Stolt or Phase Shift 3D Migration

Stolt or Phase Shift 3D Migration727ProMAX® ReferenceStolt or Phase Shift 3D MigrationTheoryStolt or Phase Shift 3D Migration migrates or demigrates3D stacked seismic volumes using Stolt’s f-k method or avariation of Gazdag’s phase-shift method. Stolt or PhaseShift 2D Migration is a 2D companion that providesconsistent geophysical treatment of the input data. Byapplying the migration to moveout-corrected common-offsetvolumes, a prestack time migration can be achieved.Migration MethodsStolt MigrationStolt migration is computationally efficient and very accuratefor constant velocity, but has difficulty imaging steep dips inareas where there are large vertical or lateral velocityvariations. This algorithm uses a method analogous to Stolt’sstretching technique to account for vertical and spatialvelocity variations.For steep dips, a further improvement is obtained via thestretch factor, often simply referred to as W. This factor isused, after time stretching and Fourier transforming, to alterthe Stolt mapping of frequencies. When this factor is omitted(equivalent to letting W = 1.0), simple time stretching tends toover-migrate steeply dipping reflectors. Decreasing this factorto, for example, W = 0.6 may more accurately position steeplydipping reflectors. As you experiment with this W parameter,remember that fast Stolt migration, even with this stretchfactor, cannot be a substitute for a more costly and moreaccurate migration method.For fairly constant velocity media, the primary advantage ofStolt’s method is speed. In typical Gulf Coast variable velocitysettings, where a significant amount of trace stretching isrequired to precondition the data for Stolt applications, thedifference in speed between Stolt and Phase Shift migrationcan be insignificant.Other DocsSearch PageKnown Problems

Stolt or Phase Shift 3D Migration728ProMAX® ReferencePhase Shift MigrationPhase Shift migration handles steeply dipping, evenoverturned, reflectors when velocity varies with depth.However, like all time migration methods, it cannot properlyimage steep reflectors when velocity significantly varieslaterally.To image turning rays, which typically require longermigration apertures and recording times, you need anaccelerating interval velocity field. Do not select this option ifyou do not have the potential for imaging turning rays, asyou will only cause additional noise to be incorporated intoyour migrated section.The computational efficiency of Phase Shift migrationoriginates from the assumption that velocity is laterallyinvariant. Using a method analogous to Stolt’s stretchtechnique, the program attempts to handle lateral velocityvariations by time stretching seismic traces to approximatetraces with laterally invariant velocity. Once the algorithm isapplied to the migrated traces, they are unstretched. Thissimple time stretching is most accurate for reflectors withmoderate dip.A Rule of Thumb: any velocity change should be subtle. Inthe case of a gentle lateral velocity gradient, it has beenobserved that the effect of this internal stretch is to imagefault-plane reflectors closer to their true lateral location thanmost other time migration methods.Refer to the Migration Overview for more information.Applying NMO and DMOIn prestack usage, Stolt or Phase Shift 3D Migration isapplied to common-offset volumes that have had NMO andDMO applied. After migration, the NMO corrections can beremoved and a final velocity analysis performed for stack.Note: This approach approximates a prestack time migration,but it is not equivalent.Reversing the Migration ProcessThere are circumstances in which it can be useful to reversethe migration process.Other DocsSearch PageKnown Problems

Stolt or Phase Shift 3D Migration729ProMAX® Reference• You want to forward model a synthetic stacked section inorder to test some processing flow or analysis tool.• After aligning and stacking common-offset time migrations,you want to generate a zero-offset section suitablefor poststack depth migration. In effect the Stolt orPhase Shift 3D Migration is used to generate a betterstack to avoid the expense of 3D prestack depth migration.Stolt or Phase Shift 3D Migration provides the followingtwo options for reversing the migration process:• demigration is the classic zero-offset exploding reflectorsforward modeling algorithm upon which the correspondingmigration, either Phase Shift or Stolt, is based.It is a very stable processing operation and in most casesthe preferred tool when subsequent analysis and interpretationis not critically dependent on amplitudes.• inverse migration is, at least approximately, the linearinverse of the corresponding migration algorithm.Because it necessarily boosts the energy of dippingevents, it takes care and experimentation to control artifactssuch as steep linear noise trains.When using either of these options, you should be aware ofthe following:• Migration followed by demigration does not reproducethe original input data set. Generally speaking, steeperdips are attenuated by a factor proportional to the cosineof the subsurface dip. This is because migration is notan inversion process.• Inverse migration does not produce the same data set asforward modeling does. It does, however, avoid much ofthe steeper dip attenuation associated with demigration.• For the Stolt algorithm, demigration is the inverse ofmigration with the obliquity explicitly turned off.• Unlike Stolt migration, Phase Shift migration is not tractablyinvertible. We use the amplitude correction procedurefrom inverse Stolt migration to approximate theinverse of Phase Shift migration.• Theoretically, a “perfect” migration reduces the RMSenergy of dipping events, but not their spectral amplitudes.Thus, time-spectral analyses of steeply dippingOther DocsSearch PageKnown Problems

