Geoacoustic inversion using combustive sound ... - Semantic Scholar

Potty et al.: JASA Express Letters

关DOI: 10.1121/1.2960974兴

Published Online 28 August 2008

Geoacoustic inversion using combustive sound source signals Gopu R. Potty and James H. Miller Department of Ocean Engineering, University of Rhode Island, Narragansett, Rhode Island 02882 [email protected], [email protected]

Preston S. Wilson Applied Research Laboratory, University of Texas, P.O. Box 8029, Austin, Texas 78713-8029 [email protected]

James F. Lynch and Arthur Newhall Applied Ocean Physics and Engineering, Woods Hole Oceanographic Institution, Woods Hole, Massachusetts [email protected], [email protected]

Abstract: Combustive sound source (CSS) data collected on single hydrophone receiving units, in water depths ranging from 65 to 110 m, during the Shallow Water 2006 experiment clearly show modal dispersion effects and are suitable for modal geoacoustic inversions. CSS shots were set off at 26 m depth in 100 m of water. The inversions performed are based on an iterative scheme using dispersion-based short time Fourier transform in which each time-frequency tiling is adaptively rotated in the time-frequency plane, depending on the local wave dispersion. Results of the inversions are found to compare favorably to local core data. © 2008 Acoustical Society of America PACS numbers: 43.30.Pc, 43.60.Hj, 43.60.Mn [WC] Date Received: March 26, 2008 Date Accepted: April 10, 2008

1. Introduction The “long range sediment tomography technique,” developed by Potty et al. (2000), uses the arrival time dispersion of acoustic normal modes to estimate the compressional wave speeds of the ocean sediment. The technique is based on matching the observed modal arrival times with predicted ones for various “candidate models.” The search for the model which produces the best match is carried out using a global optimization scheme. Time-frequency analysis using the short time Fourier transform (STFT) or the wavelet transform (WT) enables us to accurately observe the modal arrival times. Time-frequency analysis of combustive sound source (CSS) data collected during shallow water (SW06) shows fewer mode arrivals (3–5 modes) compared to explosive sources (7–9 modes; Potty et al., 2000). These arrivals are in the frequency range 20– 200 Hz and resolution of the modal arrivals is poor at the lower frequencies 共20– 100 Hz兲. Considering the fewer number of mode arrivals present in the data it is important to increase the quality of the available arrivals especially at lower frequencies. In order to achieve this we use a new adaptive approach which utilizes the local group velocity in the time-frequency analysis. An iterative scheme inputting acoustic data collected during the (SW06) experiment is used to estimate the compressional wave speeds of the sediments in the New Jersey shelf area. These results will be compared to other bottom property studies in the region. 2. Dispersion based short time Fourier transform (DSTFT) Conventional time-frequency analysis techniques such as the STFT and the WT have often been used for the analysis of dispersive waves. However, their time-frequency tilings do not consider the dispersion effect explicitly. We have modified these approaches and used an adaptive timefrequency analysis method, originally proposed by Hong et al. (2005), whose time-frequency tilings depend on the dispersion characteristics of the signal to be analyzed. This method, called

EL146 J. Acoust. Soc. Am., Vol. 124, No. 3, Pt. 2, September 2008

© 2008 Acoustical Society of America

关DOI: 10.1121/1.2960974兴



Fig. 1. Determination of the rotation parameter 共left panel兲 and the steps involved in the inversion process using DSTFT 共right panel兲

the dispersion based short time Fourier transform (DSTFT), is performed by adaptively rotating each of the analysis atoms in the time-frequency plane with respect to the wave dispersion relationship. For a square integrable function f共t兲, the DSTFT at any time-frequency location 共u , ␰兲 is defined as follows: Df共u, ␰兲 =

冕

⬁

冕冋冑冉冊 ⬁

f共t兲g¯共s,u,␰,d兲共t兲dt =

−⬁

f共t兲

−⬁

1

s

g

册

t−u 2 丢共id兲−1/2e−i共t /2d兲 e−i␰tdt, 共1兲 s

where g¯ denotes the complex conjugate of the analysis window g共t兲 which is given by g共s,u,␰,d兲共t兲 =

冋冑冉冊 1

s

g

册

t−u 2 丢共id兲−1/2e−i共t /2d兲 ei␰t . s

共2兲

The symbol 丢 denotes the convolution operator, parameter s determines the size of the window, and the parameter d determines the amount of rotation of the time-frequency tile in 共u , ␰兲, such that d = d共u, ␰兲 =

⌬u . ⌬␰

共3兲

The group delay of the basis function of Eq. (2) in the time-frequency plane is given by Hong et al. (2005)

