Theoretical and Computational Acoustics 2005

PREFACE.

ORGANIZING COMMITTEES AND SPONSORS.

CONTENTS.

This talk discusses an inverse problem of acoustic. The aim is to reconstruct the sound pressure field of a cavity based on a small number of measurements. In the calculation, arbitrary admittance boundary conditions are considered. Therefore, the inverse formulation requires to include the boundary admittance as a coefficient of the Robin boundary condition for the Helmholtz differential equation. In order to support a minimization of the necessary number of measurements, the new approach is based on an inverse formulation of the finite element method for the acoustical boundary value problem, of which its facility to extract a modal solution can be advantageous.

The seabed parameters are especially important in underwater sound propagation in shallow water. A long range geoacoustic inversion experiment was conducted in January 2005, in winter conditions in the South China Sea where the bottom is mostly sand and silt. In this experiment, single frequency CW pulse signals were transmitted from a suspended source, and received by a vertical array of hydrophones. The data were inverted for the geoacoustic properties of the seabed using a hybrid inversion method—the adaptive simplex simulated annealing (ASSA). Owing to the identical inversion procedures, the favorable results were obtained for 6 unknown geometrical and geoacoustic parameters by the semi-infinite seabed model. It is shown that seabed inversion parameters are consistent for the different time arrival signals. By comparing with the inversion for a sediment over basement bottom model, the single layer seabed geoacoustic model is adequate to obtain the equivalent seabed parameters very well for the long range experiment site.

Radon transform (RT) has been widely applied in seismic data processing and interpretation, it owns fine effect in the events identification, wavefield separation, de-multiples, velocity analysis etc. This paper discusses the factors that affect the resolution of RT and the strategies for achieving the high resolution. We solve the spare matrix by the conjugate gradient [6], which does not affect the resolution and improves the computation efficiency. On the basis of the differences of velocity and intercept time between p-wave and s-wave, we separate the seismic waves by the high resolution hyperbolic RT. With theoretical models and the practical data, it makes clear that the resolution and computation efficiency of the conjugate gradient for solving the hyperbolic RT algorithm is better and more practical to separate the wavefields.

Nonlinear internal wave (NIW) packets cause ducting and whispering gallery effects in acoustic propagation. The acoustic energy restricted within the internal wave crests (crest-crest) on the shelf is the ducting effect, and the energy confined along the crest when the source is located upslope from the NIW crest is the whispering gallery effect. This paper presents the simulation results concerning the phenomena of whispering gallery by FOR3D wide-angle version. It appears that energy emerges right before and along the wave crest and then vanish right in the back of the wave crest and then converges again, especially with the lower frequency band (150Hz ~ 600Hz).

Estimates of shear wave velocity profiles in seafloor sediments can be obtained from inversion of measured dispersion relations of seismo-acoustic interface waves propagating along the seabed. The interface wave velocity is directly related to shear wave velocity with value of between 87-96% of the shear wave velocity, dependent on the Poission ratio of the sediments. In this paper we present two different techniques to determine the dispersion relation: a single-sensor method used to determine group velocity and a multi-sensor method used to determine the phase velocity of the interface wave. An inversion technique is used to determine shear wave velocity versus depth and it is based on singular value decomposition and regularization theory. The technique is applied to data acquired at Steinbåen outside Horten in the Oslofjorden (Norway) and compared with the result from independent core measurements taken at the same location. The results show good agreement between the two ways of determining shear wave velocity.

An approach of extracting the modal back-scattering matrix from the reverberation data in shallow-water is proposed recently (Shang, Gao and Tang, 2002). The kernel matrix of the inversion is constructed by the square of the modal function. The singularity of this matrix (or the stability of the inversion) is the crucial issue to be considered. In this paper, we discuss this issue analytically for a Pekeris waveguide with limited mode number M. The method that we used for singularity analysis is to calculate the maximum value of the determinant of this kernel matrix. We found that there is an optimum source depth distribution corresponding to the maximum value of the determinant of the kernel matrix. That means that by choosing the optimum source depth distribution we can get the most stable inversion. The conclusion is that under a quite tolerant condition the matrix is not singular.

