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WO1993007512A1 - Methodes et appareils concernant des enregistrements sonores multipolaires a frequence constante - Google Patents

Methodes et appareils concernant des enregistrements sonores multipolaires a frequence constante Download PDF

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Publication number
WO1993007512A1
WO1993007512A1 PCT/US1991/007493 US9107493W WO9307512A1 WO 1993007512 A1 WO1993007512 A1 WO 1993007512A1 US 9107493 W US9107493 W US 9107493W WO 9307512 A1 WO9307512 A1 WO 9307512A1
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WIPO (PCT)
Prior art keywords
multipole
wave
sonic
borehole
shear
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PCT/US1991/007493
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English (en)
Inventor
Shu-Kong Chang
Original Assignee
Chang Shu Kong
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Publication date
Application filed by Chang Shu Kong filed Critical Chang Shu Kong
Priority to PCT/US1991/007493 priority Critical patent/WO1993007512A1/fr
Publication of WO1993007512A1 publication Critical patent/WO1993007512A1/fr

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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
    • G01V1/00—Seismology; Seismic or acoustic prospecting or detecting
    • G01V1/40—Seismology; Seismic or acoustic prospecting or detecting specially adapted for well-logging
    • G01V1/44—Seismology; Seismic or acoustic prospecting or detecting specially adapted for well-logging using generators and receivers in the same well
    • G01V1/48—Processing data

Definitions

  • the present invention is directed to logging of formation shear in a borehole traversing an earth formation. More particularly, the present invention is directed to logging of formation shear using discrete frequency measurements, as well as to logging in the frequency domain.
  • Shear wave data has been found useful in lithology and fluid identification, porosity determination, measurement of rock elastic and inelastic properties, and as an adjunct to shear seismic data. See, for example, H. LESLIE and F. MONS, SONIC WAVEFORM ANALYSIS: APPLICATIONS, presented at the Society of Professional Well Log Analysts (SPWLA) Annual Logging - Symposium, New Orleans, Louisiana, June 10-13, 1984.
  • sonic borehole logging tools have been used to acquire formation shear data. Such tools employ a monopole transmitter which emits a broad ⁇ band sound pulse, and one or more receivers which detect the pulse as it passes. A number of such sonic logging tools have been widely used, including Schlumberger's BHC* borehole compensated sonic tool, LSS* long-spaced sonic
  • Propagation of the broad-band, monopole sound pulse in a borehole is governed by the mechanical properties of several separate acoustic domains. These include the formation, the borehole fluid column, and the logging tool itself. Wide-band sound energy emanating from the monopole transmitter impinges on the borehole wall, establishing compressio ⁇ ar and shear waves in the formation, surface waves along the borehole wall, and guided waves within the fluid column.
  • the borehole wall, formation bedding, borehole rugosity, and fractures can all represent significant acoustic discontinuities. T e phenomena of wave refraction, reflection and conversion lead to the presence of many acoustic waves in the borehole when a sonic log is being run. Thus, many acoustic energy arrivals are seen by the receivers of a sonic logging tool.
  • the more usual acoustic energy arrivals at the receivers of a sonic logging tool having a wide-band monopole energy source are shown in the waveform examples of Figure 1.
  • the distinct changes corresponding to the onset of the compressio ⁇ al and shear arrivals and the tube (Stoneley) arrival can be seen in these examples, although the wave packets are not totally separated in time.
  • the first arrival (the compressio ⁇ al wave) has traveled from the transmitter to the formation as a fluid pressure wave, has been refracted at the borehole wall,
  • SUBSTITUTE SHEET has traveled within the formation at the compressional wave velocity of the formation, and has traveled back to the receiver as a fluid pressure wave.
  • the shear wave has traveled from the transmitter to the formation as a fluid pressure wave, has traveled within the formation at the shear wave velocity of the formation, and has traveled back to the receiver as a fluid pressure wave.
  • the mud wave (not strongiy evident in the wavetrain examples of Figure 1) has traveled directly from transmitter to receiver in the mud column at the compressional wave velocity of the borehole fluid.
  • the Stoneley wave is of large amplitude and has traveled from transmitter to receiver with a velocity less than that of the compressio ⁇ al waves in the borehole fluid.
  • the slowness-time coherence technique uses a semblance algorithm to detect arrivals that are coherent across the array of receiver waveforms and to estimate their interval transit time. Applying this semblance algorithm to the waveforms of Figure 1 produces the coherence map of Figure 2, in which regions of large coherence correspond to the compressional, shear, and Stoneley arrivals. The apex of each region defines the slowness of that wave. This process is repeated for each set of waveforms acquired by the tool and is used to produce a log of slowness versus depth such as shown in Figure 3. In a slow formation (a formation having a shear velocity less than the borehole fluid velocity), the tool obtains real-time measurements of compressional, Stoneley and mud wave velocities, but shear wave values must be derived from these velocities.
  • STC slowness-time coherence technique
  • SUBSTITUTE SHEET wave is insufficient for effective processing and analysis. And because the first shear wave arrival follows the compressional wave arrival, identifying the first shear arrival can be difficult or impossible.