Stolt or Phase Shift 3D Migration730ProMAX® Referenceevents will see the same spectral amplitudes compressedinto a smaller bandwidth.If the data to be demigrated or inverse migrated are a subsetof the data that were originally migrated, you may need tooutput padded traces to prevent the loss of events that moveoutside of the input volume. Use Pad 3D Stack Volume toadd padded traces. To pad both inlines and crosslinesrequires two passes through the data. In Stolt or Phase Shift3D Migration include the padded traces in Minimum andMaximum inline and crossline numbers. Select None toRekill dead traces or else the padded traces are rekilled onoutput. The following is an example of how to pad:Disk Data InputPrimary sort XLINE_NOSecondary sort INLINE_NOPad 3D Stack VolumePrimary sort XLINE_NOCode first and last inline values to force creation of desired padDisk Data OutputDisk Data InputPrimary sort INLINE_NOSecondary sort XLINE_NOPad 3D Stack VolumePrimary sort INLINE_NOCode first and last crossline values to force creation of desired padStolt or Phase Shift 3D MigrationCode Minimum and Maximum inline numbers and Minimum and Maximumcrossline numbers to match values in Pad 3D Stack VolumeSet Rekill dead traces to NoneDisk Data OutputIf the input traces are shorter than the traces that wereoriginally migrated, use Output trace length to increase theoutput trace length and prevent the loss of events that movedownward in time during demigration or inverse migration.Other DocsSearch PageKnown Problems

Stolt or Phase Shift 3D Migration731ProMAX® ReferenceUsageResamplingStretchingVelocitiesStolt or Phase Shift 3D Migration resamples and, ifnecessary, antialias filters the data. Input data are resampledto an internal sample interval of 0.6*0.5/fmax, where fmaxis the maximum frequency to migrate. (The 0.6 comes fromthe accuracy of the 8-point sinc interpolator used to stretchthe data.) Data are resampled after migration to therequested output sample rate. During both resamplings, ifthe sample rate increases, a zero-phase high-fidelity antialiasfilter is applied before resampling. Both resampling andantialias filtering are done using the methods ofResample/Desample.Stolt or Phase Shift 3D Migration stretches resampledinput data via a method analogous to Stolt’s stretchtechnique that uses interval velocities instead of RMSvelocities. The same stretching method is used for both Stoltand Phase Shift migration, but the reference velocity differs.For Stolt migration, the reference velocity is a single velocity,the minimum at any time and place in the input velocity field.For Phase Shift migration, the reference velocity is a singlevelocity function, the minimum at each time for any place inthe input velocity field. Because the reference velocity is theminimum velocity, data are always stretched, nevercompressed; therefore, data are not aliased during thestretch and subsequent migration.As with any migration method, accurate specification ofmigration velocities is critical. The reliability and accuracy ofthe results of any migration are highly dependent on thequality of the velocity model used to migrate the data.Therefore, it is strongly recommended that you use theInteractive Velocity Editor for QC and velocity smoothing,particularly in the lateral direction. An unsmoothed velocityfield can introduce spurious migration artifacts.You can also use a single interval velocity function in time byusing Velocity Manipulation to derive a spatially-averagedfunction. Alternatively, since averaging may not produce aOther DocsSearch PageKnown Problems

