акустика / gan_ws_acoustical_imaging_techniques_and_applications_for_en

storage devices – such as charge-coupled devices (CCDs) or bulk constant delay lines – which have the appropriate speed, linearity, dynamic range and uniformity from device to device. With the increasing availability of good CCDs, this technique is coming into greater usage.

Another aspect of the beamforming system relevant to acoustical imaging is the ability to stack two sets of linear beamformers, one set following the other, to achieve a two-dimensional beamformer. For an array of N × M hydrophones, one set of N-point beamformers (M of them) forms beams in one direction, while another set of M-point beamformers (N of them) uses the outputs of the first set of beamformers to form beams in the other direction. The result is a set of N × M image points. Then for an N × Marray of hydrophones, N × N + M × M taps and 2 × N × M summing junctions are necessary.

11.6.2.2Phased Array Beamformer

The phased array beamformer is a narrow-band approximation to the delay and sum type. It uses some form of properly phased reference signal to sample or mix with the incoming acoustic signal to achieve the proper signal addition for beam formation.

The beam output from such a beamformer is given by

where φ is the phase step between hydrophone elements.

In order to implement the phase concept, refer again to Figure 11.9. Here φ is rewritten as (2π d sin θ )/λ. To represent these phases as one of N equally spaced phase delays, the φ term can be replaced by 2π l/N radian, where l runs from 0 to N − 1, to give

Implementations often use a delay line of some sort to obtain reference signals with the desired phase at each hydroplane (Figure 11.10). Each microphone signal is then multiplied by the correspondence reference signals and added to the rest of the products. Only those signals arriving at the angle being examined will have phases that add coherently after multiplication by the reference waves. Inserting a sine wave into a uniformly tapped delay line produces the desired reference waves whose phases vary linearly with distance for one scan angle. Inserting a slowly varying sine wave causes the reference signal phases to vary linearly with time, thus scanning out a variety of angles. Chirps have been sent down delay line made from many technologies including surface acoustic waves (SAW) [9], CCD, shift registers [10] and conventional delay lines, as well as generated in READ-ONLY memories (ROMs). The technique of stacking two sets of beamformers described previously, works for these phase beamformers as well.

Hydrophones

Multipliers

Summation Reference line signals

Frequency

Tapped delay line

chirp

Figure 11.10 Delay line beamformer. Only sound arriving at one angle to the array will have the signal phases that match the reference phases present at the delay line taps at any one reference frequency. As the frequency sweeps, so does the received beam (Lee and Wade [8] © IEEE)

11.6.2.3Correlation Beamformer

The third type of beamformer is the correlation beamformer. The principle is when a planar sine wave arrives at some angle to an array of sensors, it produces a sinusoidal pattern of amplitudes across the array at any one instant. By looking for those spatial sinusoids at variety of frequencies using matched spatial correlators, a multibeam beamformer results. A simple example of a correlator is just a series of resistors, each attached to one hydrophone and each having a value corresponding to one point of one sinusoid extending across the array. The outputs of all the resistors are summed together so that when the right plane wave is incident on the array, all of the outputs add with the proper amplitude to form a signal (Figure 11.11). When plane waves arrive from other angles, the amplitudes are at random values and the resulting sum tends towards zero. This implies that the correlation beamformer is necessarily narrow band.

A difficulty of beamformed acoustic imaging is that virtually all of the circuitry must operate at the acoustic frequency (unless converted to an intermediate frequency, a process that has its own problems). At lower acoustic frequencies and in synthetic aperture system, this is not a serious drawback. However, as the frequency goes up or as the number of parallel circuits increases, generally so does the power required to run the high-frequency electronic circuits, especially integrated circuits. Total system power can be quite high (100’s to 1000’s of watts) with completing filled arrays at high frequencies.

Correlator output

Acoustic wavefronts Hydrophones

Figure 11.11 Correlation beamformer. At any one instant, a plane wave has a spatial sinusoidal amplitude across the array that can be detected by the sum of appropriately weighted resistors (Lee and Wade [8] © IEEE)

11.6.3Holographic Acoustical Imaging

Holograph acoustical imaging is a narrow bandwidth phase sensitive technique that usually processes all of the beams simultaneously. Since it is phase sensitive during the acquisition of the acoustic hologram, a holographic acoustic imaging system must either employ many channels of parallel processing, maintain extreme stability during the acquisition period, on the order of a tenth wavelength, or use some fairly sophisticated means to detect the motion and motion compensating signal processing to remove its effects. In holographic acoustical imaging, the sound field of a narrow band signal is spatially sampled by a hydrophone array and is immediately converted to a stable set of DC values called a hologram. Since it is holographic, the signal present at each point in the receiving array is mixed with a reference signal of the same frequency to produce a DC component. This value represents the term A cos φ, where A is the acoustic amplitude and φ is the phase relative to the reference signal.

