Unified escription of cattering and ropagation FY13 Annual Report

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1 DISTRIBUTION STATEMENT A. Approved for public release; distributio is ulimited. Uified escriptio of catterig ad ropagatio FY13 Aual Report David Paul Kobles Applied Research Laboratories The Uiversity of Texas at Austi PO Box 8029 Austi, TX phoe: (512) fax: (512) Award Number: N LONG-TERM GOALS The log-term goal of the research is to icrease the physical uderstadig of acoustic propagatio ad scatterig i cotietal shelf ad slope eviromets i the Hz bad. This icludes both the physics of the seabed ad the couplig to physical mechaisms i the water colum i complex rage- ad azimuth-depedet littoral waveguides. OBJECTIVES For FY13, the first objective was to ivestigate the statistics of the mode itesity ad cross-mode coherece that result from scatterig from a radomly rough seabed surface i a shallow water eviromet. The secod objective was to extract iformatio about the frequecy depedece of seabed atteuatio for a soft thick sedimet. APPROACH This research represets a collaborative effort betwee David Kobles ad Dr. Jaso Sagers, also with the Applied Research Laboratories, The Uiversity of Texas at Austi. The methods used to achieve the scietific goals ad objectives are based o theoretical advaces made over the previous two years. Two ideas i particular are uique to the aalysis approach. For shallow water eviromets ad acoustic frequecies below about 500 Hz, a coupled mode itegral equatio method that separates forward ad backward propagatig modal amplitudes i a physically cosistet maer [1] is employed to ivestigate the statistics of propagatio ad scatterig from a radomly rough seabed. For statistical iferece of sedimet atteuatio dispersio, a maximum etropy method [2] is applied to ewly recovered acoustic broadbad data collected i the Gulf of Oma basi. 1

2 1. Statistics of propagatio ad scatterig The approach employed to examie the statistics of scatterig ad propagatio, i a uified maer, utilizes a itegral equatio coupled mode method that was recetly placed ito a formulatio that splits the modal amplitudes ito forward ad backward compoets. The critical aspect of the splittig is that the amplitudes are costraied to satisfy the appropriate asymptotic boudary coditios [1]. I cotrast the backward compoet of the modal amplitudes i the COUPLED algorithm developed by Evas [3] does ot satisfy the boudary coditio (amplitude must be fiite) at the origi i a cylidrical coordiate system. The appropriate boudary coditios deped o the choice of coordiate system. The 2-D coupled mode equatios of dimesio 2N for the forward ad backward modal amplitudes ( R + + (x) = [R 1, R + 2,..., R + N 1, R + ] ad R (x) = [R 1, R 2,..., R N 1, R N ] ) i Cartesia coordiates are R x x N x N + (x) = G + (x, x")s (x")dx"+ G + + (x, x") C m (x")r m (x")dx"+ G + (x, x") C m (x")r m (x")dx" 0 0 m=1 0 m=1 N N. (1) R (r) = G (x, x")s (x")dx"+ G + (x, x") C m (x")r m (x")dx"+ G (x, x") C m (x")r m (x")dx" x x m=1 x m=1 where S is the modal source fuctio for the th mode, C m is the mode couplig matrix operator, ad + N is the total umber of modes. G ad G are the forward ad backward propagatig Gree s fuctios that satisfy the appropriate asymptotic boudary coditios The seabed possesses spatial ihomogeeities i the form of fie-scale iterface roughess ad volume fluctuatios i the soud speed ad desity. Thus, a sigle ocea acoustic measuremet (or predictio) of propagatio ad scatterig should be treated as a sample from a esemble of possible acoustic field microstates. The, like may other areas of physics, the meaigful quatities of iterest become averages of physical quatities over a esemble of sample measuremets or predictios. Radom realizatios of the seabed roughess are geerated from a roughess power spectrum. For each + realizatio Eq. (1) is solved for R (r) ad R (r). The, the esemble averages of the modal itesities < R + 2 > ad < R 2 >, ad the cross-mode cohereces < R + (R + ) * >, < R (R ) * m m >, ad < R + (R ) * m > are computed for a sufficiet sample size. 2. Maximum etropy based approach to statistical iferece A statistical iferece approach seeks to aswer the questio, Give data D what iformatio ca be iferred about model parameters M? A Bayesia approach is a well-defied method to aswer this questio. A likelihood fuctio is costructed ad Bayes s formula the yields a posterior probability distributio (PPD) from which the iformatio cotet for various model parameters are quatified. The key step is the costructio of the likelihood. I this step it is ecessary to make prior assumptios about the statistics of data-model errors. I Ref. 2 a maximum etropy (ME) approach was itroduced that also computes a PPD. However, istead of first costructig a likelihood ad usig Bayess rule, the PPD is directly obtaied i the form of a caoical distributio, the most coservative distributio possible. No prior assumptios are made about the distributio of model ad data errors. Rather, the caoical distributio becomes uique oce certai costraits o the average error are specified. Referece 2 itroduced a method where the costrait values ca be estimated whe there exist a 2

