HARNESSING THE GHOST

S. Norman Domenico
Tulsa

A previous field experiment demonstrated that the interface between an air-water mixture of very low fractional air volume (say, 0.005) and air-free water is a very effective reflector of acoustic waves, suggesting that acoustic waves in water might be beamed downward by placing the energy source at the focus of a paraboloidic interface. When this interface is concave downward, wave energy traveling upward and outward from the source at the focus is reflected (beamed) downward, and the surface reflection (ghost) is eliminated. Accordingly, a paraboloid reflector consisting of perforated circular air pipes was constructed and tested with a small water gun at its focus. The structure, suspended from its apex, had a height of 4 ft (1.2 m), a base diameter of 8 ft (2.4 m), and a focus 1 ft (0.3 m) below the apex.

The wave field with an air-bubble stream emanating from the perforated pipes, constructed by contouring the maximum amplitude of hydrophone signals, displays a beam with a nearly constant half width of 22 ft (6.7 m). Signal amplitudes directly below the paraboloid on an extension of its axis are as much as 9 dB above, and off-axis amplitudes are as much as 17 dB below, signal amplitudes for no air-bubble stream. The ghost is not evident, the characteristic precursor of the water-gun signal is diminished greatly, and the dominant frequency is approximately 1200 Hz. Comparison with theoretical monofrequency wave fields indicates that the experimental horizontal beam profile 20 ft (6.1 m) below the source approaches that of a 1000-Hz monofrequency signal; at 60 ft (18.3 m) below, that of a 2000-Hz monofrequency signal; and at 100 ft (30.5 m) below, that of a monofrequency signal substantially below 2000 Hz.

A potential application of the paraboloid reflector is in marine vertical seismic profiling (VSP) for which well seismometer signals from an energy source within the reflector would be enhanced by elimination of the source ghost signal, of water-layer multiple reflections resulting from the ghost signal, and of bore-hole waves caused by the direct source wave striking the riser pipe. Another potential application is in shallow-water seismic surveys for which the recording cable and source are stationary during each recording. Reflection resolution and penetration should be improved substantially.

The effect of gas bubbles in a liquid on acoustic (pressure) waves propagating through the mixture has been studied extensively (e.g., Silberman, 1957; Cartensen and Foddy, 1947; Fox, et al., 1955; Macpherson, 1957). It is well known that a small fractional volume (say, 0.005) of gaseous bubbles in a liquid reduces acoustic wave velocity and increases attenuation several fold from values to a gas-free liquid. A previous field experiment (Domenico, 1982).

Norshir Inc., Tulsa, demonstrated the effect of closely and uniformly-spaced, parallel air-bubble curtains on acoustic waves propagating normally through the curtains. The reflection coefficient at the interface between the air-bubble curtain and the adjoining air-free corridor was - 0.82 when the pressure of air issuing from the compressed-air source was 50 psi (3.45-105 Pa).

The high reflectivity of the air-bubble curtain/water interface suggested that air-bubble curtains might be used effectively to concentrate and beam an acoustic wave from an underwater source. A device for beaming an acoustic wave by generation of an air-bubble curtain is illustrated in Fig. 1 and is described in more detail elsewhere (Domenico, 1986a). A paraboloid, shown in vertical cross-section with the base downward, is formed by a series of circular, horizontal, perforated air pipes. Horizontal spacing of the pipes is uniform; thereby, providing a uniform fractional air volume in the overall air-bubble stream emanating from the pipes. The acoustic-wave source, of course, is placed at the paraboloid focus. As indicated in Fig. 1 by the raypaths, a portion of the acoustic wave is reflected vertically downward by the paraboloidic interface between the air-water mixture above and air-free water below. Traveltimes along all reflected raypaths from the source to the paraboloid base are equal, resulting in a plane circular wavefront. The portion of the acoustic wave penetrating into the air-bubble stream above the paraboloid is attenuated quickly. In effect, the water surface reflection (ghost) is eliminated and a large portion of the acoustic-wave energy is beamed downward. The effectiveness of this device, which is called a paraboloid reflector, is a function of its size; the greater the vertical distance between the apex and focus and the greater the height, the larger the horizontal extent of the vertically beamed acoustic wave. The concentration of the acoustic energy into a beam is, of course, frequency dependent.

In this paper a field experiment of the paraboloid reflector is described, followed by a brief discussion of experiment results and a comparison of these with theoretical results.