Stolt or Phase Shift 3D Migration732ProMAX® ReferenceInput Datarepresentative velocity function, you can select a singlevelocity function from your original interval velocity field. Theprimary advantages of this approach are speed and accuratehandling of high dips.Older Stolt migration programs used RMS velocities to do aStolt stretch. To get approximately the same results here, useVelocity Manipulation to resample the RMS velocities to thesample rate of the seismic data and to convert them tointerval velocities in time using the smoothed gradientsmethod.Data input to this migration are corrected to a flat datum. Ifyour data are referenced to a floating datum, apply datumstatics to move your data to a flat datum. If your velocity fieldis referenced to a floating datum, modify the velocity fieldwith Velocity Manipulation.Input must be normal stacked data with primary sort key ofILINE_NO and secondary sort key of XLINE_NO. Data mustbe in order with no missing traces. Within the migration job,use Pad 3D Stack Volume with ILINE_NO as the primarysort to pad in any missing traces within an inline ensemble. Ifentire inline ensembles are missing, see the section Reversingthe Migration Process for an example of how to pad them in.Stacked DataAdditional steps to prepare stacked data for migration are:• Consider using CDP Taper instead of the internal inlineand crossline tapers. The internal tapers are applied tothe ends of each inline and crossline regardless ofwhether the traces are live or dead. Since 3D data setsare usually padded with dead traces to form a rectangulargrid, the true edges of the data are not tapered. CDPTaper designs and applies a taper based on the CDP foldstored in the database for each trace and its neighbors.Therefore, it finds and tapers the true edges of the input3D data plus the edges of any holes.Common-Offset VolumesAdditional steps to prepare prestack data for migration are:Other DocsSearch PageKnown Problems

Stolt or Phase Shift 3D Migration733ProMAX® Reference• Apply Normal Moveout Correction followed by DMO toGathers 3D.• Use a tertiary sort key of DMOOFF when sorting the datato select a single offset bin. Each job can migrate onlyone common-offset volume.• Use Trace Header Math to change the data type to Normalstacked before migration and back to Normalunstacked afterwards.• Do not use CDP Taper. It is for poststack data only.Output Trace LengthDuring migration, it is often desirable for the output migratedtraces to be much shorter than the input stacked traces,particularly for sections with steep or overturned dips thatwere recorded at very large times, but which migrate torelatively small times.For similar reasons, during demigration or inverse migration,it is often desirable for the output demigrated traces to belonger than the input migrated traces, especially if the inputtraces are shorter than the traces that were originallymigrated. Increasing the output trace length prevents theloss of events that move downward in time duringdemigration or inverse migration.If the output trace is shorter than the input trace, the bottommute is reset to the lesser of the input bottom mute and thenew, shorter, trace length. In addition, if the top mute isgreater than or equal to the new trace length, the trace iskilled.If the output trace is longer than the input trace, the bottommute is reset to the new, longer, trace length so that the extrasamples at trace end are not rezeroed by remute.Scratch SpaceStolt or Phase Shift 2D Migration uses scratch files andscratch directories. Scratch directories must be crossmounted on all hosts so each host can read and write allscratch files.Other DocsSearch PageKnown Problems

Stolt or Phase Shift 3D Migration734ProMAX® ReferenceThere are two types of scratch files. The following paragraphsexplain how to estimate the amount of scratch space neededfor each.• The first type stores trace headers. File size in bytes isnx*ny*nb, where nx and ny are the inline and crosslinedimensions of the data, and nb is the length of the traceheader in bytes. 268 bytes/trace is a typical poststacktrace header size. For the exact length, use MB2 to lookat the data set information.• The second type holds intermediate results. File size inbytes is approximately 4.1*(nx+nxpad)*(ny+nypad)*nt,where nx and ny are the inline and crossline dimensionsof the data, nxpad and nypad are the inline andcrossline pad, and nt is the input trace length. Actualdimensions are nxfft by nyfft/2+1 by 8*MAX(nt, ntau,nu), where nxfft and nyfft are the inline and crosslinelengths after padding and nt, ntau and nu are thelengths in samples of the input, output and stretchedtraces. nu depends on the velocity field, the maximumfrequency to migrate, and the migration method, Stolt orPhase Shift.Intermediate data are spread over an ntile by ntile array ofscratch files. ntile=ncpu*ffactor, where ncpu is the numberof migration server nodes and ffactor is the file refinementfactor. ffactor is increased internally as needed to preventindividual files from being more than 1 gigabyte in size. Thearray of scratch files enables parallel I/O by allowing eachmigration server to have exclusive access to a subset of thedata during each processing step.The dimensions and sizes of all scratch files are calculatedand printed during the Initialization Phase. At that time allscratch files are explicitly filled with zeroes to guarantee thatneeded scratch space is available.Stolt or Phase Shift 3D Migration can use extended scratchspace. Please refer to Adding Extended Scratch Space inthe System Administration Guide for a complete description ofextended scratch space setup and requirements.The FFTX and FFTY phases can be I/O bound. Each server isassigned a row or column of scratch files to transform. Theserver must read from, then write to, all files in its assignedrow or column. With 8 servers, there are at least 64 files opensimultaneously for read and write. One solution is to useOther DocsSearch PageKnown Problems

