GB2295014A - Acoustic logging - Google Patents

Abstract

A method of separating a predetermined wave propagation mode from signals generated by an acoustic array well logging tool is disclosed. Receiver signals from the tool are digitized (40) and converted to a 2-dimensional (2-D) array. The 2-D array is converted (46) to an (f,k) array by a 2-D Fourier transform. The (f,k) array is velocity bandpass filtered (48) to separate the predetermined propagation mode. The filtered (f,k) array is converted back (50) to the time-position domain by applying an inverse 2-D Fourier transform. In a particular embodiment of the invention, the filtered time-domain data are semblance correlated to determine an acoustic velocity in the predetermined propagation mode in an earth formation. <IMAGE>

Description

ACOUSTIC LOGGING The present invention relates to the field of wireline wellbore logging and concerns, more specifically, a method of processing data from a plurality of acoustic sensors in a wireline tool. Such processing is applicable to determining acoustic wave transmission properties in an earth formation penetrated by a wellbore.

Electric wireline logging tools include various types of acoustic logging instruments. Acoustic logging instruments are used, among other things, for determining the velocities at which acoustic waves propagate through earth formations. Acoustic waves can propagate through a particular earth formation at several different velocities depending on the mode of propagation of the acoustic waves.

Two acoustic wave propagation modes of particular interest in the evaluation of earth formations are compressional and shear. Compressional propagation takes the form of alternate compressions and rarefactions of the formation. The direction of propagation of compressional waves is in the same plane as the motion of the particles of the formation. Shear wave propagation comprises particle motion occurring at right angles to the direction of propagation. Shear waves typically cannot travel through fluids.

Measurement of shear velocities by typical well logging tools requires a conversion of the wave propagation mode of acoustic energy emitted by the tool into shear waves in the formation. Shear waves can be generated at the wellbore wall, for example, when compressional energy strikes the wall.

Acoustic logging tools typically include acoustic energy sources and receivers combined in a single instrument. An acoustic measurement is made first by activating the source so that acoustic energy radiates into the wellbore, refracts at the wellbore wall so that it propagates along the wellbore wall, and then re-refracts into the wellbore so that the acoustic energy can be detected by at least one receiver disposed in the instrument. Refraction of the energy so that it travels along the wellbore wall is a result of typical acoustic velocity contrasts between the formation and fluid filling the wellbore.

Acoustic logging instruments include monopole devices which have acoustic energy sources, or transmitters, that approximate a point source of energy, meaning that acoustic energy radiates away from the transmitter substantially as if the energy came from a single point. Monopole devices are used for determining the velocities of acoustic waves which propagate in certain specific propagation modes such as compressional and Stoneley modes. In earth formations having shear wave velocities exceeding the compressional velocity of the fluid in the wellbore, monopole devices can also be used to measure the velocity of shear wave propagation because the shear waves will also refract so as to propagate along the wellbore wall.

Dipole instruments determine velocities of acoustic waves propagating in a flexural mode and can be used to determine shear wave velocities when the earth formation has a shear wave velocity lower than the compressional velocity of the fluid filling the wellbore. In such a case compressional energy from a monopole transmitter, which converts to shear energy at the wellbore wall, usually cannot be detected by the receivers in the instrument because the shear waves are refracted out into the formation rather than along the wellbore wall. In order to overcome this limitation, the transmitter in a dipole instrument usually comprises a "bender bar" or similar type transmitter which creates undulations in the fluid in the wellbore.

Undulations can be described as a transverse motion of the particles in a material being energized, in which a portion of the material moves in one direction and another portion of the material displaced along a central axis of the bender bar moves in the opposite direction. The particle motion is perpendicular to the direction of wave propagation, as it is with shear wave propagation. The undulations in the wellbore fluid generate similar undulations in the wall of the wellbore, which propagate along the wellbore wall substantially at the shear velocity of the formation.

Monopole and dipole instruments can be combined in a single tool. For example, "The Multipole Array Acoustilog", Atlas Wireline Services, Houston, TX, 1991, describes a combination monopole/dipole tool.

Typically, the combination tool comprises at least one monopole transmitter, at least one dipole transmitter, and a plurality of receivers at spaced apart locations along a tool housing. The transmitters, receivers and housing can be designed to minimize detection of waves propagating in unwanted modes during a measurement cycle for a particular wave propagation mode. For example, "The Multipole Array Acoustilog" tool comprises dipole receivers which are highly sensitive to the undulations, or flexural, waves but tend to reject detection of waves transmitted through the wellbore fluid as monopole compressions; the tool also comprises monopole receivers which are highly sensitive to compressional waves.

