Perfectly matched layers for modelling seismic oceanography experiments

Kormann, Jean; Cobo, Pedro; Prieto, Andrés

doi:10.1016/j.jsv.2008.03.024

Cited by 13 publications

(12 citation statements)

References 15 publications

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“…In recent years other authors (e.g. [37,38]) have also considered this class of functions and have conducted studies on the variation of the various parameters in their respective formulations (e.g. [26,39]).…”

Section: Discussionmentioning

confidence: 99%

A parameter-free perfectly matched layer formulation for the finite-element-based solution of the Helmholtz equation

Cimpeanu

Martinsson

Heil

2015

Journal of Computational Physics

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This paper presents a parameter-free perfectly matched layer (PML) method for the finite-element-based solution of the Helmholtz equation. We employ one of Bermúdez et al.'s unbounded absorbing functions for the complex coordinate mapping underlying the PML. With this choice, the only free parameter that controls the accuracy of the numerical solution for a fixed numerical cost (characterised by the number of elements in the bulk and the PML regions) is the thickness of the perfectly matched layer, δ PML . We show that, for the case of planar waves, the absorbing function performs best for PMLs whose thickness is much smaller than the wavelength. We then perform extensive numerical experiments to explore its performance for non-planar waves, considering domain shapes with smooth and polygonal boundaries, different solution types (smooth and singular), and a wide range of wavenumbers, k, to identify an optimal range for the normalised PML thickness, kδ PML , such that, within this range, the error introduced by the presence of the PML is consistently small and insensitive to change. This implies that if the PML thickness is chosen from within this range * Corresponding author URL: http://www3.imperial.ac.uk/people/radu.cimpeanu11 (Radu Cimpeanu), http://www.maths.manchester.ac.uk/~mheil/ (Matthias Heil) Preprint submitted to Journal of Computational PhysicsMay 4, 2015 no further PML optimisation is required, i.e. the method is parameter-free. We characterise the dependence of the error on the discretisation parameters and establish the conditions under which the convergence of the solution under mesh refinement is controlled exclusively by the discretisation of the bulk mesh.

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Section: Discussionmentioning

confidence: 99%

A parameter-free perfectly matched layer formulation for the finite-element-based solution of the Helmholtz equation

Cimpeanu

Martinsson

Heil

2015

Journal of Computational Physics

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“…It is worthwhile to emphasize that, to observe the reflections yielded by the inhomogeneous water clearly, spurious numerical reflections at the lateral PML boundaries must be at least one order smaller than the magnitude of the physical phenomena of interest. Thus, the first-order PML introduced by Kormann et al [16] is used in this paper. Our physical model is depicted in Figure 1(a).…”

Section: To What Degree Is a Seismic Image Influenced By Inhomogeneoumentioning

confidence: 99%

The effect of inhomogeneous water on seismic imaging in deepwater areas of the South China Sea

Lin

Hao

2013

Chin. Sci. Bull.

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This paper examines the effect of inhomogeneous water on seismic imaging in deep water areas. An appropriate partial differential equation is derived for the acoustic pressure field in inhomogeneous water, including current effects. Seismic wavefields are simulated and the results show that the traveltime of seismic waves can be affected. The maximum traveltime perturbation at zero offset is 20 ms. In particular, the structure of horizontal reflectors below the water is distorted by mesoscale eddies. Variations of water temperature are the fundamental cause of the distortion. Finally, a calibration method for the distortion of seismic imaging caused by inhomogeneous water is presented.

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“…Even in the simplest case where both media are homogeneous and isotropic, the problem remains open. However, in the literature there exists a wide range of works dealing with stratified media, for instance, among many other areas, in geophysics (see [26]) or in underwater acoustics (see [53]), all of them with a common assumed claim: if the interface among the different media is perpendicular to the interface between the physical domain and the PML and continuous straight in the PML domain, then a good numerical accuracy is expected from the PML technique. To the best knowledge of the authors, this claims has not theoretical support yet.…”

Section: Semi-buried Rigid Object In Underwater Sedimentsmentioning

confidence: 99%

Perfectly Matched Layers for Time-Harmonic Second Order Elliptic Problems

Bermúdez

Hervella-Nieto

Prieto

et al. 2010

Arch Computat Methods Eng

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The main goal of this work is to give a review of the Perfectly Matched Layer (PML) technique for time-harmonic problems. Precisely, we focus our attention on problems stated in unbounded domains, which involve second order elliptic equations writing in divergence form and, in particular, on the Helmholtz equation at low frequency regime. Firstly, the PML technique is introduced by means of a simple porous model in one dimension. It is emphasized that an adequate choice of the so called complex absorbing function in the PML yields to accurate numerical results. Then, in the two-dimensional case, the PML governing equation is described for second order partial differential equations by using a smooth complex change of variables. Its mathematical analysis and some particular examples are also included. Numerical drawbacks and optimal choice of the PML absorbing function are studied in detail. In fact, theoretical and numerical analysis show the advantages of using non-integrable absorbing functions. Finally, we present some relevant real life numerical simulations where the PML technique is widely and successfully used although they are not covered by the standard theoretical framework.

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Perfectly matched layers for modelling seismic oceanography experiments

Cited by 13 publications

References 15 publications

A parameter-free perfectly matched layer formulation for the finite-element-based solution of the Helmholtz equation

A parameter-free perfectly matched layer formulation for the finite-element-based solution of the Helmholtz equation

The effect of inhomogeneous water on seismic imaging in deepwater areas of the South China Sea

Perfectly Matched Layers for Time-Harmonic Second Order Elliptic Problems

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