␶共␻兲 =

冋

册

d d u共␻ − ␰兲 + 共␻ − ␰兲2 = u + d共␻ − ␰兲. d␻ 2

共4兲

Equation (4) implies that the time-frequency tile in 共u , ␰兲, using the basis function of Eq. (2), can be obtained by rotating or shearing the time-frequency tile of the standard STFT, using the parameter d共u , ␰兲. Therefore if we choose d共u , ␰兲 with respect to the local wave dispersion, the resulting time-frequency tiling will correspond to the entire wave dispersion behavior. To use the DSTFT, the value of the parameter d has to be evaluated, based on the local dispersion behavior, at all the locations of interest 共u , ␰兲 in the time-frequency plane. The procedure for the calculation of “d” is graphically illustrated in Fig. 1 (left panel). The parameter d共u , ␰兲 can be written as

J. Acoust. Soc. Am., Vol. 124, No. 3, Pt. 2, September 2008

Potty et al.: Geoacoustic inversion EL147

关DOI: 10.1121/1.2960974兴


d共ui, ␰j兲 =


⌬t ti+1 − ti−1 D/Cg共␰i + 1兲 − D/Cg共␰i − 1兲 = = , ⌬␻ ␰j+1 − ␰j−1 ␰j+1 − ␰j−1

共5兲

where D is the range and Cg is the group velocity at the location 共ui , ␰j兲. To begin the inversion process we need to assume background values for the group speeds as a function of frequency corresponding to various modes. Based on these values we can initialize the inversion process by calculating the rotation parameter d共u , ␰兲 using Eq. (5). Using the values of d at all timefrequency locations, the DSTFT can now be computed and the arrival times corresponding to individual modes can be picked as a function of frequency. These modal arrival times form the input data for our sediment tomography technique (Potty et al., 2000). Output of this inversion provides values of the compressional wave inversion of the sediments. The group velocities of the normal modes are then recomputed based on these new sediment sound speed values and new estimates of the rotation parameter d共u , ␰兲 are found using Eq. (5). Time-frequency analysis can now be performed again, using these new values of the rotation parameter, to recompute the modal arrival times. These iterative steps are repeated to achieve convergence of the group velocity estimates. Figure 1 (right panel) summarizes the steps involved in the inversion scheme described above. 3. Shallow water experiment 2006 (SW06) and combustive sound sources (CSS) During the SW06 experiment, the combustive sound source (CSS) was deployed at 26 m depth from R/V Knorr in water depths of approximately 100 m. A combustible gas mixture of electrolytically derived hydrogen and oxygen was captured in the combustion chamber of the CSS and ignited with a spark. The ensuing burning produced expanding gases which in turn produced high intensity, low frequency acoustic pulses (Wilson et al., 1995). The left panel in Fig. 2 shows the various stages of CSS generation for a conical shaped source. Cylindrical shaped sources were used in the SW06 experiment but the CSS generation is similar. These acoustic signals were received at the single hydrophone receiver units (SHRUs) deployed by the Woods Hole Oceanographic Institution. The time-frequency diagram of the received acoustic signal is shown in the right panel of Fig. 2. The first three acoustic mode arrivals are clearly seen and also modes 4 and 5 which are only partly present in the data. The SHRUs were deployed at water depths ranging from 65 to 110 m. The results presented here correspond to the CSS deployed at 39° 5.5174⬘ N and −73° 5.5816⬘ E and the receiver (SHRU) was located at 38° 57.6715⬘ N, −72° 54.8139⬘ E. The source to receiver range was 21.24 km. The bathymetry is range dependent and hence the acoustic propagation was modeled using adiabatic mode theory assuming six range sections. The sediment properties were assumed range independent and the depth variation of the sediments was modeled using sediment layers of unknown thickness over an acoustic basement. 4. Iterative scheme to estimate the compressional wave speed A geoacoustic model based on historic data from the experimental location (Jiang et al., 2007) was used in the beginning to initialize the parameter d共u , ␰兲. Group velocities corresponding to each normal mode were used to compute d共u , ␰兲 which were then assigned to time-frequency locations in the neighborhood of the normal mode. This is the key step in the time-frequency analysis and the inversion process—the modal group speeds as a function of frequency need to be mapped correctly into the time-frequency plane. The modal arrival times are thus chosen from the DSTFT and the tomography inversion is carried out using these values. A new estimate of the modal group speeds is made and the steps are then repeated to get a new estimate until the group speed values converge. Figure 3 (left panel) shows the compressional wave speeds in the top 40 m of the sediments estimated by the inversion scheme. The dashed line is the geoacoustic model proposed by Jiang et al. (2007). They suggested this model for the SW06 experimental area based on chirp sonar inversions, grab samples, in situ probes, and shallow core measurements. The middle panel in Fig. 3 shows the standard deviations associated with these compressional wave


