Journal of Computational Acoustics

Computer simulation techniques, such as the Local Interaction Simulation Approach (LISA), allow us to predict accurately and efficiently the propagation of acoustic and ultrasonic waves or pulses in complex (heterogeneous and/or anisotropic) media. For a quantitative comparison with experimental results it is necessary to properly include in the model the attenuation and dispersion properties of the propagation medium. A spring model is used to derive heuristically the iteration equations, which yield stable and convergent simulations of the wave propagation even in the case of attenuative, dispersive and/or nonlinear media. To illustrate the procedure several examples of propagation of monochromatic waves and pulses are presented.

A numerical method for computing the influence of Doppler due to source/receiver platform motion in a parabolic equation model is introduced. Both source/receiver speeds and angles of motion in the vertical plane are included in the specification of the motion. By necessity, it is shown that the source function must be defined in the vertical wavenumber domain. Furthermore, the source amplitude spectrum must be defined prior to the calculation, in contrast to previous implementations which would allow for application of variable spectra in post-processing. Examples are given for simple environments demonstrating the expected influence of Doppler due to source motion.

An implicit high-order compact unconditionally stable finite-difference time-domain (FDTD) method is proposed here for numerical solution of point sources over an impedance plane. In this method, the linearized Euler equations are split into three directional sets and twelve simple wave components, or six when equivalent sources are adopted with no mean flow. Each component is solved using a fourth-order Padé approximant in space and second-order trapezoidal integration in time. The concept of reflection coefficient is used and algebraically modeled to develop time-domain impedance-equivalent boundary conditions. Comparisons with established methods for reflections of harmonic or impulsive sources demonstrate the applicability of this method for general impedance value, source type, or their arbitrary distributions. Examples of using typical wool felt and grass ground impedances are given to illustrate its practicality and effectiveness. This method provides a means through which time-domain theories and procedures for in-situ characterization of impedance surfaces can be developed.

The paper presents estimates of the S-wave velocity and the crack density at which fractured reservoirs begin to play an important role in oil exploration. Transverse isotropy with a horizontal axis of symmetry (HTI) is the simplest azimuthally anisotropic model used to describe fractured reservoirs that contain parallel vertical cracks. A double profile concept is used to develop an equation for the P-S wave normal-moveout (NMO) velocity. The azimuthal NMO velocities of the P- and P-S waves can then be used to estimate the velocities of the S-waves and Thomsen's coefficient, γ. For multilayered media, a recursive equation is developed for the NMO velocity in each layer. The numerical results indicate that the S-wave NMO velocity can be accurately estimated using the P- and P-S wave NMO velocities in HTI media. An important parameter of fracture systems that can be measured from seismic data is the crack density which can be estimated using the NMO velocities of the P- and S-waves from horizontal reflectors. Therefore, fractures can be completely characterized by the joint inversion of P-waves and converted P-S waves in HTI media.

In this paper we study a mathematical model to describe a three dimensional acoustic scattering problem associated to a "vibrating" obstacle that is a bounded simply connected domain contained in the three dimensional real Euclidean space whose shape changes in time. In particular we propose a numerical method based on a perturbation series and the operator expansion method to solve the mathematical model considered. This method makes possible to obtain highly parallelizable algorithms able to compute the solution of the problem considered order by order in perturbation theory, and able to obtain the required solution of the scattering problem summing up the perturbation series. Really impressive speed up factors are observed and reported when the algorithm is executed on the Chiba Cluster, a parallel machine of the Argonne National Laboratory, USA. We validate the mathematical model and the numerical method proposed solving some test problems. The quantitative character of the numerical results obtained is established. The results obtained on the test problems are discussed both from the numerical and the physical point of view. In particular we show that the Doppler spectrum associated to the far field patterns of the scattered acoustic fields depends mainly from the incoming wave and from the excited vibrational modes (Figs. 9–13). The website: shows some Applets relative to the numerical examples.