See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/229917517 2D PP/PS-stereotomography: application to a real 2D-OBC dataset ARTICLE in GEOPHYSICAL PROSPECTING · FEBRUARY 2008 Impact Factor: 1.47 · DOI: 10.1111/j.1365-2478.2008.00681.x · Source: OAI CITATIONS 2 READS 30 5 AUTHORS, INCLUDING: Gilles Lambaré MINES ParisTech 48 PUBLICATIONS 565 CITATIONS SEE PROFILE Reda Baina Université de Pau et des Pays de l'Adour 20 PUBLICATIONS 47 CITATIONS SEE PROFILE Soazig Le Bégat Independent Researcher 13 PUBLICATIONS 113 CITATIONS SEE PROFILE Available from: Soazig Le Bégat Retrieved on: 15 January 2016
2D PP/PS-stereotomography: Application to a real 2D-OBC dataset
M. Alerini1,∗,†, G. Lambare1,‡, R. Baina2, P. Podvin1 and S. Le Begat1,∗∗
1Ecole des Mines de Paris, Fontainebleau, France, and 2OPERA, Pau, France
Received May 2007, revision accepted September 2007
ABSTRACTIt has been shown on an ‘ideal’ synthetic dataset that PP/PS-stereotomography canestimate an accurate velocity model without any pairing of PP- and PS-events. TheP-wave velocity model is first estimated using PP data and then, fixing this velocityfield, the S-wave velocity is estimated using the PS data. This method needed to beevaluated further and we present here the first application of PP/PS-stereotomographyto a real dataset: the 2D East-West Mahogany OBC line (Gulf of Mexico). We are hereconfronted with data which do not fit our working assumptions: coherent noise (dueto an approximate separation of PP- and PS-events and some remaining multiples),probably some anisotropy and 3D effects. With a careful selection of the stereotomo-graphic picks, which allows one to decrease the effect of the picked coherent noiseby the automatic picker, our application can demonstrate the relevance of our ap-proach in the upper part of the profile, where anisotropy and 3D effects might below. We can thus estimate, without any pairing of PP- and PS-events, a velocity fieldwhich provides not only flat common image gathers, but also PP- and PS-depth mi-grated images located at the same positions. For the deeper part of the profile, asignificant shift in depth appears. In addition to possible anisotropy, 3D effects anda more complex velocity field (‘salt body’), this is due to the quality of the PZ- andX-components profiles: The PZ-component profile where the PP-stereotomographicpicking is performed, is polluted by conflicting converted or multiple events and theX-component profile, where the PS-stereotomographic picking is performed, is highlynoisy. This study emphasizes the need to develop accurate selection criteria for thestereotomographic picks.
I N T R O D U C T I O N
The use of converted waves in reflection seismic imaging canbe a significant improvement. Indeed P- and S-reflected wavesbear complementary information about the elastic propertiesof the medium. It concerns both the reference velocity model(P- and S-wave velocities) and the short wavelength compo-nents of the elastic parameters describing the model (reflectiv-ity).
The propagation of S-waves can be advantageously usedfor structural imaging, as for example in gas cloud contexts
†Now at: SINTEF Petroleum, Trondheim, Norway‡Now at: Compagnie Generale de Geophysique, Massy, France∗ ∗
Now at: Geophysical Consulting, Pau, France
where the S-wave propagation is far less affected by gas thanP-wave propagation (Thomsen et al. 1997; Gaiser et al. 2001).Concerning the short wave-length components of the elasticparameters, in addition to AVA/AVO analysis of convertedwaves (Garotta and Granger 1987), linearized inversions ofPP- and PS-diffracted/reflected wave fields have been proposed(Tarantola 1986; Jin et al. 1992; Nicoletis et al. 1997). Theyallow a better lithological identification (Polskov et al. 1980),a better fracture characterization (Kendall and Kendall 1996;Granger et al. 2001) and better rock property analysis (Kendallet al. 1998b).
In marine environments, with the development of 4-component (4C) receivers laid on the sea bottom, convertedwaves have received increasing attention from the explorationgeophysics community (Garotta, Granger and Dariu 2000).These 4C are one hydrophone recording the pressure and
three geophones recording the particle displacement (or ve-locity). The most commonly used acquisition system is theso-called OBC, for ocean bottom cable (Caldwell 1999). Acable containing 4C receivers is laid on the seabed and a ves-sel pulls a source at the sea surface. In recent years, the useof S-waves through PS-conversions in marine reflection seis-mics has shown better quality results than the use of PP-datain some configurations. For example, real improvements havebeen reported when imaging through a gas cloud (Thomsenet al. 1997; Granli et al. 1999).
