SEMs of the mineral sands examined, showing (a) quartz, (b) shell, (c) magnetite, and (d) muscovite mica. The scale bar in each SEM depicts 500 μm.
Particle size distributions by mass [(a) and (b)] and PDF spectra [(c) and (d)] for mixed sediments i and ii, respectively. The mass distributions of the constituent mineral sands and the total mass distribution (—) are shown in (a) and (b). The single mineral (SM) and mixed sediment (MS) PDFs were calculated following Eqs. (16) and (19) , respectively in (c) and (d).
(Color online) The sediment tower, showing the ABS transducers, mixing assemblage, and pumps.
Comparison of measurements of χ with the sphere model predictions of χS (—) obtained using Eq. (4) for each mineral sand as labeled. The results of fitting the MSMs to the experimental data following Schaafsma and Hay (1997) , denoted MSM-1 (···), and following Thorne and Buckingham (2004) , denoted MSM-2 (– – –), are also shown.
Comparison of measurements of f with the sphere model predictions of fS (—) obtained using Eq. (5) , for each mineral sand as labeled. Two versions of the measurements of f are presented, those obtained by modeling χ using MSM-1 ( Schaafsma and Hay, 1997 ) in (a)–(d), and those obtained by modeling χ using MSM-2 ( Thorne and Buckingham, 2004 ) in (e)–(h). The results of applying each MSM to the predictions of fS are also shown for MSM-1 (···), MSM-2 (– – –), and MSM-3 (-.-).
Results of fitting the sphere model predictions of fS (—) to the experimental data, following Eq. (8) for MSM-1 (···), for each mineral sand as labeled.
Variation of the weighted mean form function, fWM , with x for mixed sediment ii, calculated using Eq. (21) , at 2 MHz (◻) and 4 MHz (•). For comparison, the modified sphere models (MSM-2) for the three minerals in the mixture, quartz (—), shell (···), and magnetite (– – –), are also shown.
Measurements of χ 0 [(a) and (b)] and f 0 [(c) and (d)] obtained from mixed sediments i and ii, respectively. Theoretical predictions of ensemble scattering following the mixed sediment (MS) method (—) and single mineral (SM) method (···) are also shown. The envelope of the intrinsic scattering properties for the constituent minerals in each mixture is shown by the shaded area.
Mean particle aspect ratio, ar , number of particles measured, Sn , and physical characteristics of each mineral sand examined. S.E. denotes the standard error about the mean, and ε is the uncertainty associated with the laboratory volume displacement measurements.
Summary of grain size distribution statistics for each mixed sediment (MS) shown in Fig. 2 . See text for definition of symbols.
Normalized rms differences, expressed as percentages, between the theoretical predictions and laboratory measurements of χ and f, for each mineral sand and each MSM examined (defined in Secs. II B and IV B ).
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