An Integrated Pre-Stack Depth Migration Workflow Using ... · An Integrated Pre-Stack Depth Migration Workflow Using Model-Based Velocity Estimation And Refinement Andy Furniss *

GEOHORIZONS Vol . 5 No. 1July 2000

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An Integrated Pre-Stack Depth Migration Workflow Using Model-Based Velocity Estimation And Refinement

Andy Furniss *

Abstract:

The advent of velocity-sensitive depth imaging techniques such as pre-stack depth migra-tion has created a demand for more accuracy in velocity model building. Traditional methods thatuse seismic processing velocities are limited by many assumptions inherent in the Dix formula andthe distortion caused by complex ray paths. Techniques based on model ray-tracing allow moreaccurate estimates of interval velocity to be made, which, when constrained by an interpreter’sgeological knowledge of an area, have the ability to produce superior velocity models for depthconversion or pre-stack depth migration.

The role of the interpreter in any depth imaging project is often understated because of alack of understanding of velocity modelling and depth imaging techniques. The purpose of thispaper is to introduce some of these concepts to interpreters in an attempt to promote more activeinvolvement in velocity modelling projects and for them to not simply rely on the processing ex-perts to build geologically consistent velocity models.

Velocity estimation techniques such as stacking velocity inversion and coherency inversionare-equally applicable to depth conversion projects as they are to pre-stack depth migration. Coupledwith map migration techniques, these methods allow the interpreter to reduce the uncertainty ofconventional depth conversion and ultimately reduce the geological risk of prospects.

Pre-stack depth migration and tomographic model refinements are an essential and power-ful tool to produce the optimum seismic data quality. These methods are described to give theexplorationist a practical understanding of the workflows involvedin depth imaging.

Introduction:

Recent advances in computer-based in-terpretation systems have significantly reducedthe cycle time for exploration projects while im-proving the accuracy of interpretations in themigrated-time domain. However, as every inter-preter knows, the final test for any interpretationlies in the ability to produce an accurate progno-sis in the depth domain. It is inadequacies in thisstep of converting an interpretation from the timeto the depth domain that are commonly the causeof poor predictions, leading to increased drillingcosts or at worst, creating prospects that simplydo not exist.

There are several approaches that can betaken to improve our predictions in the depth

domain, from simply improving our initial ve-locity models using model-based ray-tracingtechniques through to the ultimate in depth im-aging, pre-stack depth migration (PSDM).Whether we interpret on time migrated data andscale our maps to depth or choose to interpret ondepth migrated data, there are many tools avail-able that can assist in building more accuratedepth models. Whatever approach we take, ouraccuracy in depth is wholly dependent on ourability to produce an accurate interval velocitymodel and this can only be achieved by taking amodel-based approach using the interpreter’sknowledge of the region to constrain that model.Model refinement techniques that rely on auto-mated tomographic approaches should be usedin conjunction with model-based approaches asthey have been shown to give erratic and unreli-able results when used as the sole method of


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model building or refinement. This paper de-scribes some of the available technologies thatcan be applied to produce better velocity modelswithout labouring on the theory behind the meth-ods. Interpreters are encouraged to play an ac-tive role in the building of velocity models andnot to leave this Critical step of the interpreta-tion process to the local ‘velocity expert’ whomay not have all the geological constraints ormodels at hand.

From Conversion to Inversion

Traditionally, the interpretation cycle fora project consisted of mapping key horizons ontime migrated seismic data followed by ‘depthconversion’ using a combination of well and/orseismic velocities to derive a regional velocityfield. While application of this technique has re-sulted in the discovery of some of the world’slargest oil and gas fields, it is flawed for a num-ber of reasons.

Table 1: An example illustrating how a 1% error in ve-locity creates the same depth error as 1% error in twoway time. While a 20 ms mistie in time would be deemedunacceptable, a 30 m/s velocity mistie would be frequentlyoverlooked

Firstly, an explorationist may spend manymonths interpreting structural horizons in fastidi-ous detail and then discard that precision byspending only a matter of days or a week build-ing the velocity model for depth conversion.Table I emphasizes the importance of producingaccurate velocity models. For the example given,a 1% error in two-way-time gives the same 30meter error in depth as a 1% error in averagevelocity. Few interpreters would accept a 20 msmistake in their interpretation while a 30 m/s er-ror in velocity is often overlooked.

