Acoustic Localization of an Intruder in a Strongly Scattering Medium

Localizing an intruder submerged in a strongly scattering medium, such as a dense granular suspension, is a practical challenge. Here we extract the coherent ultrasonic echo from a steel ball submerged in a dense glass-bead packing saturated by water, by using a standard single-element ultrasonic transducer thanks to a configuration averaging process. Different configurations of the granular packing are created by the nonaffine motion of the beads with a mixing blade, akin to the Brownian motion, in the vicinity of the intruder. We investigate the efficiency of this process to reduce the so-called material noise from multiply scattered ultrasound, as a function of the configuration number, the shear rate and the blade-intruder distance. Nonaffine motions of the beads in the shear zone induced by the blade are then analyzed on the basis of a split-bottom rotating shear cell. This method helps to develop not only ultrasonic imaging tools of buried objects in turbid marine sediments, but also the local rheology based on a ball falling monitored by ultrasonic tracking.

Figure 1

Schematic of the experimental setup. A ball with a diameter of $D=3\mathrm{cm}$ is submerged at depth $Z$ in a suspension of glass beads ($d\sim 425–850\text{μ}\text{m}$) in water. A piezoelectric transducer $(A)$ is used to send short pulses and measure the echoes from the interface and the surface of the ball. The scatter configuration in the granular packing may by modified by a mixing blade with size $L=5$ cm and rotation speed $\mathrm{\Omega }$ placed at a distance $\chi$ from the ball.

Figure 2

Effect of configuration averaging for $\chi =8$ cm. (a1) Acoustic signal obtained at $\mathrm{\Omega }=0$. (a2) Spectrogram of the acoustic signal in (a). (b1),(c1),(d1) Acoustic signals obtained for $\mathrm{\Omega }=23$ rpm and after averaging $N=2$, 20 and 50 signals, respectively. (b2),(c2),(d2) Spectrograms of the signals in (b1),(c1),(d1). The coherent echo from the surface of the ball is indicated by the black arrow. The color indicates the log amplitude. (e) Power spectrum of the signals in (a1),(d1) in gray and black, respectively. (f) The energy of the propagating wave normalized by the energy of the wave at $\mathrm{\Omega }=0$, versus the number $N$ of signals averaged (semi-logarithmic plot).

Figure 3

Effect of the rotation speed of the blade observed at $\chi =7$ and 9.5 cm, respectively. (a1) Acoustic signal obtained for $\mathrm{\Omega }=0$ at $\chi =7$ cm. (b1),(c1),(d1) Acoustic signals at $\chi =7$ cm for $\mathrm{\Omega }=20$, 62, 121 rpm. (a2),(b2),(c2),(d2) Spectrograms of the signals in (a1),(b1),(c1),(d1). (e1) Acoustic signal obtained for $\mathrm{\Omega }=0$ at $\chi =9.5$ cm. (f1),(g1),(h1) Acoustic signals at $\chi =9.5$ cm for $\mathrm{\Omega }=22$, 75, 119 rpm. (e2),(f2),(g2),(h2) Spectrograms of the signals in (e1),(f1),(g1),(h1). The coherent echo from the surface of the ball is indicated by the black arrow. (i) The energy of the transmitted wave normalized by the wave energy for $\mathrm{\Omega }=0$ is plotted versus the rotation speed, showing a clear decrease with increasing $\mathrm{\Omega }$. Solid points are $\chi =7$ cm, open circles are $\chi =9.5$ cm.

Figure 4

Effect of the blade-intruder distance. (a1) Trace at $\chi =7$ cm for $\mathrm{\Omega }=0$ rpm with its spectrogram in (a2). (b1) Trace at $\chi =8.2$ cm for $\mathrm{\Omega }=0$ rpm with its spectrogram in (b2). (c1) trace at $\chi =9.5$ cm for $\mathrm{\Omega }=0$ rpm with its spectrogram in (c2). (d1) Trace at $\chi =11$ cm for $\mathrm{\Omega }=0$ rpm with its spectrogram in (d2). (e1) Trace at $\chi =7$ cm for $\mathrm{\Omega }=40$ rpm with its spectrogram in (e2). (f1) Trace at $\chi =8.2$ cm for $\mathrm{\Omega }=40$ rpm with its spectrogram in (f2). (g1) Trace at $\chi =9.5$ cm for $\mathrm{\Omega }=40$ rpm with its spectrogram (g2). (h1) Trace at $\chi =11$ cm for $\mathrm{\Omega }=40$ rpm with its spectrogram in (h2). The coherent echo from the ball is indicated by the black arrow. (i) The energy ratio of the averaged acoustic trace to the signal obtained for $\mathrm{\Omega }=0$ versus the blade-intruder distance. This energy ratio increases with increasing $\chi$, suggesting that the averaging process becomes less efficient further from the shear zone.

Figure 5

Time necessary to randomize the scattering waves. (a) Normalized energy calculated from the data in Fig. 2 ($\chi =8$ cm and $\mathrm{\Omega }=23$ rpm) by averaging two signals ($N=2$) for increasing time lag between them. To completely randomize the scattering waves $\delta t^{\ast }\sim 30$ s. (b) The normalized energy of the wave versus the delay time for $\mathrm{\Omega }=20$, 62, and 121 rpm (blue, red, and yellow, respectively) at a distance $\chi =7$ cm calculated from the data in Fig. 3. The dotted arrow indicates the decrease of $\delta t^{\ast }$ with increasing $\mathrm{\Omega }$. Error bars represent the standard error of the mean.

Figure 6

(a) Sketch of side view and (b) top view of the shear zone (in green) induced by the mixing blade (split-bottom-like shear cell). The location of tracer beads is indicated (right) for illustration. (c)–(f) Images obtained from averaging 6000 frames from a movie (about 100 s) at rotating speeds $\mathrm{\Omega }=31$, 68, 95, 120 rpm, respectively. The texture of the image is smoothed due to the particle motion by shear. The dotted lines are a guide to the eye, they indicate $\chi$ for which ${\sigma }_L=0.9$ and illustrate the increase of the flowing zone with $\mathrm{\Omega }$. (g) $(1-{\sigma }_L)$ as a function of $\chi$ for the images in (c)–(f) colors blue, red, yellow, and green are $\mathrm{\Omega }=31$, 68, 95, 120 rpm, respectively. Open circles depict ${\sigma }_L=0.75$. The black lines are models of $\omega (\chi )$ obtained from Eq. (1) by setting $R_c$ and $W$. Inset shows a typical trace of $\omega (\chi )$ with $R_c=50$ mm and $W=10$ mm. (h) The $W$ (points) and $R_c$ (circles) used for the models in (f) versus $\mathrm{\Omega }$. The black line corresponds to a power law $W\sim {\mathrm{\Omega }}^{0.38}$ [39].