The dipole receivers are designed to generate a large output signal, only in response to flexural waves because residual components of waves propagating in monopole type modes can be time coincident at the receivers with the flexural waves. Dipole receiver insensitivity to the monopole wave components reduces the amplitudes of the monopole wave components in the dipole receiver output. It is therefore easier to make measurements from the flexural waves.

Velocity of wave propagation is typically determined by calculating the amount of time elapsed between corresponding detections of a wave by each receiver in a plurality of receivers at spaced apart locations along the instrument. The distance between each of the receivers is known, so the velocity can be calculated directly from the elapsed time determined between detections of the wave at the corresponding receivers.

The time difference between detections at corresponding receivers can be determined by a method known as semblance correlation. The output of each receiver resulting from the detection of a wave typically comprises an electrical signal representing acoustic amplitude. The signal can be digitized into a series of numbers which represent samples of the signal taken at spaced apart time intervals. The digitizing can be done either by circuits in the instrument or by equipment located at the earth's surface. The samples can then be processed by equipment typically located at the earth's surface. A time window can be chosen by the tool operator, typically by visually examining a graphic representation of the signals to determine a time span during which the signal appears to have sufficient amplitude. Within the chosen time window, the signal from each receiver is then correlated with signals from the other receivers and the time difference between signals which yields the highest correlation value, or degree of correspondence, is determined to be the time difference between wave detection at each receiver. The time difference is used to calculate the velocity directly since the distance between receivers is known.

Semblance correlation processing can be difficult because acoustic wave propagation modes other than compressional and flexural occur in the wellbore as a result of excitation of the wellbore wall by the energy radiated from the transmitters. These other propagation modes may create waves which interfere with identification of the desired wave mode in the receiver signal. For example, propagation modes such as Stoneley waves and pseudo-Rayleigh waves propagate within a wellbore along the interface between the liquid filling the wellbore and the wellbore wall.

"Vertical Seismic Profiling", by Bob A. Hardage, Geophysical Press, London, 1985, describes the Stoneley and pseudo-Rayleigh propagation modes (pp. 75-76). The interference created by Stoneley and pseudo-Rayleigh waves can be particularly difficult to resolve if the Stoneley and pseudo-Rayleigh waves have very high amplitudes or if parts of the Stoneley and pseudo-Rayleigh waves are time coincident with the flexural or compressional waves.

It is possible to separate different wave propagation mode waves by using frequency bandpass filters. For example, the Stoneley wave components which can be present in a monopole receiver signal typically have a high amplitude in a much lower frequency range than compressional waves occurring in the same signal. Application of a high-pass filter to the receiver signal can attenuate the Stoneley wave component of the receiver signal.

Frequency bandpass filtering reduces the bandwidth of the isolated mode signal, which can make the data from the isolated mode signal less useful, particularly if the earth formation is dispersive, that is the formation has velocities which are frequency dependent.

Frequency bandpass filtering is also relatively ineffective if there is substantial frequency coincidence between the desired wave mode and the unwanted wave mode. Frequency coincidence typically occurs in dipole receiver signals, where the flexural and Stoneley waves can have substantial overlap in their respective frequency contents.

The (f,k) filter can sometimes be used in geophysical exploration for processing vertical seismic profile (VSP) surveys and for processing surface seismic surveys. The (f,k) filter can be used to remove acoustic energy propagating in an undesired direction. For example, in a VSP survey so-called upgoing waves, which reflect from seismic events deeper than a borehole geophone deployed in the wellbore, can be separated from so-called downgoing waves, which reach the borehole geophone directly through the earth from a seismic source at the earth's surface, by use of the (f, k) filter. The (f,k) filter can also be used in surface seismic surveys to attenuate multiple reflections caused by seismic reflectors near the earth's surface, or by the water surface in a marine seismic survey.For example, "Vertical Seismic Profiling" (pp 174-181) describes the process of (f,k) filtering as related to VSP data.