The second flaw in the interpretationworkflow is the inaccuracy caused by traditionaldepth conversion methods where time structure

maps are vertically scaled to depth using an av-erage velocity map or a series of interval veloc-ity maps. This process is adequate in areas oflow dip without lateral or vertical velocity varia-tions or faults but unfortunately, these areas arerarely of interest to us in the search for hydrocar-bons. Map migration is a ray-traced depth con-version technique that produces more accuratedepth maps and also compensates for the spatialpositioning errors that are left uncorrected by timemigration. Significant lateral errors may be ob-served where there is very little velocity varia-tion in the overburden and only map migrationtechniques can accurately reposition this data.

The third flaw lies in the actual imagingof the seismic data in the time domain. Althoughwe are taught that time migration will image seis-mic reflections in their correct spatial position,most of us are aware that this is not the case wherelateral velocity variations, velocity gradients andscattering distort the seismic ray paths. Conse-quently, our seismic gathers do not stack or mi-grate correctly, leaving us with a distorted andinferior image of the subsurface in the time do-main. If we can produce an accurate velocity-depth model, PSDM will give us a far superiorimage of the subsurface by correctly positioningtraces during migration. By scaling the depthmigrated data back to time, calibrating veloci-ties to well data then rescaling back to depth, wenot only have the optimum image quality of ourseismic but also a seismic line or volume thatcan be interpreted in the depth domain. Addingadditional well control simply means re-calibrat-ing the velocity field and rescaling the data todepth.

Fig 1. A typical workflow used for building and refininginterval velocity models for use in pre-stack depth

migration


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While PSDM is often seen as a panaceafor seismic imaging it must be remembered thatthe process itself is dependent on the raw inputgathers and the accuracy of the velocity-depthmodel used for the migration. PSDM has pro-duced spectacular results in most of the petro-leum producing basins around the world and willadd value to any interpretation project by improv-ing the seismic image. However, its limitationsmust be recognised and there are many caseswhere data imaging problems will not be com-pletely resolved by this process.

Figure 1 outlines a workflow that will notonly improve the interpretation of seismic databut also provide more accurate depth predictions.The workflow replaces traditional depth conver-sion with depth inversion by using sophisticatedvelocity modelling and refinement tools andPSDM. With this new workflow, interpretationis finished. Advances in computer hardware andimproved software algorithms are rapidly put-ting this technology into the hands of the inter-preter. Whereas the desktop workstation wasonce used only for creating time interpretationsand maps, it is now capable of producing depthmigrated data, the input model for which is theinterpretation.

Model-Based Interval Velocity Estima-tion

For many years, the process of depth con-verting time structure maps relied on the use ofaverage velocity maps hand contoured from welldata. This method is perfectly adequate in areaswhere there is sufficient well control, velocityvariation is small and the structure does not varysignificantly away from the control points. Ob-viously, in new exploration areas there is insuf-ficient well control to allow this accurate map-ping and therefore additional velocity controlmust be employed. Velocities derived during theprocessing of seismic data provide substantialadditional control away from wells but are sel-dom accurate representations of the earth veloc-ity. The most common approach to using thisvelocity information is to use the Dix equation(Dix, 1955), which relates interval velocity toroot-mean-square (RMS) velocities. Equation (1)

shows that interval velocity, Vintn, can be calcu-

lated for the nth interval where Vrmsn-l

, tn-l

, andVrms

n, t

n are the root-mean-square velocity and

travel times to the n-1th and nth layers respectively.

V2rmsn

tn - V2rmsn-1

tn-1

(1) tn - tn-1

ÖThe Dix transform from RMS velocity

to interval velocity is based on many assump-tions and is frequently applied in areas wherethose assumptions are invalid. Interpreters com-monly use stacking velocity as input into Equa-tion (1) assuming they approximate to RMS ve-locity. However, stacking velocity will only ap-proach RMS velocity in areas with no structuraldip, no lateral or vertical velocity gradients, andwhen common midpoint (CMP) gathers havevery restricted offsets. In the real world, whereatleast one of these assumptions is invalid, seis-mic raypaths will show non-hyperbolic moveoutcausing stacking velocity and RMS velocity todiffer. This produces inaccurate results from theDix equation. In 2D a simple correction to re-move the effect of structural dip, q, can be ap-plied using the formula from Levin (1971) asshown in Equation (2).

Vstack = Vrms (2)

Cosq

The Levin equation shows that for areaswith structural dip, stacking velocity will alwaysbe faster than RMS velocity. In 3D, the dip cor-rection becomes more complicated and terms toaccount for the dip azimuth must also be intro-duced. Despite these corrections, the Dix trans-form will still produce incorrect results as raybending still occurs due to velocity variationswithin layers and at layer boundaries.

