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PHASE VELOCITY PROCESSING FORACOUSTIC LOGGING-WHILE-DRILLING

FULL WAVEFORM DATA

Marek Kozak, Magnetic Pulse Inc., Paul Boonen and Doug Seifert, PathFinder Energy Services

ABSTRACT

This paper presents the principle and demonstratesthe advantages of using a Phase Velocity Processingtechnique (PVP) applied to the full wave acousticdata recorded by a logging-while-drilling tool. PhaseVelocity Processing is particularly well suited forhandling the characteristics of LWD data that maydegrade the results of Semblance method. Amongthem are: large tool-mode content, high signalattenuation across the receiver array, and strong roadnoise. Another advantage of applying PVP is its highvertical resolution: due to the common receiver modeof operation vertical resolution of the calculatedslowness is equal to the offset between adjacentreceivers. By comparison, the Semblance methoddelivers results averaged across the entire receiverarray span.

The PVP algorithm employs series of Fast FourierTransform procedures to (a) filter the data usingHeisenberg’s method, (b) define time domaindistribution of the phase arrivals using a Hilberttransform, and finally (c) perform the Phase Velocityanalysis. Large number of phase arrival pointsprovides efficient mechanism to calculate standarddeviation of the results, quality indicators are addedto show how well the algorithm was able to calculateboth compressional and shear slownesses. Processingpackage includes filters operating in the frequency,time, slowness or space domains to minimizecompeting acoustic modes, especially the toolarrivals that are frequently present in LWD waveformdata.

Examples demonstrate improvement of the slownesscalculation performed with the PVP over the resultsdelivered by the Semblance method. The resultsobtained in attenuating formations, across the bedboundaries, and in thin beds are presented. Theability of the new filtering technique to identify andsuppress the tool mode arrivals is also demonstrated.

INTRODUCTION

The acoustic logging-while-drilling tools that wereintroduced six years ago (Minear et. al., 1995, Heysseet. al., 1996, Minear et. al., 1996) are by necessityfull waveform recording devices. The drilling noiseand the requirement for rigidity in an LWDenvironment prevented the use of a simple thresholdtechnique as employed in the older wireline acoustictools. The semblance method was the mostcommonly utilized processing technique at the time.It was implemented in the form of embeddedfirmware for downhole processing and as the surfacesystem application for memory waveform dataanalysis.

Semblance processing has a number of drawbacks,such as its requirement for constant amplitude andvelocity across the receiver array, the smoothing ofthe waveforms across the receiver span, the ability tomask defective data collected by an under performingtool, and not in the least its numerical complexity andtherefore long execution time. We introduce here thePhase Velocity Processing algorithm implemented toprocess full waveform data recorded with a logging-while-drilling acoustic tool.

ACOUSTIC LWD WAVEFORM AND LWDTOOL ARCHITECTURE

The very nature of acoustic measurements performedunder drilling conditions has necessitated therecording of full waveform data. This hascomplicated not only the construction of the acousticLWD tools but also the downhole processing, as real-time sonic slowness calculations are required.

A constant presence in LWD waveforms is toolmode, defined as the signal traveling from thetransmitters to the receivers, either directly in the toolbody or deflected by the borehole wall. The isolatorsections in acoustic LWD tools are not perfect due tothe fact that the LWD devices, contrary to wirelineunits, need to be absolutely rigid: the collar strengthcannot be compromised by the introduction of theelectronics and isolators. Tool mode signal is

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characterized by the constant arrival time and agenerally constant amplitude reduced by the isolator.Compressional and flexural tool modes can berecognized.

The acoustic LWD tool in Figure 1 has twotransmitters located symmetrically on both sides ofan array of four receivers: one transmitter ispositioned above and one below the array. Alltransmitters and receivers are aligned on one side ofthe tool. Such a configuration shows advantages overthe typical omnidirectional monopole acoustic tool:

• Single side architecture is similar to that of adipole tool, where the transmitters and receiversare aligned to perform directional measurements.The acoustic source located on one side of the toolgenerates both monopole and dipole excitations.Therefore this source can be considered as ahybrid between a monopole and a dipole sourceand can be called a unipole transmitter. A unipoletool generates simultaneously formationcompressional and borehole flexural waves duringa single recording cycle.