3 sufficiet umber of data samples that form a esemble. This idea of data esembles is cosistet with the cocept of computig/measurig esemble averages of acoustic fields i the ocea. The data curretly beig aalyzed are well suited for the ME approach as a result of a large umber of data samples ad its aalysis could potetially provide useful iformatio o the seabed atteuatio dispersio. The data were take i the Gulf of Oma basi i the form of received time series sigals geerated by SUS explosios alog a 200 km track. The physics that drives the iformatio part of the process is that the received sigals are composed of arrivals that have refracted withi the body of the sedimet. The approach attempts to obtai margial distributios for the soud speed ratio ad a gradiet, assumig omial atteuatio values. Oce parameter values are established that adequately predict the arrival time structure of the various refractig multipaths, the statistics of the frequecy depedet atteuatio are the established. WORK COMPLETED The work completed i FY13 icludes the applicatio of the split itegral equatio coupled mode methodology to quatify the esemble-averaged modal itesity ad cross-mode coherece for a case of strog (Bor series does ot coverge) seabed scatterig. Also, prelimiary results have bee obtaied for the frequecy depedece of the atteuatio for a soft seabed sedimet usig data collected i the Gulf of Oma. A mauscript is i preparatio for the applicatio of ME to obtai the soud speed structure of the sedimet. RESULTS 1. Statistics of the mode itesity ad cross-mode coherece The effect of seabed roughess o the modal itesities ad cross-mode coherece as a fuctio of rage was examied for a shallow water waveguide [4]. The backgroud waveguide is 50 m deep with a stratified soud speed profile (SSP) over a half-space. The half-space soud speed ad desity are 1645 m/s ad 1.9 g/cm 3, respectively. The SSP was oe measured durig the SW06 experimet ad has a thermoclie depth at about 20 m. The roughess waveumber power spectrum employed to geerate a 1-D rough seabed realizatio is K L h 2 P(k) = π (K L + k 2 ), (2) 2 γ /2 where h, K L, γ, ad k are the rms roughess height, the roll-off waveumber give by the reciprocal of the roughess correlatio legth, the scatterig expoet, ad the spatial waveumber, respectively. Values selected for γ, K L, ad h i Eq. 2 were 2.0, 0.1 m -1, ad 0.25 m, respectively. These parameters geerate realizatios that are cosistet with a very rough seabed surface classificatio. The roughess realizatios were the superimposed oto the 50 m flat bathymetry. For the computatios i this study the depth of the waveguide was set to its backgroud value for x < x a ad x > x b, with x a ad x b set to 1000 ad 9000 m, respectively. Computatios were made with the seabed atteuatio set to 0.0 for the purpose of testig the predictio of modal equipartitio assumig that < R + 2 R 2 > ad < > satisfied a master equatio [5-6]. Also, computatios were made for a seabed atteuatio set to 0.4 db/λ for the purpose of testig the effect of the esemble-averaged modal itesities ad cross-mode coherece to a typical atteuatio for a sad sedimet. 3

4 FIGURE 1. Esemble-averaged modal itesities for zero atteuatio case: (a) forward compoet 50 m source depth, (b) backward compoet 50 m source depth, (c) forward compoet 38 m source depth, ad (d) backward compoet 38 m source depth. Figure 1 shows < R + 2 > ad < R 2 > for the zero-atteuatio case. The acoustic frequecy is 300 Hz. R + 2 While < > does ot have the high variability observed for a sigle realizatio, it does possess a complex structure o both small ad large spatial scales. Geerally, eve though there is sigificat modal scatterig from for x a < x < x b the asymptotic (x > x b ) modal itesity distributios do ot exhibit equipartitio for either the 50 m ad the 38 m source depth case as would be predicted by a solutio to a master equatio without atteuatio [5-6]. Rather, the asymptotic distributio for the forward propagatig modes is strogly iflueced by the iitial distributio of mode itesity at x=0. Figure 2 shows < R + 2 > ad < R 2 > for the o-zero atteuatio case. The additio of atteuatio chages the ature of the modal evolutio with rage i a profoud maer sice the propagatio provided by G + is damped as a result of atteuatio give by the imagiary part of the horizotal waveumber eigevalues; < R + 2 > has the characteristic feature of a decrease i mode itesity with icreasig x ad mode umber. This is a mode strippig effect. The atteuatio also causes < R 2 > to be substatially differet from the zero atteuatio case. As a result of the atteuatio mode 8 o loger cotais the largest portio of the backscattered field. While it is still true that < R 2 > will icrease, albeit i a o-uiform maer, for decreasig x, the additioal factor of atteuatio causes peaks i < R 2 > for x > 0. 4