The Dix equation itself is based on sev-eral assumptions that are rarely honoured in thereal world. Equation (1) assumed that the traveltimes to the two layers bounding a given inter-val are essentially identical apart from the traveltime within the layer itself. When the layers arenot parallel, have structural dip or have long off-

Vintn=


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sets, the Dix equation will give erroneous results.Similarly, when the time interval in the Dix equa-tion. dt, becomes small, the resulting intervalvelocity becomes very large, and the results be-come unstable. A cut-off should be applied tothe isochron such that values of dt below somethreshold value are not used in the Dix trans-form. A dt threshold of 200 ms is typically usedin areas with dips between 5 and 15 degrees, re-ducing as the dip decreases.

Several model-based techniques existthat can estimate the interval velocity of a layerfrom the travel time through it, giving more ac-curate results by avoiding the Dix equation andits many assumptions. To accurately estimateinterval velocity, travel times must be calculatedby CMP ray tracing through an interval veloc-ity-depth model and comparing these modelledtravel times with those actually recorded by theCMP gathers.

Stacking velocity inversion and coher-ency inversion (Landa et. al„ 1999) are two suchprocesses but differ in the type of input data usedfor the comparison. Coherency inversion usesactual pre-stack CMP gathers in the time domainto correlate with the modelled travel time curves,whereas stacking velocity inversion correlates themodelled Raypath with a hyperbolic traveltimecurve implied by the stacking velocity.

Coherency Inversion

The key advantage of coherency inver-sion over Dix-based methods is that it uses ray-traced modelled traveltime curves to comparewith actual travel times recorded from the earth.Lateral or vertical variations in velocity, refrac-tion according to Snell’s Law, and structural dipwithin the model are all accounted for by ray trac-ing and we are therefore no longer limited by thehyperbolic moveout assumption of the Dix equa-tions. Coherency inversion also provides a sta-tistical estimate of uncertainty in the velocitymodel (Landa et.al., 1991)

Coherency inversion beings with the in-terpretations of key velocity horizons in thestacked time (unmigrated) domain. Coherency

Fig 2a. Principles of coherency inversion Normal incidenceraypaths are modelled by velocity inversion methods todetermine zero-offset travel time through the model

inversion is a layer-stripping approach and there-fore requires an interval velocity and depth modelfor all layers above the interval under investiga-tion. For the layer being modelled, a range ofinterval velocities is given for each CMP alongthe line. At each CMP, local normal incidenceray migration is used to migrate the time inter-pretation to its correct position in depth. Normalincidence ray tracing is than performed on theinterval velocity model to calculate the raypathand its travel time through the model (Figure 2a).This horizon depth-migration and ray tracingprocedure is than repeated for each constant in-terval velocity in the given range.

Semblance is calculated at each CMP tomeasure the correlation between the recordedCMP gathers and the modelled traveltime curvefor each interval velocity tested (Fig 2b). Thehighest semblance value represents the velocitythat successfully flattens the CMP gathers im-plying that the model honours the velocities alongthe actual raypath through the earth. At eachCMP, the moveout corrected gathers are dis-played (Figure 3a) and a histogram of semblanceagainst velocity can be observed for QC (Figure3b). A semblence display is created for the hori-zon (Figure 4) that is then used to pick the opti-mum interval velocity at each CMP. The veloc-ity profile is used to ray migrate the horizon todepth and the process is continued for the nextlayer in the model.

Coherency inversion uses curved rays and


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Fig 2b. Principles of coherency inversion. The modelledzone offset travel are correlated against recorded CMP

gathers to determine the optimum interval velocitywithin a layer

Fig 3a. The result of coherency inversion are a set ofCMP gathers flattened according to the interval velocity

model used.

Fig 3b. The optimum interval velocity will produce flatgathers and will have the highest semblance versus

interval velocity

accounts for vertical and lateral velocity gradi-ents allowing modellec travel time curves to ac-curately match those recorded in theCMP gathers.

Fig 4 : When run in continuous mode, coherency inver-sion and stacking velocity inversion produce a semblancedisplay along a given horizon. By intepreting the maxi-mum semblance(blue), the interpreter builds up a velocityprofile this is used to construct the velocity depth model.

