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Acoustic inversions for measuring boundary layer suspended sediment processes
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10.1121/1.3618728
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Affiliations:
1 National Oceanography Centre, Joseph Proudman Building, 6 Brownlow Street, Liverpool, L3 5DA, United Kingdom
2 Laboratory of Geophysical and Industrial Flows (LEGI), CNRS UMR 5519, Grenoble, France
3 National Oceanography Centre, Joseph Proudman Building, 6 Brownlow Street, Liverpool, L3 5DA, United Kingdom
a) Author to whom correspondence should be addressed. Electronic mail: pdt@pol. ac.uk
J. Acoust. Soc. Am. 130, 1188 (2011)
/content/asa/journal/jasa/130/3/10.1121/1.3618728
http://aip.metastore.ingenta.com/content/asa/journal/jasa/130/3/10.1121/1.3618728
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## Figures

FIG. 1.

(a) Lognormal mass distribution, m(a) (···), and particle size distribution, n(a) (–), vs particle radius a. am , a 50, and ac are the radius respectively for the mean mass, median mass and mean particle size. (b) Form functions for the intrinsic scattering characteristics of the sediments fio (‐‐) and the ensemble f (–) with x. (c) Normalized total scattering cross sections for the intrinsic scattering characteristics χ io (‐‐) and the ensemble χ (–) with x. x = ka for the intrinsic scattering and x = kac for the ensemble scattering. k is the wavenumber.

FIG. 2.

Variation with x of (a) the ensemble form function f and (b) the ensemble normalized total scattering cross section χ, for β = 0.8 (‐‐), 1.0 (–), and 1.2 (···). The two vertical lines indicate the values of x = kac used in the simulated suspension inversions.

FIG. 3.

Profiles of the variation with height above the bed, z, of (a) the normalized mean particle radius, ac/ar , for l = 0 (–) and l = 0.1 m (‐‐) and (b) the normalized mass concentration, C/Cr .

FIG. 4.

Profiles from the iterative implicit inversion of the variation with range, r, of (a) normalized concentrations, Ms/Cr , when the particle size was range independent and known, (b) mean normalized particle size, as/ar , and (c) normalized concentration, Ms/Cr , when both mean particle size and concentration were unknown. The three lines are for β = 0.8 (‐‐), 1.0 (–), and 1.2 (···), the symbols represent Cr  = 1.0 (○), 5.0 (□), and 20 (▵) kgm−3.

FIG. 5.

(a) Profiles from the dual frequency inversion of the variation with range, r, of the normalized concentrations when the particle size was range independent and known. Profiles with range, r, from the hybrid constrained iterative implicit and dual frequency inversion of (b) the mean normalized particle size, as/ar and (c) the normalized concentration, Ms/Cr , when both mean particle size and concentration were unknown. The three lines are for β = 0.8 (‐‐), 1.0 (–), and 1.2 (···), the symbols represent Cr  = 1.0 (○), 5.0 (□), and 20 (▵) kgm−3.

FIG. 6.

Profiles of the variation with range, r, of the normalized concentration, Ms/Cr , from the constrained iterative implicit inversion when both the mean particle size and concentration were unknown. The three lines are for β = 0.8 (‐‐), 1.0 (–), and 1.2 (···), the symbols represent Cr  = 1.0 (○), 5.0 (□), and 20 (▵) kgm−3.

FIG. 7.

(a) Profiles of the variation with range, r, of the normalized concentration, Ms/Cr , from the dual frequency inversion when the particle size was range dependent and known. Profiles of the variation with range, r, from the hybrid constrained iterative implicit and dual frequency inversion of; (b) the mean normalized particle size, as/ar and (c) the normalized concentration, Ms/Cr , when both the mean particle size and concentration were unknown. The three lines are for β = 0.8 (‐‐), 1.0 (–), 1.2 (···) and Cr  = 20 kgm−3. The input profile for ac and C are given by the symbol (×).

FIG. 8.

Profiles of the variation with range, r, of the normalized concentration profiles, Ms/Cr , when the particle size was range independent and known. (a) Iterative implicit inversion and (b) dual frequency inversion. The lines are from simulated inversions and the open circles are from inversions using the measured backscattered signal. The symbol represent the different values for β; 0.9 (*), 0.95 (▵), 1.0 (×), 1.05 (□), 1.1 (+).

FIG. 9.

Profiles of the variation with range, r, of the normalized mean particle size, as/ar and the normalized concentration, Ms/Cr . (a) and (b) were obtained using the iterative implicit inversion and (c) and (d) were obtained using the hybrid constrained iterative implicit dual frequency inversion. The lines are from simulated inversions and the open circles from inversions using the measured backscattered signal. The lines are for β = 0.95 (‐‐), 1.0 (–), 1.05 (···).

FIG. 10.

Plot of the ratio of the concentration noise relative to the backscatter signal noise, σ(me )/σ(ve ), with the ratio of the normalized total scattering cross sections, χ12. The solid circles were obtained using Eq. (15) and the solid line is given by (1− χ12)−1.

/content/asa/journal/jasa/130/3/10.1121/1.3618728
2011-09-02
2014-04-20

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Scitation: Acoustic inversions for measuring boundary layer suspended sediment processes
http://aip.metastore.ingenta.com/content/asa/journal/jasa/130/3/10.1121/1.3618728
10.1121/1.3618728
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