Journal of Computational Acoustics

In this paper, FD formulations in cylindrical coordinates are used to model the field radiated, by a circular source, in fluid and solid media.

The stability of the used schemes is controlled by a proper choice of time and space steps. Absorbing boundary conditions are introduced to satisfy the assumption of a propagation in a half space medium. In order to minimize the CPU time, calculations are limited for regions disturbed by the propagating ultrasonic pulse then the calculus zone is incremented.

Some numerical results are presented to illustrate the effect of the medium nature, source vibration profiles and eventually the presence of targets in the acoustic field. A spatio-temporal description of the diffraction phenomena is given. The radiated field is interpreted in terms of plane and edge waves. For solid media, this interpretation allows the determination of the arrival times which are compared with those numerically predicted. Numerical results corresponding to fluid media are compared to those obtained by the Impulse Response Method. The good agreement obtained justifies the choice of the FDM for the modeling of the wave propagation problems.

Modeling of acoustic pulse propagation in nonideal fluids requires the inclusion of attenuation and its causal companion, dispersion. For the case of propagation in a linear, unbounded medium Szabo developed a convolutional propagation operator which, when introduced into the linear wave equation, accounts for attenuation and causal dispersion for any medium whose attenuation possesses a generalized Fourier transform. Utilizing a one dimensional Finite Difference Time Domain (FDTD) model Norton and Novarini showed that for an unbounded isotropic medium, the inclusion of this unique form of the convolutional propagation operator into the wave equation correctly carries the information of attenuation and dispersion into the time domain. This paper addresses the question whether or not the operator can be used as a basic building block for pulse propagation in a spatially dependent dispersive environment. The operator is therefore used to model 2-D pulse propagation in the presence of an interface separating two dispersive media. This represents the simplest description of a spatially dependent dispersive media. It was found that the transmitted and backscattered fields are in excellent agreement with theoretical expectations demonstrating the effectiveness of the local operator to model the field in spatially dependent dispersive media. [Work supported by ONR/NRL.]

Modes and wavenumbers are the principal ingredients that characterize the pressure field in an oceanic waveguide. However, wavenumber and mode inversions are well-known to be a difficult task in underwater acoustics. Moreover, this double inversion has never been performed simultaneously from the same configuration of emitters and receivers. We present a new approach to this problem in a shallow water environment between two vertical arrays of sources and receivers. Starting from a classical modal decomposition of the pressure field, our algorithm focuses on a specific treatment of phase and amplitude variables. The key idea is to run a three-stage optimization by working separately on the phase and amplitude of the acoustic field. The high number of variables of the problem is turned into an advantage by using an adjoint code generated by an Automatic Differentiation software. Numerical results in the presence of noise show that modes and wavenumbers are estimated with a high accuracy.

Taking the Astley element for example, the conventional mapped infinite element is theoretically dissected in this paper. The study brings to light the reason why the results from the mapped infinite elements vary with the location of the mid-side points used in the geometry mapping. To remedy this deficiency, a new conjugated mapped infinite element is proposed whose shape functions exactly satisfy the multi-pole expansion in the infinite direction. Within the framework of this infinite element, shape functions for any type of wave are composed of the one in the conventional finite element for the same order multiplied by a factor that contains the information of the geometry mapping and the decay behavior of wave. In addition to the slight modification to the phase factor and the weighting factor, the present element permits a free geometry mapping, and therefore greatly expands the applicability of the mapped infinite element methods. To display the performance of the proposed element, typical examples are finally given.

An algorithm has been developed to implement synthetic aperture focusing technique for B-scan. This is made at a several transmitter/receiver locations to form a map of ultrasonic reflectivity on the insonified region, considering the path travelled by the ultrasonic pulse from the transducer to the target and back again. To reconstruct the image, a time domain beam-former is applied to the envelope of the detected signals. This method minimizes the side-lobe amplitude and the restriction of λ/2 distance between two adjacent transducer positions can be neglected without loosing image resolution.

The present work is focused on the location of the in-homogeneities, caused by the presence of a phantom immersed in a water tank. The results are presented when the distance between two adjacent transducer positions are varied from 0.5λ to 2.5λ showing that the longitudinal resolution is not affected but the lateral resolution becomes poorer when the distance is about 2λ. The error in the longitudinal location of in-homogeneities is within the minimum detectable distance of the system, while the lateral location error is increased when the distance between any two adjacent transducer positions is larger than 1.5λ.

In ultrasound inverse problems, the integral equation can be nonlinear, ill-posed, and computationally expensive. One approach to solving such problems is the conjugate gradient (CG) method. A key parameter in the CG method is the conjugate gradient direction. In this paper, we investigate the CG directions proposed by Polyak et al. (PPR), Hestenes and Stiefel (HS), Fletcher and Reeves (FR), Dai and Yuan (YD), and the two-parameter family generalization proposed by Nazareth (TPF). Each direction is applied to three test cases with different contrasts and phase shifts. Test case 1 has low contrast with a phase shift of 0.2π. Reconstruction of the object is obtained for all directions. The performances of the PPR, HS, YD, and TPF directions are comparable, while the FR direction gives the poorest performance. Test case 2 has medium contrast with a phase shift of 0.75π. Reconstruction is obtained for all but the FR direction. The PPR, HS, YD, and TPF directions have similar mean square error; the YD direction takes the least amount of CPU time. Test case 3 has the highest contrast with a phase shift of 1.003π. Only the YD direction gives reasonably accurate results.

A simple model displaying structural-acoustic behavior is considered. The model comprises of two parallel infinitely-long flat membranes lying on elastic foundations and the acoustic medium separating them. The structural-acoustic coupling manifests itself in that a vibrational excitation of one of the membranes triggers vibrations in the other. The governing equations are stated, and the associated finite element formulation is constructed. The model is then analyzed numerically and its vibrational properties are investigated. The proposed model is especially simple, being two-dimensional and involving a small number of parameters, but at the same time it brings to light some important features associated with structural-acoustic coupling. Therefore it may serve as a benchmark for evaluating structural-acoustic numerical schemes and as an educational tool for studying structural-acoustic coupling in a simple context.

Acoustic wave propagation is sensitive to many rock properties including fluid content, porosity, and pore structure, among others. Pore structure is one of the important parameters in controlling both seismic wave velocity and permeability in sandstones and carbonate rocks. For a given porosity of two similar rocks with different pore structure, their acoustic wave speeds can differ 2 km/s and permeability can span nearly six orders of magnitude from 0.01 mD to 20 D in both sandstones and limestones. In this paper, we introduce a two-parameter velocity model defined by porosity and a new pore structure parameter called as frame flexibility factor. Using this model, we define three pore structure types (PST) to quantify the pore structure effects on elastic properties of sedimentary rocks. These three PSTs have their distinct characteristics on synthetic shot gathers and common midpoint gathers. This study indicates that it may be feasible to use this new concept and method to detect pore structure variations in reservoir rocks from field seismic data. This study also helps explain why analysis of amplitude variation with offset (AVO) in some cases fails for fluid detection: pore structure effect on seismic waves can mask all the fluid effects, especially in carbonate rocks.

In a recent paper (J. Computational Acoustics10 (2002) 387–405) Tam has claimed that the famous Lighthill Acoustic Analogy predicts the wrong flow field for the simple problem of the propagation of a normal shock. However, we show that Tam has misinterpreted the results of his analysis, and that when this error is corrected the results of the Acoustic Analogy are brought into exact agreement with the well-known Rankine–Hugoniot solution of the Euler equations.