Stacking Velocity Inversion

Stacking velocity inversion uses a simi-lar process to coherency inversion but does notuse pre-stack gathers for the correlation of mod-elled travel time curves. Instead, stacking veloci-ties are interpolated to the key horizons identi-fied on the stack section. These velocities are thenused to calculate a hyperbolic moveout curve thatis correlated with the modeled travel time curve(Figure 5). The outputs from stacking velocityinversion are similar to coherency inversion andprovide an estimate of interval velocity alongeach horizon. The main assumption of this pro-cess is that the stacking velocity measured fromthe data represents the hyperbola that best fitsthe data. Clearly, this may not be a valid assump-tion in areas of poor signal to noise ratio or atgreater depths where moveout discrepancy ismore difficult.

Both coherency inversion and stackingvelocity inversion are equally applicable in the3D world although full 3D ray tracing is requiredto accurately model rays from varying offsets andazimuths. The output from 3D coherency inver-sion or 3D stacking velocity inversion are mapsof interval velocity for each layer. These mapscan be used directly as an initial model for PSDMor can be calibrated to well data and used fordepth conversion of time structure maps.


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Fig 5: Stacking velocity inversion uses a hyperbolictravel time curve calculated from the input stacking

velocity model to correlate with modelled travel times.The correlation is then used to calculate semblance and

determine the optimum interval time

Travel time inversion techniques can besuccessfully used to build initial velocity mod-els for depth conversion or depth migration. Themodel based approaches, particularly those us-ing pre-stack CMP gathers, give more accurateand reliable estimates of interval velocity thanmethods based on the Dix equations.

Map Migration

The traditional method of depth conver-sion in which time migrated maps are verticallyscaled to the depth domain, has many inherentproblems caused by lateral velocity variationsthat result in horizons being spatially misplaced.Additional problems include holes in the timestructure grids caused by faults, pinchouts orunconformities. All of these problems can besuccessfully resolved using a model-based mapmigration approach.

Map migration is a zero-offset 3-D in-version and is one of the most powerful toolsthat can be applied to most structural interpreta-tions. Given accurate time structure maps andan accurate layered interval velocity model, mapmigration transforms maps from time to depthwhile correcting the spatial error caused byraypath bending and velocity variations withinand between layers.

The need for map migration is often over-looked by interpreters who assume that their in-terpretation is correctly positioned if it is pickedon time-migration data. Unfortunately, most time

migration algorithms use simplifying assump-tions to improve computation speeds and thisresults in residual errors particularly where thereare lateral velocity variations. Also, time migra-tion algorithms do not take into account any ve-locity variations and simply collapse hyperbolicdiffraction curves to the minimum travel time.These velocity variations may be the result ofintra-formational vertical or lateral velocitygradients or cross-fault juxtaposition of differ-ent formations.

Fig 6: Schematic illustrating how reflections aremispositioned by time migrated and how image rays can

be used to correct for this error(After Fagin, 1991)

Following time migration, the residualspatial error at a given CMP may be calculatedusing image rays (Hubral, 1977). These rays canbe used to position the reflector to its true spatialposition as shown in (Figure. 6). Time migrationalgorithms works by collapsing a hyberbolic dif-fraction curve on a CMP gather to its point ofminimum travel time, which will generally be atthe apex of the diffraction. The misplacement ofthe reflector is caused by the assumption that thecrest of the diffraction curve lies vertically be-neath the CMP surface location. In any situation.where the true raypath is bent or refracted byvelocity gradients or contrasts, this assumptionis invalid and the reflector will be mispositioned(Figure 7)

Any model with structural dip or veloc-ity variation will benefit from map migrationwhich can be applied in the same time that it takesto perform the more conventional vertical scal-


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ing depth conversion. Figure 8 compares the re-sults of a ‘standard ‘ depth conversion using ver-tical scaling (Figure 8a) with a map migration ofthe same event (Figure 8b). The difference map,shown as Figure 8c shows depth shifts of up to100m as a result of the map migration. Figure 8dis a displacement map showing the lateral move-ment of grid modes from the migrated time do-main to the depth domain with displacements ofup to 130 m observed.

Many mapping packages now offer mapmigration as an option for depth conversion. Anyprospect that has even moderate velocity varia-tions, structural dips greater than 3 degrees, orfaulting should use map migration techniques inplace of the conventional scaling methods.

Pre-Stack Depth Migration

The ultimate goal of any seismicprogramme is to provide an accurate image ofthe subsurface that will enable a reliable geologi-cal interpretation. Few seismic surveys ever re

Fig 7: Schematic showing focussing distortion andpositioning error caused by time migration. Depth

migration corrected in both

Fig 8(a): Depth structure map produced by verticalscaling of migrated time depth structure map

Fig 8(b) : Depth structure map produced by image raymap migration.