Recently, an analytic adjoint-based method of optimal nonlocal boundary control has been proposed for inversion of a waveguide acoustic field using the wide-angle parabolic equation [Meyer & Hermand, J. Acoust. Soc. Am. 117, 2937–2948 (2005)]. In this paper a numerical extension of this approach is presented that allows the direct inversion for the geoacoustic parameters which are embedded in a discrete representation of the nonlocal boundary condition. The adjoint model is generated numerically and the inversion is carried out jointly across multiple frequencies. To demonstrate the effectiveness of the implemented numerical adjoint, an illustrative example is presented for the geoacoustic characterization of a Mediterranean shallow water environment using realistic experimental conditions.

In the past few decades the elastic properties of ocean bottom were usually ignored to simplify problems by assuming a fluid seabed. Nevertheless, while it is acceptable to make such assumptions in deep water, the effects of shear waves can never be omitted as long as sound waves penetrates into ocean bottom, especially in shallow water where interactions between sound waves and elastic bottom are very frequent. Hence, seabed has to be considered as elastic solids to correctly reveal the propagating behavior of sound waves. A novel mathematical model and an implicit finite difference method to obtain a numerical solution for predicting wave propagation in a 3D ocean coupled with irregular fluid/solid interface are presented and developed into a computer code. Theoretical and computational aspects of the proposed parabolic equation solution procedure are investigated. Several numerical examples are included to show satisfactory results after comparing to known reference solutions with shear effects.

A thin rubber coating with cavities in a doubly periodic lattice can redistribute sound energy, normally incident on a steel plate, in the lateral direction. At high frequencies, propagating reflected beams appear in a discrete set of nonnormal directions in the surrounding water. The phenomenon is illustrated by pulse measurements in a water tank. The results are modeled by adapting modern computation techniques for electron scattering and band gaps in connection with photonic and phononic crystals. At lower frequencies, with only one propagating reflected beam in the water, differential evolution and winding-number integral algorithms are applied to design coatings with low reflectance. A stochastic resampling algorithm is adapted for accurate characterization of the parts of parameter space with favorable properties.

Thin-layer reservoir has great significance for oil exploration and development. Seismic characterization and monitoring of thin-layer reservoir has spatial advantage. New seismic attributes and attributes combination analysis are proposed, including attributes versus incidence angle, attributes versus scale, reflection coefficient spectrum and time-frequency analysis for detailed thin-layer reservoir characterization.

In 1974 a model was introduced by Frederick D. Tappert for predicting long-range wave propagation in a range-dependent environment. He applied the parabolic Equation approximation to transform the Helmholtz equation into a parabolic equation, the very first Parabolic Equation (PE). A pressure-release surface boundary is considered along with an artificial bottom boundary treatment. This paper proved that the Tappert model is energy-conserving.

Routine P-wave seismic data processing is tailored for isotropic rocks. Such assumption typically works well for small incidence angles and weak anisotropy. However, in the last decade it has become clear that seismic anisotropy is commonplace. Moreover, its magnitude often severely violates the presumptions taken for routine processing. Consequently reservoir characterization may be significantly distorted by anisotropic effects. In particular the intrinsic shale (often sealing rock) anisotropy often has first order effect on AVO gradient. Hence an assessment of the shale properties from surface seismic data may be of the primary importance for quantitative interpretation. There are several inversion approaches which require full set of geological information. In reality we expect to have at least the log and surface seismic data available for such a task. We present here a newly developed hybrid inversion method which is suitable for the recovery of anisotropic parameters of sealing rocks under such conditions. The effectiveness of this approach was successfully tested on seismic data recorded in the North West Shelf, Australia.

A numerical code using Gaussian Beam Model (NTUGBM) is developed for underwater acoustic propagation at high frequency (larger than 1 kHz) in oceans with penetrating slope bottom. Several test cases are used to benchmark NTUGBM. Cases include continental shelf and continental slope. The results of NTUGBM are compared with results using EFEPE and FOR3D (Nx2D version). Results of NTUGBM agree well with those of both codes.