Processing of converted waves requires a significant adapta-tion of the sequence such as wavefield separation, convertedwaves migration or velocity model building (Stewart et al.
2002, 2003; Boelle and Ricarte 2003). An additional diffi-culty may arise when the analysis needs a matching of PP- andPS-events. In depth imaging it means determining P- and S-wave velocity models migrating PP- and PS-data at the samedepth and the same horizontal position. Considering the poorconditioning of the estimation of the reference velocity mod-els, the matching of PP- and PS-images is generally insured bypairing a priori PP- and PS-reflected events. In standard trav-eltime tomography, this seriously complicates the picking step(Gerea, Nicoletis and Rakotoarisoa 2001; Stopin 2001; Brotoet al. 2003), even if some practical solution can be found (Foss,Ursin and de Hoop 2005).
Alerini et al. (2007) presented an extension of stereotomog-raphy to converted PP/PS-waves. A 2D approach was devel-oped for inverting P-wave and S-wave isotropic reference ve-locity models in a nearly fully automatic way. They showedthat for a synthetic data example and optimal preprocessingand picking, PP/PS-stereotomography allowed one to invert,without any pairing of events, both P- and S-wave velocitymodels, providing PP- and PS-migrated images at the samepositions. It appeared, thus, important to further test the ap-proach in a real data context, where coherent noise, 3D effectsand anisotropy could alter the results.
In the present paper we first recall some basic ideas of PP/PS-stereotomography and then present the first application on areal dataset, the East-West 2D-4C OBC Mahogany line (Cald-well et al. 1998). The quality of the inverted velocity modelis assessed in terms of flatness of common image gathers andin terms of focusing depths of PP- and PS-reflections. Eventhough the automatic picking used for stereotomography ismuch easier than the one used for picking global events, itremains the bottleneck of the method. Indeed, we use herean automatic approach which can be inaccurate in (coherent)noise context. We emphasize here the practical difficulties ofthe application of PP/PS-stereotomography and in particular,
the difficult selection of the stereotomographic picks after theautomatic stereotomographic picking (Billette et al. 2003).
P P / P S - S T E R E O T O M O G R A P H Y
Stereotomography is a slope tomography which was intro-duced, developed and applied by Billette and Lambare (1998).Alerini et al. (2007) presented an extention to converted PS-waves. We shall here just briefly recall the basis of PP/PS-stereotomography. Stereotomography is based on the use oflocally coherent events for estimating velocity macro-modelsfrom seismic reflection data. Such locally coherent events aredefined by their positions at the surface (source and receiverfor example, s, r), their two-way traveltimes, Tsr, and theirtwo slopes in the common source and common receiver gath-ers (ps, pr), which are the local tangents to the locally coherentevents. For PP/PS-stereotomography, those events have to beidentified as primary PP- or PS-reflections/diffractions. A PP/PS-stereotomographic dataset consists then of NPP PP-stereo-tomographic picks and NPS PS-stereotomographic picks:
d ={(s, r, ps, pr, Tsr)
NP Pi=1 , (s, r, ps, pr, Tsr)
NPSj=1
}. (1)
This data will allow us to invert a model defined by
m ={(X, βs, βr, Ts, Tr)
NP Pi=1 , (X, βs, βr, Ts, Tr)
NPSj=1 , (CP )MP
k=1,
(CS)MSl=1
}(2)
where (CP )MPk=1 and (CS)MS
l=1 denote respectively the MP andMS parameters describing the P- and S-wave reference veloc-ity models, X the position of the diffraction/reflection point,(βs, βr) the two shooting angles and Ts and Tr the two one-way traveltimes, for the rays propagating from X towards thesource in the P-wave velocity model and towards the receiverin the S-wave velocity model, respectively.
In PP/PS-stereotomography we can first invert the PP-stereotomographic dataset into the P-wave reference veloc-ity model. This is done by standard stereotomography. Wethen fix the P-wave reference velocity model and invert the PS-stereotomographic dataset into the S-wave reference velocitymodel.
PP/PS-stereotomographic optimization was described inAlerini et al. (2007). We would like to focus here more onthe stereotomographic picking, which is, although easier thanthe picking in traveltime tomography, definitively the mainbottleneck in our later application to real data.