Potty et al.: Geoacoustic inversion


关DOI: 10.1121/1.2960974兴


Fig. 2. 共Color online兲. Left panel shows cross section of the CSS combustion chamber. The right panel shows the time-frequency diagram calculated using the wavelet 共top兲 and DSTFT 共bottom兲 methods. The continuous lines in the DSTFT diagram represent theoretical modal arrival times computed using the inversion results.

speed inversions. The standard deviations are of the order of 20 m / s except at 20 m depth where the uncertainty is higher. Compressional wave speeds in the top 15 m of the sediment are compared (right panel in Fig. 3) with data from the AHC-800 core (Norfjord, 2005) which was close to the source-receiver path. The AHC-800 data show the type of sediments and the sediment acoustic velocities in various layers. The sediments in the top 15 m are generally sandy in nature and interbedded with mud and shells. The inversion captures the trend present in the core data very well, though the average values of the compressional wave speeds are lower than the core data (but higher than the model of Jiang et al.). The maximum difference between the inversion and the core data as well as the model of Jiang et al. occurs in the near surface sediments 共0 – 3 m兲. This could be due to the fact that only the lower order modes (in the frequency range 20– 200 Hz) were used for the inversion. It should be also be noted that the inversions correspond to much lower frequencies compared to the frequencies at which the cores are usually logged 共⬃20 kHz兲. This can cause differences in values of compressional wave speeds obtained from cores and inversion if frequency dispersion effects are present. The timefrequency diagram was calculated using the DSTFT with input geoacoustic values corresponding to the inversion is shown in Fig. 2. We can note that the modes are now better resolved in time at lower frequencies, which is particularly evident in the case of mode 1. The solid lines in

J. Acoust. Soc. Am., Vol. 124, No. 3, Pt. 2, September 2008

Potty et al.: Geoacoustic inversion EL149


关DOI: 10.1121/1.2960974兴


Fig. 3. 共Color online兲 The inversion results for the top 40 m of the sediment 共left panel兲 and the standard deviation 共middle panel兲. The dashed line in the left panel is the Jiang-Chapman geoacoustic model 共2007兲. The right panel shows the comparison of the inversion with data from AHC-800 core. The continuous black line in the right panel is the inversion result.

the figure correspond to the theoretical arrival times calculated based on the inversion. They agree well in most of the frequency bands, except for modes 1 and 3 in the 140– 200 Hz band. Efforts are currently under way to repeat the inversions using data from other sources/receivers to explore the spatial variability of geoacoustic properties. Inversions to estimate the compressional wave attenuation will also be carried out using the CSS data. 5. Conclusions Geoacoustic inversions were successfully performed using CSS data collected during the SW06 Experiment. A new time-frequency analysis approach is introduced which uses the local group velocity values to rotate the time-frequency tiles. The time-frequency analysis is linked to the inversion which, after each iteration, provides new estimates of the modal group velocity values based on the inversions (compressional wave speeds). The results of the inversion compare well with published core data from the region. Acknowledgments This study was supported by Office of Naval Research, Ocean Acoustics Program (Code 321 OA). The authors would also like to thank Professor Yoon Young Kim (Seoul National University) for providing the software for the dispersion based short-time Fourier transform analysis and helping with its implementation. References and links Hong, J.-C., Sun, K. H., and Kim, Y. Y. (2005). “Dispersion based short-time Fourier transform applied to dispersive wave analysis,” J. Acoust. Soc. Am. 117(5), 2949–2960. Jiang, Y.-M., Chapman, N. R., and Badiey, M. (2007). “Quantifying the uncertainty of geoacoustic parameter estimates for the New Jersey shelf by inverting air gun data,” J. Acoust. Soc. Am. 121(4), 1879–1894. Norfjord, S. (2005). Late Quaternary geologic history of New Jersey middle and outer continental shelf, PhD thesis, University of Texas at Austin, p. 202. Potty, G. R., Miller, J. H., Lynch, J. F., and Smith, K. B. (2000). “Tomographic Inversion for sediment parameters in shallow water,” J. Acoust. Soc. Am. 108(3), 973–986. Wilson, P. S., Ellzey, J. L., and Muir, T. G. (1995). “Experimental investigation of the Combustive Sound Source,” IEEE J. Ocean. Eng. 20(4), 311–320.


Potty et al.: Geoacoustic inversion