Anthony L. Bonomo

A comparison of finite element and analytic models of acoustic scattering from rough poroelastic interfaces

The finite element method is used to model acoustic scattering from rough poroelastic surfaces. Both monostatic and bistatic scattering strengths are calculated and compared with three analytic models: Perturbation theory, the Kirchhoff approximation, and the small-slope approximation. It is found that the small-slope approximation is in very close agreement with the finite element results for all cases studied and that perturbation theory and the Kirchhoff approximation can be considered valid in those instances where their predictions match those given by the small-slope approximation.

Acoustic scattering from a sand layer and rock substrate with rough interfaces using the finite element method

The finite element method is used to study the acoustic scattering from a layer of sand overlying a rock substrate. All the modeling is done in two dimensions. Both the water-sand interface and the sand-rock interface are modeled as random rough surfaces following a modified power law spectrum. The rock substrate is assumed to be an elastic solid. Three sediment models are used for the sand layer: the full Biot model for poroelastic media, an effective density fluid model based on the Biot model, and a simple fluid model. The effect of the choice of sediment model used for sand is studied. The finite element results are also compared with perturbation theory and the Kirchhoff approximation in order to further evaluate the validity of considering the underlying interfaces to be flat as a rough sand-rock interface cannot be handled by these models. [Work supported by ONR, Ocean Acoustics.]

Comparison of the finite element method with perturbation theory and the small-slope approximation for acoustic scattering from one-dimensional rough poroelastic surfaces

The finite element method is used to address the problem of acoustic scattering from one-dimensional rough poroelastic surfaces. The poroelastic sediment is modeled following the Biot-Stoll formulation. The rough surfaces are generated using a modified power law spectrum. Both backscattering strengths and bistatic scattering strengths are calculated. These results are compared with lowest order perturbation theory and the lowest order small-slope approximation, as extended to the case of scattering from poroelastic surfaces. It is known that these approximate methods are sufficient for the study of rough surface scattering in the case of sediments modeled as fluids. This work seeks to assess whether or not these methods are accurate when applied to the case of poroelastic sediments. [Work supported by the Office of Naval Research, Ocean Acoustics Program.]

A study of the reflection coefficients and backscattering effects of one-dimensional rough poroelastic surfaces using the finite element method

Acoustic reflection and scattering effects of one-dimensional rough poroelastic surfaces are studied using the finite element method. The poroelastic sediment layer is modeled following the classical work of Biot as extended by Stoll, which assumes that two attenuating compressional waves and one attenuating shear wave propagate in the sediment. The rough surfaces are generated using power-law type spectra and the incident wave used is a Gaussian tapered plane wave. This work seeks to assess how the reflection coefficients and backscattering effects of a poroelastic bottom vary as a function of frequency, roughness, and sediment type. Special consideration is given to the mesh required to accurately resolve the effects of the slow compressional and shear waves, which often have wave speeds slower than the fast compressional wave by an order of magnitude or more. [Work sponsored by the Office of Naval Research, Ocean Acoustics.]

Geoacoustic sediment model discrimination using acoustic color comparison

Many competing geoacoustic models exist to represent sandy sediments. These models can be fluid, elastic, or poroelastic, depending on the number and types of waves the sediment is assumed to support. In this talk, a fully scattered field finite element approach is utilized to construct acoustic color templates for a buried spherical aluminum shell and a spherical bubble. The simulated results are then used to assess the ability of target strength measurements to discriminate between the predictions of the competing sediment models. Such discrimination may help determine the physical validity of a given geoacoustic model and aid in model selection. Five geoacoustic sediment models are considered: a simple fluid, constant-Q fluid model, the effective density fluid model of Williams, the viscous grain shearing model of Buckingham, the Biot-Stoll poroelastic model, and the extended Biot model of Chotiros. [Work supported by ONR, Ocean Acoustics.] Many competing geoacoustic models exist to represent sandy sediments. These models can be fluid, elastic, or poroelastic, depending on the number and types of waves the sediment is assumed to support. In this talk, a fully scattered field finite element approach is utilized to construct acoustic color templates for a buried spherical aluminum shell and a spherical bubble. The simulated results are then used to assess the ability of target strength measurements to discriminate between the predictions of the competing sediment models. Such discrimination may help determine the physical validity of a given geoacoustic model and aid in model selection. Five geoacoustic sediment models are considered: a simple fluid, constant-Q fluid model, the effective density fluid model of Williams, the viscous grain shearing model of Buckingham, the Biot-Stoll poroelastic model, and the extended Biot model of Chotiros. [Work supported by ONR, Ocean Acoustics.]

On the validity of the effective density fluid model as an approximation of a poroelastic sediment layer

The effective density fluid model (EDFM) was developed to approximate the behavior of sediments governed by Biots theory of poroelasticity. Previously, it has been shown that the EDFM predicts reflection coefficients and backscattering strengths that are in close agreement with those of the full Biot model for the case of a homogeneous poroelastic half-space. However, it has not yet been determined to what extent the EDFM can be used in place of the full Biot-Stoll model for other cases. Using the finite element method, the flat-interface reflection and rough-interface backscattering predictions of the Biot-Stoll model and the EDFM are compared for the case of a poroelastic layer overlying an elastic substrate. It is shown that considerable differences between the predictions of the two models can exist when the layer is very thin and has a thickness comparable to the wavelength of the shear wave supported by the layer, with a particularly strong disparity under the conditions of a shear wave resonance. For thicker layers, the predictions of the two models are found to be in closer agreement, approaching nearly exact agreement as the layer thickness increases.