We use an automatic picking tool (Billette et al. 2003) theprinciple of which is to compute the slope of the locally coher-ent events by local slant stack and the coherency of this events
x0 is the position of the central trace, p, the investigated slopeand L is the width of window over the traces in which wecompute the local semblance. H is the normalized Hammingwindow and u is the analytic trace defined by u = (1 + iHilb)u(Hilb being the Hilbert transform operator). The denomina-tor in this expression is the energy of the data, which also al-lows one to pick energetically low but highly coherent events.The a posteriori selection criteria for the automatically pickedstereotomographic events can be first based on the semblanceand energy of the events (provided that a proper gain hasbeen applied). The selection can also be based on the equiv-alent model (Billette et al. 2003), which is the interpretationof any individual stereotomographic events in terms of indi-vidual reflection. There, events are pieces of flat reflectors in auniform medium. The equivalent velocity, Veq, and the equiv-alent diffration point position, xeq, can be computed and theirexpressions found in Billette et al. (2003).
For PS-stereotomography, the only assumptions arethat the reflections correspond to primary PP- or PS-reflections/diffractions and that the P-to-S conversion occursat the reflection/diffraction point. In terms of preprocessing,PP/PS-stereotomography requires multiple removal, wavefieldseparation and static correction. Concerning wavefield sepa-ration, due to the high S-wave velocity gradient, PP-reflectionscan be mainly observed on the PZ-component profile, whilethe PS-reflections can be mainly observed on the horizontalcomponent profile. We make this assumption here, althoughbetter strategies exist (Edme et al. 2005).
T H E M A H O G A N Y F I E L D
The Mahogany field has a very specific importance for thehistory of oil prospection in the Gulf of Mexico. It was dis-covered in 1993 by a well operated by Philips Petroleum and itbecame, after starting production in December 1996, the firstcommercial oil field beneath salt in the Gulf of Mexico.
Imaging beneath salt is usually difficult using standard pro-cessing (Caldwell et al. 1998). The strong velocity contrastsand the roughness of the boundary of the salt body are cer-tainly difficult challenges for seismic imaging techniques. An-other supposed reason for this difficulty is the strong con-version of P-waves into S-waves at the boundaries of the saltbody. These conversions are frequently stronger than the non-converted waves. In some cases, the base of the salt can only
be observed using converted waves and they have to be takeninto account rigorously during the preprocessing and the in-terpretation (Ogilvie and Purnell 1996).
In order to assess the potential of seismic imaging with con-verted waves on the Mahogany field, a 2D multicomponent(4C) test was decided and the acquisition was completed inearly 1998. The goal was to determine if coherent S-wave en-ergy generated and/or reflected beneath salt could be recordedand identified (Caldwell et al. 1998). It was one of the firstmulti-component acquisitions in the Gulf of Mexico (the for-mer OBC acquisitions had essentially been done in the NorthSea). Two lines were recorded: an East-West line, that we usedfor this study, and a North West-South East line to the east ofthe Mahogany platform. The East-West line was chosen in or-der to minimize the 3D effects (Caldwell et al. 1998). Numer-ous studies have been devoted to the processing of this dataset(Kendall et al. 1998a; Herrenschmidt et al. 2001; Gerea et al.
2001; Stopin 2001; Jin et al. 2002) and it was a very interestingopportunity for us to test PP/PS-stereotomography.
Indeed, the application to Mahogany was our first appli-cation to a real dataset and we did not expect to solve theproblem of imaging beneath the salt. More modestly, ourgoal was to investigate the robustness of our approach in acase where no rigorous splitting of PP- and PS-events couldhave been applied to the dataset and where strongly corre-lated noise existed. In addition, some authors (Gerea et al.
2001; Stopin 2001) found some anisotropy, which we did nottake into account in our inversion scheme. In this context werather focused on the shallowest part of the profile, where thesignal-to-noise ratio was significantly higher especially for theX-component section where we picked PS-events.
T H E M A H O G A N Y D ATA S E T
The 2D-4C East-West Mahogany line was recorded by Geco-Prakla. The acquisition was performed using a 1.5 km longcable which has been laid 7 times in order to cover a 10.5 kmlong receiver line. A 4C Nessie cable was used with a 25 mreceiver group spacing. The coupling with the sea bottom wasonly ensured by the weight of the cable (Ronen et al. 2000).The source was a 5400 in3 airgun at 6 m depth. Shot spacingwas 25 m and the maximum recorded offset was 10 km. 10 swere recorded with a 2 ms sampling. (We resampled to 4 ms.)According to Caldwell et al. (1998), the quality of the recordeddata was good, with, for example, most of the PS-convertionsoccuring at depth and not at the sea bottom.
Some preprocessing had been applied (Herrenschmidt et al.
2001) to the raw (4C) dataset: first a P-Z summation(Soubaras 1996) and then various surface consistent statics
Figure 1 2D 4C Mahogany dataset, PZ-component. Common receiver gather for Xr = 688, 305 km. (a) the data used for the migration, (b) thedata used for the stereotomographic picking. An AGC, a high pass filter and internal and external mutes were applied to the traces used for thestereotomographic picking.
corrections at the receivers for the horizontal component. Evenif the splitting of PP- and PS-events into the PZ-componentand the X-component profiles was not perfect, we decidedto use the PZ-component profile for PP-stereotomographyand PP-migration and the X-component profile for PS-stereotomography and PS-migration.
