Atmospheric Acoustic Remote Sensing - Chapter 4

4 Sound Transmission and Reception The essence of an acoustic remote-sensing system is in generating sound into a well-formed beam which interacts with the atmosphere in a known manner and then detecting that interaction. In Chapter 2 we learned about the nature of the atmo-sphere into which the sound is projected, and in Chapter 3 the way in which sound travels. In this chapter we describe how to form a beam of sound, how scattered sound is detected, and how systems are designed to optimize retrieval of various atmospheric parameters. The main emphasis of Chapter 4 is on geometry and tim-ing, but details on some of these aspects are left to Chapter 5. 4.1 GEOMETRIC OBJECTIVE OF SODAR DESIGN The boundary layer atmosphere is often strongly varying in the vertical, but hori-zontally much more homogeneous. The geometric design objective for vertically profiling instruments is therefore to localize the acoustic power sufficiently in space so that atmospheric properties are obtained from well-defined height intervals at a particular time. This means that the vertical resolution has to be defined, typically by using a pulsed transmission. But since sound will spread spherically from the source, height resolution also depends on angular width of the beam transmitted. Here we concentrate on SODAR (SOund Detection And Ranging) systems, for which the acoustic beams are often non-vertical, as shown in Figure 4.1. Here the pulse duration is Υ and the angular width of the acoustic beam is ±∆Γ in azimuth angle and ±∆Ρ in zenith angle. From Figure 4.1, the vertical extent of the pulse volume is ≈ cΥcos Ρ + 2z∆sinΡ∆Ρ, which has a term increasing with height z. Taking cΥ =20 m, and Ρ = 20°, the vertical extent of the pulse volume near the ground is cΥ cos Ρ = 18.8 m but, for a beam half-width of ∆Ρ = 5°, this increases to 50 m at z = 500 m. This emphasizes the need to keep the product sinΡ∆Ρ small. Also, if ∆Ρ is too large then the pulse volume will include a wide range of radial velocity, the Dop-pler spectrum will be wider, and the ability to detect the peak position of the Doppler spectrum, in the presence of noise, will be compromised. But we will see later that the wind velocity component estimates of u and v have errors which depend on 1/sinΡ, so it is important that Ρ not be too small. On the other hand, Ρ must also not be so large that the volumes sampled by the various SODAR beams which point in differ-ent directions, are so spatially separated that their wind components become uncor-related. The resulting design must therefore be a delicate balance between modest Ρ values and a narrow beam width ∆Ρ. Typical designs have 15°<Ρ<25° and 4°<∆Ρ <8°. Obtaining such a small beam width ∆Ρ requires an antenna, since the beam widths of individual speakers are typically much greater. Use of an antenna has the added advantage of increasing the collecting area for echo power. 55 © 2008 by Taylor & Francis Group, LLC 56 Atmospheric Acoustic Remote Sensing z q c q x y FIGURE 4.1 The pulse volume for a tilted acoustic beam. 4.2 SPEAKERS, HORNS, AND ANTENNAS 4.2.1 SPEAKER POLAR RESPONSE Figure 4.2 shows several typical speakers. The TOA SC630 is a double re-entrant horn 30-W speaker producing a sound pressure level (SPL) of 113 dB at 1 m and at 1.5 kHz. The FourJay 440-8 “Thundering Mini” is a compact 40-W re-entrant horn speaker with an SPL = 110 dB peaking at 2 kHz. The Motorola KSN1005A is a small piezo-electric horn speaker producing an SPL of 94 dB at 5 kHz. Horn speakers consist of a driver, which includes a diaphragm, and a horn-shaped cone of plastic or metal to efficiently couple energy from the small driver into the atmo-sphere. Re-entrant horn speakers have the cone split into a backward-facing part connected to the driver and a forward-facing part exiting into the atmosphere; they have the advantage of being more weatherproof and can in many cases be mounted facing upward. Figure 4.3 shows polar plots of the sound intensity produced by these speakers at selected frequencies. It is clear from these polar plots that a typical half-power, or −3 dB, beam width is 30° rather than the desired 5°. There are two ways in which a narrow beam is generally achieved, while still using such speakers. One is to re-shape the beam pattern by using a parabolic reflec-tor, in much the same way as car headlights re-shape the broad beam from a light bulb into a narrow forward beam. The other method is to use multiple speakers, driven synchronously. The sound waves from multiple speakers reinforce in one direction and gradually cancel at angles further away from this direction. This is the principle of the phased array antenna. © 2008 by Taylor & Francis Group, LLC Sound Transmission and Reception 57 285m 85 m 140 m FIGURE 4.2 TOA SC630 (left), FourJay 440-8 (center), and Motorola KSN1005A (right). 