5 FIGURE 2. Esemble-averaged modal itesities for o-zero atteuatio case: (a) forward compoet 50 m source depth, (b) backward compoet 50 m source depth, (c) forward compoet 38 m source depth, ad (d) backward compoet 38 m source depth. Figure 3 shows < R + (R + ) * >, < R (R ) * >, ad < R + (R ) * m m m > for zero atteuatio ad the source depth at 50 m. The cross-mode cohereces i Fig. 3 have bee ormalized such that they have values betwee 0 ad uity. There are sixtee subpaels, each cotaiig sixtee esemble-averaged crossmode coherece versus mode umber ad rage. Overall, < R + (R + ) * m > is ear uity betwee 0 ad 5 km ad the decreases very slightly for rages greater tha 5 km. This observatio is cosistet with the observatio i Fig. 1 that < R + 2 > does ot show sigs of equipartitio. O the other had < R (R ) * > is sigificatly smaller tha < R + (R + ) * m m > ad the cross-coherece with rage might be described as complicated. For < R + (R ) * > coherece levels are about the same size as < R (R ) * m m >. However, much of the structure i the cross-mode coherece is idepedet of the th modal idex. This is evidet i either the upper half of the first group of eight subpaels or the lower half of the secod group of eight subpaels i Fig. 3. 5

FIGURE 3. Esemble-averaged modal cross-mode coherece for zero atteuatio case with source depth of 50 m. 2. Frequecy depedece of seabed atteuatio i a soft thick seabed.

6 FIGURE 3. Esemble-averaged modal cross-mode coherece for zero atteuatio case with source depth of 50 m. 2. Frequecy depedece of seabed atteuatio i a soft thick seabed. Addressed is the statistical iferece of the soud speed depth profile ad atteuatio of a thick soft seabed from broadbad soud propagatio data recorded i the Gulf of Oma basi. The acoustic data are i the form of time series sigals recorded i 1977 o a sparse vertical lie array ad geerated by explosive sources deployed alog a 250 km track. A maximum etropy (ME) method is employed to obtai margial probability distributios for values of the soud speed ratio ad the soud speed gradiet. The specific types of data from which iformatio about the sedimet soud speed structure is iferred are those where most of the eergy travels alog sedimet refractig paths. The ME aalysis of the Gulf of Oma data reveals a rage-depedece of the margial distributios for the soud speed ratio ad the gradiet. There is o evidece for a o-liear depth profile. This rage-depedece appears to be drive by a iheret parameter ambiguity betwee the ratio ad the gradiet. This aalysis is icomplete; however, a prelimiary result is show here. A more complete discussio will be provided i Ref. 7. 6

a Time - sec Time - sec Level - db rel 1 upa 2 b % Time - sec Time - sec FIGURE 4.

receiver depth ad (b) 3321 m receiver depth. Source depth is 88 m.

$A icrease i the arrival umber correspods to a icrease i the umber of bottom iteractios or equivaletly the grazig agle of the refracted$ raypaths icrease with icreasig time of arrival.

raypaths icrease with icreasig time of arrival.