• Simplicity of the unipole tool architectureprovides higher quality data since there is no needfor well balanced sources and carefully matchedreceivers as required by true dipole setup.

• Much simpler electronics are needed for a unipoletool design improving the failure rate overequivalent monopole/dipole tool configuration.

PHASE VELOCITY PROCESSING METHOD

The Phase Velocity Processing (PVP) method, whichis sometimes referred to as a complex signal analysis(Tanner, 1979), is based on the Hilbert transform ofthe recorded real time domain waveforms. Theslowness of the acoustic mode of interest(compressional, shear) is computed by findingconstant phase trajectories. The data flow illustratingthe PVP algorithm is shown in Figure 2. Thisalgorithm represents the Phase Velocity Picking stepin the full processing flow diagram in Figure 3.

In the initial step, input time domain waveforms areconverted to the complex form using a Hilberttransformation. Figure 4 shows the raw data andFigure 5 shows the Hilbert transformed waveforms.As the result, the data measured by each receiver areconverted to its time domain real and imaginarycomponents. The real part of the Hilbert transformedsignal is identical to that of the input data. Theimaginary part, in conjunction with the real part,

represents the magnitude and the phase of each timedomain point of the input data.

In the second step, the Hilbert transformed signal ofeach receiver is used to compute its time domainphase arrivals Φi(t), utilizing equation (1).

ΦI(t) = arctan im[H( xi(t))] / re[H( xi(t))] (1)

where: xi(t) is the input time domain data recordedwith i-th receiver and the H( ) function is its Hilberttransform. In the absence of competing acousticmodes, functions of class (1) vary quasi linearlywithin the range of (-π, +π), and with a periodicityequal to that of the input signal (Figure 6).

Next, the time domain slowness distribution of eachreceiver pair is calculated by means of a constantphase trajectory (Figure 7), using equation (2).

Si,j(t) = [Φ−1j(t) - Φ

−1i(t)] / z (2)

where the symbol Φ−1i(t) denotes an inverse solution

to equation (1) and z is the spatial interval betweenreceivers i and j (j>i). In the absence of interferingacoustic modes, functions of class (2) show semi-constant slowness values across the entire processingwindow width (Figure 7). Should frequencydispersion affect the data, as often happens whenrecording borehole flexural wave, the slowness timedomain distribution curve will show some variability(Figure 8). In such a case equation (2) can beutilized to estimate and compensate for the dispersioneffects.

Finally, a single slowness value is computed byintegrating (averaging) equation (2) over the desiredtravel time interval as follows:

∆Ti, j=(Σ Si, j(t))/(tmax-tmin) (3)

where summing is performed over the travel timeinterval limited by the tmin and tmax.

PHASE VELOCITY PROCESSING

Data flow utilized by the Phase Velocity Processingalgorithm that is implemented for LWD full waveacoustic tool is shown in Figure 3. The PVPalgorithm employs a sequence of digital signalprocessing techniques to:

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• Suppress tool mode arrivals using a depth domainfilter. This filter is optional and is invoked by theuser if needed.

• Reduce high frequency road noise by utilizing 5-thorder moving average depth domain kernel filterThis filter is also optional.

• Extract desired acoustic arrivals (compressional orflexural) by simultaneously employing Heisenbergzero phase shift frequency filter (Figure 9) and thetime domain tracking routine.

• Calculate formation slowness by performingHilbert transformation and the Phase Velocityanalysis as illustrated earlier.

All of the processing steps described above arerepeated iteratively for each of the transmitter firings.Final formation slowness is calculated as thecorrelation weighted average of the results obtainedwith each of the transmitters individually. Whenshear wave arrivals are present in the recorded data,the PVP calculations are repeated with differentfrequency and time domain tracking filters.

VERTICAL RESOLUTION

The Phase Velocity Algorithm has an option tocompute the slowness in common receiver mode(CRM) instead of common transmitter mode (CTM),which is the basic method for semblance processing.Figure 10 shows the difference between these twoprocessing techniques.

In common transmitter mode, CTM, four receiversignals are processed for the same transmitter firing.The vertical resolution of the computed slowness isequal to the span of the receiver array, three feet inthe discussed tool.