Figures 1(a) and 2(a), show a PZ- and X-component com-mon receiver gather for receiver position Xr = 688.305 km.From these figures it is clear that the splitting of PP- of PS-events was not fully obtained in the PZ- and X-componentprofiles. For example, some PS reflected events appear on thePZ-component common receiver gather: e.g. between 1.5 sand 2 s, at short offsets we can see strongly curved events(1a). These effects may be due to some coupling between thedifferent geophones of the receivers. However, those gathers oftraces are directly used for PP and PS prestack depth migrationin our application.
Since an accurate splitting of PP- and PS-events is impor-tant for PP- and PS-stereotomography, we tried to apply some
further preprocessing before stereotomographic picking. Con-sidering Fig. 1(a) we see that PS-events have a lower frequencycontent than PP-events. So we applied to the PZ-componenta high-pass filter with a ramp between [15, 25] Hz, and weapplied to the X-component a low pass filter with a rampbetween [40, 50] Hz. Finally an AGC with a 0.5 s time win-dow, followed by external and internal mutes (with a 40 mstaper) was applied before the stereotomographic picking. Fig-ures 1(b) and 2(b) show the resulting data for receiver posi-tion, Xr = 688.305 km. These figures show that most of theshear waves have been removed from the PZ-component, forinstance. The mutes ensure the localization of the stereotomo-graphic automatic picking in the convenient time windows ofthe traces, i.e. those where the signal to noise ratio is the bestin terms of splitting of PP/PS-events and those with the high-est stereotomographic information (no short offsets, which donot allow one to solve the velocity to depth ambiguity).
Figures 1 and 2 allow a comparison between the data formigration and the data for stereotomography.
Figure 2 2D 4C Mahogany dataset, X-component. Common receiver gather for Xr = 688, 305 km. (a) the data used for the migration, (b) thedata used for the stereotomographic picking. An AGC, a low pass filter and internal and external mutes were applied to the traces used for thestereotomographic picking.
S T E R E O T O M O G R A P H I C I N V E R S I O N
We emphasize here that the main point of our study was toinvestigate whether our approach could provide good resultswhen confronted with real data. The problems we faced were:� presence of remaining multiples (internal multiples for in-
stance)� aliasing in the data� strong velocity variation in shallow layers requiring statics
corrections� imperfect splitting of PP- and PS-events� anisotropy� 3D effects
In order to eliminate some of these problems, we performeda careful selection of the picks. As this dataset was the firstreal dataset on which PS-stereotomography was applied, welacked experience for an automatic selection of stereotomo-graphic picks and we decided to check interactively the qual-ity of each pick on the gather of traces and on the local slant
stack panel (Billette et al. 2003). The aliasing in the data wasactually easy to identify, considering local slant stack panels(Figs 3 and 9), but also in terms of equivalent model (Billette et
al. 2003). It was thus possible to do a first automatic selectionof the events according to this velocity.
In both, P- and S-wave velocity models estimation, we triedto apply the strategy we tested on the ‘ideal’ dataset shownin Alerini et al. (2007). Our idea there was to do first an au-tomatic picking (for central traces spaced at 150 m both inthe shot and receiver directions) and from this initial stereoto-mographic dataset, to perform various selections among thestereotomographic picks. Just after the automatic picking,a first interactive selection was made eliminating outliers interms of equivalent model parameters and keeping the mostcoherent events and those with the strongest energy (an AGCwas applied to the dataset!). We then did a visual interactivequality control of the picks and further eliminated the events,which we suspected to be erroneous according to our hypoth-esis. We give more details about these selections below.
Figure 3 PP stereotomographic picking. Interactive quality control ofthe automatically picked events. At the top the common shot gather(left) and the associated local slant stack gather (right). At the bottomthe common receiver gather (left) and the associated local slant stackgather (right). The vertical axis is the time for both types of panels,while the horizontal axis is the trace number for the gathers of traces,and slope, i.e. horizontal slowness, for the local slant stack panels.The two gathers of traces are centred around the same central trace(in black, while the other traces are in grey). On both local slant stackpanels automatically picked events are indicated by crosses. They cor-respond to high values of the envelope of the local slant stack indicatedin blue (red corresponds to poor values). Among these events, the onewith a superimposed square corresponds to an aliased event, whichclearly appears, considering the associated slopes reported on the tracegather. On the top panel the value of the time, of the slope and of thesemblance of the event is also indicated at the top of the panel, as wellas at the bottom the characteristics of the associated equivalent model(Billette and Lambare 1998), which could not be calculated here.