A forward modeling of P-wave propagation in a bi-layer model of an isotropic layer overlying an orthorhombic layer is performed. The observation data of four differently oriented common-midpoint (CMP) lines show that P-wave amplitude exhibit strong azimuthal anisotropy. A formula is deduced to obtain the azimuth angle by using the amplitude variation of four differently oriented lines. Thomsen anisotropic parameters and the ratio of SV-wave and P-wave vertical velocity can be inverted from Amplitude Versus Offset and Azimuth (AVOA) by using the Niche Genetic Algorithms (NGA).The numerical simulation shows that the inversion method has enough stabilization and precision.

In this paper we focus our attention on the Marchenko inversion method which requires as input the reflectivity sequence of the medium with the view to reconstructing the seismic impedance from seismic reflection data. The reflectivity sequence and the relevant seismic wavelet are extracted from marine reflection data by applying the statistical estimation procedure known as Markov Chain Monte Carlo method to the problem of blind deconvolution. In order to implement the inversion method, the assumption of pure spike trains that was used previously has been replaced by amplitudes having a narrow bell-shaped form to facilitate the numerical solution of the Marchenko integral equation from which the underlying profile of the medium is obtained. Various aspects of our inversion procedure are discussed. These include questions related to the handling of experimental data and the numerical solution of the Marchenko integral equation using piecewise polynomials.

A novel statistical scheme for the characterization of underwater acoustic signals is tested in a shallow water environment for the classification of the bottom properties. The scheme is using the statistics of the 1-D wavelet coefficients of the transformed signal. For geoacoustic inversions based on optimization procedures, an appropriate norm is defined, based on the Kullback-Leibler divergence (KLD), expressing the difference between two statistical distributions. Thus the similarity of two environments is determined by means of an appropriate norm expressing the difference between two acoustical signals. The performance of the proposed inversion method is studied using synthetic acoustic signals generated in a shallow water environment over a fluid bottom.

A spectral element method has been recently developed for solving elastodynamic problems. The numerical solutions are obtained by using the weak formulation of the elastodynamic equation for heterogeneous media and by the Galerkin approach applied to a partition, in small subdomains, of the original physical domain under investigation. In the present work some mathematical aspects of the method and of the associated algorithm implementation are systematically investigated. Two kinds of orthogonal basis functions, constructed with Legendre and Chebyshev polynomials, and their related Gauss-Lobbatto collocation points, used in reference element quadrature, are introduced. The related analytical integration formulas are obtained. The standard error estimations and expansion convergence are discussed. In order to improve the computation accuracy and efficiency, an element-by-element pre-conditioned conjugate gradient linear solver in the space domain and a staggered predictor/multi-corrector algorithm in the time integration are used for strong heterogeneous elastic media. As a consequence neither the global matrices, nor the effective force vector is assembled. When analytical formula are used for the element quadrature, there is even no need for forming element matrix in order to further save memory without loosing much in computational efficiency. The element-by-element algorithm uses an optimal tensor product scheme which makes spectral element methods much more efficient than finite-element methods from the point of view of both memory storage and computational time requirements. This work is divided into two parts. The second part will give the algorithm implementation, numerical accuracy and efficiency analyses, and then the modelling example comparison of the proposed spectral element method with a conventional finite-element method and a staggered pseudo-spectral method that is to be reported in the other work.

The normal mode model of reverberation in shallow-water waveguides has been presented based on Born approximation. The key component of this model is the modal back-scattering matrix. The characteristics of the modal back-scattering caused by (1) the roughness of the bottom interface and (2) the volume inhomogeneities under the interface are discussed. Approaches of inversion of the matrix from reverberation data are proposed. Examples of the inversed result are shown both for numerical simulation and experiment.

To include the sound scattering caused by limited size of surfaces in room acoustic computer simulations, some model for scattering must be included in room acoustics computer models. A large concert hall usually contains a variety of small and complex surfaces and it is not practical to obtain accurate scattering coefficients of all these surfaces. Even if these frequency dependent coefficients could be obtained in the design phase, the modeling process would become more time consumed and increase the cost of design. In such a case, the appropriate simplification of the model and the definition of scattering coefficients by experience will become important. But in some other cases, calculation of a detailed model is necessary and possible. For these different cases, practical methods to define or calculate scattering coefficients, which include a new approach of modeling surface scattering and scattering caused by edge diffraction, have been presented. The predicted and measured acoustic parameters have been compared in order to testify the practical approaches recommended in the paper.