In common receiver mode, CRM, the slowness iscomputed from the three pairs of receivers located atthe same depth, by utilizing three different transmitterfirings. This method of slowness calculationenhances the vertical resolution of the measurementto the offset between two adjacent receivers, one footin the figured tool. The quality of the CRM results inan LWD environment depends on depth samplingrate, which in turn depends on the drilling rate ofpenetration and the tool time sampling rate. At depthsampling rates different than one sample per foot, aninterpolator is utilized to provide CRM with thewaveforms aligned at proper depth intervals.

PHASE VELOCITY VERSUS SEMBLANCEPROCESSING

The Phase Velocity Processing method shows severalmajor advantages over the semblance technique:

• It can be derived from equation (1) that timedomain phase arrivals of the receiver waveform donot depend on the amplitude of the signal. Due tothe self-normalization of the Hilbert transform,two identical signals (in the sense of shape) willhave exactly the same phase distributions, even iftheir amplitudes differ by orders of magnitude. Inpractice it means that the PVP algorithm willprovide valid slowness calculations even if therock is either highly attenuating or the receiverarray is poorly calibrated for amplitude.Furthermore, the number of calculated phasepoints is limited only by the numerical capabilitiesof the computer system used to execute thealgorithm (Equation 3), thus yielding highaccuracy of slowness computations.

• The PVP method will compute formationslowness based entirely on the waveform transittime measurements. By comparison, the semblancealgorithm calculates amplitude weighted groupvelocities. Therefore semblance results arestrongly affected by propagation losses andreceiver amplitude characteristics.

• The PVP method, due to its high verticalresolution in Common Receiver Mode, provides astable response that is not affected by the receiverarray crossing a boundary with a high acousticimpedance contrast. Again by comparison,semblance will produce erroneous multiple peaksyielding not only data smoothing but also false orfrequently artificial slowness readings. Userdefined processing setup also might affectsemblance response. En example of such abehavior is discussed in the examples.

• The PVP method provides a way to monitor theresponse of each receiver pair (Equation 2).Therefore as long as there are at least two reliablereceiver signals, the raw data can be utilized toproduce valid slowness log.

• The PVP method is based on the Hilberttransform, closely related to the Fast FourierTransform, which makes it an order of magnitudefaster then the semblance algorithm. Therefore it iswell suited for all the applications that demandreal-time or very short turn around time.

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EXAMPLES

Tool Mode Removal: Tool mode is the signaltraveling in the tool body from the transmitters to thereceivers. Because the isolator sections in sonic LWDtools are not perfect, as LWD tools need to beabsolutely rigid for the drilling operations to whichthey are subjected, tool mode is a constant presencein the LWD waveform. Figure 11 shows a 150 ftsection of raw waveforms (left) compared to thesignal with the tool mode removed (right). The wavesare presented in a variable density log format from200 to 600 microseconds after the start of therecording. The constant arrivals that can be seen atabout 330, 410 and 500 microseconds in the rawwaveforms mask the underlying compressionalarrival. The tool mode removal filter has successfullysuppressed the constant component of the waveform(tool mode) while properly maintaining slowlychanging compressional arrivals.

Comparison of formation slowness estimationdelivered by PVP with the Semblance Processingresults: The semblance processing response isaffected by the presence of thin beds in conjunctionwith processing setup parameters as shown in Figure12. Track 1 and track 2 present the results obtainedfrom semblance processing and PVP respectively.The processing window width was varied from 100µsec (black curves) up to 250 µsec (green curves).Track 3 shows the raw waveforms and track 4 thefiltered data with tool mode suppressed. The PVPalgorithm delivers matching slowness curves that arevirtually independent from the processing setup. Thesemblance response shows high susceptibility to theprocessing parameters. The semblance processingeither over- or under-estimates the formationslowness depending on the selected processingwindow width, especially where the receiver array iscrossing thin beds or high acoustic impedancecontrast zones. In the presence of competing modesas shown in the later part of the wave train shown onthe Figure 13, semblance will generate erroneousresults, computing slowness readings affected bylarge bias (Figure 12).

A Gulf of Mexico data set comparing Semblanceprocessing results and those of the Phase Velocitymethod is shown in Figure 14. This is a 200-footinterval of sandstone, siltstone and shale. There is agood agreement between the PVP compressionalslowness (DTP) which is the correlation weightedaverage of the upper and lower calculated delta-tvalues and the semblance processing results for bothupper and lower transmitter data sets, curves labeled

DTP1_sem and DTP2_sem respectively. Additionallythe PVP processing delivers a better overall bedresolution.