  • various sonic tools have been proposed for directly logging formation shear, particularly in slow formations where the conventional tools having a monopole source cannot give shear wave logs directly.
  • These tools employ dipole or other multipole (e.g., quadrupole) source and receiver transducers (rather than monopole transducers as in conventional sonic logging tools) for direct logging of shear in both fast and slow formations.
  • a monopole source excites azimuthally symmetric acoustic waves around the borehole, as shown diagrammatically in Figures 4a and 4b.
  • a dipole source can be synthesized from two monopole sources of opposite polarity (i.e., the pressure of one source is positive when the other is negative and vice versa) placed on a plane perpendicular to the borehole axis. Since one side of a dipole source pushes the fluid with a positive pressure and the other side pulls with a negative pressure, a dipole source acts as a point force moving the fluid transversely to the borehole wall. Therefore, propagation of a dipole wave causes the formation surrounding the borehole to flex sideways, as shown diagrammatically in Figures 5a and 5b.
  • a dipole source must move the borehole fluid to vibrate perpendicularly to the borehole axis. This can be achieved by moving a plate in the hole.
  • One way to move the plate is to use the concept of moving coils in a magnetic field, similar to loudspeakers.
  • Another way is to use piezoelectric bimorphic or mo ⁇ omorphic benders.
  • a bimorphic bender is made of two thin piezoelectric plates of opposite polarity bonded together. As a voltage is applied across the plates, one plate extends while the other contracts. Thus, the composite plate bends in response to applied voltage much as a bimetallic plate does in response to temperature change. When supported at the edges, the bender will move the fluid sideways as a dipole source.
  • Other dipole source configurations are also known, such as dual volume sources, expanding rods, rare earth transducers, split cylinders, etc.
  • a dipole receiver must be able to sense either pressure gradient, particle acceleration, particle velocity, or particle displacement. Measuring the differential output of two hydrophones will give the pressure gradient. Accelerometers and geophones will sense particle acceleration and velocity, respectively. Variable capacitance microphones can sense the displacement of the fluid particle vibrations. These transducers vary in their sensitivities and frequency characteristics.
  • a quadrupole transducer In contrast to the dipole transducers, which excite and detect pressure gradient or particle vibrations, a quadrupole transducer can excite and detect waves with 90-degree asymmetry. That is, as a quadrupole wave travels up the borehole, the borehole vibration will be like squeezing a paper cup in one direction. In the cross-sectional plane, the wall will squeeze in toward the axis in one direction and expand out away from the axis in the perpendicular direction. Thus, quadrupole transducers will excite and detect shear/screw waves, in contrast to the shear/flexural of dipole transducers.
  • SUBSTITUTE SHEET transducers is mounted on each of several pads which are pressed against the borehole wall.
  • the transducers of each pad are oriented along mutually orthogonal axes and selectively activated to apply force to the borehole wall in a desired direction.
  • the tool can be operated in one of four different modes to produce torsional, flexural, radial and axial vibrations, by suitable application of voltage pulses to the source transducers.
  • the flexural (sideways) mode of vibration is that of a dipole source.
  • the transducers in that arrangement are each formed of two half-cylinder segments of piezoelectric material (barium titanate), assembled to form a cylindrical body.
  • the segments are connected electrically such that the application of a voltage causes one segment to expand in the radial direction when the other segment contracts in the radial direction, and vice versa, thereby generating a dipole wave in the borehole.
  • the receiver transducers are of the same construction, acting as a pressure gradient sensor at low frequencies.
  • a voltage pulse is applied to the source transducer to produce a flexural wave in the borehole, and the response of the receiver transducer is displayed in time domain.
  • the receivers are geophone-like devices with a neutrally-buoyant body which moves relative to the logging tool in response to passage of the asymmetric dipole pressure wave.
  • a pulse is applied to the source transducer, and the waveforms detected at the receivers are recorded in the time domain.
  • the tool must be stationary while taking measurements.
  • An alternate transducer construction proposed in U.S. Patent No. 4,207,961 to Kitsunezaki has diaphragms which move up and down such that a pair of fluid chambers displace fluid in opposite directions to generate a dipole wave.
  • Kitsunezaki's electrodynamic transducer disclosed in U.S. Patent No. 4,383,591 to Ogura, generates both monopole and dipole signals. Since the original design by Kitsunezaki was unsuitable for logging shear in fast formations, a new design was developed which uses a stationary coil and a moving magnet or a magnetic material block. The moving magnet is used as a hammer to drive either a rubber or a metal plate. The frequency was extended to several kHz and the power output was increased by the new design. See K. TANAKA, S. INOUE and K. OCURA, DEVELOPMENT OF A SUSPENSION PS LOGGING SYSTEM'S SEISMIC SOURCE FOR HARD GROUND, presented at the 56th SEG Annual Meeting, Houston, Texas, November 2-6, 1986.
  • SUBSTITUT transducers are of similar construction.
  • the benders have a resonant frequency such that, when a broad-band voltage pulse is applied to them, the frequency of the resulting acoustic signal ranges from about 1 kHz to 6 kHz with a predominant frequency of about 3 kHz. Benders of lower resonant frequency are also discussed.
