Paul J. Vidmar

Matched mode localization

In this article, a method of passively localizing a narrow‐band source in range and depth in a waveguide is presented based on ‘‘matching’’ predicted normal mode amplitudes to measured mode amplitudes. The modes are measured by using a vertical array of hydrophones and performing mode filtering. Previous studies of mode filtering have considered only the overdetermined case, i.e., where there are more hydrophones than discrete modes present in the waveguide. In this study, mode filtering is considered for the underdetermined case, i.e., where there are fewer hydrophones than the total number of discrete modes in the waveguide, but only a subset of the total number of modes is to be estimated. Previous studies of matched field localization have been based on matching the entire pressure field. In this study, the pressure field is expressed in terms of normal modes, and only a subset of the total number of modes is used for localization. Using a subset of modes allows trade‐offs to be made between localizat...

Eigenray finding and time series simulation in a layered‐bottom ocean

A ray theory approach for simulating the propagation of broadband signals interacting with a layered ocean bottom is presented. The range‐invariant environment consists of the ocean and an arbitrary number of bottom layers. Each bottom layer has profiles of compressional and shear wave velocity, attenuation, and density. Eigenrays, including those with multiple interactions and refractions in the ocean and bottom layering, are found using a thorough and efficient algorithm based on an analysis of the sound velocity profile and the dependence of ray path geometry on the Snell invariant. The time series at a receiver due to an arbitrary source waveform is obtained by constructing a frequency domain transfer function from the eigenray characteristics. Several example applications demonstrate the potential use of this approach and show that reflection from relatively simple layering can severely distort a received time series.

On the calculation of normal mode group velocity and attenuation

The group velocity for a normal mode can be calculated without invoking a finite difference approximation requiring a second eigenmode calculation. The reciprocity relation is employed in a derivation of the normal mode group velocity and attenuation coefficient. The group velocity thus calculated is more accurate than a comparable finite difference approximation. Arbitrarily arranged layers of solid and fluid media are considered.

Normal mode identification for impedance boundary conditions

When using the plane wave reflection coefficient (impedance condition) to represent bottom interaction for a normal mode calculation, counting the number of eigenfunction zeroes to identify normal modes is impractical. A method for identifying these modes by knowing the characteristics of the reflection coefficient is presented [R. A. Koch, P. J. Vidmar, and J. B. Lindberg, J. Acoust. Soc. Am. (to be published)]. In the absence of attenuation, the mode number is the number of eigenfunction zeros for the water column plus a contribution given by the number of times that, as a function of horizontal wavenumber, the reflection coefficient circles the origin in the complex plane. [This work was sponsored by the Office of Naval Research.]

Acoustic reflection from transversely isotropic consolidated sediments

Measurements of an excess of horizontal to vertical velocity (averaging 10% for shales) have been made in consolidated marine sediments and in sedimentary rocks. In this paper, the proposed causes of such anisotropies are reviewed, and the reflection coefficient for a homogeneous, solid, transversely isotropic seafloor is derived from plane‐wave solutions of the anisotropic wave equations. Bottom loss calculations are used to show that anisotropy can affect the reflectivity of exposed consolidated sediments at the ocean floor. Studies of bottom loss are also used to develop a method for estimating the elastic parameter C13 (frequently not measured for sedimentary material) for consolidated materials.

Simulation of bottom interacting waveforms

Current understanding of the acoustic processes occurring in the seafloor is used to develop a detailed ray approach for simulating the received time series of a broadband acoustical signal interacting once with the seafloor. The environment is assumed to be horizontally stratified, and the seafloor is described in terms of a geoacoustic profile. The frequency response is constructed from the superposition of the individual responses of each of the eigenrays. The ray approach includes the effects of reflection from the water–sediment interface, penetration into the sediment, refraction due to a constant compressional sound‐speed gradient in the sediment, absorption within the sediment, phase shifts due to caustics, and multipaths. The one‐bounce time series is constructed from the inverse Fourier transform of the product of the source spectrum and the eigenray frequency response. As an example application, the one‐bounce time series for an explosive source in a deep water environment is calculated and ana...

The effect of near‐surface layering on the reflectivity of the ocean bottom

The effect of near‐surface layering in marine sediments on the plane‐wave reflection coefficient R of the ocean bottom is examined using a numerical model. A comparison of bottom reflection loss, BRL = −20 log10 (‖R‖), from a 500‐m‐thick sediment with and without realistic near‐surface layering shows that additional reflections from the layering can reduce 1/3‐ octave averaged BRL (BRLA) by more than 10 dB at 1600 Hz for grazing angles above 20°. This results in a frequency inversion since, at lower frequencies, the effect of the layering is much smaller; at 50 Hz there is almost no effect. An important feature of this dramatic decrease in BRLA is its relative independ‐ ence from the details of the layering structure. However, the exact nature of the layering does have an important effect on BRL and the phase of R at a single frequency, and on BRLA at about 800 Hz. Studies of an artificial layered structure made up of equally spaced, identical layers show that the physical process producing the decrease i...

Shear Wave Effects on Propagation to a Receiver in the Substrate

Some effects produced by shear wave processes in a layered seafloor are examined. Normal mode theory is used to calculate the displacement produced by a low frequency source in the water column at a receiver located inside the seafloor. The effects of the seafloor are represented by an impedance boundary condition obtained from the plane wave reflection coefficient. Shear wave processes are included by using the reflectivity of a solid, layered seafloor. A comparison of displacements obtained for solid and fluid descriptions of the seafloor is made to isolate the role of shear waves. Both vertical and horizontal displacements are found to increase significantly when shear wave processes are included. An analysis of the range dependence of displacement suggests that shear wave propagation is the major acoustical mechanism producing this increase.

Shear wave effects on propagation to near‐bottom and sub‐bottom receivers

Some effects of shear wave processes in a multilayered ocean bottom are examined. Normal mode theory is used to calculate the stress and displacement components at receivers in and on the bottom. The effects of the seafloor on normal modes are contained in a bottom boundary condition involving the impedance derived from the plane‐wave reflection coefficient. Shear wave processes are included when the reflectivity is calculated using a solid description of the bottom. Comparisons of the range dependence of stresses and displacements calculated using fluid and solid descriptions of the seafloor indicate that shear wave processes significantly affect the phase of all acoustic field components, both on and in the bottom. Within the bottom, all acoustic component amplitudes may be 10 dB greater if the solid, instead of the fluid, seafloor description is used. On the seafloor, the only acoustic component amplitude substantially affected by shear wave processes is the vertical displacement, which may be 10 dB sm...

Plasma wave reflection from sharp density gradients

Electrostatic wave reflection from density gradients is studied using an expansion in the ratio of the time an electron spends in the gradient to the wave period. The reflection coefficient is of order unity under rather general conditions.