Ocean acoustic interferometry.

Ocean acoustic interferometry refers to an approach whereby signals recorded from a line of sources are used to infer the Green's function between two receivers. An approximation of the time domain Green's function is obtained by summing, over all source positions (stacking), the cross-correlations between the receivers. Within this paper a stationary phase argument is used to describe the relationship between the stacked cross-correlations from a line of vertical sources, located in the same vertical plane as two receivers, and the Green's function between the receivers. Theory and simulations demonstrate the approach and are in agreement with those of a modal based approach presented by others. Results indicate that the stacked cross-correlations can be directly related to the shaded Green's function, so long as the modal continuum of any sediment layers is negligible.

[1]  N. Chapman,et al.  Bayesian geoacoustic inversion in a dynamic shallow water environment. , 2008, The Journal of the Acoustical Society of America.

[2]  Richard A. Tapia,et al.  A trust region strategy for nonlinear equality constrained op-timization , 1984 .

[3]  Mickael Tanter,et al.  Recovering the Green's function from field-field correlations in an open scattering medium. , 2003, The Journal of the Acoustical Society of America.

[4]  Richard L. Weaver,et al.  On the emergence of the Green's function in the correlations of a diffuse field: pulse-echo using thermal phonons. , 2001, Ultrasonics.

[5]  P. Schultz,et al.  Fundamentals of geophysical data processing , 1979 .

[6]  Peter Gerstoft,et al.  Effect of ocean sound speed uncertainty on matched-field geoacoustic inversion. , 2008, The Journal of the Acoustical Society of America.

[7]  G. M. Wenz.  Acoustic Ambient Noise in the Ocean: Spectra and Sources , 1962 .

[8]  Yingjie Yang,et al.  Processing seismic ambient noise data to obtain reliable broad-band surface wave dispersion measurements , 2007 .

[9]  K. Wapenaar,et al.  Green's function representations for seismic interferometry , 2006 .

[10]  M. Fink,et al.  Ultrasonic pulse compression with one-bit time reversal through multiple scattering , 1999 .

[11]  W. Kuperman,et al.  Passive in vivo elastography from skeletal muscle noise , 2007 .

[12]  S. Glenn,et al.  Shallow Water '06: A Joint Acoustic Propagation/Nonlinear Internal Wave Physics Experiment , 2007 .

[13]  M. Porter,et al.  Gaussian beam tracing for computing ocean acoustic fields , 1987 .

[14]  D. V. Holliday.  Fundamentals of acoustical oceanography , 1999 .

[15]  James D. Irish,et al.  Acoustic and oceanographic observations and configuration information for the WHOI moorings from the SW06 experiment , 2007 .

[16]  T. Coleman,et al.  On the Convergence of Reflective Newton Methods for Large-scale Nonlinear Minimization Subject to Bounds , 1992 .

[17]  J. Claerbout,et al.  Acoustic daylight imaging via spectral factorization: helioseismology and reservoir monitoring , 1999 .

[18]  Homer Bucker.  A simple 3‐D Gaussian beam sound propagation model for shallow water , 1994 .

[19]  Stephen Bannister,et al.  Ambient noise Rayleigh wave tomography of New Zealand , 2007 .

[20]  F. B. Jensen,et al.  Wave theory modelling: a convenient approach to CW and pulse propagation modelling in low-frequency acoustics , 1988 .

[21]  Eric Larose,et al.  Lunar subsurface investigated from correlation of seismic noise , 2005 .

[22]  M. Siderius,et al.  Bottom profiling by correlating beam-steered noise sequences. , 2008, The Journal of the Acoustical Society of America.

[23]  Claude C. Leroy,et al.  Depth-pressure relationships in the oceans and seas , 1998 .

[24]  Michel Campillo,et al.  High-Resolution Surface-Wave Tomography from Ambient Seismic Noise , 2005, Science.

[25]  R. Francois,et al.  Sound absorption based on ocean measurements: Part I: Pure water and magnesium sulfate contributions , 1982 .

[26]  K. Mackenzie.  Nine‐term equation for sound speed in the oceans , 1981 .

[27]  W.A. Kuperman,et al.  Using ocean ambient noise for array self-localization and self-synchronization , 2005, IEEE Journal of Oceanic Engineering.

[28]  Peter Gerstoft,et al.  Seismic interferometry-turning noise into signal , 2006 .

[29]  Ralph A. Stephen.  Solutions to range‐dependent benchmark problems by the finite‐difference method , 1990 .

[30]  W. Kuperman,et al.  Extracting coherent wave fronts from acoustic ambient noise in the ocean , 2004 .

[31]  Kees Wapenaar,et al.  Green's function retrieval by cross‐correlation in case of one‐sided illumination , 2006 .

[32]  P. Gerstoft,et al.  Array shape estimation from sources of opportunity , 2003, Oceans 2003. Celebrating the Past ... Teaming Toward the Future (IEEE Cat. No.03CH37492).

[33]  Mark Porter,et al.  The KRAKEN normal mode program , 1992 .

[34]  Mathias Fink,et al.  Green's function estimation using secondary sources in a shallow water environment. , 2003, The Journal of the Acoustical Society of America.

[35]  H. Medwin.  Speed of sound in water: A simple equation for realistic parameters , 1975 .

[36]  J. Goff,et al.  Seabed characterization on the New Jersey middle and outer shelf: correlatability and spatial variab , 2004 .

[37]  Michel Campillo,et al.  Emergence of broadband Rayleigh waves from correlations of the ambient seismic noise , 2004 .