The (f,k) filter is difficult to use on seismic data, however, because transformation of data in the time-position domain, which is how the seismic or VSP data are recorded, into the frequency-wavenumber (or f,k) domain requires uniformly spaced data samples in both time and position for the filter to work without distorting the results. Control of the interval between sample depths in VSP data or of the geophone locations in surface seismic data can be inadequate to prevent distortions of the data on transformation to the (f,k) domain. Consequently, (f,k) filtering has generally been replaced in the art by other methods.

For example, "Seismic Data Processing", by Ozdogan Yilmaz, Society of Exploration Geophysicists, Tulsa, 1987, (pp. 68-73,79) describes the limitations of (f,k) filtering.

Various aspects of the present invention are exemplified by the attached claims. Another aspect of the present invention is a method of separating a component of an acoustic wave propagating in a predetermined mode from data recorded by a wireline acoustic array logging tool wherein the data from a plurality of spaced-apart receivers in the acoustic logging tool are converted from time-domain waveforms by a 2-dimensional Fourier transform into data in the frequency-wavenumber, or (f,k) domain, a velocity bandpass filter is applied to the (f,k) converted data, and the filtered data are reconverted to the time domain.

In one embodiment of the invention, the velocity filtered time domain data are semblance correlated to determine the time difference between detections of the component of the wave propagating in the predetermined mode at corresponding receivers. Values of compressional and flexural velocity can be calculated from the time differences so determined.

For a better understanding of the invention, and to show how the same may be carried into effect, reference will now be made, by way of example, to the accompanying drawings, in which: Figure 1 shows an acoustic array logging tool disposed within a wellbore; Figure 2 shows a graphic representation of signals generated by receivers in the tool of Fig. 1; Figure 3 shows the placement of transmitters and receivers on the tool of Fig 1 in more detail; Figure 4 shows a flow chart of the processing steps performed on receiver signals of the tool of Fig 1; Figure 5 shows a graphic display of signals from the plurality of receivers before filtering; Figure 6 shows a graphic representation of a combined correlogram generated from the receiver signals before filtering; Figure 7 is a graphic representation of the amplitude of the signals in Figure 5 after conversion to the f,k domain;; Figure 8 is a contour graph of the same data as shown in Figure 7, the contour graph also having boundaries of a velocity filter to be applied according to one embodiment; Figure 9 shows the data as presented in Figure 7 after application of the velocity filter of Figure 8; Figure 10 shows the data as displayed in Figure 8 after application of the velocity filter; Figure 11 shows the filtered data of Figure 10 after application of an inverse 2-D Fast Fourier transform; and Figure 12 shows a graphic representation of a combined correlogram generated from the filtered data shown in Figure 11.

Figure 1 is a simplified illustration of an acoustic array well logging tool 2 showing how the tool 2 is typically used in a wellbore 10 penetrating an earth formation 12. The tool 2 comprises at least one transmitter 14 and a plurality of receivers 16 positioned at equally spaced apart locations along the tool 10. The tool 2 is lowered into the wellbore 10 by means of a cable 8 comprising at least one insulated electrical conductor (not shown). The cable 8 is lowered into the wellbore 10 by means of a surface logging unit 4. The surface unit 4 typically comprises winch equipment 4A for moving the cable 8 into and out of the wellbore 10, and a computer 4B for receiving and processing signals (not shown) transmitted by the tool 2 to the computer 4B along the cable 8.

Periodically the at least one transmitter 14 is energized to emit acoustic energy pulses 18 which travel through a fluid 6 filling the wellbore 10 until they reach the wall of the wellbore 10. The pulses 18 then interact with the wall of wellbore 10.

Interaction of the acoustic energy pulses 18 with the wall of the wellbore 10 causes modified acoustic energy waves to travel along the wall of the wellbore 10, and eventually enables the modified acoustic waves 18 to reach the receivers 16 in the tool 2. The receivers 16 generate electrical signals (not shown) which correspond to the amplitude of the further modified acoustic pulses 18 which reach each of the receivers 16.

Information about acoustic properties of the earth formation 12 can be determined by processing the signals generated by the receivers 16 in the computer 4B, as will be explained in more detail.