P-wave velocity model
For the P-wave velocity model estimation, we first selectedaround 7000 stereotomographic events according to their co-herency, their energy and the equivalent model parameters.
We then performed a visual quality control of the picks andeliminated about 3% of them (see Fig. 3 with an eliminatedpick associated to aliasing). We finally kept only 5347 events,the traveltime of which was less than 3 s (at greater times, weestimated the signal to noise ratio to be too low).
For the optimization, we tested both ‘multi-scale’ and ‘timestripping’ (Alerini et al. 2007) approaches, which gave similarresults. We present here the results given by the ‘time stripping’approach which allows a better control on the selected events.The data were split into four subsets, i.e.� 555 stereotomographic events with time <1 s,� 2252 stereotomographic events with time <2 s,� 3779 stereotomographic events with time < 2.5 s,� 5347 stereotomographic events with time <3 s,which were successively introduced in the optimization. Thisprogressive increase of the number of stereotomographic dataallows one to bypass the nonlinearity.
The a priori model was an homogeneous velocity modelwith a velocity of 1500 ms−1. The spacing of the B-splinesnodes was 500 m vertically and horizontally. For the a priori
covariance matrix in the data space, we considered uncorre-lated errors of 5 m on the positions, of 10 sm−1 on the slopesand of 5 ms on the two-way travel time. The final model al-lowed us to fit about 50% of the observed events within thesea priori error bars. The regularization is insured by a smooth-ing (a weighted Laplacian type operator) as defined in Aleriniet al. (2007).
Figure 4 shows the final VP velocity model. We superim-posed the dip bars corresponding to the recovered pairs of raysegments. It gives an idea of the coverage of the model andof the geological structure. Dip bars are small segments posi-tionned at the inverted diffraction point position and with theinverted local geological dip.
The migrated images give an idea of the quality of the in-verted velocity model. The prestack migrated image (Fig. 5)exhibits good focus. The quality of this image (assessed interms of focus and depth of the geological structures) is equiv-alent to the one of the result obtained by Stopin (2001)by standard travel time tomography, assuming an isotropicpropagation.
We show some common-image gathers in angle domain (Xuet al. 2001) in Fig. 6. The common-image gathers are flat upto two kilometres depth, even if strong frowning events revealthat PS arrivals still exist in the PZ-component profile. Below2. km depth, we observe that the top of the salt (about 2.6 kmdepth at X = 688. km) is slightly frowning in the common-image gathers (the recovered velocity is too high!), while thebase of the salt (about 3.2 km depth at X = 688. km) is strongly
Figure 4 Final PP stereotomographic model.Dip bars have been superimposed on the VP
velocity model expressed in kms−1. 5347‘picks’ or ‘locally coherent events’ wereused for estimating this velocity model. Asmoothing along the dip bars, instead ofa Laplacian type regularization, would cer-tainly provide a more geologically plausiblemodel.
Prestack PP depth migrated image for thePZ-component profile using the final PPstereotomographic model shown on Fig. 4.
687. 689. 691. 693.0.
1.
2.
3.
Distance (km)
Dep
th (
km)
685. 686. 688. 690. 692. 694.
Figure 6 PP common-image gathers in theangle domain. Incidence angles range from−60◦ to +60◦. The final PP stereotomo-graphic model (Fig. 4) was used for the mi-gration. The migration stack is shown in Fig.5). Strong frowning events observed in theshallowest part may correspond to remain-ing PS events. We see that the top of the saltbody is slightly frowning, while its bottomis strongly smiling. We also observe between2 km and 3.5 km depth conflicting frowningand smiling events, which bias the stereoto-mographic optimization.
smiling (the recovered velocity is too low). Furthermore, in-side the salt body we observe conflicting frowning and smilingevents, which certainly bias the stereotomographic optimiza-tion in this area.
Figure 7 focuses on the first two kilometres depth. This zonecorresponds to the best imaged part of the model and we willalso focus on this part for the PS-stereotomography results.
S-wave velocity model
The S-wave velocity model estimation was more difficult thanthe P-wave one. This is due to the lower signal-to-noise ratioin the PS-data, making the automatic picking less efficient, butalso due to the strong S-wave velocity variations in the shallowlayers. A uniform smoothing of the velocity model, such as the
Figure 7 PP prestack depth migration.Zoom in the prestack PP depth migrated im-age for the Z-component of the data (Fig. 5).Note for the first layers the small oscillationscreated by the interpolation scheme used inour migration code (Thierry et al. 1999).