Finite element computation of the scattering response of objects buried in ocean sediments

To assist in locating objects at or near the ocean floor, there is a need for computational models that can predict the scattering response of objects fully or partially buried in ocean sediments such as sand. In reality, sand can best be understood as a two-phase porous medium and the shear waves supported by the sediment can contribute meaningfully to the acoustic signature of the buried objects. Due to the slow phase speeds of these shear waves, the computational burden of finite element models can be excessive. In this talk, efficient modeling techniques and methods for reducing the computational time of these models are covered. [Work supported by ONR, Ocean Acoustics.]To assist in locating objects at or near the ocean floor, there is a need for computational models that can predict the scattering response of objects fully or partially buried in ocean sediments such as sand. In reality, sand can best be understood as a two-phase porous medium and the shear waves supported by the sediment can contribute meaningfully to the acoustic signature of the buried objects. Due to the slow phase speeds of these shear waves, the computational burden of finite element models can be excessive. In this talk, efficient modeling techniques and methods for reducing the computational time of these models are covered. [Work supported by ONR, Ocean Acoustics.]

On the use of model truncation to extend the applicability of the finite element method to higher frequencies

Many structural acoustics problems of interest can be modeled as a vibrating elastic structure situated in and fully coupled to an infinite acoustic fluid domain. To model such problems using the finite element method, techniques have been developed to approximately enforce the Sommerfeld radiation condition at the boundary of the computational domain and prevent spurious boundary reflections from adversely affecting the calculated solution. These techniques include radiation boundary conditions, infinite elements, and perfectly matched layers. It is well known that due to computational constraints, the finite element method is often restricted to relatively low frequencies. However, many of the same techniques that have been used to enforce the Sommerfeld radiation condition can also be used to truncate the computational domain further and allow the finite element method to be used to study higher frequency problems where the structural acoustic response is relatively localized. This talk explores this model truncation application.Many structural acoustics problems of interest can be modeled as a vibrating elastic structure situated in and fully coupled to an infinite acoustic fluid domain. To model such problems using the finite element method, techniques have been developed to approximately enforce the Sommerfeld radiation condition at the boundary of the computational domain and prevent spurious boundary reflections from adversely affecting the calculated solution. These techniques include radiation boundary conditions, infinite elements, and perfectly matched layers. It is well known that due to computational constraints, the finite element method is often restricted to relatively low frequencies. However, many of the same techniques that have been used to enforce the Sommerfeld radiation condition can also be used to truncate the computational domain further and allow the finite element method to be used to study higher frequency problems where the structural acoustic response is relatively localized. This talk explores this m...

Model/data comparisons and numerical experiments for the comparison of sandy sediment models

Many geoacoustic models have been proposed to study the acoustic behavior of sandy sediments to predict the propagation within the sediment and the reflection loss from waterborne waves. Sandy sediments have been described as a two-phase porous medium using the theoretical framework developed by Biot. Other proposed theories were developed under the assumption that sandy sediments possess no effective skeletal matrix and instead describe the acoustic behavior of the sediments using grain-to-grain contacts. This talk summarizes model/data comparisons and numerical experiments in an attempt to determine which of these two theoretical frameworks is more suitable for the modeling of sandy sediments. Recommendations are made for future experiments that can aid in resolving this issue. [Work supported by ONR, Ocean Acoustics.]Many geoacoustic models have been proposed to study the acoustic behavior of sandy sediments to predict the propagation within the sediment and the reflection loss from waterborne waves. Sandy sediments have been described as a two-phase porous medium using the theoretical framework developed by Biot. Other proposed theories were developed under the assumption that sandy sediments possess no effective skeletal matrix and instead describe the acoustic behavior of the sediments using grain-to-grain contacts. This talk summarizes model/data comparisons and numerical experiments in an attempt to determine which of these two theoretical frameworks is more suitable for the modeling of sandy sediments. Recommendations are made for future experiments that can aid in resolving this issue. [Work supported by ONR, Ocean Acoustics.]

A comparison of three geoacoustic models using Bayesian inversion and selection techniques applied to wave speed and attenuation measurements

Many geoacoustic models have been developed to study sandy sediments. In this work, Bayesian inference techniques are used to compare three such models: the VGS(λ) model, the most recent of Buckinghams viscous grain-shearing models, the Biot-Stoll poroelastic model, and an extension to the Biot-Stoll model proposed by Chotiros called the corrected and reparametrized extended Biot (CREB) model. First, Bayesian inversion is applied to wave speed and attenuation measurements previously made in the laboratory to determine the degree to which each of the model input parameters can be resolved by wave speed and attenuation data. Then, Bayesian model selection techniques are utilized to assess the degree to which the predictions of these models match the measured data and to ascertain the Bayesian evidence in favor of each. Through these studies it is determined that the VGS(λ) and CREB models outperform the Biot-Stoll model, both in terms of parameter resolution and in their ability to produce predictions in agreement with measurements. The VGS(λ) model is seen to have the highest degree of Bayesian evidence in its favor.