Stolt or Phase Shift 3D Migration735ProMAX® ReferenceReferencesextended scratch to distribute scratch files over multiple filesystems. Another solution is to set the number of spatial FFTservers to a number smaller than the number of migrationservers, until a balance is reached between I/O and computedemands.Claerbout, J. F., 1985, Imaging the Earth’s interior: Blackwell Scientific Publications.Gazdag, J., 1978, Wave-equation migration by phase shift: Geophysics, 43, 1342-1351.Stolt, R. H., 1978, Migration by Fourier transform: Geophysics, 43, 23-48.Yilmaz, O., 1987, Seismic data processing: SEG.ParametersName of migration server host(s)Enter the name of the host(s) for the migration servers.Scratch directories must be cross mounted on all hosts. If nohost name is specified, the process executes on the samehost as the ProMAX® executive.Number of migration server nodesEnter the total number of migration servers. In a distributedparallel environment, this number usually matches thenumber of migration server hosts. For shared parallelenvironments, this number corresponds to the number ofCPUs to use for the migration.Number of spatial FFT server nodesEnter the total number of spatial FFT servers. This numbermust be less than or equal to the number of migrationservers.The FFTX and FFTY phases can be I/O bound. See the lastparagraph of Scratch Space in the Usage section for detailson why. If they are I/O bound, one solution is to set thenumber of spatial FFT servers to a number smaller than thenumber of migration servers, until a balance is reachedbetween I/O and compute demands.Other DocsSearch PageKnown Problems

Stolt or Phase Shift 3D Migration736ProMAX® ReferenceMigration algorithmSelect the migration algorithm from the following choices:• Phase Shift• StoltMigrate, Demigrate or Inverse Migrate?Select:• Migrate input data• Demigrate input data• Inverse migrate input dataMigration of dipsThis appears if Phase Shift to Migration algorithm. Selectto migrate (or demigrate):• Up to 90 degrees only• Beyond 90 degrees only• Up to and beyond 90 degreesStolt stretch factorThis appears if Stolt to Migration algorithm or Inversemigrate input data to Migrate, Demigrate or InverseMigrate. Enter the (W) factor to use with time stretching tomake the constant-velocity Stolt migration algorithm moreaccurately handle velocity variations with depth. A value of0.6 is appropriate for young, uncompacted sediments inwhich velocity increases gradually with depth. Decreasing thestretch factor tends to lessen the effect of over migration ofsteep dips. Use 1.0 for constant velocity.Apply Stolt obliquity correction?This appears if Stolt to Migration algorithm and Migrateinput data to Migrate, Demigrate or Inverse Migrate.Select Yes to apply the obliquity correction. The obliquitycorrection is proportional to the cosine of the subsurface dip.Applying it during the forward migration reduces theamplitude of the migration operator for steeper dips. SelectOther DocsSearch PageKnown Problems

Stolt or Phase Shift 3D Migration737ProMAX® ReferenceNo only when you plan to do a Stolt demigration on the datalater.Start of high-dip taperThis appears if Inverse migrate input data to Migrate,Demigrate or Inverse Migrate. Enter the angle in degrees atwhich the high-dip taper starts in inverse migration. Theamplitude of the cosine-squared taper is 1.0 at the startingangle and 0.0 at 90 degrees.The high-dip taper reduces the amplitude of dipping linearartifacts created by inverse migration. Inverse migrationapplies a scale factor proportional to one over the cosine ofthe subsurface dip. The scale factor is 1.0 at 0 degrees, 2.0 at60 degrees, 5.0 at 78.463 degrees and infinite at 90 degrees.Large scale factors near 90 degrees produce dipping linearnoise; therefore, they are tapered.Select interval velocity fileSelect an Interval Velocity in Time file from the database.Minimum inline numberMaximum inline numberMinimum crossline numberMaximum crossline numberEnter the minimum and maximum inline and crosslinenumbers of the output image volume. Input traces outsidethe image volume are neither migrated nor output.Output trace lengthEnter the trace length in ms for output migrated ordemigrated data. The default, 0.0, means use the input tracelength.Output sampling intervalEnter the sampling interval in ms for output migrated ordemigrated data. The default, 0.0, means use the inputsampling interval.Other DocsSearch PageKnown Problems