[38]  C. Holland.  Seabed reflection measurement uncertainty. , 2003, The Journal of the Acoustical Society of America.

[39]  Anatoli L. Levshin,et al.  Ambient noise Rayleigh wave tomography across Europe , 2007 .

[40]  Jon F. Claerbout,et al.  Synthesis of a layered medium from its acoustic transmission response , 1968 .

[41]  H. W. Marsh,et al.  Sound Absorption in Sea Water , 1962 .

[42]  John S. Perkins,et al.  An approximation to the three‐dimensional parabolic‐equation method for acoustic propagation , 1982 .

[43]  V. A. D. Grosso.  New equation for the speed of sound in natural waters (with comparisons to other equations) , 1974 .

[44]  K. van Wijk,et al.  On estimating the impulse response between receivers in a controlled ultrasonic experiment , 2006 .

[45]  Peter Gerstoft,et al.  Extracting time‐domain Green's function estimates from ambient seismic noise , 2005 .

[46]  R. Weaver,et al.  Ultrasonics without a source: thermal fluctuation correlations at MHz frequencies. , 2001, Physical review letters.

[47]  K. Wapenaar.  Retrieving the elastodynamic Green's function of an arbitrary inhomogeneous medium by cross correlation. , 2004, Physical review letters.

[48]  F. N. Frenkiel,et al.  Waves In Layered Media , 1960 .

[49]  M. Porter,et al.  A passive fathometer technique for imaging seabed layering using ambient noise , 2006 .

[50]  Peter Gerstoft,et al.  P‐waves from cross‐correlation of seismic noise , 2005 .

[51]  James F. Lynch,et al.  Temporal and azimuthal dependence of sound propagation in shallow water with internal waves , 2002 .

[52]  C. Farrar,et al.  SYSTEM IDENTIFICATION FROM AMBIENT VIBRATION MEASUREMENTS ON A BRIDGE , 1997 .

[53]  Andrew Curtis,et al.  Modeling of wave propagation in inhomogeneous media. , 2005, Physical review letters.

[54]  P. Zweifel.  Advanced Mathematical Methods for Scientists and Engineers , 1980 .

[55]  Peter Gerstoft,et al.  Surface wave tomography from microseisms in Southern California , 2005 .

[56]  Mark R. Loewen,et al.  A model of the sound generated by breaking waves , 1991 .

[57]  W. Kuperman,et al.  Ambient noise cross correlation in free space: theoretical approach. , 2005, The Journal of the Acoustical Society of America.

[58]  R. Snieder.  Extracting the Green's function from the correlation of coda waves: a derivation based on stationary phase. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[59]  Michael B. Porter,et al.  Computational Ocean Acoustics , 1994 .

[60]  Robert J. Urick,et al.  Principles of underwater sound , 1975 .

[61]  Michael A. Ainslie,et al.  A simplified formula for viscous and chemical absorption in sea water , 1998 .

[62]  Thomas G. Muir,et al.  Experimental investigation of the combustive sound source , 1995, IEEE Journal of Oceanic Engineering.

[63]  Francisco J. Sánchez-Sesma,et al.  Elastodynamic 2D Green function retrieval from cross‐correlation: Canonical inclusion problem , 2006 .

[64]  W. Kuperman,et al.  Passive acoustic and seismic tomography with ocean ambient noise , 2005 .

[65]  Peter Gerstoft,et al.  Green’s functions extraction and surface-wave tomography from microseisms in southern California , 2006 .

[66]  Philippe Roux,et al.  Arrival-time structure of the time-averaged ambient noise cross-correlation function in an oceanic waveguide. , 2005, The Journal of the Acoustical Society of America.

[67]  Ding Lee,et al.  A finite‐difference treatment of interface conditions for the parabolic wave equation: The irregular interface , 1982 .

[68]  P. Gerstoft,et al.  Multichannel array diagnosis using noise cross-correlation. , 2008, The Journal of the Acoustical Society of America.

[69]  Garry J. Heard,et al.  Experimental validation of regularized array element localization , 2004 .

[70]  S. Orszag,et al.  Advanced mathematical methods for scientists and engineers I: asymptotic methods and perturbation theory. , 1999 .

[71]  Peter Gerstoft,et al.  Full Field Inversion Methods In Ocean And Seismo Acoustics , 1995 .

[72]  A. Paul,et al.  Long-Range Correlations in the Diffuse Seismic Coda , 2003, Science.

[73]  P. Gerstoft,et al.  STRUCTURE OF A CARBONATE/HYDRATE MOUND IN THE NORTHERN GULF OF MEXICO , 2008 .

[74]  Kees Wapenaar,et al.  Spurious multiples in seismic interferometry of primaries , 2006 .

[75]  William S. Hodgkiss.  Shape Determination Of A Shallow-water Bottomed Array , 1989, Proceedings OCEANS.

[76]  J. Harvey,et al.  Time–distance helioseismology , 1993, Nature.

[77]  P. Gerstoft,et al.  Passive fathometer processing. , 2008, The Journal of the Acoustical Society of America.

[78]  Francisco J. Sánchez-Sesma,et al.  Retrieval of the Green’s Function from Cross Correlation: The Canonical Elastic Problem , 2006 .

[79]  J. Robertson.  Wave scattering from rough surfaces , 1995 .

[80]  J. Scales,et al.  Extracting the Green function from diffuse, equipartitioned waves. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[81]  K. Wapenaar,et al.  Green's function representations for seismic interferometry , 2006 .