EXPERIMENT DESCRIPTION

A photograph of the prototype paraboloid pipe structure tested in a field experiment is shown in Fig. 2. The device consisted of 22 horizontal, circular, and the perforated air pipes at a horizontal spacing of 2 in. (5.1 cm). Pipe diameters varied from 8 ft (2.4 m) at the base to 0.8 ft (0-2 m) at the top. Air was supplied to these pipes through 8 radial pipes. Height is 4 ft (1.2 m) and the focus is 1 ft (0.3 m) below the apex.

The source was a water gun that created an acoustic wave by abruptly ejecting water from a 15-cu.-in. (97-cu.cm) chamber by an air-driven piston. Unlike the commonly used airgun, the water gun does not create additional source waves by repeated expansions and contractions of an air bubble.

Detectors were Geospace MP-4 hydrophones, each containing four piezoelectric crystals. The recorder was a 12-channel, digital, high-resolution system. Recordings were made with a sample interval of 0.25 msec.

The experiment was conducted in Loche Linnhe, one of the deep-water loches along the Great Glen Fault in Scotland. The paraboloid focus (source position) was placed at a depth of 40 ft (12.2 m) and recordings were made of signals from a vertical hydrophone array extending from 30 ft (9.1 m) above to 140 ft (42.7 m) below the source. The array was positioned successively on one side of the source at horizontal distances from the source of 0 to 50 ft (15.2 m) at 10-ft (3.0-m) intervals. Origin of the horizontal x and vertical z coordinates was at the source. Recordings were made at each array position with and without the paraboloid reflector; that is, with and without the air-bubble curtain above the paraboloid.

EXPERIMENT RESULTS

Signals recorded from 10 hydrophones in a vertical array, suspended 20 ft (6.1 m) horizontally from the source, are displayed in Fig. 3. These were recorded for each of three source conditions; namely, (a) water gun only (i.e., with the paraboloid pipe structure removed), lb) water gun mounted inside the paraboloid pipe structure with no air flow (i.e., no air-bubble stream and, accordingly, no reflector), and (c) water gun with the paraboloid reflector. Signal amplitudes are normalized; that is, maximum signal amplitudes have been equalized. The surface reflection (ghost) is prominent in Figs. 3a and b and is imperceptible in Fig 3c. Thus, the paraboloid reflector effectively eliminates the surface reflection. However, signals in Fig. 3b differ moderately from those in Fig. 3a, indicating that the paraboloid pipe structure without the air-bubble stream modifies the source signal. Specifically, the direct signal becomes increasingly oscillatory with increasing distance below the source. In Fig. 4c, signals recorded at and above the source depth [z=3, -10, and -30 ft (0.9, -3.0, and -9.1 m)] are distorted severely. In addition to absence of the ghost, signals from hydrophones below the source depth are modified further by the paraboloid reflector. The precursor, which is characteristic of water-gun signals and is prominent in Figs. 3a and b, is diminished by the paraboloid reflector. Also, additional cycles of nearly equal periods have developed, indicating a concentration of energy at the frequency of the dominant spectral component, about 1200 Hz.

After correction for variations in hydrophone sensitivity and source signal level, amplitude of the first positive peak on signals recorded with the paraboloid reflector were contoured as shown in Fig. 4a. Hydrophone positions are indicated by dots. Signals from hydrophones above the paraboloid reflector are severely attenuated and distorted; thus, these could not be used. Contour values are in dB below the amplitude of the signal from the hydrophone 3 ft (0.9 m) vertically below the source. Beaming effect of the paraboloid reflector is obvious. A trough (amplitude minimum) occurs that approximately parallels the paraboloid axis (z-axis) at a horizontal distance of about 22 ft from the source. In Fig. 4b, the ratio of the signal amplitude with the paraboloid reflector to that without the air-bubble stream, expressed in dB, is contoured. The ratio varies from a maximum of about 9 dB, observed on the paraboloid axis (z-axis) to a minimum of -17 dB in the trough directly opposite the paraboloid base. Corresponding power ratios are 7.94 and 0.02.

EXPERIMENT AND THEORETICAL RESULTS

Theoretical wave fields were derived for comparison with that obtained experimentally for the paraboloid reflector (Fig. 4a). Displayed in Fig. 5 are wave fields for monofrequency source signals at frequencies of 100, 400, 600, 800, 1000, and 2000 Hz. Each is over the same area as that for the experimental wave field (Fig. 4). Contour values are pressure in dB relative to the pressure at a distance of 1 ft from the source. At 100 Hz the wave field is essentially that of a point source. The beaming effect is perceptible at 400 Hz and, as expected, increases with frequency. At 2000 Hz side lobes are developed.

