004, Virtual sources, a new wayto remove overburden problems: 66th Annual Conference and Exhibition,EAGE, ExtendedAbstracts, 234–237.

laerbout, J., 1976, Fundamentals of geophysical data processing: McGraw-Hill Book Co.

oates, R., M. Kane, C. Chang, C. Esmersoy, M. Fukuhara, and H. Yama-moto, 2000, Single-well sonic imaging: High-definition reservoir cross-sections from horizontal wells: SPE/Petroleum Society of CIM,65457-MS.

aley, T., E. Majer, and R. Gritto, 2000, Progress and issues in single wellseismic imaging: 70th Annual International Meeting, SEG, Expanded Ab-stracts, 1552–1555.

erode, A., E. Larose, M. Campillo, and M. Fink, 2003, How to estimate theGreen’s function of a heterogeneous medium between two passive sen-sors? Application to acoustic waves: Applied Physics Letters, 83,3054–3056.

ink, M., 1999, Time reversed acoustics: ScientificAmerican, 281, 91–97.—–, 2006, Time-reversal acoustics in complex environments: Geophys-ics, 71, no. 4, SI151–SI164.

letcher, R., P. Fowler, P. Kitchenside, and U. Albertin, 2005, Suppressingartifacts in prestack reverse time migration: 75th Annual InternationalMeeting, SEG, ExpandedAbstracts, 2049–2051.

ortin, J. P., N. Rehbinder, and P. Staron, 1991, Reflection imaging around awell with the EVAfull-waveform tool: LogAnalyst, 32, 271–278.

ray, S., 2005, Gaussian beam migration of common-shot records: Geo-physics, 70, no. 4, S71–S77.

ray, S. H., and W. P. May, 1994, Kirchhoff migration using eikonal equa-tion traveltimes: Geophysics, 59, 810–817.

uitton, A., B. Kaelin, and B. Biondi, 2006, Least-square attenuation of re-verse-time-migration artifacts: 76th Annual International Meeting, SEG,ExpandedAbstracts, 2348–2351.

ale, D., N. R. Hill, and J. Stefani, 1992, Imaging salt with turning seismicwaves: Geophysics, 57, 1453–1462.

ill, N. R., 1990, Gaussian beam migration: Geophysics, 55, 1416–1428.—–, 2001, Prestack Gaussian-beam depth migration: Geophysics, 66,1240–1250.

okstad, K., R. Mittet, and M. Landrø, 1998, Elastic reverse time migrationof marine walk away vertical seismic profiling data: Geophysics, 63,1685–1695.

ornby, B., 1989, Imaging of near-borehole structure using full-waveformsonic data: Geophysics, 54, 747–757.

ornby, B., and J. Yu, 2007, Interferometric imaging of a salt flank usingwalkaway VSP data: The Leading Edge, 26, 760–763.

ornby, B. E., J. Yu, J. A. Sharp, A. Ray, Y. Quist, and C. Regone, 2006,VSP: Beyond time-to-depth: The Leading Edge, 25, 446–452.

orneev, V., and A. Bakulin, 2006, On the fundamentals of the virtual sourcemethod: Geophysics, 71, no. 3, A13–A17.

u, R., X. Campman, M. E. Willis, M. N. Toksöz, and M. V. de Hoop, 2006,An application of TRA to the pre- and post-stack imaging of a salt-domeflank: 68th Annual Conference and Exhibition, EAGE, Extended Ab-stracts, H043.

u, R., M. E. Willis, X. Campman, J. Ajo-Franklin, and M. N. Toksöz, 2006,Imaging dipping sediments at a salt dome flank — VSP seismic interfer-ometry and reverse-time migration: 76th Annual International Meeting,SEG, ExpandedAbstracts, 2191–2194.ajer, E., J. Peterson, T. Daley, B. Kaelin, L. Myer, J. Queen, P. D’Onfro,and W. Rizer, 1997, Fracture detection using crosswell and single well sur-veys: Geophysics, 62, 495–504.ateeva, A., J. Ferrandis, A. Bakulin, P. Jorgensen, C. Gentry, and J. Lopez,

R

S

S

S

S

S

V

W

W

W

W

W

W

X

Y


Dow

nloa

ded

09/1

5/13

to 1

28.8

3.63

.20.

Red

istr

ibut

ion

subj

ect t

o SE

G li

cens

e or

cop

yrig

ht; s

ee T

erm

s of

Use

at h

ttp://

libra

ry.s

eg.o

rg/

2007, Shell steers virtual sources for salt, subsalt imaging: Offshore, 67,94–96.

ickett, J., and J. Claerbout, 1996, Passive seismic imaging applied to syn-thetic data: Stanford Exploration Project, Report 92, 83–90.

chuster, G., F. Followill, L. Katz, J. Yu, and Z. Liu, 2003, Autocorrelogrammigration: Theory: Geophysics, 68, 1685–1694.

chuster, G., J. Yu, J. Sheng, and J. Rickett, 2004, Interferometric/daylightseismic imaging: Geophysical Journal International, 157, 838–852.

iddiqui, K., S. Clark, D. Epili, N. Chazalnoel, and L. Anderson, 2003, Ve-locity model building methodology and PSDM in deep water Gulf of Mex-ico: A case history: 73rd Annual International Meeting, SEG, ExpandedAbstracts, 442–445.

nieder, R., 2004, Extracting the Green’s function from the correlation ofcoda waves: A derivation based on stationary phase: Physical Review E,69, 046610.

un, Y., F. Qin, S. Checkles, and J. P. Leveille, 2000, 3-D prestack Kirchhoffbeam migration for depth imaging: Geophysics, 65, 1592–1603.

an Manen, D. V., J. O. A. Robertsson, and A. Curtis, 2005, Modeling ofwave propagation in inhomogeneous media: Physical Review Letters, 94,164301.ang, B., F. Audebert, D. Wheaton, and V. Dirks, 2006, Subsalt velocityanalysis by combining wave equation based redatuming and Kirchhoff

based migration velocity analysis: 76th Annual International Meeting,SEG, ExpandedAbstracts, 2440–2444.ang, B., F. Qin, F. Audebert, and V. Dirks, 2005, Afast and low cost alterna-tive to subsalt wave equation migration perturbation scans: 75th AnnualInternational Meeting, SEG, ExpandedAbstracts, 2257–2260.apenaar, K., 2004, Retrieving the elastodynamic Green’s function of an ar-bitrary inhomegeneous medium by cross correlation: Physical ReviewLetters, 93, 254301.apenaar, K., and J. Fokkema, 2006, Green’s function representations forseismic interferometry: Geophysics, 71, no. 4, SI33–SI46.apenaar, K., J. Fokkema, and R. Snieder, 2005, Retrieving the Green’sfunction in an open system by cross correlation: A comparison of ap-proaches: Journal of theAcoustical Society ofAmerica, 118, 2783–2786.illis, M. E., R. Lu, X. Campman, M. N. Toksöz, Y. Zhang, and M. de Hoop,2006, Anovel application of time-reverse acoustics: Salt dome flank imag-ing using walkaway VSP surveys: Geophysics, 71, no. 2, A7–A11.

u, S., and S. Jin, 2006, Wave equation migration of turning waves: 76thAn-nual International Meeting, SEG, ExpandedAbstracts, 2328–2331.

oon, K., K. Marfurt, and W. Starr, 2004, Challenges in reverse-time migra-tion: 74thAnnual International Meeting, SEG, ExpandedAbstracts, 1057–1060.

Documents

Redatuming through a salt canopy and target-oriented salt-flank imaging