The advantage of the holographic acoustic imaging system is that physically it is as compact as a beamformer system since no lens is used and the signal processing to perform the image reconstruction can be conveniently separated from the data collection. This separation enables existing high-speed general purpose signal processors such as digital minicomputers and optical processors to be adapted for use, relieving some of the need for specialized hardware. Another advantage is that the processing electronics can be located somewhere other than in the hydrophones array, thus relieving some of its bulk.

The acoustical hologram contains the minimal amount of information that describes the narrow bandwidth signals at each hydrophone. The array freezes a representation of the acoustic field containing phase information (the acoustical hologram) present at the face of

the array. This information is then sent to a signal processor that can evaluate all of the data contained in the hologram simultaneously in the most efficient manner possible.

The image reconstruction process in acoustical holography can be done in one of at least three ways: (1) optical diffraction, (2) backward propagation and (3) Fourier/Fresnel transformation.

11.6.3.1Optical diffraction

In optical diffraction, a coherent light beam from a laser is bounced off the acoustic hologram as it exists on the surface of the water or is refracted through the hologram that has been copied onto some form of transparent surface, much as in reconstruction of optical hologram [11]. The results are nearly identical to those in optical holography as well. There is a zero-order bright spot, a real image and an out-of-focus conjugate image. If the spatial sampling rate in the receiving aperture is not fine enough (relative to a half-wavelength) the conjugate image will lie on top of the real image, obscuring it. The departure from optical holography is that the difference in optical and acoustical wavelengths causes the two (range) dimensions to be greatly magnified with respect to the lateral dimension in the reconstructed image. This means that only a short depth of field can be in focus at any one time.

11.6.3.2Backward Propagation

Backward propagation consists of solving the inverse integral equation to the acoustic propagation equation at a specific range. The result is nearly exact and works even in the very near field of the acoustic array. The details were discussed in equations (11.19)–(11.22). The following is the procedure of the backward propagation algorithm:

(a) Take the Fourier transform of the array dot.

(c) Take the inverse Fourier transform of the result.

These operations can be performed on a digital computer.

11.6.3.3Fourier/Fresnel Transformation

In the Fourier/Fresnel transformation technique of reconstruction, use is usually made of the near-field or Fresnel approximation to the propagation equation such that a spatial Fourier transform of the spatial hologram data results. The equation that describes this process was given in equations (11.11) and (11.12). Since most acoustical imaging is of objects in the moderately near field (or Fresnel region), a quadratic phase factor precedes the Fourier transform to compensate for wavefront curvature. This is sometimes called the focus factor, since it focuses the image at the desired range. The primary advantage of using this approximation is that a fast Fourier transform (FFT) algorithm can be implemented on a

(a)

(b)

Figure 11.13 Holographic acoustic image of a 1-sq ft steel plate at 12 ft. (a) Metal target 12 × 12 in (300 × 300 mm). (b) Image reconstructed with the target at a range of 12 ft (3.7m) (Lee and Wade [8] © IEEE)

The system’s resolution is 0.3 degree and range 1–30 m. It follows the performance gap between sonar and underwater telecom cameras. It has 48 × 48 array of piezoelectric hydrophones on the lower front and a separate acoustic projector above. The projector is capable of transmitting 250 W of acoustic energy at 642 kHz into an 11×11 degree field of view. Inside the housing are 48 electronic channel processor cards, which detect the acoustic hologram. The data from the channel processor is digitized and transmitted to the control panel for further processing

Figure 11.13 is an example of an object and its acoustic image obtained with the system, where the object was 4 m away in ocean water that had an optical visibility of about 0.3 m.

Other research centres on the underwater acoustical imaging systems are at Bendix Research Labs, Southfield, MI, Bendix Electrodynamics, Sylmar, CA and OKI Electri Industrial Company in Japan, which uses a synthetic aperture technique.

As a whole, the research on underwater acoustic imaging system is not of as strong desire as for medical and nondestructive testing areas and so it continues at a slower pace. Additionally the reverse environmental requirement that underwater systems meet also makes development in this area more expensive.

11.7Application of Robotics to Underwater Acoustical Imaging

With the increase of oil exploration activities in deep-sea water, the use of robotics in underwater acoustical imaging becomes indispensable. An example would be the use of robot for deep-sea structural inspection [13]. The ultimate purpose is to produce a 3-D acoustical image of the structure. The objective is to develop technology to autonomously construct 3-D models of marine structures. The following are required:

(a)Hardware system

(b)Algorithm and software for autonomous model reconstruction of marine structures

(c)Algorithm and software to generate motion strategies for the robot.

The hardware will include robotic platform such as the SCOUT autonomous surface craft and sensors such as Velodyne 3D and Blueview microbathymetry.