Stolt or Phase Shift 3D Migration738ProMAX® ReferenceMigration tends to downshift the frequency content,especially for steep dips. Therefore, the sampling interval ofthe output migrated data can be greater than that of theinput unmigrated data.Demigration and inverse migration tend to upshift thefrequency content, especially for steeper dips, compensatingfor the downshift that migration applies. Therefore, if thesampling interval was changed during migration, it may beworthwhile to change the output sampling interval for thedemigrated data back to the sampling interval beforemigration.Minimum frequency to (de)migrateThis appears if Phase Shift to Migration algorithm. Enterthe minimum frequency in Hz to migrate or demigrate.Minimum frequency is always 0 Hz for Stolt migration.To avoid artifacts due to the abrupt truncation of thefrequency band, ensure that the input traces have littleenergy below the minimum frequency.Maximum frequency to (de)migrateEnter the maximum frequency in Hz to migrate or demigrate.The default, 0.0, means set maximum frequency to 0.6 *Nyquist frequency, for example, 75 Hz for 4-ms data. The 0.6comes from the accuracy of the 8-point sinc interpolator usedto stretch the data.Maximum frequency has a strong impact on run time. Itaffects the sampling interval and number of samples of thestretched traces. Much computation time and scratch spacecan be saved by not migrating frequencies above the signalband of the input data. To avoid artifacts due to the abrupttruncation of the frequency band, ensure that the inputtraces have little energy above the maximum frequency.Number of inline traces to padNumber of crossline traces to padEnter the number of zero-amplitude traces to add to eachinline and crossline to avoid f-k migration wrap around.Theoretically, padding in both directions should be the widthof the migration operator, but in practice much smaller padsOther DocsSearch PageKnown Problems

Stolt or Phase Shift 3D Migration739ProMAX® Referencecan be used, particularly if the dips near the edges of thestacked section are moderate.An equation that can be used to estimate the amount ofpadding is x = v/2 * t * sin(theta), where v is the migrationvelocity at time t, t is the two-way traveltime in seconds, andtheta is the dip of events near the edge of the section at timet. Divide x by the inline or crossline spacing to get thenumber of traces to pad.Inline taper length (in traces)Crossline taper length (in traces)Enter the inline and crossline taper lengths in traces toprevent migration artifacts due to abrupt data truncation. AHamming taper is used, which consists of a cosine weightingthat varies from 100% to 8% over the length of the taper.Top time taper (in ms)Bottom time taper (in ms)Enter the top and bottom taper to prevent migration artifactsdue to abrupt data truncation or irregular amplitudes atsmall or large times. A Hamming taper is used over the lengthof the taper time.Reapply trace mutes?Select Yes to reapply the input top and bottom mutes fromthe trace headers to the output data. For any traces that weredead on input but are live on output (see Rekill DeadTraces), new mute header values are calculated and applied.Select No to have no mutes applied to the output data. For alloutput live traces, top mute header values are reset to zeroand bottom mute header values are reset to output tracelength.Rekill dead traces?Select from the following choices:• All: traces that were dead on input are rezeroed andremain dead on output.Other DocsSearch PageKnown Problems

Stolt or Phase Shift 3D Migration740ProMAX® Reference• None: traces that were dead on input are output as live,with TRC_TYPE changed to 1.• Edges only: rekill behavior depends upon the location ofthe dead trace. A polygon is found that marks the outeredge of live input data. If an input dead trace is outsidethe polygon, then it is rezeroed and output as dead. If aninput dead trace is inside the polygon, then it is outputas live, with TRC_TYPE changed to 1.If the input live traces are not contiguous, then morethan one polygon is found and used. Dead traces in thegaps between polygons are output as dead. A simpleexample of a data set with two noncontiguous regions oflive traces is one with an entire inline or crossline that isdead.Any trace with TRC_TYPE not equal to 1 is considered to be adead trace. No check is made on whether or not a tracecontains nonzero samples.File refinement factorEnter a file refinement factor, ffactor. The intermediate dataare spread over an ntile by ntile array of scratch files.ntile=ncpu*ffactor, where ncpu is the number of migrationserver nodes and ffactor is the file refinement factor. ffactoris increased internally as needed to prevent individual filesfrom being more than 1 gigabyte in size.Increasing the file factor above its minimum default value canmarginally improve performance by more evenly subdividingwork amongst multiple processes and by allowing the job tomore fully use available scratch file space. Each process hasup to ntile scratch files open at the same time. If ntile is toolarge, the job may fail because a process runs out of availablefile descriptors. The ProMAX® processing system ensuresthat at least 1024 file descriptors are available to eachprocess.Scratch file IDEnter a flow-specific prefix to identify scratch files. Usedifferent IDs to run multiple jobs at the same time from thesame flow.Other DocsSearch PageKnown Problems

Stolt or Phase Shift 3D Migration741ProMAX® ReferenceVerbose listing?Select Yes to receive verbose printout about what is going on,especially migration servers.Other DocsSearch PageKnown Problems

Stolt or Phase Shift 3D Migration742ProMAX® ReferenceOther DocsSearch PageKnown Problems