In Fig. 6 amplitudes of field-recorded signals (solid lines) and amplitudes of various theoretical monofrequency signals (dashed lines) are plotted versus horizontal distance (x) at axial distance (z) of (a) 20 ft (6.1 m), (b) 60 ft (18.3 m), and (c) 100 ft (30.5 m) below the source. Amplitude values for each curve are in dB relative to the respective axial (x=O) value; thus, each curve has an axial value of 0 dB. At z = 20 ft (Fig. 6a) the experimental curve (field-recorded signals) for no air-bubble stream is essentially that for a point source which is the same as that for a theoretical 0-Hz monofrequency signals with the paraboloid reflector. Experimental amplitudes with the paraboloid reflector decrease appreciably from the axial value, becoming nearly equal to that of the 1000-Hz signal at x=20 ft (6.1 m). At z = 60 ft (Fig. 6b) the experimental curve for the paraboloid reflector is nearly coincident with the 2000-Hz theoretical curve out to a horizontal distance (x) of 20 ft (6.1 m), and at z = 100 ft (Fig. 6c) it is appreciably below this theoretical curve. Beyond a horizontal distance of 20 ft (6.1 m) the experimental amplitudes tend to increase moderately at each of the three axial distances (z). This departure from the theoretical curves likely is due to diffraction around the perimeter of the paraboloid base, a phenomenon not accounted for in development of the theoretical wave fields.

CONCLUDING REMARKS

Results of the field experiment demonstrate that an acoustic wave in water can be beamed downward effectively by placing the source at the focus of a paraboloidic interface, concave downward, between water below and an air-water mixture above. A very small fractional volume of air (e.g., 0.005), reduces acoustic-wave velocity to approximately one-tenth that in air-free water, resulting in a reflection coefficient near -0.8.

Additional research is required to determine more precisely the effect of the paraboloid reflector on signal characteristics. Because of its high-frequency content due to the small size of the reflector, the beamed signal achieved here is not suitable for typical seismic exploration surveys. It is likely that paraboloid reflectors useful in seismic exploration must be appreciably larger than the prototype used in this experiment.

An obvious application of the paraboloid reflector is in marine vertical seismic profiling (VSP). The paraboloid reflector with a suitable source at its focus would be suspended in water from an offshore well platform, beaming signals downward for recordings from a well seismometer. The recorded signals should be simplified and enhanced by exclusion of the ghost, as well as of all water-layer multiple reflections resulting from the ghost. Also, the acoustic wave that strikes the well riser pipe is diminished, thereby reducing the amplitude of interfering borehole waves. Another possible application is in shallow-water seismic surveys for which the recording cable and sources are stationary for each recording. One or more paraboloid reflectors might be suspended from a barge or other suitable vessel. Reflection resolution and penetration should be enhanced. In conventional deep-water seismic surveys other air-pipe structures may be used (Domenico, 1986b) to attenuate that portion of the acoustic wave traveling upward and outward from a moving source, thereby attenuating the ghost and other noise waves.

ACKNOWLEDGEMENTS

The author is indebted to several individuals who contributed substantially to the pursuit and successful completion of the field experiment reported here. In particular he acknowledges the contributions of Frank Haines, Ken Kelly, and Jana Walker at Amoco's Tulsa Research Center, and those of Bert Pengelley, Derek March, and Peter Kennett at Seismograph Service's London facility. The author also is indebted to Amoco Production Co. for permission to publish this paper and for assistance in its preparation.

This paper is a shortened version of one accepted for publication in Geophysics, a journal of the Society of Exploration Geophysicists. The SEG, assigned copyright of the paper, has given permission for publication of this version in the OGJ.

BIBLIOGRAPHY

Cartensen, E.E. and Fody, L.L., 1947, Propagation of sound through a liquid containing bubbles: J. Acoust. Soc. Am., v. 19, p 481. Domenico, S.N., 1982, Acoustic wave propagation in air-bubble curtains in water, Part II: Field experiment, Geophysics, v.47, p 354-375.

Domenico, S.N., 1986a, Seismic source system for use in water-covered area: U.S. Patent No. 4,632,213.

Domenico, S.M., 1986b, Moving seismic source system for use in water-covered area; U.S. Patent No. 4,618,02.

Fox, F.E., Curley, S.R., and Larson, G.S., 1955, Phase velocity and adsorption measurements in water containing air bubbles: J. Acoust. Soc. Am., 27, p. 534.

Macpherson, J.D., 1957, Effect of gas bubbles on sound propagation in water: Proc. Phys. Soc., London, B70, p. 85.

Silberman, E., 1957, Sound velocity and attenuation in bubbly mixtures measured in standing wave tubes: J. Acoust. Soc. Am., v.29, p. 925-933.