  • U.S. Patent No. 4,606,014 to Winbow et al. discloses an acoustic dipole logging device in which the transducers comprise either a bimorphic bender clamped at one edge or a pair of bimorphic benders clamped at opposing edges.
  • the source transducer is driven by a voltage pulse.
  • the outputs of the receiver transducers are band-pass filtered and processed in time domain.
  • U.S. Patent No. 4,649,526 to Winbow et al. discloses an acoustic logging device with dipole or higher-order multipole transducers having multiple piezoelectric members of split-cylinder or bimorphic plate form.
  • the source transducers are driven by voltage pulses.
  • a dipole source excites not only the desired shear waves, but also a borehole flexural wave.
  • A. KURKJIAN and S. CHANG Acoustic Multipole Sources in Fluid-Filled Boreholes, 51 GEOPHYSICS 1 (January, 1986), at 148-163, and U.S. Patents Nos. 4,698.792 and 4,703,460 to Kurkjian et al.
  • the flexural wave is dispersive (its phase velocity varies with frequency) and is excited at a greater amplitude than the formation shear by a wide-band dipole source.
  • Figure 6 illustrates the dispersive nature of the flexural waves as a function of frequency.
  • the flexural wave phase velocity approaches the formation shear velocity at low frequency and gradually becomes slower at higher frequencies.
  • Figure 7 shows one example of the relative excitation amplitudes of the shear wave and flexural mode as functions of frequency.
  • the direct formation shear is much weaker than the flexural wave at higher frequencies, but stronger than the flexural wave at low frequencies where the flexural wave phase velocity is close to that of the shear velocity. (As shown in the example of Figure 7, the flexural mode is more than 20 dB stronger than the shear wave above a certain frequency.)
  • the formation shear is excited more than the flexural wave.
  • the dipole signals can be viewed approximately as a mixture of shear and flexural wave, with a velocity dispersion following that of the flexural wave. Since the drop in low-frequency amplitude of the shear wave is quite steep, it is difficult to obtain reasonable shear signal strength without also exciting the flexural mode.
  • road noise the noise generated by the sonde traveling in the borehole
  • Transverse vibration of the tool is generally detected by the dipole receivers. It has been found that road noise energy is mainly concentrated below 1 kHz and that, in general, road noise increases with increased logging speed.
  • sonic logging measurements have traditionally been made in time domain: a broad-band sonic energy source excites propagation of sonic waves in the borehole, and waveforms detected at an array of receiver locations spaced from the source in the borehole are recorded as functions of time. Shear wave velocity at the dominant frequency is then estimated by waveform stacking techniques, such as semblance or radon transforms.
  • time- domain recording has several disadvantages if the frequency domain results are desired.
  • the waveforms must be sampled in small time steps over a long period, resulting in a large set of data to transmit, store, and process. The truncation in time can cause interference in the processing.
  • SUBSTIT signal to noise ratio can be quite small for the wide-band transient measurements.
  • the noise problem can be significant for low frequency data (less than 1000 Hz) because of the noises generated by the sonde traveling in the borehole.
  • measurements are taken in frequency domain, thereby avoiding the above-noted problems.
  • a frequency domain measurement is desirable for a tool that gives a single dominant arrival. This is particularly true if the arrival is dispersive, as is the case with the shear/flexural arrival of dipole waves.
  • a variety of such techniques are disclosed, involving wavelength tuning by varying frequency and/or phase shift. In all the techniques, frequency and/or phase shift is adjusted until an amplitude peak is observed, the frequencies which produce such amplitude peaks are noted, and wave, propagation velocity is calculated from the expression given above.
  • the wavelength of the transmitted signal is tuned to a fixed wavelength of the transmitting and receiving arrays by varying its frequency.
  • the wavelength of the arrays is tuned to a fixed value of the transmitted wavelength by varying the phase shift between adjacent transducer elements.
  • the frequency of the transmitted signal or the phase shift between adjacent receiving transducers, or both are varied.
  • both amplitude and phase (or real and imaginary parts) of shear wave energy are needed to understand the dispersion.
  • the disclosed method requires downhole tuning of the frequency and/or the wavelength while acquiring the data. The method is not directly applicable to obtain the frequency dependent characteristics of dispersive waves, such as the shear/flexural or shear/screw waves.
  • U.S. Patent No. 4,419,748, issued December 6, 1983 to R.W. Siegfried, II. proposes a continuous wave sonic logging method in which a continuous sine wave at a single frequency is emitted and received, and a spatial Fourier transform is performed over the receiver array. The resulting spatial frequency components are then used to indicate the velocities of various sonic paths.
  • the logging method of U.S. Patent No.4,419,748 would have several disadvantages for multipole shear logging. For example, the method requires a large number of receivers in order to facilitate the spatial Fourier transforms. Further, the disclosed method records the instantaneous values of the received signal; that is, it is recorded in time domain.
  • the measurement is subject to noise interferences. No improvement in the signal to noise ratio is realized by the proposed method. Furthermore, the measurement can only be done one frequency per logging run (due to the time domain recording). This would require numerous logging runs for the dispersive waves, for which the wave characteristics are functions of frequency. Since the logging time is a costly factor in wire line logging services, the method is not practical for logging dispersive waves.