Individual waveform data for the lower transmitterfiring and for the depth indicated by the arrow inFigure 14 are shown in Figure 15. The figure showsthe waveforms recorded for each of the four receiversand a hand picked correlation. Note how the handpicked delta-t of 112.3 µsec/ft correlates well withboth processing methods, of approximately 112µsec/ft slowness.

Another section of the log, at a shallower depth, isshown in Figure 16. There is a large discrepancybetween the PVP slowness, curve labeled DTP, andthe semblance processed delta-t values, curvesDTP1_sem and DTP2_sem, over the whole 125 footinterval shown. At the depth indicated by the arrownear the top of a siltstone, the two processingtechniques disagree by approximately 25 µsec/ft (130µsec/ft versus 106 µsec/ft). The interval is comprisedof shale and siltstone. Examination of the individualwaveforms indicate excellent waveform data qualityas shown in Figure 17. Manual correlation of thedata indicates a clear 106 µsec/ft slowness, whichmatches the Phase Velocity Processing result. Thefaster delta-t is the correct one. It can be clearlycorrelated with the waveform data and it matches theGamma Ray response (faster delta-t in the siltstonethan in the above shale). The waveform data in track3 of Figure 16 indicate a faster formation than theoverlying shale by the earlier arrival in transit time ofthe compressional wave.

The only distinctive feature about this interval is theattenuation of approximately 4.2 db/ft. This is notunreasonably high, but indicates fairly attenuatingstrata. Such conditions are encountered quitefrequently, primarily due to the fact that drilling noiseforces the tool to operate in a frequency bandwidthabove 10 kHz. On Figure 17 a manual correlation isalso shown that matches the semblance correlationresults of approximately 130 µsec/ft slowness. Thesemblance processing correlated peaks of samerelative amplitude. This is one of the majordrawbacks of the semblance correlation technique; ityields an amplitude weighted group velocity.

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CONCLUSION

A new technique for correlating acoustic waveformdata, Phase Velocity Processing (PVP), has beenintroduced and described. The technique works verywell with the LWD full waveform data. PVP resultsdo not depend on the amplitude of the processedwaveform, nor are they sensitive to the formationattenuation. Additionally, the slowness calculation isbased entirely on the measurement of the waveformtransit time and thus has a high vertical resolution,essentially equal the receiver spacing. The PVPmethod is also much faster in execution than thesemblance correlation technique traditionally used.

ACKNOWLEDGEMENTS

The authors wish to thank the management ofMagnetic Pulse Inc. and Pathfinder Energy Servicesfor the permission to publish this paper. The PhaseVelocity Algorithm is protected under U.S. Patent #5,831,934.

REFERENCES

Heysse, D., Robbins, C., Minear, J., 1996, “FieldTests of an Acoustic Logging-While-Drilling Tool inVarious Borehole Environments”, SPWLA 37thAnnual Logging Symposium, New Orleans, June 16-19, paper EE.

Minear, J., Birchak, R., Robbins, C., Linyaev, E.,Mackie, B., 1995, “Compressional Wave SlownessMeasurement While Drilling”, SPWLA 36th AnnualLogging Symposium, Paris, June 26-29, paper VV.

Minear, J.W., Heysse, D., Boonen, P., 1996, “InitialResults from an Acoustic Logging While DrillingTool”, SPE Annual Technical Conference andExhibition, Denver, Co, Oct. 6-9, SPE 36543.

Taner, M. T., Koehler, F., Sheriff, R.E., 1979,“Complex trace analysis”, Geophysics, v. 44, p.1041-1063.

ABOUT THE AUTHORS

Marek Kozak holds a Ph.D. in EE/ MeasurementSystems from the Warsaw University of Technologyin Poland. He has been instrumental in thedevelopment of MPI's pulsed power wirelineinduction and acoustic logging tools, and processingsoftware. Prior to joining MPI in 1990 he was for 10years with the Warsaw University of Technology,conducting research in theoretical and appliedmagnetics sponsored by Polish Academy of Sciences,teaching classes in measurement of non-electricalquantities, and working as the industry consultant inDSP systems. He is a member of SEG and PlanetarySociety.

