Frequency variability of modal attenuation coefficients
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1 Frequency variability of modal attenuation coefficients Wendy Saintval and William L. Siegmann Rensselaer Polytechnic Institute Troy, New York William M. Carey and Allan D. Pierce Boston University Boston, Massachusetts 153 rd Meeting of the Acoustical Society of America Salt Lake City, Utah
2 Motivation and Objectives Modal attenuation coefficient (MAC) Fundamental for TL decrease with range Tolstoy, Tindle, Ingenito Experimental results NJ Continental Shelf Gulf of Mexico Examine parameter sensitivity of MACs Variation of depth gradients in water, upper sediment Frequency dependence of intrinsic attenuation in upper sediment Analyze overall trends of transmission loss June 5, 2007 ASA-Salt Lake City 2
3 Governing Equations For Biot medium* Pressure solution (stratified environment) complex wavenumber *Simplified model of Pierce, Carey, Lynch, JASA (2003) and Pierce, Carey, Zampolli, Oceans IEEE-Brest (2005) June 5, 2007 ASA-Salt Lake City 3
4 ~ Modal Eigenvalue Problem for к 2 n BC Interface conditions (j = 0, 1) Radiation condition z s * H 0 H 1 r ρ 0, c 0 ρ 1, c 1 α 1 f m ρ 2, c 2, α 2 f z June 5, 2007 ASA-Salt Lake City 4
5 Modal Attenuation Coefficient (MAC) Normalization condition Rayleigh quotient MAC result MAC modal phase speed June 5, 2007 ASA-Salt Lake City 5
6 Three-layer Model Environment Simplified environment of NJ Continental Shelf Investigate dependence of MAC on SSPs Water Isospeed Linear gradients Upper sediment Isospeed Linear gradients Biot-model gradients z s = 36 m * H 0 = 73 m H 1 = 78 m z ρ 0 = 1025 kg/m 3 c 0 (z) ρ 1 (z), c 1 (z) α 1 (z, f ) f 2 r ρ 2 = 2650 kg/m 3 c 2 = 1740 m/s α 2 = 0.34 f /f 0 db/m June 5, 2007 ASA-Salt Lake City 6
7 Biot-Model Profiles (I) q(z) = Porosity profile Density ρ 1 (z)=qρ(h 0 )+(1-q)ρ(H 1 ) Compression index C I (Cederberg, et al., 1993, 1995) 78 June 5, 2007 ASA-Salt Lake City 7
8 Biot-Model Profiles (II) Given q(h 1 ), C I q(z), ρ 1 (z) q(z), ρ 1 (z) c 1 (z), α 1 (z, f 0 ) Near surface value from Hamilton (1980) with f 0 = 1 khz 78 June 5, 2007 ASA-Salt Lake City 8
9 SSPs: Water Isospeed, Sediment Linear Mode 1 ζ June 5, 2007 ASA-Salt Lake City 9
10 SSPs: Water Isospeed, Sediment Biot Mode 1 ζ June 5, 2007 ASA-Salt Lake City 10
11 SSPs: Water Linear, Sediment Linear Mode 1 ζ June 5, 2007 ASA-Salt Lake City 11
12 SSPs: Water Linear, Sediment Linear Mode 1 ζ June 5, 2007 ASA-Salt Lake City 12
13 SSPs: Water Linear, Sediment Biot Mode 1 ζ June 5, 2007 ASA-Salt Lake City 13
14 SSPs: Water Linear, Sediment Linear Mode 6 ζ June 5, 2007 ASA-Salt Lake City 14
15 Results: MAC SSP Dependence MAC (Δ n ~ f ζ n ) sensitive to water SSPs For isospeed water, intrinsic sediment attenuation α ~ f 2 à -0.9 < ζ n < -0.7 Downward refracting water à 0.9 < ζ n < 1.1 MAC values increase with water gradient MAC robust to sediment SSPs Linear, Biot gradients à similar ζ n Higher modes à similar ζ n June 5, 2007 ASA-Salt Lake City 15
16 Effective Attenuation Coefficient (EAC) Reduced Transmission Loss [db re: P(r=1 m)] Range-window averaged Least squares fit (EAC) r + const. EAC for f large: June 5, 2007 ASA-Salt Lake City 16
17 EAC: Example ζ e 0.8 June 5, 2007 ASA-Salt Lake City 17
18 MAC/EAC Connection (I) June 5, 2007 ASA-Salt Lake City 18
19 MAC/EAC Connection (II) f = 2000 Hz = EAC within 10% June 5, 2007 ASA-Salt Lake City 19
20 MAC/EAC Connection (III) f = 500 Hz 1000 Hz 1500 Hz 2000 Hz June 5, 2007 ASA-Salt Lake City 20
21 Water SSP sensitivity Results: EAC Isospeed: MAC ~ f ζ n à ζ n -1 EAC ~ f ζ e à ζ e 0 Downward refracting: MAC, ζ n 1 ± 0.2 EAC, ζ e from 0 to 0.9 Band of mode numbers contribute to accurate estimate of EAC Agreement with EAC to within 10% appears to require MACs below 0.6 db/km June 5, 2007 ASA-Salt Lake City 21
22 Gulf of Mexico Experiment Panama City, FL Experiment (Ferris 1969) Variable depth sources Frequencies: 400, 750, 1500 Hz Water depth: 31 ± 1 m Range: 5-15 km Vertical string of 9 hydrophones Data from bottom reflection (Ferris, Kuperman 1970) Density: 1750 < ρ 1 < 1850 kg/m 3 SS ratio: < c 1 /c 0 < fa 15 fa Modes, MACs calculated using SSP measurements (Ingenito 1972) Inferred sediment attenuation: 0.50 (f /f 0 ) 1.75 db/m June 5, 2007 ASA-Salt Lake City
23 GoM Modeling, Reexamination Examined 32 measured, 4 isospeed SSPs in rangeindependent waveguide Downward refracting (24) Isospeed or nearly so (9) Upward refracting (3) Following Ingenito: analyze Two frequencies: 400, 750 Hz First two modes Results: Isospeed, weakly downward refracting SSPs agreed well with previously calculated MACs 0 m * ρ 1 : 1850 kg/m 3 c 1 : varies α 1 = 0.50 (f /f 0 ) 1.75 db/m June 5, 2007 ASA-Salt Lake City z 1525 m/s c
24 Gulf of Mexico MACs Ingenito Ingenito June 5, 2007 ASA-Salt Lake City 24
25 Results: Gulf of Mexico Modeling Environmental effects on MACs Sensitive to water SSPs Bottom density changes negligible Bottom SS changes non-negligible Comparison with previous calculations Weakly downward refracting, isospeed SSPs lead to good agreement between MAC values Upward refracting, strongly downward refracting SSPs do not agree well Possible causes of disagreement Uncertainty in environmental parameters Uncertainties from inferred intrinsic sediment attenuation June 5, 2007 ASA-Salt Lake City 25
26 Acknowledgements Office of Naval Research Colleagues Dr. M. Kupferschmid Dr. R. Evans Dr. J. Lynch Dr. D. Chu Dr. I. Herron RPI staff, Family, Friends June 5, 2007 ASA-Salt Lake City 26
27 Questions June 5, 2007 ASA-Salt Lake City 27
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inter.noise 2000 The 29th International Congress and Exhibition on Noise Control Engineering August 2000, Nice, FRANCE
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