Time dependent seafloor acoustic backscatter (10-100kHz)

A time-dependent model of the acoustic intensity backscattered by the seafloor is described and compared with data from a calibrated, vertically oriented, echo-sounder operating at 33 and 93 kHz. The model incorporates the characteristics of the echo-sounder and transmitted pulse, and the water column spreading and absorption losses. Scattering from the water–sediment interface is predicted using Helmholtz–Kirchhoff theory, parametrized by the mean grain size, the coherent reflection coefficient, and the strength and exponent of a power-law roughness spectrum. The composite roughness approach of Jackson et al. [J. Acoust. Soc. Am. 79, 1410–1422 (1986)], modified for the finite duration of the transmitted signal, is used to predict backscatter from subbottom inhomogeneities. It depends on the sediment’s volume scattering and attenuation coefficients, as well as the interface characteristics governing sound transmission into the sediment. Estimation of model parameters (mean grain size, roughness spectrum strength and exponent, volume scattering coefficient) reveals ambiguous ranges for the two spectral components. Analyses of model outputs and of physical measurements reported in the literature yield practical constraints on roughness spectrum parameter settings appropriate for echo-envelope-based sediment classification procedures

Remote sensing of sediment characteristics by optimized echo-envelope matching

A sediment geoacoustic parameter estimation technique is described which compares bottom returns, measured by a calibrated monostatic sonar oriented within 15° of vertical and having a 10°–21° beamwidth, with an echo envelope model based on high-frequency (10–100 kHz) incoherent backscattertheory and sediment properties such as: mean grain size, strength, and exponent of the power law characterizing the interface roughness energy density spectrum, and volume scattering coefficient. An average echo envelope matching procedure iterates on the reflection coefficient to match the peak echo amplitude and separate coarse from fine-grain sediments, followed by a global optimization using a combination of simulated annealing and downhill simplex searches over mean grain size, interface roughness spectral strength, and sediment volume scattering coefficient. Error analyses using Monte Carlo simulations validate this optimization procedure. Moderate frequencies (33 kHz) and orientations normal with the interface are best suited for this application. Distinction between sands and fine-grain sediments is demonstrated based on acoustic estimation of mean grain size alone. The creation of feature vectors from estimates of mean grain size and interface roughness spectral strength shows promise for intraclass separation of silt and clay. The correlation between estimated parameters is consistent with what is observed in situ

Statistical Properties of Random Banded Matrices with Strongly Fluctuating Diagonal Elements

The random banded matrices (RBM) whose diagonal elements fluctuate much stronger than the off-diagonal ones were introduced recently by Shepelyansky as a convenient model for coherent propagation of two interacting particles in a random potential. We treat the problem analytically by using the mapping onto the same supersymmetric nonlinear $\sigma-$model that appeared earlier in consideration of the standard RBM ensemble, but with renormalized parameters. A Lorentzian form of the local density of states and a two-scale spatial structure of the eigenfunctions revealed recently by Jacquod and Shepelyansky are confirmed by direct calculation of the distribution of eigenfunction components.Comment: 7 pages,RevTex, no figures Submitted to Phys.Rev.

2-D Prony-Huang Transform: A New Tool for 2-D Spectral Analysis

This work proposes an extension of the 1-D Hilbert Huang transform for the analysis of images. The proposed method consists in (i) adaptively decomposing an image into oscillating parts called intrinsic mode functions (IMFs) using a mode decomposition procedure, and (ii) providing a local spectral analysis of the obtained IMFs in order to get the local amplitudes, frequencies, and orientations. For the decomposition step, we propose two robust 2-D mode decompositions based on non-smooth convex optimization: a "Genuine 2-D" approach, that constrains the local extrema of the IMFs, and a "Pseudo 2-D" approach, which constrains separately the extrema of lines, columns, and diagonals. The spectral analysis step is based on Prony annihilation property that is applied on small square patches of the IMFs. The resulting 2-D Prony-Huang transform is validated on simulated and real data.Comment: 24 pages, 7 figure