Parabolic equation solution of seismo-acoustics problems involving variations in bathymetry and sediment thickness
04 Jan 2008-Journal of the Acoustical Society of America (Acoustical Society of America)-Vol. 123, Iss: 1, pp 51-55
TL;DR: Improvements in the parabolic equation method are combined to extend this approach to a larger class of seismo-acoustics problems, including problems involving variations in bathymetry and the thickness of sediment layers.
Abstract: Recent improvements in the parabolic equation method are combined to extend this approach to a larger class of seismo-acoustics problems. The variable rotated parabolic equation [J. Acoust. Soc. Am. 120, 3534–3538 (2006)] handles a sloping fluid-solid interface at the ocean bottom. The single-scattering solution [J. Acoust. Soc. Am. 121, 808–813 (2007)] handles range dependence within elastic sediment layers. When these methods are implemented together, the parabolic equation method can be applied to problems involving variations in bathymetry and the thickness of sediment layers. The accuracy of the approach is demonstrated by comparing with finite-element solutions. The approach is applied to a complex scenario in a realistic environment.
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TL;DR: A time-domain Legendre spectral-element method is described for full-wave simulation of ocean acoustics models, i.e., coupled fluid-solid problems in unbounded or semi-infinite domains, taking into account shear wave propagation in the ocean bottom.
Abstract: A time-domain Legendre spectral-element method is described for full-wave simulation of ocean acoustics models, i.e., coupled fluid-solid problems in unbounded or semi-infinite domains, taking into account shear wave propagation in the ocean bottom. The technique can accommodate range-dependent and depth-dependent wave speed and density, as well as steep ocean floor topography. For truncation of the infinite domain, to efficiently absorb outgoing waves, a fluid-solid complex-frequency-shifted unsplit perfectly matched layer is introduced based on the complex coordinate stretching technique. The complex stretching is rigorously taken into account in the derivation of the fluid-solid matching condition inside the absorbing layer, which has never been done before in the time domain. Two implementations are designed: a convolutional formulation and an auxiliary differential equation formulation because the latter allows for implementation of high-order time schemes, leading to reduced numerical dispersion and dissipation, a topic of importance, in particular, in long-range ocean acoustics simulations. The method is validated for a two dimensional fluid-solid Pekeris waveguide and for a three dimensional seamount model, which shows that the technique is accurate and numerically long-time stable. Compared with widely used paraxial absorbing boundary conditions, the perfectly matched layer is significantly more efficient at absorbing both body waves and interface waves.
36 citations
TL;DR: Low-frequency transmission loss data collected from an offshore seismic survey in Bass Strait on the southern Australian continental shelf are analyzed and shown to be in broad agreement with the numerical predictions based on the theoretical analysis and modeling using an elastic parabolic equation solution for range-dependent bathymetry.
Abstract: Measurements of low-frequency sound propagation over the areas of the Australian continental shelf, where the bottom sediments consist primarily of calcarenite, have revealed that acoustic transmission losses are generally much higher than those observed over other continental shelves and remain relatively low only in a few narrow frequency bands. This paper considers this phenomenon and provides a physical interpretation in terms of normal modes in shallow water over a layered elastic seabed with a shear wave speed comparable to but lower than the water-column sound speed. A theoretical analysis and numerical modeling show that, in such environments, low attenuation of underwater sound is expected only in narrow frequency bands just above the modal critical frequencies which in turn are governed primarily by the water depth and compressional wave speed in the seabed. In addition, the effect of a thin layer of harder cap-rock overlaying less consolidated sediments is considered. Low-frequency transmission loss data collected from an offshore seismic survey in Bass Strait on the southern Australian continental shelf are analyzed and shown to be in broad agreement with the numerical predictions based on the theoretical analysis and modeling using an elastic parabolic equation solution for range-dependent bathymetry.
24 citations
Cites background or methods from "Parabolic equation solution of seis..."
...II and numerical predictions for range-dependent bathymetry using an algorithm based on the parabolic approximation (Collis et al., 2008)....
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...8) and a parabolic equation (PE) solution recently developed by Collis et al. (2008)....