Next one has to find motion and sensing strategy to reach a goal region as fast as possible with lowest cost. One will be faced with the problem of state of the robot and environment, which are never known exactly. There will be significant errors in motion and sensing and environment map uncertainty. The problem definition is how should the robot move, where and when should it scan the environment so that the goal is reached with minimum cost.

To cope with the uncertainty, the POMDP approach is used. That is to plan with respect to sets of states consistent with the available information. This will be represented as distributions over state space called beliefs. The proposed solution is to plan over sampled representation of the belief space. Domain knowledge will be used to sample representative beliefs and converge to the optimal policy.

References

[1]Brekhovskikh, L.M. (1960) Waves in Layered Media, Academic Press Inc., New York.

[2]Urick, R.J. (1983) Principles of Underwater Sound, 3rd edition, McGraw-Hill, New York.

[3]Lord Rayleigh (1945) The Theory of Sound, vol. 2, Dover Publications, Inc., New York.

[4]Hamilton, E.L. (1972) Compresional wave attenuation in marine sediments. Geophys., 37, 620.

[5]Weston, D.E. (1963) Propagation of sound in shallow water, 1962 Sonar Systems Symposium, University of Birmingham, England. J. Brit. IRE, 26, 329.

[6]Thorn, J.V., Booth, N.O., Sutton, J.L. and Saltzer, B.A. (1974) Test and evaluation of an experimental holographic acoustic imaging system. Naval Undersea Center Technical Publication 398, Nov.

[7]Goodman, J.W. (1968) Introduction to Fourier Optics, McGraw-Hill, New York, Chapter 5, pp. 83–90.

[8]Lee, H. and Wade, G. (eds.) (1986) Modern Acoustical Imaging, IEEE Press, New York.

[9]Havlice, J.F., Kino, G.S., Kofol, J.S. and Quate, C.F. (1974) An electronically focused acoustic imaging device, in Acoustical Holography, vol. 5 (ed. P.S. Green), Plenum Press, New York, pp. 317–334.

[10]Young, J.W. (1977) Electronically scanned and focused receiving array, in Acoustical Holography, vol. 7 (ed. L.W. Kessler), Plenum Press, New York, pp. 387–403.

[11]Metherell, A.F., El-Sum, H.M.A. and Larmore, L. (1966) Acoustical Holography, vol. 1, Plenum Press, New York.

[12]Sutton, J.L., Thorn, J.V., Booth, N.O. and Slatzer, B.A. (1979) Description of a Navy holographic underwater acoustic imaging system, in Acoustical Holography, vol. 8 (ed. A.F. Metherell), Plenum Press, New York, pp. 219–234.

[13]Kurniawati, H. (2011) Autonomous model reconstruction of marine structures, presentation, Acoustics Research Laboratory, Tropical Marine Science Institute, National University of Singapore, October.

12

Geophysical Exploration

12.1Introduction

Geophysical imaging system was invented due to the necessity to search for oil and gas. The procedure uses explosive charges and sensitive sensors to measure the intensity and travel time of acoustic shock waves moving through the earth. These shock waves reflect sharply from hard rock, but not form soft dirt. The length of time it takes for the waves to reach an underground layer of rock and return to a sensor on the surface shows how deep the layer is. Seismic and geographical exploration consists of acquiring and recovering the data and then interpreting what has been recorded. It started off with analogue techniques but it has gone digital since the 1960s.

Geophysical seismic exploration systems were in use since the 1920s. The efficiencies of the technology have greatly increased since the arrival of the digital computer. This is due to the fact that seismic surveys are carried out over several square miles of area on surface grids to obtain the three-dimensional images of interest. For each square mile surveyed, tens of millions of bits of information will be acquired. The timely processing of the massive amount of data would be practically impossible without the use of the high-speed digital computer.

These seismic data are multidimensional because acoustic wave fields have both spatial and temporal variations. The seismic signal processing therefore must take into account the full multidimensional character of the recorded wave fields. Hence, the concepts of tomography and hologram can both be exploited here. There is already a trend in the use of these two concepts in the technique for seismic and geophysical exploration. For instance, seismic tomography can present three-dimensional image of the interior of the earth’s structure. Research along these lines could answer some long-standing fundamental questions of geodynamics in earth science. At present, the data bank is already of sufficient accuracy and size to attempt threedimensional reconstruction of the interior structure of the earth. For the first time we can see details of the deep interior of the earth. This casts light on the origin of features observed on the earth’s surface.

In tomography, three-dimensional images are determined by processing an integrated property of the specimen obtained by the ray of the probing energy in propagation through the specimen. Geophysical diffraction tomography is similar to medical ultrasound diffraction

Acoustical Imaging: Techniques and Applications for Engineers, First Edition. Woon Siong Gan. © 2012 John Wiley & Sons, Ltd. Published 2012 by John Wiley & Sons, Ltd.

tomography. The main difference is that in medical applications, we record the sound wave amplitude, while in geophysical case, the travel time or phase is recorded. The direction of geophysical diffraction tomography is towards a full reconstruction of the three-dimensional structure of the earth.

