The Energy Flux Method for Reverberation: Modeling and Inversion

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1 DISTRIBUTION STATEMENT A Approved for public release; distribution is unliited The Energy Flux Method for Reverberation: Modeling and Inversion Ji-Xun Zhou School of Mechanical Engineering Georgia Institute of Technology Atlanta, GA phone: (404) fax: (404) eail: jixunzhou@egatechedu Award Nuber: N LONG-TERM GOALS The long-ter goals of this work are: (1) to develop a reverberation odel for predicting the reverberation level and the echo-to-reverberation ratio in shallow water (SW), and () to characterize the seabed scattering in a frequency band of Hz fro long-range broadband reverberation easureents OBJECTIES The scientific objectives of this work include: (1) to integrate the energy flux ethod for SW reverberation with physics-based seabed scattering odels for reverberation prediction and inversion, and () to analyze the echaniss of low-frequency (LF) seabed scattering, obtained fro reverberation data and the Biot seabed geo-acoustic odel APPROACH (1) The energy flux (angular power spectru) ethod for reverberation, based on the WKB approxiation to the noral-ode solution [1], is integrated with physics-based seabed scattering odels [] to get SW reverberation expressions; () The effective Biot acoustic odel for sandy and sand-silt ixture bottos, derived fro broadband LF field easureents at any locations [3], is used to odel two-way sound propagation in the reverberation; (3) The broadband reverberation data are used to characterize the seabed scattering; (4) The LF seabed scattering cross-sections, derived fro the long-range reverberation data, will be used to estiate the geo-physical paraeters of the seabed roughness and the sedient inhoogeneity, and to analyze LF seabed scattering echaniss RESULTS (1) The energy flux ethod for SW reverberation is integrated with the rough botto scattering (RBS) odel and the sedient volue scattering (SS) odel This integration directly and intuitively results in general expressions for SW reverberation in the angular doain and in the odal doain The resultant reverberation expressions can conveniently be used for predicting SW reverberation for the Pekeris waveguide or non-pekeris waveguide, respectively The reverberation intensity in shallow water, derived fro the energy flux ethod, can be expressed by a suation over noral odes: 1

2 Rrzz (,; ) c τ k k k β r w 0 α ( 1) exp( ) w r + 0 = e 1 1 π r n kw( z0) D( z0) + kw( z0) k kw( h) D( h) + kw( h) k kn( kn kn+ 1) exp( βnr) σθ (, θn) (1) 1 1 kw( h) D( h) + kw( h) kn kw( z) D( z) + kw( z) kn where kn is the longitudinal wave nuber of the nth ode, and βn is the odal attenuation coefficient r is distance, and h is the water depth; z 0 is the source depth and z is the receiver depth αw is the water absorption coefficient σθ [, θ n] is the botto scattering cross section per unit area; θ ( h) is the incident grazing angle of ode at the botto; and θn( h ) is the scattering angle of ode n kw( z) = π f / cw( z) is the wave nuber in the water τ 0 is the signal pulse duration Dz ( ) is a inor odification factor for overcoing a proble when a receiver is near a turning point, 1 dcw( z) Dz ( ) = 0875 () π f dz 3 For arbitrary velocity profiles, Eq (1) can be used to calculate SW long-range reverberation intensity by using the classic cross sections of seabotto scattering and any available noral-ode code This only requires two paraeters: real and iaginary parts of the odal eigenvalue k, and β () The integration of the energy flux ethod with seabed scattering odels also results in a siple relationship between the classic boundary scattering cross sections and the odal scattering atrix in SW waveguides: Φ( h) Φn( h) MSM (, n) = σθ (, ) (3) θn 1 + ( θ ) 1 + ( θ ) ww ww n Here MSM (, n ) is defined as the odal scattering atrix in the SW waveguide between an incident ode and a scattering ode n Φ ( h ) is the aplitude of th ode at the water-botto interface 1 where the odal angleθ = cos [ k / kw( h)] σθ (, θn) can be either the RBS cross section or the SS cross section ww is the sound reflection coefficient with the scripts ww added to indicate that the incident and reflected fields are both in the water (3) The data-odel coparisons show that the reverberation can alost be equally well predicted by using the RBS odel and SS odel Thus, the scattering paraeters for the RBS odel and the SS odel have been inverted fro reverberation data However, the reverberation level as a function of tie, RL() t, at one single frequency cannot uniquely deterine the seabed scattering paraeters As an exaple, Figure 1 shows the internal paraeter coupling for the RBS odel between the spectral exponent and the spectral strengthω : three different pairs of and ω would result in an identical RL() t An increase (decrease) in can be copensated for by an increase (decrease) inω (4) The wideband reverberation data as a function of frequency, ( ) RL f, at given reverberation ties can uniquely deterine a set of the botto roughness spectra or the sedient volue scattering cross