Fig 8(c) : Difference map between scaled and mapmigrated structure.


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ally achieve the desired level of imaging for manyreasons including distortion of the seismic sig-nal by noise, earth filtering effects or simply pooracquisition geometry. As discussed above, thedata represented in the migration time domainare seldom the best image of the subsurface andreflectors are often spatially mis-positioned.There is an obvious trade-off between precisionand cost during time domain processing of seis-mic data that stems from the immense numberof computations required to process a seismicsurvey. This trade-off is normally achieved bymaking simplifications and assumptions in someof the computing algorithms that often results ina less than optimal product.

Advances is computing technology meanthis trade-off should no longer be necessary or

Fig 8(d) : Displacement map showing lateral movementof subsurface points when map is migrated to the depthdomain. The maximum displacement shown is 130m.

Note the significant lateral shift in areas with dip.

acceptable. New algorithms and techniques cannow process seismic data faster (cheaper) thanever before and produce superior images of thesubsurface. One such technology that is beingrapidly accepted world wide, is the use of pre-stack depth migration (PSDM). Until only re-cently, PSDM was reserved for the biggest supercomputers and the process took weeks to com-plete a single 2D seismic line. Table 2 shows acomparison of how this technology can easilybe applied today in a matter of hours using aninexpensive desk-side workstation. With the re-cent increases in processing speed, a projectionis made 5 years from now showing that PSDMwill be in the hands of every interpreter and willeventually become the accepted standard for anyseismic interpretation project.

So why is PSDM becoming the preferredprocess? As discussed, time-migration algo-rithms result in events being spatially mis-posi-tioned and the results have the obvious draw-back of being represented by a two-way traveltime. Depth migration provides an image indepth, but more importantly, pre-stack algorithmsavoid the many assumptions and simplificationsthat cause mis-positioning of events in the timedomain. The reflections are not only positionedcorrectly but also, as a by-product of this theircontinuity and discontinuities affecting them(faults) are better imaged.

Figures 9a and 9b respectively, show acomparison of a post-stack time migrated sec-tion and a pre-stack depth migrated section. Theprimary objective in this prospect was the tiltedfault block to the right of the well track, indi-cated by the arrow. The well was planned on the

Table 2: Illustrative runtimes for depth migrating processing. Computer hardware and software advances will soonmake pre-stack depth migrated data the interpreters main tool.

Process Desk top workstation Runtimes(illustratives only)1990 1995 Today 5 years from now ?

2 D Post Stack Depth Migration 5 hrs 1 hr 15 min <1 min 2 D Pre-Stack Depth Migration Several days 4 hrs 1 hr 2 mins

(current running time on 8 CPU parallel machine)

3D Post-Stack Depth Migration(25 sq Km) N/A 1 day 4 hrs 30 mins 3D Pre-Stack Depth Migration(100) sqKm) N/A N/A 4 weeks 2 days (4 CPU paralleled machine)


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post-stack time migrated section to intersect thefault block well away from the bounding fault.However, during drilling, the well missed theprimary objective and encountered the fault asseen or the PSDM data that was completed afterthe well was drilled This is a classic example in

Fig 9(a): Comparison of Post Stack time migrated dataand Pre-Stack depth migrated data. A well was drilled,based on the post-stack time migrated data, to test the

titled fault-block indicated by the arrow. The well failedto intersect th eprognosed reservoir and following thedry hole, pre-stack depth migration was performed on

the line.

Fig 9(b) : With the correct velocity model and accuratepositioning in depth, it is clear to see why the well failed.

The original primary target was not intersected by thewell bore that passed straight through the fault plane

adjacent to the prospect.

which velocity contrast across the fault resultedin severe ray-bending and consequent mis-posi-tioning of data in the migrated time domain.

Amplitude preserving 3D PSDM algo-rithms are now available that not only improvestructural interpretations, but will also have adramatic effect on stratigraphic inversion toolsand AVO analysis.

While PSDM will generally give the in-terpreter the best possible with today’s technol-ogy, one must remember that depth migrationalgorithms are far more sensitive to the inputvelocity model than their time-domain equiva-lents, making accurate velocity modelling a criti-cal factor in the successful application of themethod. PSDM is often seen as a remedy for allseismic imaging problems but the method canonly help where an accurate velocity field in thesubsurface can be determined.