Another application of geophysical acoustical imaging is the use of sound to penetrate the opaque brilliance of the solar surface. Continuous sound waves after propagating through the exterior of the sun are visible on the sun’s surface. One can probe the sun’s interior from the observation of these sound waves. The period and pattern of the oscillation of sound waves will provide important clues to the composition structure and dynamics of the sun’s interior. The velocity and direction of the sound wave’s propagation depend on the temperature, composition and motion within the sun. Thus, they provide a sensitive indication of conditions in the sun’s interior.

12.2Applications of Acoustical Holography to Seismic Imaging

Seismic or geophysical acoustical imaging technique has seen steady improvements during the first half of the twentieth century with the arrival of cheap and high-speed computers. Many complicated algorithms for obtaining seismic images can now be implemented. The early proposals of Metherell et al. [1], Farr [2] and Silverman [3] already made suggestions on the applications of acoustic holography to seismic imaging. The approach used in seismic applications of acoustical holography is a bit different from the conventional acoustical holography technique. In conventional acoustical holography, an effective reference wave is mixed with the received signals to produce a true interference pattern or acoustical hologram. Furthermore, in conventional acoustical holography, it is the analysis of this hologram and its reconstruction rather than an analysis of the individual time traces that leads to a reconstructed image. Most conventional acoustical hologram also usually involve an effective two-dimensional recording array. In seismic acoustical holography, one-dimensional recording array is used in the oil industry for surface prospecting and in borehole geophysical application. Also, in seismic acoustical holography, the use of geophones that are linear detectors not square law detectors, and as a consequence, amplitude and phase information have always been rapidly available in seismic data, unlike conventional acoustical holography where a reference wave is needed in order to record the phase information.

The traditional problem in seismic imaging has been to find ways to extract from the phase information and the amplitude data, information regarding the scattering targets and other structural features of interest. In the early days, the only way was to perform a pulse-echo analysis in which certain structural features or characteristics were identified by eye on the geophone traces themselves and these features were used to obtain a map of the geological structure.

In the modern era, wave-equation migration techniques and related approaches are used. However, these techniques still need a full-time trace for the geological detector or group of detectors to be recorded and stored.

The advantage of recording seismic data by conventional holography is not only that it opens up new possibilities for reconstructing and interpreting the data, but it also means that no recording of the time traces per second is required. All that is required is that the time-dependent record signal, call it S(x, y, z, t ), be mixed in real time with a local oscillator

reference wave R(t ) and the time average intensity taken to produce the acoustical hologram values H(x, y, z).

There are many applications, especially small-scale applications, where the traditional techniques for taking data and interpreting the data are no longer strictly necessary or desirable in order to obtain good image of geological structure.

Once the data have been recorded holographically, a large variety of schemes for analyzing, interpreting and reconstructing the data become possible. Holograms may be added, subtracted, filtered, correlated and so on before being reconstructed. This capability allows one to take advantage of a large variety of existing computer-assisted techniques originated from modern optics and optical data processing for the improvement and interpretation of reconstructed images of geological structure.

12.3Examples of Field Experiments

12.3.1One-Dimensional Holographic Arrays

An example is the experiment of Mueller and Steinberg of Bendix Research Laboratories Southfield, MI and Farr of AMOCO [4]. This experiment was done in the Gulf of Mexico over a thoroughly salt-dome structure. The active line of hydrophones detectors measured 1350 ft and the spacing between individual hydrophones was about 8 ft. The maximum acoustic frequency used in this experiment was about 70 Hz. Both the seismic source and the receivers were towed by a ship. Spatial location of the detectors was determined by constant updating of information from several microwave navigation buoys. The entire scan length was about 2.5 miles.

The received signals were mixed with local oscillator signals 90◦ out of phase producing phase-quadrature intensities. The hologram with amplitudes A cos φ and A sin φ were produced and recorded where A is the amplitude of the mixed signals and φ is the phase difference between the local oscillator and the recorded signal. A cross-correlation imaging technique [5] was used for reconstruction, instead of the conventional wavefront reconstruction technique with laser or a computation algorithm such as fast Fourier transformation (FFT). A correlator is needed for image formation and this was done using a velocity versus depth model first constructed using other available data.

The cross-correlation imaging technique is performed in the following way. Take an imaginary point scatterer located at some point at depth z below the hologram array where the image value was to be computed. The expected hologram values in the surface line (or the surface array) or the response expected from this single point scattered can then be computed using the velocity versus depth model. This gives the synthetic correlator Hc (z), which also consists of real and imaginary parts in quadrature.

The full hologram Hs measured at the surface was a complex hologram.