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...Exposure of calcium-carbonate rich marine sediments to fresh water from atmospheric precipitation resulted in the calcium carbonate in the top layer of sediment partly dissolving, penetrating deeper as a pore fluid and then re-crystallizing, cementing the remaining sediment grains together....
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TL;DR: An almost optimal error estimate is presented for the finite element solution of a nonlinear parabolic interface problem, where the coefficient depends on the unknown variable and is discontinuous along an interface inside the computational domain.
Abstract: We present an almost optimal error estimate for the finite element solution of a nonlinear parabolic interface problem, where the coefficient depends on the unknown variable and is discontinuous along an interface inside the computational domain. A linearized second-order backward difference formula is used for the time discretization, and piecewise linear interpolation is used to approximate the interface. We do not assume Lipschitz continuity of the nonlinear coefficient.
22 citations
TL;DR: A stepwise coupled-mode model with the use of the direct global matrix approach, capable of handling two-dimensional problems with either a point source in cylindrical geometry or a line source in plane geometry that is numerically stable and free from the numerical overflow problem.
Abstract: In this paper, a stepwise coupled-mode model with the use of the direct global matrix approach is proposed. This method is capable of handling two-dimensional problems with either a point source in cylindrical geometry or a line source in plane geometry. With the use of the direct global matrix approach, this method is numerically stable. In addition, by introducing appropriately normalized range solutions, thismodel is free from the numerical overflow problem. Furthermore, we put forward source conditions appropriate for the line-source problem in plane geometry. As a result, this method is capable of addressing the scenario with a line source on top of a sloping bottom. Closed-form expressions for coupling matrices are derived and applied in this paper for handling problems with pressure-release boundaries and a homogeneous water column. The numerical simulations indicate that the proposed model is accurate, efficient, and numerically stable. Consequently, this model can serve as a benchmark model in range-dependent propagation modeling. Although this method is verified by an ideal wedge problem in this paper, the formulation applies to realistic problems as well.
20 citations
TL;DR: Building on recent elastic seafloor modeling developments, a range-dependent parabolic equation solution that treats the ice as an elastic medium is presented and is benchmarked against a derived elastic normal mode solution for range-independent underwater acoustic propagation.
Abstract: Sound propagation predictions for ice-covered ocean acoustic environments do not match observational data: received levels in nature are less than expected, suggesting that the effects of the ice are substantial. Effects due to elasticity in overlying ice can be significant enough that low-shear approximations, such as effective complex density treatments, may not be appropriate. Building on recent elastic seafloor modeling developments, a range-dependent parabolic equation solution that treats the ice as an elastic medium is presented. The solution is benchmarked against a derived elastic normal mode solution for range-independent underwater acoustic propagation. Results from both solutions accurately predict plate flexural modes that propagate in the ice layer, as well as Scholte interface waves that propagate at the boundary between the water and the seafloor. The parabolic equation solution is used to model a scenario with range-dependent ice thickness and a water sound speed profile similar to those observed during the 2009 Ice Exercise (ICEX) in the Beaufort Sea.
18 citations
References
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TL;DR: In this article, the authors present state-of-the-art numerical techniques to solve the wave equation in heterogeneous fluid-solid media and present a comprehensive and modern introduction to computational ocean acoustics accessible to students.
Abstract: Senior level/graduate level text/reference presenting state-of-the- art numerical techniques to solve the wave equation in heterogeneous fluid-solid media. Numerical models have become standard research tools in acoustic laboratories, and thus computational acoustics is becoming an increasingly important branch of ocean acoustic science. The first edition of this successful book, written by the recognized leaders of the field, was the first to present a comprehensive and modern introduction to computational ocean acoustics accessible to students. This revision, with 100 additional pages, completely updates the material in the first edition and includes new models based on current research. It includes problems and solutions in every chapter, making the book more useful in teaching (the first edition had a separate solutions manual). The book is intended for graduate and advanced undergraduate students of acoustics, geology and geophysics, applied mathematics, ocean engineering or as a reference in computational methods courses, as well as professionals in these fields, particularly those working in government (especially Navy) and industry labs engaged in the development or use of propagating models.