340° 350° 0° 10° 20° 330° 30° 320° 40° 310° 50° 300° 60° 290° 70° 280° 80° 270° 90° –25 –20 –15 –10 –5 0dB 260° 100° 250° 110° 240° 120° 230° 130° 220° 140° 210° 150° 200° 190° 180° 170° 160° FIGURE 4.3 Polar response of some typical horn speakers, normalized to 0 dB in the for-ward direction. Heavy line (FourJay 440-8 at 3 kHz) and light line (TOA SC630 at 2 kHz). 4.2.2 DISH ANTENNAS A parabolic dish antenna consists of a speaker situated at the focus of a parabolic reflector and facing downward toward the center of the reflector. An example is shown in Figure 4.4 and the geometry is shown in Figure 4.5. It can be shown that if sound from the speaker is projected downward at an angle Ρ to the vertical, then its angle to the perpendicular from the dish surface is [ = Ρ/2. The law of reflection gives [ = Ρ/2 between the perpendicular and the verti- © 2008 by Taylor & Francis Group, LLC 58 Atmospheric Acoustic Remote Sensing cal. This means that all sound from the focal point is reflected directly upward and, regardless of the speaker’s polar response, the upward beam is perfectly collimated. There are a number of rea- sons why this “perfect” situation is not observed in practice. The first is that the speaker cone has finite diameter d. The effect of this can be estimated using Figure 4.6. In this figure we know that a down-ward ray from the center of the speaker (at the focus) will be reflected verti- cally upward. So, using the fact that sound propagation is reversible, a ver-tically downward ray from the edge of the speaker (at x = d/2) will be reflected back through the focus, and on past the used in. an early AV2000 AeroVironment speaker at antangle Z to theovertical. If the dish, then the beam will now have a width of approximately ± Zqd/2b rad. For example, a dish having b = 570 mm and a speaker of diameter d = 100 mm would produce a beam nominally of width ±5°. In practice, the actual half-angle width of the beam (measured out to where the sound intensity is at half the intensity at the center of the beam) will depend on the angular or polar response of the speaker, and will generally be less than od / 2a , where a is the dish radius. Very approximately, the speaker polar response within angles tan1(b / a) to tan1(b / a) , will be com-pressed into angles tan1(d / 2b) to tan1(d / 2b). A second cause for non-perfect collimation is whether some of the sound from the speaker reaches the edges of the dish. This creates diffraction (discussed in Chapter 3) with the upward traveling sound being equivalent to coming through a b z xb x FIGURE 4.5 Geometry for a SODAR using a dish antenna. The downward-facing speaker is at the focal point of the parabolic dish. © 2008 by Taylor & Francis Group, LLC Sound Transmission and Reception 59 b x d FIGURE 4.6 7KHHIIHFWRIÀQLWHVSHDNHUGLDPHWHURQGLVKDQWHQQDEHDPZLGWK hole with the same diameter as the dish. If the dish is uniformly covered by sound energy from the speaker, the upward intensity pattern is proportional to §2J1(kasinY)·2 © kasinY ¹ where J1 is the Bessel function of order 1, k the wavenumber of the sound, and a the dish radius. This gives a beam pattern which has an angular half-power width of about o2 / ka rad, but which also has subsidiary peaks at greater angles (known as side lobes), as shown in Figure 4.7. For example, if ka = 33, then Figure 4.8 shows that the polar response of the diffraction pattern from the dish has a side lobe peak about 17 dB below the main lobe intensity and at an angle to the vertical of about Z = 9°. ka FIGURE 4.7 The polar intensity pattern from a uniformly radiated dish of radius a. © 2008 by Taylor & Francis Group, LLC ... - tailieumienphi.vn