  • the present invention is directed to methods and apparatus for sonic shear logging of boreholes using discrete frequency measurements.
  • a multipole source transducer emits sonic energy at a location in a borehole of at least one discrete frequency which induces propagation of multipole sonic waves in the borehole; sonic energy of the multipole sonic waves is received at multiple multipole receiver locations in the borehole, the multiple receiver locations being spaced apart from one another and from the source transducer location; and for each receiver location, amplitude of the received sonic energy of the multipole sonic waves is detected
  • the source transducer may be driven continuously at one or a plurality of discrete frequencies, or may be driven intermittently, or may be driven alternately from a plurality of sources which provide one or a plurality of discrete frequencies.
  • the source transducer is driven from a repetitive signal pattern to emit sonic energy at a plurality of discrete frequencies.
  • the phase reference is preferably derived from the same signal source which drives the source transducer.
  • Shear logs are preferably obtained by sorting the dispersion results after processing the discrete frequency data.
  • the detected amplitude and phase of the received sonic energy of the multipole sonic waves may be processed to determine wave phase velocity and wave attenuation at discrete frequencies and to calculate velocity and attenuation as a function of frequency.
  • the multipole some wave data are useful, for example, in lithology and fluid identification, porosity determination, measurement of rock elastic and inelastic properties, and as an adjunct to shear seismic data.
  • a number of different techniques may be used to process the multipole sonic wave data, such as three receiver analytical solutions, least square fittings, two receiver phase difference and amplitude ratio, Prony's method, conventional beamforming, and the maximum likelihood method.
  • Figure 1 shows waveform displays of typical acoustic energy arrivals at the receivers of a sonic logging tool having a wide-band monopole energy source
  • Figure 2 shows a slowness-time coherence map resulting from the application of a typical semblance algorithm to the waveforms of Figure 1;
  • Figure 3 shows a log of slowness versus depth for the data of Figures 1 and 2;
  • Figures 4a and 4b illustrate diagrammatically in cross-sectional elevation and plan views, respectively, the azimuthally-symmetric acoustic waves excited by a monopole source in the formation surrounding a borehole;
  • Figures 5a and 5b illustrate diagrammatically in cross-sectional elevation and plan views, respectively, the azimuthally-asymmetric acoustic waves excited by a dipole source in the formation surrounding a borehole;
  • Figure 6 is an example of a plot of the ratio of flexural mode phase velocity to shear wave velocity as a function of frequency, illustrating the dispersive nature of flexural waves, and illustrating that the flexural wave phase velocity approaches the formation shear velocity at low frequency and gradually becomes slower at higher frequencies;
  • Figure 7 is an example of a plot of flexural mode and shear wave amplitude as a function of frequency
  • Figure 8 shows in schematic block form a first preferred embodiment of a discrete-frequency dipole logging apparatus for shear/flexural logging in accordance with the invention
  • Figure 9 shows in schematic block form a modification of the embodiment of Figure 8 which permits multiple, discrete frequencies to be emitted sequentially in bursts for shear/flexural logging in accordance with the invention
  • SUBSTITUTE SHE Figure 10 shows amplitude of a periodic signal as a function of time, the signal having a discrete frequency spectrum as shown in Figure 11;
  • Figure 11 shows amplitude of the discrete frequencies of the signal of Figure 10.
  • Figure 12 shows in schematic block form a further modification of the embodiment of Figure 8 which permits multiple, discrete frequencies to be emitted simultaneously for shear/flexural logging in accordance with the invention.
  • FIG 8 shows in schematic block form a first preferred embodiment of a • logging apparatus in accordance with the present invention, useful for obtaining shear/flexural data at discrete frequencies.
  • acoustic logging sonde 10 is shown suspended by cable 12 in borehole 14 in the earth. Borehole 14 is filled with drilling mud or other fluids (not illustrated).
  • Logging sonde 10 preferably includes dipole transmitting, or source, transducer 16 and a plurality of dipole receiving transducers 20 - 26 arrayed at locations spaced apart from one another and from source transducer 16 along sonde 10. While Figure 8 shows four receiving transducers, more or fewer transducers may be used, although it will be seen from the data processing techniques described below that at least two receiving transducers are preferred.
  • Narrow-band transducer drivers (such as discrete frequency oscillators) 28, 30, 32 and 34, generate sinusoidal signals at one or more discrete frequencies f , f ⁇ f 3 , ... reckon. If multiple discrete frequencies are produced, the signals are then mixed in signal mixer 36. The output signal from mixer 36 is then passed through amplifier 38 to drive source transducer 16.
  • the signals may be continuous, or may be transmitted in brief bursts of sufficient duration (for example, on the order of 10 or 20 cycles per burst) to approximate a continuous wave for purposes of exciting propagation of shear/flexural waves in the borehole at the desired frequency or frequencies.
  • source transducer 16 induces propagation of shear/flexural waves in the earth formation surrounding the borehole at the prescribed frequency or frequencies.
  • the shear/flexural waves are detected at receiving transducers 20 - 26.
  • the signal output from each of receiving transducers 20 - 26 is separated into a respective signal at each of the discrete frequencies of interest (f f 2 , f 3 , ... / classroom) by a plurality of band-pass filters (shown generally at 40).