3 section As an exaple, Figure shows that the wideband reverberation data are used to uniquely invert a set of seabed scattering paraeters for the RBS and SS odels The botto roughness spectru and the sedient volue scattering cross section, inverted fro the broadband long-range reverberation data at the ASIAEX site, exhibit different characteristics fro those coonly used in HF For the HF, the roughness spectru exponent is restricted to the range of 4 with a ean value of 30; the LF roughness spectru exponent fro long-range reverberation data has saller values with a ean value around 13 The HF sedient volue scattering cross section σ is generally assued to have linear frequency dependence However, Figure 3 shows that theσ, inverted fro long-range reverberation data, exhibits uch stronger frequency dependence in the 150- (3805± 001) 500 Hz range: α = (00038 ± ) f, here f is frequency in a unit of khz (5) All the LF seabed scattering paraeters for the RBS odel and the SS odel, inverted fro the long-range (3 to 1 s) reverberation data, are listed in Table I The standard deviations between the easured reverberation data and the theoretical predictions for all the frequencies are also listed in Table I These seabed scattering paraeters for the RBS odel and the SS odel ay be used for future analyzing which one (or both) is doinating LF scattering echanis at low grazing angles In Figure and Table I, α p (in a unit of db/) is the sound attenuation in the sea bottos that obeys the Biot odel [3] IMPACT/APPLICATIONS The resultant reverberation expressions with the physics-based seabed scattering odels can conveniently be used to predict the SW reverberation and to characterize the LF seabed scattering RELATED PROJECTS NONE REFERENCES 1 JX Zhou, The Analytical ethod of angular power spectru, range and depth structure of the echo-to-reverberation ratio in shallow water Sound Field, (Chinese) ACTA ACUSTICA, 5 (), (1980) DR Jackson and MD Richardson, <High-frequency Seafloor Acoustics>, 616 pages, Springer, JX Zhou, XZ Zhang, and DP Knobles, Low-frequency geoacoustic odel for the effective properties of sandy seabottos, J Acoust Soc A, 15, (009) PUBLICATIONS 1 JX Zhou and X Z Zhang, Shear wave velocity and attenuation in the upper layer of ocean botto fro long-range acoustic field easureents, J Acoust Soc A, 13(6), , Dec 01 [published, refereed] JX Zhou and XZ Zhang, Integrating the energy flux ethod for reverberation with physicsbased seabed scattering odels: Modeling and inversion, J Acoust Soc A, 134 (1), 55-66, July 013 [published, refereed] 3

4 Fig 1 Internal paraeter coupling between the spectral exponent and the spectral strengthω for the RBS odel Three different pairs of and ω result in a identical RL() t An increase in can be copensated for by an increase in ω Fig Wideband reverberation data at the ASIAEX site are used to invert a set of seabed scattering paraeters for the RBS and SS odels 4

5 Fig 3 The sedient volue scattering cross section, inverted fro long-range reverberation data at 3805 the ASIAEX site, exhibits strong frequency dependence: α = f ( f in khz) Table I The LF seabed scattering paraeters for the RBS odel and the SS odel, inverted fro long-range (3 to 1 s) reverberation data at the ASIAEX site Models RBS : Botto roughness spectru W( K) = ω ( K) SS: olue scattering cross section: σ = σα * n v p Rev tie and rang-to-depth ratio 5 ω 10 std RBS ( db ) * σ n stdss ( db ) v t R = 30 r/ h =