Figure 8 Initial velocity models for PSstereotomography. (a) the VP velocity modelrecovered by PP stereotomography andfixed during PS stereotomography (It hasbeen extended laterally in order to avoidboundary effects); (b) the initial VS velocitymodel derived from the VP velocity modelusing a slight variation from Han’s (1986)expression.
one we use, may not always be the most appropriate solution.S-wave propagation is also sensitive to anisotropy, which isnot taken into account in our inversion.
We start from an initial S-wave velocity model derived fromthe final P-wave using the empirical law given by Han, Nur andMorgan (1986) and slightly corrected for the unconsolidatedshallow layers. In addition, we had to extend the VP modellaterally due to an increased offset range for the preprocessedX-component data compared to the PZ one. The a priori S-wave velocity model is described by B-spline nodes spaced by
500 m laterally and by 120 m vertically in order to be able todescribe the strong velocity variations in the shallow part ofthe model. The extended VP model and the a priori VS one areshown on Figures 8(a) and 8(b) respectively.
Considering a realistic VS model will allow us to improvethe selection of the picks. Indeed, the automatic picking forPS-stereotomography on the X-component did not provide asgood picks as for PP-stereotomography on the PZ-component.After the first selection of steps based on equivalent modelparameters, coherency and energy, we did an interactive
Figure 9 PS stereotomographic picking. Interactive quality control ofthe automatically picked events. See caption of Fig. 3 for an expla-nation of the display. The event indicated by a square and a crosscorresponds to a spurious aliased event. It clearly appears consideringthe associated slopes reported on the trace gathers. On the bottompanel the value of the time, the slope and the semblance of the eventare indicated at the top of the panel, as well as at the bottom the char-acteristics of the associated equivalent model (Billette and Lambare1998), which could not be calculated here. This type of event waseliminated from the PS stereotomographic dataset.
quality control of the PS-stereotomographic picks. Three maintypes of spurious stereotomographic picks could be identified:aliased events (Fig. 9), ambiguous conflicting events (Fig. 10),or events picked on poorly coherent traces gathers (Fig. 11).In the case of crossing events, the difficulty relied in the factthat there is an ambiguity about the pairing of slopes. Allthese spurious stereotomographic picks (output of automaticpicking) were eliminated interactively during the visual check.About 65% of the PS-stereotomographic picks remained afterthis selection (compare to 97% in the PP case!), giving a totalnumber of 5210 PS-stereotomographic events.
Figure 10 PS stereotomographic picking. Interactive quality controlof the automatically picked events. See caption of Fig. 3 for an ex-planation of the display. The event indicated by a square and a crosscorresponds to an ambiguous stereotomographic event. It correspondto simultaneously crossing events in the common shot and commonreceiver gathers and there is an ambiguity concerning the associationbetween the events. We prefered to eliminate this type of event fromthe PS stereotomographic dataset. On the top panel the value of thetime, the slope and the semblance of the event are indicated at thetop of the panel, as well as at the bottom, the characteristics of theassociated equivalent model (Billette and Lambare 1998).
The poor convergence of PS-stereotomography using thisdataset revealed that the selection was not sufficient. We thendecided to perform an additional selection during the stereoto-mographic optimization step (Lambare et al. 2004a). Indeed,since we could expect our initial S-wave velocity model to besufficiently accurate for discriminating between PP- and PS-stereotomographic events, we decided to identify PP-events asthose having a too large misfit after the relocalization step(optimization of the pairs of ray segments fixing VP and VS
velocity models (Billette et al. 2003)). We eliminated themfrom the PS-stereotomographic dataset. Practically, we did the
Figure 11 PS stereotomographic picking. Interactive quality controlof the automatically picked events. See caption of Fig. 3 for an expla-nation of the display. The event indicated with a square and a crosshas been picked by our automatic stereotomographic picking tool.However, it does not seem to correspond to any significant stereoto-mographic event, and we prefered to eliminate it from the PS stereoto-mographic dataset. On the bottom panel the value of the time, theslope and the semblance of the event are indicated at the top of thepanel, as well as at the bottom, the characteristics of the associatedequivalent model (Billette and Lambare 1998).
selection after the second iteration of the relocalization stepand eliminated PS-stereotomographic events having a misfiton positions larger than 2. km, or a misfit on slopes bigger than5. s/km or finally a misfit on the travel time bigger than 2. s.This was not really a drastic selection but we had to considerthat our initial VS velocity model was not optimal and had tobe improved from the remaining misfits. This led to keep 5161events out 5210. Then, we finally used only the events up to6 s, which corresponds roughly to the same imaged region asthe one inverted in PP-stereotomography and resulted in theselection of 2875 PS-events.
