##### Author

Brown, Elisabeth, M.

##### Other Contributors

Siegmann, William, L; Pierce, Allan, D; Lin, Ying-Tsong; Kovacic, Gregor; Banks, Jeffrey, W;

##### Date Issued

2019-08

##### Subject

Mathematics

##### Degree

PhD;

##### Terms of Use

This electronic version is a licensed copy owned by Rensselaer Polytechnic Institute (RPI), Troy, NY. Copyright of original work retained by author.;

##### Abstract

A research problem of considerable interest in underwater acoustics is accurately modeling the frequency-dependent geoacoustic properties of marine mud sediments. Marine mud is composed of seawater and clay mineral platelets, and typically contains varying amounts of silt, sand, and other organic and non-organic materials. Geoacoustic models for mud-like sediments ideally should provide estimates for bulk density and for the frequency-dependent compressional and shear wave speeds and attenuations. Previous models of marine mud offer reasonable estimates for some, but not all, of these properties. The recent card-house theory, for example, successfully develops very good estimates of compressional and shear sound speeds, and density for high-porosity marine sediments. The Mallock-Wood equation gives reasonable values for compressional wave speed, and the same density value as the card-house theory, in terms of the physical parameters porosity and the bulk moduli and densities of seawater and clay. However, a physically-based approach that successfully predicts attenuation in marine mud has been a critical need. A very recent silt-suspension theory hypothesizes that embedded silt particles are the dominant contributors to compressional attenuation in muddy marine sediments, as well as to the variability in compressional sound speeds. The card-house structure of aggregated clay platelets plays a key role in supporting the silt particles and keeping them separated. A classic experiment in propagation through mud is re-examined to determine how a narrow-band sound source (as opposed one at a single-frequency) affects transmission loss. A quantitative explanation is proposed for the behavior of measured loss patterns with range for higher center frequencies of the source. The demonstration uses a two-layer Pekeris waveguide model, with a Cauchy distribution of source frequencies, to capture the signal level fluctuations at all frequencies. Variations of the silt-suspension theory are investigated, including those using single representative silt-particle sizes or a distribution of sizes, and lower-order (dilute) and higher-order (non-dilute) versions. Predictions from the single-size particle version are compared with archival data for 14 mud sites worldwide. The data arranged by increasing porosity shows significant variability in compressional sound speed and attenuation measurements. It is found that among the physical parameters examined, the representative silt-particle size has the largest influence on both sound speed and attenuation predictions. Most importantly, an experimentally estimated version of such a parameter, used in combination with the silt-suspension theory, is best able to capture sound speed and attenuation variability in the data. The single-size particle version is also capable of predicting a Linear Frequency Band (LFB), an interval of application interest within which attenuation increases nearly linearly with frequency. Another variant of silt-suspension theory is an extension with contributions from a distribution of silt particle sizes. For examples, the latter are specified from piston core data obtained during the Seabed Characterization Experiment (SBCEX). Frequency dependence of attenuation, including a process to determine the LFB, is illustrated for both dilute and non-dilute theory versions. At both low and high frequencies, effective particle sizes, specified by the moments of the distribution, are discussed that produce the same attenuation as the full distribution. Such quantities are larger for low frequencies, and smaller for high. These dominant moments (for the dilute theory) suggest bounds on a frequency-dependent effective particle size that applies over all frequencies. Relations predicted by silt-suspension theory between physical sediment parameters are consistent with SBCEX core data, validating the applicability of the theory for modeling transmission loss over a SBCEX17 AUV propagation track. Variations in porosity depth dependence, seen in the uppermost portion of core data, significantly affect both sound speed and attenuation predictions, and consequently transmission loss. For example, with a frequency of f = 800 Hz, with a near- bottom source and receiver separated by 8 km, transmission loss differences occur up to about 20 dB. The silt-suspension theory is combined with commonly-applied Bayesian-inference inversion methods to determine geoacoustic properties of marine mud. This physically-based approach is distinctive because it is an inversion for physical parameters that represent mud-layer properties. Sensitivity analyses provide useful assistance to determine the most effective physical parameters for inversion. The selected parameters can then be used to produce estimates of geoacoustic properties, including their frequency dependence. WHOI data from a SBCEX17 propagation track are employed, with low frequency components from combustive source signal sent to a single hydrophone on a receiver array. Very good estimates of mud density, sound speed, and attenuation show the feasibility of this inversion approach, which is also validated by a very good match between predicted and observed pulses at the receiver. The frequency dependence of attenuation is estimated over the full low-frequency source band, showing an approximate power exponent of 1.72 that is consistent with expected low-frequency behavior.;

##### Description

August2019; School of Science

##### Department

Dept. of Mathematical Sciences;

##### Publisher

Rensselaer Polytechnic Institute, Troy, NY

##### Relationships

Rensselaer Theses and Dissertations Online Collection;

##### Access

Restricted to current Rensselaer faculty, staff and students in accordance with the
Rensselaer Standard license. Access inquiries may be directed to the Rensselaer Libraries.;