A common misconception is that PSDMseismic volumes will perfectly tie well data wheninterpreted. This is not the case for a very simplereason - the velocity model used for PSDM isdesigned to give the best seismic image qualityin exactly the same way that stacking velocitiesand RMS velocities do in the time and migrated-time domains respectively. Velocities from wellbores effectively measure the vertical componentof the velocity field, whereas seismic velocitiestypically measure the horizontal component. Inany situation where there are vertical or lateralvelocity variations anywhere along the seismicraypath, the two velocities will not be coincident.Consequently, the seismic reflectors correspond-ing to a well marker will not tie the seismic eventsprecisely. To correct for this, the depth migratedvolume is scaled back to the’ lime domain usingthe PSDM velocity model, the interval velocitymodel is then calibrated to the wells, and thevolume is scaled (not migrated) back to depthwhere it will tie the well markers.

A second misconception is that PSDMis only of benefit in structurally complex areas.This is certainly not the case. Any situation thathas imaging problems caused by ray bending orvelocity problems will benefit from PSDM. Im-aging problems associated with, for example,shallow gas accumulations, fault shadows, overthrusts, reefs or a hard seafloor can all be suc-cessfully resolved given an accurate velocitymodel, although they may not be considered tobe structurally complex. Because PSDM process-ing can now be completed in the same time as aconventional time processing workflow, depthimaging is being used increasingly in explora-


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tion areas, where until recently, only time imag-ing would have been considered.

The third misconception is that PSDM isa complex process that should be left in the handsof the specialist processing geophysicist. Whilstthe mathematics behind the PSDM algorithmsmay be daunting, the process should never beapplied without substantial input from the inter-preter. Indeed, some of the best PSDM resultshave been created by interpreters because theyusually have a better understanding of the earthmodel than their processing geophysicist coun-terparts. This knowledge of what is geologicallyreasonable is the key to building a robust, accu-rate velocity model that will provide outstand-ing results in the depth domain.

Velocity Model Refinement

The quality of a velocity model used forPSDM can be assessed by analysing the outputcommon reflection point (CRP) gathers. For agiven CRP gather, all rays will have sampled thesame point on the subsurface irrespective of theirsource - receiver geometry, and it would be flatif the correct velocity model was used for migra-tion.

Fig 10. Typical work flow for refining velocity modelsby global tomography

Any residual delay in the CRP gathersnot only degrades the migrated image but alsoimplies that the spatial position of the reflectorswill be incorrect because of an incorrect model.By analysing these residual delays, the model isrefined through a number of techniques rangingfrom hyperbolic delay corrections to horizon-

Fig 11. Depth CRP gather showing residual delayscaused by depth migration using an incorrect velocity

model. The delay dz is determined and used as input to

tomography.

based and grid-based global tomography. Thenew velocity model resulting from the updatesis then used to re-run the PSDM, after which theprocess is repeated until the depth CRP gathersare flat. Figure 10 shows a typical tomographyworkflow to refine the velocity depth model.

Fig 12: Schematic showing how the error in travel timeat reflection point A is the result of an accumulation oferrors, åd ti, within each layer where the ray has trav-elled. The objective of tomography is to determine dti,the error in travel time within each layer, and derivefrom that, the error in velocity, dvi; and the error in

depth dzi, each parameter is then used in the tomographyequation to update the model.


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Tomography is a sophisticated tool thatattempts to correct errors in the velocity depthmodel by analysing the residual delays afterPSDM. Tomography is a global approach thatcan translate an error in time at one location toan error in depth or velocity at any point in themodel through which the ray has travelled. Theseerrors are solved simultaneously by makingchanges to the velocity and depth model acrossthe entire section.

Migration with an incorrect velocity willresult in depth delays, dz on the CRP gather (Fig-ure II). The first step in tomography is to scalethe depth-migrated gathers to tune and whereerrors exist, the time at far offset, t, will differfrom the time at zero offset, t

0 This delay, dt, is

measured for each CRP and used as input to thetomography algorithms.

The tomographic approach attributes thedelay, 4t that was measured from the CRP gather,to an accumulation of errors within each layeralong the raypath. The objective is to obtain theerror in velocity and the error in depth withineach layer from the error in travel time withineach layer. For example, in Figure 12, the residualtime delay observed at point A is an accumula-tion of velocity and depth errors in each layeralong the raypath. By updating the velocity-depthmodel in all the layers, the residual travel timeerror at point A can be minimised. An importantfeature of global tomography is that errors aresimultaneously solved using least squares tominimise the error in travel time across the wholemodel.

