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Sarkar, J, Cornuelle BD, Kuperman WA.  2011.  Information and linearity of time-domain complex demodulated amplitude and phase data in shallow water. Journal of the Acoustical Society of America. 130:1242-1252.   10.1121/1.3613709   AbstractWebsite

Wave-theoretic ocean acoustic propagation modeling is used to derive the sensitivity of pressure, and complex demodulated amplitude and phase, at a receiver to the sound speed of the medium using the Born-Frechet derivative. Although the procedure can be applied for pressure as a function of frequency instead of time, the time domain has advantages in practical problems, as linearity and signal-to-noise are more easily assigned in the time domain. The linearity and information content of these sensitivity kernels is explored for an example of a 3-4 kHz broadband pulse transmission in a 1 km shallow water Pekeris waveguide. Full-wave observations (pressure as a function of time) are seen to be too nonlinear for use in most practical cases, whereas envelope and phase data have a wider range of validity and provide complementary information. These results are used in simulated inversions with a more realistic sound speed profile, comparing the performance of amplitude and phase observations. (C) 2011 Acoustical Society of America. [DOI: 10.1121/1.3613709]

Raghukumar, K, Cornuelle BD, Hodgkiss WS, Kuperman WA.  2010.  Experimental demonstration of the utility of pressure sensitivity kernels in time-reversal. Journal of the Acoustical Society of America. 128:989-1003.   10.1121/1.3466858   AbstractWebsite

Pressure sensitivity kernels were recently applied to time-reversal acoustics in an attempt to explain the enhanced stability of the time-reversal focal spot [Raghukumar et al., J. Acoust. Soc. Am. 124, 98-112 (2008)]. The theoretical framework developed was also used to derive optimized source functions, closely related to the inverse filter. The use of these optimized source functions results in an inverse filter-like focal spot which is more robust to medium sound speed fluctuations than both time-reversal and the inverse filter. In this paper the theory is applied to experimental data gathered during the Focused Acoustic Fields experiment, conducted in 2005, north of Elba Island in Italy. Sensitivity kernels are calculated using a range-independent sound-speed profile, for a geometry identical to that used in the experiment, and path sensitivities are identified with observed arrivals. The validity of the kernels in tracking time-evolving Green's functions is studied, along with limitations that result from a linearized analysis. An internal wave model is used to generate an ensemble of sound speed profiles, which are then used along with the calculated sensitivity kernels to derive optimized source functions. Focal spots obtained using the observed Green's functions with these optimized source functions are then compared to those obtained using time-reversal and the inverse-filter. It is shown that these functions are able to provide a focal spot superior to time-reversal while being more robust to sound speed fluctuations than the inverse filter or time-reversal. (C) 2010 Acoustical Society of America. [DOI: 10.1121/1.3466858]

Skarsoulis, EK, Cornuelle BD, Dzieciuch MA.  2009.  Travel-time sensitivity kernels in long-range propagation. Journal of the Acoustical Society of America. 126:2223-2233.   10.1121/1.3224835   AbstractWebsite

Wave-theoretic travel-time sensitivity kernels (TSKs) are calculated in two-dimensional (2D) and three-dimensional (3D) environments and their behavior with increasing propagation range is studied and compared to that of ray-theoretic TSKs and corresponding Fresnel-volumes. The differences between the 2D and 3D TSKs average out when horizontal or cross-range marginals are considered, which indicates that they are not important in the case of range-independent sound-speed perturbations or perturbations of large scale compared to the lateral TSK extent. With increasing range, the wave-theoretic TSKs expand in the horizontal cross-range direction, their cross-range extent being comparable to that of the corresponding free-space Fresnel zone, whereas they remain bounded in the vertical. Vertical travel-time sensitivity kernels (VTSKs)-one-dimensional kernels describing the effect of horizontally uniform sound-speed changes on travel-times-are calculated analytically using a perturbation approach, and also numerically, as horizontal marginals of the corresponding TSKs. Good agreement between analytical and numerical VTSKs, as well as between 2D and 3D VTSKs, is found. As an alternative method to obtain wave-theoretic sensitivity kernels, the parabolic approximation is used; the resulting TSKs and VTSKs are in good agreement with normal-mode results. With increasing range, the wave-theoretic VTSKs approach the corresponding ray-theoretic sensitivity kernels. (C) 2009 Acoustical Society of America. [DOI: 10.1121/1.3224835]

Raghukumar, K, Cornuelle BD, Hodgkiss WS, Kuperman WA.  2008.  Pressure sensitivity kernels applied to time-reversal acoustics. Journal of the Acoustical Society of America. 124:98-112.   10.1121/1.2924130   AbstractWebsite

Sensitivity kernels for receptions of broadband sound transmissions are used to study the effect of the transmitted signal on the sensitivity of the reception to environmental perturbations. A first-order Born approximation is used to obtain the pressure sensitivity of the received signal to small changes in medium sound speed. The pressure perturbation to the received signal caused by medium sound speed changes is expressed as a linear combination of single-frequency sensitivity kernels weighted by the signal in the frequency domain. This formulation can be used to predict the response of a source transmission to sound speed perturbations. The stability of time-reversal is studied and compared to that of a one-way transmission using sensitivity kernels. In the absence of multipath, a reduction in pressure sensitivity using time reversal is only obtained with multiple sources. This can be attributed both to the presence of independent paths and to cancellations that occur due to the overlap of sensitivity kernels for different source-receiver paths. The sensitivity kernel is then optimized to give a new source transmission scheme that takes into account knowledge of the medium statistics and is related to the regularized inverse filter. (c) 2008 Acoustical Society of America.

Skarsoulis, EK, Cornuelle BD.  2004.  Travel-time sensitivity kernels in ocean acoustic tomography. Journal of the Acoustical Society of America. 116:227-238.   10.1121/1.1753292   AbstractWebsite

Wave-theoretic ocean acoustic propagation modeling is combined with the peak arrival approach for tomographic travel-time observables to derive the sensitivity kernel of travel times with respect to sound-speed variations. This is the Born-Frechet kernel relating the three-dimensional spatial distribution of sound-speed variations with the induced travel-time variations. The derivation is based on the first Born approximation of the Green's function. The application of the travel-time sensitivity kernel to an ocean acoustic waveguide gives a picture close to the ray-theoretic one in the case of high frequencies. However, in the low-frequency case, of interest in ocean acoustic tomography, for example, there are significant deviations. Low-frequency travel times are sensitive to sound-speed changes in Fresnel-zone-scale areas surrounding the eigenrays, but not on the eigenrays themselves, where the sensitivity is zero. Further, there are areas of positive sensitivity, where, e.g., a sound-speed increase results in an increase of arrival times, i.e., a further delay of arrivals, in contrast with the common expectation. These findings are confirmed by forward acoustic predictions from a coupled-mode code. (C) 2004 Acoustical Society of America.