  • the output signal from each of band-pass filters 40 is supplied to a respective one of lock-in amplifier and phase-detector circuits 42, 44, 46, 48, which detects the amplitude and phase (or real and imaginary pans) of the received waves at a respective one of the selected discrete frequencies /,, f 2 , f 3 , ... / classroom.
  • Each of lock-in amplifier and phase-detector circuits 42, 44, 46, 48 also receives a phase reference signal from a respective one of oscillators 28, 30, 32, 34.
  • the phase reference signals are preferably the signals generated by oscillators 28, 30, 32, 34 for driving source transducer 16.
  • Data detected by lock-in amplifiers 32 is passed to conventional telemetry circuitry 50 for transmission to up-hole system 52 where the data is recorded and/or processed.
  • Oscillators 28, 30, 32, 34, mixer 36, power amplifier 38, band-pass filters 40, lock-in amplifier and phase-detector circuits 42, 44, 46, 48 and telemetry circuitry 50 are preferably built into sonde 10.
  • Telemetry circuitry 50 preferably transmits data output from lock-in amplifiers 36 to up-hole recording and processing system 52 via cable 12 or any other suitable means. Alternatively, the data may be stored in the sonde and retrieved once the sonde has been removed from the borehole.
  • Source transducer 16 may be any type of dipole wave source suitable for
  • Transducer 16 may be made of piezoelectric ceramics made in benders or cylindrical sections, magnetostrictive transducers, or electrodynamic vibrators, or may be of any other suitable construction.
  • the preferred source transducers are moving coil electrodynamic transducers, piezoelectric bimorph benders, or piezoelectric monomorph benders.
  • Source transducer 16 may be driven in any manner suitable for exciting propagation of shear/flexural waves in the formation surrounding the borehole at one or more discrete frequencies, only some of which will be described herein.
  • Receiving transducers 20 - 26 are likewise any type of dipole transducers which detect pressure gradients or panicle vibrations (acceleration, velocity or displacement).
  • the preferred receiver transducers include dual hydrophones, benders, and electrodynamic transducers.
  • the source and receiving transducers should satisfy the usual logging tool specifications on temperature, pressure, maximum diameter, shock and vibration, and mechanical strength.
  • the frequency at which the flexural waves have near shear velocity can be estimated by the following formula:
  • v s is the formation shear velocity and a is the borehole radius. It is preferred that the excitation frequency be kept as low as possible to ensure that the formation shear is measurable.
  • the circumference of the borehole should be larger than a shear wavelength and smaller than twice the shear wavelength. That is. the preferred frequency band is:
  • the frequency range is about 1 kHz to 2 kHz for an 8-inch diameter hole with a 450 ⁇ s/ft shear slowness.
  • the frequency range would be reduced to between 500 Hz and 1 kHz for a 16-inch diameter hole with the same shear slowness.
  • the frequency for dipole shear logging should be lower for larger holes and for formations with slower shear.
  • a typical frequency band is from 500 Hz to 5 kHz, for shear slowness up to 450 ⁇ s/ft and borehole diameter up to 16 inches.
  • Another consideration is the shale alteration, where the formation near the well is substantially softer than the unaltered formation. In this case, the effective size of the borehole is bigger and the frequency range employed should be lower than that used for a simple borehole in a faster formation.
  • cased holes it is preferred to limit the frequency to a frequency lower than that which gives a casing shear wavelength equal to the casing circumference.
  • the preferred frequency / should also be selected such that / ⁇ [(velocity of shear in the steel casing) / (2 ⁇ r x mean casing radius)]. This is a frequency at which the mean circumference of the casing is one wavelength of the shear in the casing steel.
  • sonde housing wave coupling is to reduce the mass of the vibrating element of the source transducer, so that the mass of the vibrating element is small relative to that of the stationary sonde structure. It is also preferred to mechanically isolate the transducers from the rigid sonde housing structure, such as by means of an isolation section.
  • Figure 9 shows in schematic block form a modification of the embodiment of Figure 8 which permits multiple, discrete frequencies to be emitted in sequential bursts for shear/flexural logging in accordance with the invention.
  • a plurality of oscillators for example three oscillators 60, 62 and 64, generate sinusoidal signals at respective frequencies suitable for exciting shear/flexural waves in the borehole, for example at frequencies of 1 KHz, 3 KHz and 5 KHz.
  • Suitable switching means 68 alternately passes multi-cycle bursts of the respective frequencies to power amplifier 38 to drive transducer 16 and to lock- in amplifiers 42 - 48 ( Figure 8) for use as phase references.
  • the multi-cycle bursts are of sufficient length (for example, 10 to 20 cycles) to effectively simulate a continuous signal for purposes of exciting shear/flexural propagation in the borehole at the selected frequencies.
  • the amplitude distribution for the frequencies of interest can be designed by the shape of the waveform of the sequence.
  • the shape of the waveform can be designed such that a desired discrete frequency spectrum is obtained. This may be achieved by first specifying the amplitude distribution for the discrete frequencies, and then by summing the Fourier series of all the discrete frequency terms with the pre-assigned amplitude distribution.
