Composite boundary‐valued solution of the 2.5-D Green’s function for arbitrary acoustic media

Geophysics ◽  
1998 ◽  
Vol 63 (5) ◽  
pp. 1813-1823 ◽  
Author(s):  
Bing Zhou ◽  
Stewart A. Greenhalgh
Keyword(s):  
Boundary Condition ◽  
Green’S Function ◽  
Frequency Domain ◽  
Green's Function ◽  
Mixed Boundary ◽  
Waveform Inversion ◽  
Acoustic Medium ◽  
Model Parameters ◽  
Low Velocity ◽  
Acoustic Media

Theoretically, the Green’s function can be used to calculate the wavefield response of a specified source and the Fréchet derivative with respect to the model parameters for crosshole seismic full‐waveform inversion. In this paper, we apply the finite‐element method to numerically compute the 2.5-D Green’s function for an arbitrary acoustic medium by solving a composite boundary‐valued problem in the wavenumber‐frequency domain. The composite boundary condition consists of a 2.5-D absorbing boundary condition for the propagating wave field and a mixed boundary condition for the evanescent field in inhomogeneous media modeling. A numerical experiment performed for a uniform earth (having a known exact solution) shows the accuracy of the computation in the frequency and time domain. An inhomogeneous medium test, involving an embedded low‐velocity layer, demonstrates that the permissible range of [Formula: see text] at each frequency can be determined rationally from the critical wavenumber value of the medium around the source. Furthermore, it shows that the frequency‐domain solution is not improved continuously by increasing the number of [Formula: see text] samples because of the complicated nature of the wavefield. Both experiments show that the proposed method is effective and flexible for computing the 2.5-D Green’s function for arbitrary acoustic media.

Propagation of a Radar Modulated Ocean Wave Field

2014 ◽  
Author(s):  
M. S. M. Paalvast ◽  
P. Naaijen ◽  
H. R. M. Huijsmans
Keyword(s):  
Boundary Condition ◽  
Free Surface ◽  
Green’S Function ◽  
Wave Field ◽  
Frequency Domain ◽  
Green's Function ◽  
Propagation Model ◽  
Surface Boundary ◽  
Surface Source ◽  
Wave Elevation

In this article a study has been carried out to explore the feasibility of a wave propagation model that is able to predict the wave field in a deterministic sense, based on remote observations of the sea surface. The surface is modulated in order to simulate images created by a marine radar operating at grazing incidence. The developed model uses an integral equation method, utilizing the frequency domain Green’s function which fulfills the linear free surface boundary condition. Synthesized observations of either the wave elevation or surface tilt at the source points are used to initialize the wave model. At each of the locations of the added remote free surface panels, time traces of the observed wave elevation or surface tilt can be recorded. A Fourier Transform (FFT) of these time traces yields the frequency domain description of the boundary condition that has to be satisfied by the wave potential. The derived Green’s function for the free surface source panels is then used to solve the source of strength at these panels. Once values have been found for the sources, the potential, and thus the surface elevation, may be calculated at the ship’s location.

scholarly journals Pole-skipping and hydrodynamic analysis in Lifshitz, AdS2 and Rindler geometries

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Haiming Yuan ◽  
Xian-Hui Ge
Keyword(s):  
Boundary Condition ◽  
Green’S Function ◽  
Green's Function ◽  
Equations Of Motion ◽  
Equation Of Motion ◽  
Boundary Theory ◽  
Hydrodynamic Analysis ◽  
Dimensionless Variables ◽  
Pass Through ◽  
Special Points

Abstract The “pole-skipping” phenomenon reflects that the retarded Green’s function is not unique at a pole-skipping point in momentum space (ω, k). We explore the universality of pole-skipping in different geometries. In holography, near horizon analysis of the bulk equation of motion is a more straightforward way to derive a pole-skipping point. We use this method in Lifshitz, AdS2 and Rindler geometries. We also study the complex hydrodynamic analyses and find that the dispersion relations in terms of dimensionless variables $$ \frac{\omega }{2\pi T} $$ ω 2 πT and $$ \frac{\left|k\right|}{2\pi T} $$ k 2 πT pass through pole-skipping points $$ \left(\frac{\omega_n}{2\pi T},\frac{\left|{k}_n\right|}{2\pi T}\right) $$ ω n 2 πT k n 2 πT at small ω and k in the Lifshitz background. We verify that the position of the pole-skipping points does not depend on the standard quantization or alternative quantization of the boundary theory in AdS2× ℝd−1 geometry. In the Rindler geometry, we cannot find the corresponding Green’s function to calculate pole-skipping points because it is difficult to impose the boundary condition. However, we can still obtain “special points” near the horizon where bulk equations of motion have two incoming solutions. These “special points” correspond to the nonuniqueness of the Green’s function in physical meaning from the perspective of holography.

Development of a Computer Program for Three Dimensional Analysis of Zero Speed First Order Wave Body Interaction in Frequency Domain

2013 ◽  
Author(s):  
Amitava Guha ◽  
Jeffrey Falzarano
Keyword(s):  
Computer Program ◽  
Green’S Function ◽  
Frequency Domain ◽  
Green's Function ◽  
Early Stage ◽  
Diffraction Problem ◽  
Offshore Structures ◽  
Wave Radiation ◽  
Numerical Implementation ◽  
Strip Theory

Evaluation of motion characteristics of ships and offshore structures at the early stage of design as well as during operation at the site is very important. Strip theory based programs and 3D panel method based programs are the most popular tools used in industry for vessel motion analysis. These programs use different variations of the Green’s function or Rankine sources to formulate the boundary element problem which solves the water wave radiation and diffraction problem in the frequency domain or the time domain. This study presents the development of a 3D frequency domain Green’s function method in infinite water depth for predicting hydrodynamic coefficients, wave induced forces and motions. The complete theory and its numerical implementation are discussed in detail. An in house application has been developed to verify the numerical implementation and facilitate further development of the program towards higher order methods, inclusion of forward speed effects, finite depth Green function, hydro elasticity, etc. The results were successfully compared and validated with analytical results where available and the industry standard computer program for simple structures such as floating hemisphere, cylinder and box barge as well as complex structures such as ship, spar and a tension leg platform.

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