From this PS-stereotomographic dataset, we started the VS
velocity inversion by PS-stereotomography using the ‘timestripping’ approach. We defined six subdatasets according totheir maximum two-way travel time (same criterion as for thePP ‘time stripping’):� 75 events with Tsr < 1.5 s,� 327 events with Tsr < 2. s,� 809 events with Tsr < 3. s,� 1487 events with Tsr < 4. s,� 2070 events with Tsr < 5. s,� 2875 events with Tsr < 6. s,
The time gates here are different than for the PP data. In-deed, they are used for building the velocity model in depthprogressively from the top to the bottom (layer stripping ap-proach). Since time-to-depth conversion in PP and PS are verydifferent, there is no reason why those times gates should bethe same.
The ‘time stripping’ approach still suffered from remain-ing spurious picks and we introduced several selection stepsduring the optimization eliminating outliers characterized bytoo large misfits. Compared to PP-stereotomography, a largerregularization weight (Alerini et al. 2007) had to be used toensure a satisfactory convergence. The final model allowed usto fit about 53% of the observed data within the a priori errorbars. (In this first test on real data we chose the same error barsfor the PP and the PS data. This was certainly not optimal).
The final model (velocity and ray segments) is shown onFig. 12. We clearly see that the top of the salt was not partic-ularly emphasized by the picking, which reflects the very lowsignal-to-noise ratio at this depth and consequently a poorlyconstrained velocity. The quality of the S-velocity model canbe evaluated by considering the quality of the PS migrated im-ages. Figure 13 shows the PS-common-image gathers in theincidence angle domain, emphasizing the very poor signal-to-noise ratio of the X-component profile. In many locations(especially in depth) it may be difficult to identify events.However, the common-image gathers are flat in the upper partof the model (down to 1 km or 1.5 km). In the central partof the model (between 688 km and 691 km), they are flatdown to a greater depth but we also see that the coherencyof the common-image gathers rapidly deteriorates when wego deeper. Even the top of the salt is not very well defined, aswas revealed by the distribution of stereotomographic picks(Fig. 12). However, it appears on the final migration stack(Fig. 14). Considering these results (and the ones obtainedby PP-stereotomography) it appears reasonable to focus ouranalysis on the upper part of the model. Figures 15 and 16show the final migrated images and common-image gathers
Figure 12 Final PS stereotomographicmodel. Dip bars associated to the pairs ofPS ray segments have been superimposedon to the VS velocity model given in km s−1.Compare to the initial VS velocity modelgiven in Fig. 8.
687. 689. 691. 693.0.
1.
2.
3.
Distance (km)D
epth
(km
)685. 686. 688. 690. 692. 694.
Figure 13 PS common-image gathers in theangle domain. Incidence angles range from−60◦ to +60◦. The final P and S velocitymodels (Figs 4 and 12) were used for the PSdepth migration of the X-component pro-file.
691. 693.0.
1.
2.
3.
Dep
th (
km)
694. 695.685. 686. 687. 688. 689. 690. 692.Distance (km)Figure 14 Final PS migrated image. The fi-
nal P and S velocity models (Figs 4 and 12)were used for the PS depth migration of theX-component profile.
in this area. Only a small number of PS-stereotomographicevents have been picked for the upper layers (Fig. 12), and weobserve some slight undulations, for example around 0.6 kmand 1 km depth (Fig. 15). They could be due to lateral velocityvariations in the shallow layers, which cannot be taken intoaccount by our rough description of the velocity.
C O M PA R I S O N O F P P - A N D P S - M I G R AT E DI M A G E S
We remind the reader of the fact that stereotomographywas proposed as a solution for remedying the difficultpicking in traveltime reflection tomography. Our test of
Figure 15 Final PS migrated image. Zoomon the upper part of Fig. 14.
687. 689. 691. 693.Distance (km)
Dep
th (
km)
685. 686. 688. 690. 692. 694.
1.0
0.5
0.0
1.5
2.0
Figure 16 PS common-image gathers in theangle domain. Zoom on the upper part ofFig. 13.
PP/PS-stereotomography at Mahogany reveals that even ifstereotomographic picking provides an undisputable improve-ment compared to the one used in classical traveltime to-mography, it remains a serious difficulty for the applicationof the method. However, in the specific case of VP-VS esti-mation from multi-component seismic data, we also had theadditional advantage that it did not required a priori anypairing of PP- and PS-events. They just had to be identified asprimary reflected/diffracted PP- or PS-events. The point wasthen to investigate if an accurate and dense stereotomographicpicking could insure the co-depthing of PP and PS migratedprofiles. This fully succeeded with the ‘ideal’ synthetic datasetpresented in Alerini et al. (2005), and we had now with theapplication to Mahogany to look if it still works when usingactual ‘noisy’ data.