Hyperbolic Update of VelocityHyperbolic updating is a technique used

to flatten gathers following PSDM with an in-correct velocity model. This method is based onthe Dix formula and although it is not strictly atomographic approach, it can be successfullyapplied to update velocity models where the re-sidual delay approximates a hyperbola.

Depth CRP gathers are scaled to time and theresidual delay is measured. By using this delayin the Dix equation, we can calculate an RMSvelocity error that will flatten the gather in much

the same way as normal move out velocity is usedto flatten gathers before stacking. This residualRMS velocity is then transformed to a residualinterval velocity, which is used to update the ini-tial velocity model. It is important to rememberthat this method makes all the Dix assumptionsand therefore where the delays are non-hyper-bolic, the gathers will still not flatten correctlyand a tomographic method should be applied. Itis also important to note that any remaining er-ror in the overburden will propagate down to thenext layer and consequently the method is bestapplied in areas with simple geology with nostrong lateral velocity variations.

Global Depth Tomography

Horizon-based and grid-based tomogra-phy are global approaches that solves a simulta-neous set of equations to produce update param-eters (depth and velocity) for the model. The twotechniques differ in their inputs to the algorithms.During horizon-based tomography, the interpreteranalyses delays at each CRP along the line foreach horizon in the model and these are input tothe tomography along with the interpreted geo-logical horizons in depth. Grid based tomogra-phy is an automated approach where the delaysare picked by the computer along small, coher-ent segments of the data interpreted on the depthmigrated section. An important difference in thetwo approaches is the way in which the model isupdated. In horizon-based tomography, both thedepth interpretation and the interval velocitymodel are updated whereas grid-based tomogra-phy only updates the velocity section.

Grid tomography is useful in a numberof situations where a horizon-based method maynot be applicable. An example of this may be invery complex structures or on poor data areaswhere it is too difficult to interpret continuousreflectors through the model. In all cases, gridtomography requires a good initial velocitymodel, derived from seismic processing veloci-ties, for it to produce reliable results.

A typical workflow for horizon-based to-mography begins by analysing the residual depthdelays along the key horizons. Figure 13a showsa typical semblance display where the velocity-


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Fig 13 a. Depth migrated CRP gathers before tomogra-phy. An incorrect velocity model causes residual delays,shown by curvature on the gathers and high semblence

values away from zero line on the semblence plot.

Fig 13(b) : Horizon delay analysis. The semblencedisplay indicates where there are residual depth delays

along a given horizon. In this example, there aresignificant delays remaining on layer 4 indicating the

model needs updating.

depth model is incorrect. Where the model iscorrect (i.e. where the gathers are correctly flat-tened), the maximum semblance, indicated byblue colours, lies along the zero delay line. Posi-tive and negative delays are represented by maxi-mum semblance by lying away from the zero line.These delays are picked by the interpreter fromthe semblance displays along each horizon (Fig-ure 13b) and are used as input to the tomogra-phy. After running the tomography and re-mi-

grating the data, the resulting gathers are flat (Fig-ure 13c) and the semblance display shows noresidual error indicating that the velocity depthmodel for that layer is now correct (Figure 13d).Note the improved image quality when the datais migrated with the correct model.

Fig 13(c): Depth migrated CRP gathers after horizonbased global tomography. The CRP gathers are now flatand the maximum semblence falls along the zero delay

line.

Fig 13(d): The horizon semblance display after tomogra-phy shows zero delays remaining on Layer 4. The depthmigrated image is significantly improved on the initial

migration shown in Figure 13(b)


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For grid tomography, it is not essentialto have horizons mapped across the whole sec-tion. Instead, small segments of coherent data areinterpreted along the line and these are used toanalyse the delays for input to the tomography.The software application automatically picks theresidual delays around the small horizon seg-ments without any intervention form the user.These delays are used as input to the tomogra-phy which attempts to minimise the errors acrossthe whole section by updating the velocity fieldonly.

Fig 14(a): Effects of Global tomography on the velocitymodel a) initial velocity model used as input for pre-

stack depth migration.