7 a Time - sec Time - sec Level - db rel 1 upa 2 b % Time - sec Time - sec FIGURE 4. Modal (right) ad data (left) comparisos of spectrograms of received acoustic itesity for a source-receiver rage of about 99 km: (a) 1685 m receiver depth ad (b) 3321 m receiver depth. Source depth is 88 m. Figure 4 shows a model-data compariso of a spectrogram of the received time series i a 200 Hz bad. The sigal is characterized by multiple arrivals. A icrease i the arrival umber correspods to a icrease i the umber of bottom iteractios or equivaletly the grazig agle of the refracted raypaths icrease with icreasig time of arrival. Thus, the later the arrival time the greater depth ito the sedimet that the acoustic field peetrates. The mea soud speed ratio is ad the soud speed gradiet is about /s. Hamilto ad Bachma previously reported values of about 0.99 ad 1.3 1/s for the ratio ad gradiet, respectively, usig high agle 2-way travel time reflectio data measured o soobuoys [8]. The atteuatio is assumed to have the form of A( f ) = α( f / 1000) (4) where f is i Hz ad α is i 1 khz. A(f) has uits of db/m. 7

8 The earliest arrival saturated the data recordig o the magetic tape, ad thus appears at a lower level tha i the modeled arrival. However, the agreemet betwee the model ad the data for the remaider of the arrivals appears fairly good up to about 15 secods where the sigal to oise ratio of the data becomes too small. The values used for α ad i Fig. 4 were khz ad 1.15, respectively. At this early poit i the aalysis, the differece of the expoet from uity is too small to view the dispersio to be differet from liear. The statistical aalysis of the atteuatio is curretly uderway. IMPACT/APPLICATIONS Oe potetial impact of this research is that these studies may assist i uderstadig how to optimally combie advaced propagatio models ad iformatio iferece methods as oe proceeds to study ocea waveguides with icreasig complexity ad ihomogeeity. The issue of mode coherece is of direct importace to uderstadig soar. TRANSITIONS The combied studies of statistical iferece ad the statistical effects of seabed scatterig are expected to relate propagatio statistics to physical mechaisms o cotietal shelf ad slope eviromets. RELATED PROJECTS Related research projects iclude applyig maximum etropy to issues i passive soar. REFERENCES 1. D. P. Kobles ad J. D. Sagers, A olocal effective operator for couplig forward ad backward propagatig modes i ihomogeeous media, J. Acoust. Soc. Am (2011). 2. D. P. Kobles, J. D. Sagers, ad R. A. Koch, Maximum etropy approach for statistical iferece i a ocea acoustic waveguide, J. Acoust. Soc. Am (2012). 3. R. Evas, The decouplig of stepwise coupled modes, J. Acoust. Soc. Am. 80, (1986). 4. D. P. Kobles ad J. D. Sagers, Forward ad backward modal statistics for rough surface scatterig i shallow water, submitted to Joural of Computatioal Acoustics, August L. B. Dozier ad F. D. Tappert, Statistics of ormal mode amplitudes i a radom ocea. I. Theory, J. Acoust. Soc. Am (1978). 6. J. A. Colosi ad A. K. Morozov, Statistics of ormal mode amplitudes i a ocea with radom soud speed perturbatios: Cross-mode coherece ad mea itesity, J. Acoust. Soc. Am (2009). 7. J. D. Sagers ad D. P. Kobles, Statistical iferece of seabed soud speed structure i Gulf of Oma basi, i preparatio for the Joural of Acoustical Society of America. 8. E. L. Hamilto ad R. T. Bachma, Geoacoustic models of the sea floor: Gulf of Oma, Arabia Sea, ad Somali Basi, Techical Report 357, Naval Ocea Systems Ceter (1978). 8

9 PUBLICATIONS 1. D. P. Kobles ad J. D. Sagers, Forward ad backward modal statistics for rough surface scatterig i shallow water, udergoig peer review i Joural of Computatioal Acoustics, August D. P. Kobles, The effect of surface roughess o the iferece of frequecy dispersio of seabed atteuatio, i Advaces i Ocea Acoustics: Proceedigs of the 3rd Iteratioal Coferece o Ocea Acoustics (OA2012), Beijig, Chia, AIP Coferece Proceedigs edited by Jixu Zhou, Zhegli Li, ad Jeffrey Simme, Melville, New York Publicatio Date: December 17, N. Ross Chapma ad D. P. Kobles, Perspectives o geoacoustic iversio, i Advaces i Ocea Acoustics: Proceedigs of the 3rd Iteratioal Coferece o Ocea Acoustics (OA2012), Beijig, Chia, AIP Coferece Proceedigs edited by Jixu Zhou, Zhegli Li, ad Jeffrey Simme, Melville, New York Publicatio Date: December 17,

CHAPTER 5 A NEAR-LOSSLESS RUN-LENGTH CODER

95 CHAPTER 5 A NEAR-LOSSLESS RUN-LENGTH CODER 5.1 GENERAL Ru-legth codig is a lossless image compressio techique, which produces modest compressio ratios. Oe way of icreasig the compressio ratio of a ru-legth