For this purpose, let us now compare the PP and PS depthmigrated images. First, we can see that even if the images
exhibit similar geological structures, their frequency contentand their amplitude balancing differ significantly. Indeed, itis not easy to pair events and consequently to compare theseimages in terms of co-depthing. However, on Fig. 17 we high-lighted some significant reflections on the PP migrated imageand we superimposed these curves on the PS migrated image.Until about 1.5 km depth, the reflectors and faults are rea-sonably well positioned in depth. The zoom on the first twokilometres depth of the profile is shown on Fig. 18. In thispart the common-image gathers were flat both on the PP andPS common-image gathers, and we can confirm the reasonablefitting in depth of the PP and PS migrated profiles even if it isquite difficult to assess due to the differences in structures andin the amplitude balancing of the images.
Below 1.5 km depth the success is more difficult to assess. In-deed, the top of the salt is significantly shifted (between 100 mand 300 m), and the shift is greater for positions x < 689 km.
Figure 17 Comparison of PP and PS mi-grated images. (a) PP image, (b) PS image.The red curves highlight reflectors, while or-ange curves highlight faults. The same re-sults are shown in Figs 5 and 14 free of in-terpretation curves.
Some anisotropy had been reported by Stopin (2001), andcould explain this shift at least to some extent, as well as 3Deffects, but more probably we should blame the poor qualityof our PS-stereotomographic dataset.
C O N C L U S I O N
We have applied PP/PS-stereotomography to a real dataset,the 2D-4C OBC Mahogany dataset. Our present strategy hasbeen to first invert the P-wave velocity field using PP data,then, fixing this field, to invert the S-wave velocity field us-ing the PS data. A major difficulty has been the picking. Afterthe automatic picking, various selection steps were necessaryto clean up the stereotomographic dataset. Statistical selection(elimination of outliers) but also interactive visual quality con-trol were necessary for convergence to a reasonable VS velocitymodel.
From such a dataset, without any pairing of the PP- and PS-events we obtained PP and PS depth migrated profiles fitting indepth reasonably well up to 1.5 km depth. Below this, the poorquality of the X-component section did not allow for an accu-rate estimation of the VS velocity model. At these depths we
also observed conflicting events in the PZ-component sectionwhich strongly biased the result of the PP-stereotomographicoptimization.
Stereotomographic picking still remains a very serious bot-tleneck for an automatic application of stereotomography.Several strategies have already been proposed to improveit, while keeping it as automated as possible. For example,it has been proposed to do the picking in the post-stacktime domain (Lavaud, Baina and Landa 2004), or in theprestack depth domain (Nguyen et al. 2002), where the selec-tion of the events could be easier. While keeping the stereoto-mographic picking in the prestack time domain, some at-tempts have been made to define judicious selection crite-ria for the stereotomographic picks (Lambare et al. 2004a).First studies have already demonstrated their efficiency forPP/PS-stereotomography (Lambare et al. 2004b) and the workshould be continued.
Although some experience has to be gained on the pickingand the strategies for events selection, other improvementscould be made. First, for the regularization, the use of an ir-regular grid could allow one to better describe the strong vari-ations of the S-wave velocity in the shallow layers. A varying
Figure 18 Comparison of PP and PS mi-grated images. Zoom on the upper part ofFig. 17. (a) PP image, (b) PS image. Thered curves highlight reflectors, while orangecurves highlight faults. The same results freeof interpretations are shown in Figs 7 and15.
regularization should be introduced. Here we have probablyover-smoothed this shallow zone.
In addition, it is usually recognized that when dealing withS-waves, anisotropy has to be taken into account. An ex-tension of stereotomography to anisotropic velocity modelswould fill the gap (Barbosa et al. 2006; Nag et al. 2006).
Finally, if PP/PS-stereotomography does not require anypairing a priori, we could certainly improve the result by in-troducing the very practical strategy proposed by Foss et al.
(2005). This approach allows one to introduce pairing infor-mation in an easy way as an additional term in the cost func-tion, without modifying the stereotomographic approach.
A C K N O W L E D G E M E N T S
The authors thank Geco-Prakla for the Mahogany dataset.They also thank CGGVeritas and J.-L. Boelle (Total) forthe preprocessing of the dataset and Juergen Mann, ZenaHeilmann and an anonymous reviewer for helping to improvethe quality of this paper. This work was partly supported by
the sponsors of the DIG consortium and by the French ‘Fondsde Soutien aux Hydrocarbures’ (Ministry of Industry).
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