A graphic representation of the signals generated by the receivers 16 is shown in Figure 2. The graph in Figure 2 has time on the coordinate axis and signal amplitude corresponding to each waveform 20 on the ordinate axis. Signals from each of the receivers 16 are shown as individual waveforms 20. Each waveform 20 corresponds to one of the receivers 16. The waveforms 20 can include an indication of the time of activation of the transmitter (shown in Figure 1 as 14) as shown generally at 22. The waveforms 20 are also typically characterized by a time interval, shown generally at 24, having low signal level which occurs prior to detection of acoustic energy arriving from the wellbore 10 wall. Acoustic energy which arrives at the receivers 16 from the wellbore 10 wall is generally shown at 26.Characteristics of the signals resulting from detection of the acoustic energy, as shown at 26, depend on the type of energy imparted by the transmitter 14, the type of receiver (shown as 16 in Figure 1), and the acoustic transmission properties of the earth formation (shown as 12 in Figure 1).

Figure 3 shows the configuration of the tool 2 in greater detail. The upper part of the tool 2 comprises at least one monopole transmitter 32 and at least one dipole transmitter 34. The monopole transmitter 32 emits pulses of acoustic energy (shown as 18 in Figure 1) which interact with the fluid 6 filling the wellbore 10 substantially as a point source of energy. Acoustic waves emanating from the monopole transmitter 32 consist of substantially spherically radiating compressions and rarefactions of the fluid 6 in the wellbore 10. The dipole transmitter 34 comprises a bender bar having two active ends 35 and 37. The dipole transmitter 34 generates acoustic waves (also shown as 18 in Figure 1) which interact with the fluid 6 filling the wellbore 10 in the form undulations of the fluid 6.The undulations comprise back-and forth motion along a substantially straight-line path having a wavelength roughly equal to the distance separating the ends 35 and 37 of the dipole transmitter 34. The undulations in the fluid 6 interact with the wall of the wellbore 10 to generate similar undulations in the wall of the wellbore 10. The undulations imparted to the wellbore 10 wall travel along the wellbore 10 wall substantially at the shear velocity of the earth formation 12.

Direct coupling of acoustic energy from the transmitters 32 and 34 to receivers 31 and 33 located near the bottom of the tool 2 is substantially reduced by an acoustic isolator 38 interposed between the transmitters 32 and 34 and receivers 31 and 33.

The tool 2 typically comprises two types of receivers as shown at 31 and 33. One type of receiver is a monopole receiver as shown at 33. The monopole receivers 33 respond to compressions and rarefactions of the fluid 6 in the wellbore 10 which strike the receivers 33 from all directions simultaneously. Wave propagation modes which can be detected by the monopole receivers 33 include compressional mode, refracted shear mode generated by interaction of the wellbore 10 wall with compressional energy from the monopole transmitter 32, and Stoneley mode. Dipole receivers, shown at 31, are responsive to unidirectional motion of the fluid 6 in the wellbore, and therefore are particularly sensitive to the undulations travelling along the wall of the wellbore 10 which are induced by the dipole transmitter 34.The dipole transmitter 34 and receivers 31 are typically used to measure flexural and shear velocity, particularly when the flexural velocity of the formation 12 is slower than the compressional velocity of the fluid 6 in the wellbore so that making refractive shear velocity measurements would be impossible. The dipole receivers 31 are relatively insensitive to omnidirectional pressure variations in the fluid 6, and therefore substantially reject detection of compressional waves in the fluid 6 in the wellbore 10. The dipole receivers 31 do not entirely reject detection of compressional energy, as will be further explained.

In Figure 5, waveforms 61 to 68 from the dipole receivers (shown as 31 in Figure 3) exhibit both flexural components 81 to 88 and residual compressional components 71 to 78 prior to processing by a method according to one embodiment. In the waveform representing the receiver 31 most distant from the transmitter 34, as shown at 68, the residual compressional component 78 does not interfere with the flexural component 88, principally because of the relatively low flexural velocity and the long distance between the transmitter 34 and that particular receiver 31. Substantial interference between flexu > I 81 and compressional 71 components occurs in the waveform 61 representing the receiver 31 nearest the transmitter 34 because of the much shorter transmitter to receiver distance. Varying amounts of interference occurs in the other waveforms 62 to 67.

A combined correlogram curve generated from the waveforms 61 to 68 of Figure 5 is shown in Figure 6 at 90. The curve 90 indicates the degree of correspondence between the waveforms 61 to 68 at various values of time delay between individual receivers 31, the time delay corresponding inversely to acoustic velocity in the formation 12.

Because residual compressional components 71 to 78 are present in the waveforms 61 to 68, the correlation curve 90 exhibits velocity peaks at 91 and 92. In certain cases the peaks can be substantially coincident in velocity or can have reversed relative amplitudes, making flexural velocity determination difficult.

