COMPARISON OF TWO AND THREE SPATIAL DIMENSIONAL SOLUTIONS OF A PARABOLIC APPROXIMATION OF THE WAVE EQUATION AT OCEAN-BASIN SCALES IN THE PRESENCE OF INTERNAL WAVES: 100–150Hz

2010 ◽  
Vol 18 (02) ◽  
pp. 117-129 ◽  
Author(s):  
JOHN L. SPIESBERGER
Keyword(s):  
Wave Equation ◽  
Acoustic Wave ◽  
Internal Waves ◽  
Gravity Waves ◽  
Numerical Solutions ◽  
Internal Gravity Waves ◽  
Ocean Basin ◽  
Acoustic Wave Equation ◽  
Parabolic Approximation ◽  
Spatial Dimensions

Numerical solutions are given for a parabolic approximation to the acoustic wave equation at 100 and 150 Hz in two and three spatial dimensions to determine if azimuthal coupling in the horizontal coordinate significantly affects horizontal correlation in the presence of internal gravity waves in the sea. Coupling is a small effect at 4000 km. This implies that accurate solutions are possible using computations from uncoupled vertical slices. Shape of horizontal correlation is inconsistent with shapes given by two theories. Estimates of horizontal correlation at 4000 km and 100 and 150 Hz are about 1 km and 0.5 km respectively.

COMPARISON OF TWO AND THREE SPATIAL DIMENSIONAL SOLUTIONS OF THE WAVE EQUATION AT OCEAN-BASIN SCALES IN THE PRESENCE OF INTERNAL WAVES

2007 ◽  
Vol 15 (03) ◽  
pp. 319-332 ◽  
Author(s):  
JOHN L. SPIESBERGER
Keyword(s):  
Wave Equation ◽  
Acoustic Wave ◽  
Internal Waves ◽  
Gravity Waves ◽  
Numerical Solutions ◽  
Internal Gravity Waves ◽  
Ocean Basin ◽  
Acoustic Wave Equation ◽  
Parabolic Approximation ◽  
Spatial Dimensions

Numerical solutions are given for a parabolic approximation to the acoustic wave equation at 75 Hz in two and three spatial dimensions to determine if azimuthal coupling of the field significantly affects horizontal coherence. Coupling is a small effect at 4000 km in the presence of internal gravity waves. This implies that accurate solutions are possible using computations from uncoupled vertical slices through the field. The shape of horizontal coherence is inconsistent with shapes given by two theories. Estimates of horizontal coherence at 4000 km and 25, 50, and 75 Hz are 10, 2, and 1 km respectively.

A conservation law for internal gravity waves

1976 ◽  
Vol 78 (2) ◽  
pp. 209-216 ◽  
Author(s):  
Michael Milder
Keyword(s):  
Internal Wave ◽  
Group Velocity ◽  
Internal Waves ◽  
Gravity Waves ◽  
Conservation Law ◽  
Short Wavelength ◽  
Internal Gravity Waves ◽  
Volume Integral ◽  
Weak Density ◽  
Progressive Waves

The scaled vorticity Ω/N and strain ∇ ζ associated with internal waves in a weak density gradient of arbitrary depth dependence together comprise a quantity that is conserved in the usual linearized approximation. This quantity I is the volume integral of the dimensionless density DI = ½[Ω2/N2 + (∇ ζ)2]. For progressive waves the ‘kinetic’ and ‘potential’ parts are equal, and in the short-wavelength limit the density DI and flux FI are related by the ordinary group velocity: FI = DIcg. The properties of DI suggest that it may be a useful measure of local internal-wave saturation.

An analytic signal based accurate time-domain visco-acoustic wave equation from the Constant-Q theory

Geophysics ◽  
2021 ◽  
pp. 1-58
Author(s):  
Hongwei Liu ◽  
Yi Luo
Keyword(s):  
Wave Equation ◽  
Acoustic Wave ◽  
Time Domain ◽  
Seismic Waves ◽  
Heterogeneous Media ◽  
Relaxation Property ◽  
Analytic Signal ◽  
Acoustic Wave Equation ◽  
Real Component ◽  
Frequency Components

We present a concise time-domain wave equation to accurately simulate wave propagation in visco-acoustic media. The central idea behind this work is to dismiss the negative frequency components from a time-domain signal by converting the signal to its analytic format. The negative frequency components of any analytic signal are always zero, meaning we can construct the visco-acoustic wave equation to honor the relaxation property of the media for positive frequencies only. The newly proposed complex-valued wave equation (CWE) represents the wavefield with its analytic signal, whose real part is the desired physical wavefield, while the imaginary part is the Hilbert transform of the real component. Specifically, this CWE is accurate for both weak and strong attenuating media in terms of both dissipation and dispersion and the attenuation is precisely linear with respect to the frequencies. Besides, the CWE is easy and flexible to model dispersion-only, dissipation-only or dispersion-plus-dissipation seismic waves. We have verified these CWEs by comparing the results with analytical solutions, and achieved nearly perfect matching. Except for the homogeneous Q media, we have also extended the CWEs to heterogeneous media. The results of the CWEs for heterogeneous Q media are consistent with those computed from the nonstationary operator based Fourier Integral method and from the Standard Linear Solid (SLS) equations.

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