  • Figure 10 shows the amplitude of a periodic signal as a function of time.
  • the Fourier amplitude for each frequency is inversely proportional to f lake.
  • the Fourier spectrum of the signal of Figure 10 is as shown in Figure 11.
  • the Fourier spectrum of the signal preferably has much higher energy in its lower frequency components than in its higher frequency components. This is because the upper frequency boundary for the energy of shear/flexural waves propagating in a borehole is about 5 KHz for boreholes of a diameter typically encountered in oilfield well logging.
  • a low-pass filter can be applied to the periodic signal to eliminate the
  • SUBSTITUTE SHEET harmonics above f ⁇ naz may also be used for exciting discrete frequency signals.
  • Other e.g., square-wave, saw-tooth, specially-designed pulse shape, etc.
  • periodic signals may also be used for exciting discrete frequency signals.
  • Figure 12 shows in schematic block form a modification of the embodiment of Figure 8 which permits multiple, discrete frequencies to be emitted simultaneously for shear-wave logging in accordance with the invention.
  • the output signal from waveform generator 70 is supplied to low-pass filter 72 which passes frequencies / ⁇ f max .
  • the filtered signal is then passed through power amplifier 74 to drive source transducer 16.
  • the emitted sonic energy from source transducer 16 excites shear/flexural wave propagation in the borehole and the shear/flexural waves are received at each of the spaced-apart receiving transducers, only one of which is shown (at 20) in Figure 12.
  • phase-sensitive detector circuit (one of which is shown at 78 in Figure 12) which detects the phase of each frequency component of the filtered signal relative to a respective phase reference signal, as well as the amplitude of each frequency component.
  • the phase reference signals may be obtained from the circuitry which drives source transducer 16.
  • Phase-sensitive detector 78 may be of any suitable analog, digital or hybrid construction.
  • phase and amplitude data for each frequency is passed by suitable means (for example, via telemetry to an up-hole site) from phase- sensitive detector 78 to a processor 80 which makes use of the data for any of a number of purposes, some of which are described below.
  • the upper frequency boundary for the energy of shear/flexural waves propagating in a borehole is about 5 KHz for boreholes of a diameter
  • the discrete frequencies at which shear/flexural waves are to be excited in the borehole preferably includes a number of discrete frequencies up to the upper frequency boundary, for example, 0.5 KHz, 1 KHz, 2 KHz, 3 KHz, 4 KHz and 5 KHz. Spacing of the receiving transducers is not critical, but is preferably such that the length of the receiving transducer anay is not substantially less than the wavelength in order to accurately determine the shear/flexural wave phase velocity.
  • Dipole logging uses dipole transducers which excite and record pressure gradient or particle vibrations.
  • Quadrupole logging uses quadrupole transducers which excite and detect waves with 90-degree asymmetry. As a quadrupole wave travels up the borehole, the borehole vibration will be like squeezing a paper cup in one direction. In the cross-sectional plane, the wall will squeeze in toward the axis in one direction and expand out away from the axis in the perpendicular direction.
  • the quadrupole receivers are designed to sense this kind of vibration.
  • the quadrupole transducers will excite and detect shear/screw waves, rather than the shear/flexural waves of dipole transducers.
  • Shear/flexural wave, shear/screw waves, and other higher-order multipole waves are collectively referred to herein as multipole sonic waves.
  • the frequency selection for quadrupole logging will be different from that for dipole logging.
  • the rule of thumb will be that the circumference of the borehole should be larger than two shear wavelengths and smaller than three shear wavelengths. That is, the preferred frequency band is:
  • V s is the formation shear velocity
  • a is the borehole radius
  • Measuring multipole sonic waves in frequency domain offers several advantages. For example, measurements in frequency domain give higher signal-to-noise ratio than do time domain measurements. This is because the signal-to-noise ratio is inversely proportional to the bandwidth of the signal, and the bandwidth of the signal can be made extremely narrow when working with discrete frequencies. Also, as there is no need to record waveforms, the quantity of data to be transferred up-hole via the telemetry and cable is much less than that for traditional time-domain sonic waveforms. Thus, the logging speed can be increased. Additionally, as there is no need to transform the waveforms from time domain to frequency domain, the processing is simplified.
  • transducer calibration at specific frequencies is more reliable than is transducer calibration for the broad-band time domain sondes. Measurement in the frequency domain, as well as the use of discrete frequencies, are believed to make the methods and apparatus of the present invention more accurate than traditional time-domain sonic logging for obtaining the frequency-dependent information of multipole sonic (e.g., shear/flexural or shear/screw) waves.
  • multipole sonic e.g., shear/flexural or shear/screw
  • the data obtained with the methods and apparatus of the present invention are the complex values of the dipole (or other multipole) signal at each receiver for each frequency. It is well known that a complex value can be expressed in two forms: the amplitude and phase, or the real and imaginary parts. Since the optimal frequency for the multipole tool can vary with formation shear and borehole diameter, it is preferred that waveforms are recorded at more than one frequency. Preferably, the low and high frequency limits are first selected. For example, these may be 100 Hz and 5000 Hz for a dipole tool. Several discrete frequencies are selected between the frequency limits. The data at each frequency is preferably then processed to obtain shear velocity using one of the methods described below. By sorting the frequency-dependent velocity and amplitude data at the selected frequencies, the best choice of formation shear parameters can then be made by cross-checking with the theoretical models.