Figure 4 shows the process steps of a possible embodiment in more detail. Receiver signals 39 are digitized as shown at 40. The signals 39 are typically digitized in the tool 2, to give uniformly spaced samples in both time and position, and transmitted to the surface unit 4 for storage in a buffer.

Processing steps following digitization of the signals typically take place in the computer 4B forming part of the surface unit.

The digitized signals are then processed to equalize signal amplitudes between receivers 31 by normalizing the signals as shown at 42. As shown at 44, transmitter to receiver distances for each receiver signal, identified by the variable z, are assigned to each normalized signal. Alternatively the value of z for a selected receiver can be set to zero and all other receivers can have z values assigned corresponding to the individual receiver distances from the selected receiver.

The z values assigned at 44 are used for conversion of the time-distance domain signals into the (f,k) domain by a 2-D fast Fourier transform, as shown at 46. The (f,k) signals can be displayed graphically as shown at 48 to assist an operator, if desired, to select a velocity filter to exclude components of the signals which may be propagating in an undesired mode.

An example of the graphic display step 48 can be observed by referring to Figure 8. Optionally, the step of applying the velocity filter as shown at 48 can be automated. At this point in the process, the velocity filtered signals typically have only components propagating in the predetermined mode.

Referring back to Figure 4, the filtered signals are then converted back to the time-distance domain by application of an inverse 2-D fast Fourier transform as shown at 50. At 52, the filtered time domain signals can be stored in a buffer for later processing. If all wellbore 10 depth levels at which signals were recorded have been processed, as shown at 54, the process is complete. Otherwise, the next depth level is selected and the process is repeated.

Referring again to Figure 5, the waveforms 61 to 68 corresponding to the signals generated by the dipole receivers (shown as 31 in Figure 3) before processing by the method described can be observed. Each of the waveforms 61 to 68 displays residual compressional components 71 to 78, some of which are at least partially time correspondent with the flexural components 81 to 88. It can be observed in Figure 5 that the flexural components 81 to 88 appear to vary in amplitude and detection time between individual waveforms due to differing times of interference from the compressional components 71 to 78.

Referring again to Figure 6, the combined correlogram of the receiver signal waveforms 61 to 68 shown in Figure 5 is displayed. It can be observed that the residual compressional components 71 to 78 in the waveforms 61 to 68 cause a relative maximum correspondence value 92 to occur at a velocity which can be unrepresentative of flexural velocity in the earth formation 12. A second, higher amplitude, maximum as shown at 91 represents the flexural velocity. In certain cases the relative maximum shown at 92 can have a higher amplitude than the relative maximum shown at 91, which can cause erroneous calculation of flexural velocity.

Figure 7 shows a Z-axis contour surface of the waveforms of Figure 5 after conversion to the f,k domain by application of a 2-D Fast Fourier transform.

Many relative maxima, as shown generally at 94, can be observed. Each of these relative maxima 94 corresponds to a different value of propagation velocity. Residual compressional components present in the waveforms can be observed as a relative peak at 95.

The Z-axis contour surface in Figure 7 can be better understood as related to the present method by referring to Figure 8. In Figure 8 amplitudes are represented as a series of contours, shown generally at 96. A velocity bandpass filter is chosen by the operator or automatically so that the filter has a lower velocity limit, shown as a first line 98, and an upper velocity limit, shown as a second line 100, corresponding to maximum and minimum expected values of velocity for the predetermined propagation mode desired to be isolated from the waveforms (shown as 61 to 68 in Figure 5). Components of the signals having velocities outside the boundaries of the velocity bandpass filter limits 98 and 100 will be removed from the signal.The step of selecting the first and second lines 98 and 100 automatically in the surface computer (shown as 4B in Figure 1) can, in one example, be achieved by preselecting maximum and minimum expected values of velocity. A frequency bandpass filter may also be applied, shown as a vertical third line at 97A, if the operator determines that high frequency components of the signals will be passed by the velocity filter. For example, residual high frequency components exhibiting a contour peak at 97A will be filtered out by the frequency bandpass filter. Low frequency, low velocity, components such as those exhibiting a peak at 97B would not be removed by the frequency bandpass filter, but will be removed by the velocity filter.

A resulting velocity bandpass filtered spectrum can be observed by referring to Figure 9 and Figure 10.