1,344 citations
Book•
07 May 1997
TL;DR: This revision, with 100 additional pages, completely updates the material in the first edition and includes new models based on current research and includes problems and solutions in every chapter, making the book more useful in teaching.
Abstract: Senior level/graduate level text/reference presenting state-of-the- art numerical techniques to solve the wave equation in heterogeneous fluid-solid media. Numerical models have become standard research tools in acoustic laboratories, and thus computational acoustics is becoming an increasingly important branch of ocean acoustic science. The first edition of this successful book, written by the recognized leaders of the field, was the first to present a comprehensive and modern introduction to computational ocean acoustics accessible to students. This revision, with 100 additional pages, completely updates the material in the first edition and includes new models based on current research. It includes problems and solutions in every chapter, making the book more useful in teaching (the first edition had a separate solutions manual). The book is intended for graduate and advanced undergraduate students of acoustics, geology and geophysics, applied mathematics, ocean engineering or as a reference in computational methods courses, as well as professionals in these fields, particularly those working in government (especially Navy) and industry labs engaged in the development or use of propagating models.
523 citations
TL;DR: In this article, a higher-order elastic parabolic equation (HEPE) is derived for wave propagation in depth-dependent and weakly range-dependent fluid/solid media.
Abstract: A higher‐order elastic parabolic equation (HEPE) is derived for wave propagation in depth‐dependent and weakly range‐dependent fluid/solid media. Galerkin’s method is used to discretize the depth operators in the HEPE within layers in which depth variations in the Lame constants and density are continuous. Discontinuities in material properties are handled with centered differences for the interface conditions between layers. The numerical solution of the HEPE also involves the method of alternating directions and Crank–Nicolson integration. The HEPE is applied to underwater wave propagation problems involving a water column over an elastic bottom including a weakly range‐dependent problem. The accuracy of the HEPE is demonstrated with benchmark calculations.
128 citations
TL;DR: In this article, higher-order Pade approximations are applied to derive accurate and stable parabolic equations for sound propagation in oceans bounded below by an elastic bottom or bounded above by ice cover.
Abstract: Higher-order Pade approximations are applied to derive accurate and stable parabolic equations for sound propagation in oceans bounded below by an elastic bottom or bounded above by ice cover. Accuracy is achieved by placing constraints on the derivatives of the Pade approximations at the point corresponding to the reference wave number. Stability is achieved by requiring that the Pade approximations map part of the lower-left quadrant of the complex plane into the upper half of the complex plane. Elastic parabolic equations based on these Pade series can handle problems involving compressional, shear, and interface waves, very wide propagation angles, and large depth variations and weak range variations in the seismoacoustic parameters. A finite-difference spectral solution is developed for generating reference solutions and starting fields. The rotated elastic parabolic equation is used to investigate the accuracy of the elastic parabolic equation for range-dependent problems.
128 citations
TL;DR: A frequency-domain finite-element technique for computing the radiation and scattering from axially symmetric fluid-loaded structures subject to a nonsymmetric forcing field is presented and one particularly useful feature of the Berenger perfectly matched layer is that it can be applied across the interface between different fluids.
Abstract: A frequency-domain finite-element (FE) technique for computing the radiation and scattering from axially symmetric fluid-loaded structures subject to a nonsymmetric forcing field is presented. The Berenger perfectly matched layer (PML), applied directly at the fluid-structure interface, makes it possible to emulate the Sommerfeld radiation condition using FE meshes of minimal size. For those cases where the acoustic field is computed over a band of frequencies, the meshing process is simplified by the use of a wavelength-dependent rescaling of the PML coordinates. Quantitative geometry discretization guidelines are obtained from a priori estimates of small-scale structural wavelengths, which dominate the acoustic field at low to mid frequencies. One particularly useful feature of the PML is that it can be applied across the interface between different fluids. This makes it possible to use the present tool to solve problems where the radiating or scattering objects are located inside a layered fluid medium. The proposed technique is verified by comparison with analytical solutions and with validated numerical models. The solutions presented show close agreement for a set of test problems ranging from scattering to underwater propagation.
98 citations