  • one approach to obtain shear velocity is to select the velocity and amplitude at the lowest possible frequency which has a reasonable signal-to- noise ratio.
  • One way to judge the signal-to-noise ratio is to compare the results with those at other frequencies. Since the velocity as a function of frequency is smooth and predictable by theory, the quality of the signal, or the signal-to- noise ratio is small, when the slowness estimates are out of line from the trend produced at other frequencies.
  • Another way is to check the coherence of the signal across the receiver array. For example, the residual of the least square fitting may be checked in the Prony's method, or the value of beamforming function p(k) of equation (11) below or the likelihood value ] k) of equation (12) below at their optimal value. From the theoretical results of A. KURKJIAN and S. CHANG, Acoustic Multipole Sources in Fluid-Filled Boreholes, 51 GEOPHYSICS 1, January, 1986 (incorporated herein for all purposes by this
  • the low-frequency limit of the shear/flexural or shear/screw velocity is the formation shear velocity.
  • Another approach is to first obtain the velocity as a function of frequency from the borehole measurements, and then search for the formation shear velocity by using curve-fitting methods, such as a least-square method or a generalized linear-inversion method.
  • curve-fitting methods such as a least-square method or a generalized linear-inversion method.
  • the theory has been explicitly shown in A. KURKJIAN and S. CHANG, Acoustic Multipole Sources in Fluid-Filled Boreholes, 51 GEOPHYSICS 1, January, 1986, at 148-163. Explicitly, this procedure is expressed in two wavs:
  • ⁇ is the measured flexural- or screw-wave or other higher-order multipole wave velocity
  • ⁇ is the theoretically- calculated flexural- or screw-wave or other higher-order multipole wave velocity
  • w t - is a weighting function which can be chosen to be one or a function of wave amplitude at the z ' -th frequency.
  • the measurement can be made simultaneously for all the frequency points.
  • the frequency oscillators can be mixed and employed to drive the transmitter simultaneously at all the desired frequencies.
  • Narrow-band filters are applied to the received signals to separate the data at the different frequencies.
  • the detected-signal function can be expressed in the following form:
  • P g is the detected signal (representing pressure gradient or other received quantities such as particle displacement, velocity, acceleration, etc.);
  • A is the amplitude function which is independent of transmitter-receiver spacings;
  • z is the transmitter-receiver spacing; / is the frequency; v is the wave velocity; and a is the attenuation constant.
  • K f ⁇ 1 [ phase(P g ( 2l , f)) - phase(P g (z 2 , f)) ] I l tf (z ⁇ - z z ) (2a)
  • the two receiver method has one constraint; the wave must be traveling in only one direction. If there are significant reflection signals from tool housing structure, bed boundaries, or fractures, then other processing procedures should be used which can include both forward and backward traveling waves.
  • Waves can be reflected, either by the borehole/formation inhomogeneity or by the sonde housing structure. With the shear wave traveling up and down the borehole, the detected-signal function can be expressed as:
  • Equation (3a) Equation (3a)
  • Equations (5a) - (5c) can be reduced to a quadratic equation of G.
  • the solution of the quadratic equation is
  • the wave reflection coefficient can be obtained from the ratio of B' and A' with proper exponential factors.
  • Any of a number of known techniques may be used to process data from an array of receivers, such as: least square method, Prony's method, maximum likelihood method, and others.
  • the total number of receivers in the array is N .
  • the least square method is feasible if the waveforms have only one arrival at the receivers (so that Equation (4) is valid). If there are other arrivals, such as compressional, fluid, tool arrivals and other waves, then special spectral estimation techniques (Prony's method, conventional beam-forming, maximum likelihood method, etc.) are preferred.
  • the wave phase velocity v may be calculated from the expression:
  • the receiver response at a fixed frequency is first assumed to be
  • a linear predictor is defined as h(z) so as to satisfy the relationship
  • the spatial variables P g (z) and h(z) are first truncated to finite intervals of z.
  • the function h(z) is transformed to H(fc).
  • the wave phase velocity and attenuation are then obtained from the m 's according to Equation (3b).
  • the amplitude functions A- n 's can also be estimated by least square fitting. (This is different from the least square method described above.
  • the superscript * means complex conjugate and transpose of the matrix or vector.
  • the values of the wavenumbers k m are obtained by searching the locations of the maxima of p(k).
  • G(k) arid R are in the form described above.
  • the values of k m are obtained by searching for the locations of the local maxima of L(k) . Further * information on the maximum likelihood method may be found in Capon, Greenfield and Kolker, Multidimensional Maximum Likel iood Processing of a Large Aperture Seismic Array, 55 PROCEEDINGS OF THE IEEE, 1967 (incorporated herein for all purposes by this reference), at pages 192-211.
  • SUBSTITUTE SHEET Borehole compensation may be included in the tool or the processing algorithms.
  • One way to achieve borehole compensation is to use two source transducers, one above and the other below the receivers. The two sources are fired sequentially so that one estimate is from the upward-going waves and the other is from the downward-going waves. These two estimates (from the upward- and downward-going waves) are averaged to obtain the borehole- compensated results.