Figure 9 shows the spectrum shown in Figure 7 after application of the velocity bandpass filter. Figure 10 shows the filtered spectrum displayed in contour form, corresponding to the display of unfiltered signals shown in Figure 8. In both Figure 9 and Figure 10, all but one of the relative maxima (shown as 94 in Figure 8), as shown at 94A in Figure 9 and 94B in Figure 10, have been removed from the signals.

After the velocity filter is applied to the signals, the signals are returned to the time-distance domain by application of an inverse 2-D Fast Fourier transform. The resulting velocity filtered waveforms are shown as 101 to 108 in Figure 11. The velocity filtered waveforms 101 to 108 show a substantial reduction in variation of amplitude and appearance of the flexural components 111 to 118 compared with the flexural components, shown as 81 to 88, of the waveforms 61 to 68 shown in Figure 5.

A combined correlogram computed from the velocity filtered waveforms is shown in Figure 12 at 119. The curve 119 displays only one distinct maximum, shown at 120, which occurs at the flexural velocity. The effect of residual compressional components in the curve 119 from the unfiltered waveforms, as shown at 92 in Figure 6, has been substantially eliminated from the curve 119 of Figure 12. The elimination of the effects of residual compressional components from the curve 119 reduces the possibility of erroneous calculation of flexural velocity.

The steps described in Figures 5 through 12 to process signals from the plurality of receivers can be repeated at a plurality of depths within the wellbore 10 in order to determine velocities of earth formations at the plurality of depths within the wellbore 10.

Finally it will be seen that the method can be applied to extract components in a variety of different modes, e.g. a flexural mode, a stonely mode or a psuedo-rayleigh mode.

Claims (13)

1. A method of processing data recorded by a wireline acoustic array logging tool having a transmitter and a plurality of receivers at spaced-apart locations along said tool, the data comprising data sets from respective receivers in the time-distance domain, the method comprising: applying a 2-dimensional Fourier transform to said sets to convert said data from the time-distance domain into a frequency-wavenumber domain; applying a velocity bandpass filter to said data in said frequency-wavenumber domain; and reconverting said data to said time-distance domain by applying an inverse 2-dimensional Fourier transform, thus to separate from the recorded data a component propagating in a predetermined mode.

2. A method according to claim 1 and comprising digitizing the data generated by the plurality of receivers to generate a first plurality of number series representing acoustic amplitudes at respective receivers sampled at spaced apart time intervals, and arranging the first plurality of number series to represent a first two-dimensional array having coordinates one representing times of each corresponding number in each of the plurality of number series, and the other representing a distance from the at least one transmitter to each corresponding receiver in the plurality of receivers.

3. A method according to claim 2, wherein the reconverting comprises generating a second plurality of number series, representing signal amplitudes of the predetermined mode sampled at spaced apart time intervals, by applying the two-dimensional inverse Fourier transform to the velocity filtered array, the second plurality of number series corresponding to respective receivers located at the same distance from the at least one transmitter as the corresponding receiver of the first plurality of numbers.

4. A method according to claim 1, 2 or 3, the velocity filter having an upper velocity limit and a lower velocity limit corresponding to a maximum and a minimum velocity of the predetermined propagation mode.

5. A method according to any one of the preceding claims wherein the at least one acoustic transmitter is a monopole transmitter.

6. A method according to any one of claims 1 to 4 wherein the at least one transmitter is a dipole transmitter.

7. A method according to any one of the preceding claims wherein the predetermined mode is a flexural mode.

8. A method according to any one of claims 1 to 6 wherein the predetermined mode is a stoneley mode

9. A method according to any one of claims 1 to 6 wherein the predetermined mode is a pseudo-rayleigh mode.

10. A method according to any one of the preceding claims comprising the step of applying a frequency bandpass filter to said data.

11. A method according to claim 10, wherein the frequency bandpass filter is applied in the frequencywavenumber domain.

12. A method of determining a velocity of an acoustic wave propagating in a predetermined mode through an earth formation by using a method according to any one of the preceding claims comprising comparing each of the sets of reconverted data to at least one other of the sets of the reconverted data by calculating a degree of correspondence at a plurality of time differences between the sets being compared, determining the time difference at which the degree of correspondence reaches a maximum, and calculating the velocity from the time difference at which the degree of correspondence reaches a maximum and the distance between the receivers with which corresponding data sets are used to determine the degree of correspondence.

13. A method of separating a signal component substantially as hereinbefore described with reference to the accompanying drawings.