A common question that is asked is,whynot only use grid-based tomography that is moreautomated than horizon-based tomograpy ? Theanswer is very simple. Grid based tomographyattempts to solve the errors in a statistical sensewithout any constraint on the geological model.Without that constraint, grid-based tomographycan produce very erratic velocity models andgeologically implausible results, which in turnproduce false structures or poor imaging in depth.It is recommended that horizon-based tomogra-phy is used whenever possible, only using grid-based tomography for final, minor refinementsto the model. Figure 14a shows an inital velocitymodel, and the results following both horizonbased tomography (Figure 14b) and grid-based

Fig 14(b): Velocity model after one pass horizon basedtomography. Note the significant changes in velocity tolayer 3 and 4. Elsewhere on the section, few changes

have been made to the model.

tomography. While both models produce flatCRP gathers, the grid –based approach introducesnon-geological artefacts in the interval velocitymodel.

While automated grid-based tomographictechniques are useful in very complex data ar-eas, they should generally be avoided until themodel is very close to a solution; i.e. depth de-lays are small. There are two schools of thoughtabout how good the initial model must be fortomography to converge on a solution. Oneschool advocates using a very crude initial model,relying on numerous iterations of tomography toupdate and correct the model. The other schoolrefines the model as much as possible before run-ning PSDM and only uses tomography to makeminor adjustments. Experience with tomographyhas shown that the algorithms typically convergeon a solution within 3 iterations providing theinitial velocity model is within 15% of the finalsolution. Beyond that, the model either will notconverge or converges on a wrong solution, re-sulting in incorrect depth images. Therefore, itis recommended that the model is refined asmuch as possible before running PSDM.

Emerging Tomographic Techniques

The one obvious flaw in the tomography


14

workflow is the fact that PSDM must be run be-fore and between model updates.

Interactive tomography is an emergingtechnology that will speed up the whole tomog-raphy workflow by allowing the interpreter toperform all of the model updatesprior to running the PSDM

By creating local depth CRP panelsaround each horizon, residual interval velocitycan be analysed and interpreted. Global tomog-raphy can be run using these delays and the wholeprocess repeated until the local gathers aroundeach horizon are all flat and no residual delaysare observed. Only when the interpreter is satis-fied that the optimal model has been derived,PSDM is applied to the data. This process willresult in at least a three-fold reduction in the timerequired for the PSDM workflow as it requiredonly one pass of depth migration on the data.

Conclusion

The end objective of any exploration-mapping project is to provide a reliable under-standing of the shape and form of the subsurfacein depth. Conventional mapping techniques haverelied on interpretation of data in the time do-main followed by a depth conversion, frequentlyusing an oversimplified velocity model.

The interpreter now has many tools inhand that allow accurate imaging of the earth inthe depth domain. PSDM is considered the ulti-mate tool for seismic imaging for a good reason- the quality of the resulting images is not onlysuperior to that in the time domain, but the seis-mic data is also correctly positioned in space al-lowing the interpreter to work directly in the samedomain as the well data. The workflow used forPSDM implicitly results in an interpretation ofboth the key structural horizons in depth and anaccurate velocity model in the same timeframeas that required for conventional time process-ing.

Even where PSDM is not required, in-terpreters should be using tools such a coherencyinversion and stacking velocity inversion to moreaccurately determine interval velocity and avoidthe many problems inherent in the transforma-tion of seismic velocities by the Dix equation.Map Migration should always be used for depthconversion as method produces more accurateresults than scaling methods and accounts for thelateral mis-positioning of events introduced bytime migration algorithms.

The key message of this paper is that theinterpret geological knowledge of the region is acritical constraint any velocity model buildingor depth imaging project and role of the inter-preter should not be understated. Automatedmodel building and refinement techniques thatrequires interpreter input should be treated withconsiderable caution as they routinely produceunrealistic models of the geology.

References

Dix, C.H., 1955, Seismic velocities from surfacemeasurements: Geophysics, 20,68-86.

Fagin, S.W., 1991, Seismic modelling of geo-logic structures: applications to exploration prob-lems. Geophysical Development Series Volume2 Soc. Expl. Gophys.

Hubral, P., 1977, Time migration-some ray-theo-retical aspects : Geophys Prosp. 25,738-745

Landa, E„ Thore, P., Sorin, V, & Korcn, Z., 1991,Interpretation of velocity estimates from coher-ency inversion : Geophysics, 56(9), 1377-1383

Levin, F.K. 1971, Apparent velocity from dip-ping interface reflections: Geophysics 36, 510-516

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An Integrated Pre-Stack Depth Migration Workflow Using ... · An Integrated Pre-Stack Depth Migration Workflow Using Model-Based Velocity Estimation And Refinement Andy Furniss *