  • Another way to achieve borehole compensation is to use depth-derived borehole- compensation with only one source transducer. This is done by a synthesized array from a sequence of tool locations by picking the appropriate receiver so that the receiver location of the synthesized array is stationary. By estimating the formation quantities from the synthesized array and from the original array data, and by averaging the two estimates at a proper depth location, a borehole-compensated result may be obtained.
  • a further application is to derive the shear velocity profile as a function of radius from the borehole axis in the zone near the borehole from the collection of the dispersion data at discrete frequencies.
  • This can be done in the following way.
  • First, the flexural wave velocity versus frequency is estimated from the multipole logging tool signals and the processing described herein.
  • a theoretical model of acoustic waves in a borehole with radial velocity profile is used to calculate the flexural wave profile (for example, as described below). Then, one searches for the velocity profile until the difference between the measured and calculated (from theory) flexural velocity versus frequency is minimized.
  • the search can be done by curve-fitting methods such as a least square method or a generalized linear inversion method.
  • v n is the measured flexural wave velocity
  • v ⁇ . is the theoretically calculated flexural wave velocity
  • w t is a weighting function which can be chosen to be one or a function of wave amplitude at the z-th frequency.

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Abstract

Une invention concerne des méthodes et appareils portant sur des enregistrements sonores des cisaillement en formation dans les puits de forage grâce à des mesures à fréquence constante. Un transducteur de source multipolaire (16) émet de l'énergie sonore dans un puits de forage (14) sur au moins une fréquence constante qui induit la propagation d'ondes sonores multipolaires dans ce puits. L'énergie sonore des ondes sonores multipolaires est détectée en de multiples points situés dans le puits de forage par des récepteurs multipolaires (20, 22, 24, 26) et produit un signal sonore pour chaque point dont chacun est éloigné des autres ainsi que du transducteur de source (16). A chaque point de réception, on compare les valeurs complexes du signal sonore reçu à une référence de phase prédéterminée puis on peut les traiter pour calculer la vitesse des ondes sonores multipolaires et l'affaiblissement dû au cisaillement à des fréquences constantes et pour calculer la vitesse et l'atténuation en fonction de la fréquence.
PCT/US1991/007493 1991-10-11 1991-10-11 Methodes et appareils concernant des enregistrements sonores multipolaires a frequence constante WO1993007512A1 (fr)

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Cited By (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2000019242A3 (fr) * 1998-09-25 2000-10-05 Dresser Ind Transducteur et montage de celui-ci dans un appareil de diagraphie acoustique
US6366531B1 (en) 1998-09-22 2002-04-02 Dresser Industries, Inc. Method and apparatus for acoustic logging
US6564899B1 (en) 1998-09-24 2003-05-20 Dresser Industries, Inc. Method and apparatus for absorbing acoustic energy
FR3057978A1 (fr) * 2016-10-25 2018-04-27 Halliburton Energy Services, Inc. Determination avec une meilleure resolution de la lenteur d'ondes de volume dans une formation rocheuse a partir d'ondes guidees de trou de forage
CN108594294A (zh) * 2018-04-26 2018-09-28 河北中核岩土工程有限责任公司 孔内稳态激振剪切波测试系统及方法
US20210389487A1 (en) * 2015-10-27 2021-12-16 Schlumberger Technology Corporation Determining shear slowness from dipole source-based measurements acquired by a logging while drilling acoustic measurement tool

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US4594662A (en) * 1982-11-12 1986-06-10 Schlumberger Technology Corporation Diffraction tomography systems and methods with fixed detector arrays
US4698792A (en) * 1984-12-28 1987-10-06 Schlumberger Technology Corporation Method and apparatus for acoustic dipole shear wave well logging
US4703460A (en) * 1984-12-28 1987-10-27 Schlumberger Technology Corporation Method and apparatus for acoustic dipole direct shear wave well logging

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Cited By (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US6366531B1 (en) 1998-09-22 2002-04-02 Dresser Industries, Inc. Method and apparatus for acoustic logging
US6564899B1 (en) 1998-09-24 2003-05-20 Dresser Industries, Inc. Method and apparatus for absorbing acoustic energy
WO2000019242A3 (fr) * 1998-09-25 2000-10-05 Dresser Ind Transducteur et montage de celui-ci dans un appareil de diagraphie acoustique
US6213250B1 (en) 1998-09-25 2001-04-10 Dresser Industries, Inc. Transducer for acoustic logging
US20210389487A1 (en) * 2015-10-27 2021-12-16 Schlumberger Technology Corporation Determining shear slowness from dipole source-based measurements acquired by a logging while drilling acoustic measurement tool
FR3057978A1 (fr) * 2016-10-25 2018-04-27 Halliburton Energy Services, Inc. Determination avec une meilleure resolution de la lenteur d'ondes de volume dans une formation rocheuse a partir d'ondes guidees de trou de forage
CN108594294A (zh) * 2018-04-26 2018-09-28 河北中核岩土工程有限责任公司 孔内稳态激振剪切波测试系统及方法

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