Paul Boonen is the Regional Petrophysicist for theEastern Hemisphere at PathFinder Energy Services inAberdeen, Scotland. He holds a Ph.D. in geologyfrom the University of Leuven in Belgium. He startedhis career in the field of log analysis in 1981 withGeofiles Consultants in Brussels (Belgium), joinedHalliburton in 1983 and later transferred toPathFinder in 1998. He worked as field engineer, loganalyst, computing center manager, area marketingmanager in a variety of countries in Europe, NorthAfrica, the Far East and North America. He is amember of SPWLA, SPE and AAPG.

Doug Seifert is the Regional Petrophysicist forPathfinder in Houston where he is responsible forpetrophysics support for the Western Hemisphere.Doug was previously the Regional Petrophysicist forthe Eastern Hemisphere, located in Stavanger,Norway. Prior to joining PathFinder, he has workedfor Mærsk Olie og Gas in Denmark as the Head ofPetrophysics, for Halliburton Energy Services inOperations, Research and Technical Supportfunctions and also for Texaco in Technical Servicesand Production Operations. He is a member ofSPWLA, SCA, SPE and AAPG.

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Figure 1. Acoustic Logging-While-Drilling Tool

Figure 2. Phase Velocity Algorithm Data Flow

Figure 3. Phase Velocity Processing Data Flow

Transmitter Transmitter

IsolatorSection

IsolatorSection

Four Receiver Array

UltrasonicTransducer

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Figure 4. An example of raw LWD sonic waveforms (shown in common receiver depth mode).Right column presents receiver pair #12, the middle column – pair #23, and the left column – pair #34shown in common receiver mode.

Figure 5. Time domain complex waveforms obtained after Hilbert transform (shown in common receiverdepth mode). Dark lines denote real part of Hilbert transformed data, grey – the imaginary component.

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Figure 6. Time domain phase arrivals of the raw LWD sonic waveforms. Dark lines denote the phasedistribution of the near receivers (closest to the transmitter), grey lines – far receivers (CRM mode).

Figure 7. Time domain slowness distribution of the raw LWD sonic data obtained with each receiver pair.Right column shows the receiver pair #12, the middle column – pair #23, and the left column – pair #34(CRM mode).

Figure 8. Time domain slowness distribution of the raw LWD flexural wave obtained with receiver pair#23. Note small dispersion effect expressed as a gradual bias toward higher slowness values.

Figure 9. Frequency characteristic of typical Heisenberg filter.

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Figure 10. Comparison of CRM, Common Receiver Mode, and CTM, Common Transmitter Mode mode ofoperation.

Figure 11. Example of the effectiveness of tool mode removal algorithm over a 150-foot interval.

150ft

600200 400microseconds

Raw Data Tool Mode Removed

600200 400microseconds

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Figure 12. Comparison of Phase Velocity and Semblance Processing response to formation features, withdifferent user defined processing setups. Note how response of the Semblance method depends on theformation type and processing window width (100 µsec, 150 µsec, 200 µsec, 250 µsec). Raw waveformdata recorded at the depth indicated with the black arrow in the upper left corner is shown in the timedomain in the Figure 13.

Figure 13. Raw waveform data recorded at the depth indicated (Competing Modes) on the Figure 12, shownin the time domain. Note poor signal coherence present in the later part of wave train, causing theSemblance to overestimate formation slowness.

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Figure 14. An 200-foot interval from the Gulf of Mexico showing agreement between Semblance and PhaseVelocity processing results.

Figure 15. Waveforms at the depth indicated in Figure 14 and manual correlation of data indicating 112.3µsec/ft slowness.

200 ft

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Figure 16. A 120-foot interval from the Gulf of Mexico showing a disagreement between Semblance andPhase Velocity Processing results.

Figure 17. Waveforms from indicated depth of Figure 16 and manual correlation (red) of data indicating106.1 µsec/ft slowness. 16 and a manual correlation (green) that matches the semblance processing resultsof 130.6 µsec/ft slowness. Semblance processing found correlation of peaks of near same relativeamplitude.

120 ft

65 mv

110 mv

130 �sec/ft

106 �sec/ft