Near‐field broadband array beamforming using wave equation transformation

1996 ◽  
Vol 100 (4) ◽  
pp. 2696-2696
Author(s):  
Rodney A. Kennedy ◽  
P. Thushara ◽  
D. Abhayapala ◽  
Darren B. Ward
Keyword(s):  
Wave Equation ◽  
Near Field ◽  
Equation Transformation ◽  
Array Beamforming

Vertical seismic profile migration using the Kirchhoff integral

Geophysics ◽  
1988 ◽  
Vol 53 (6) ◽  
pp. 786-799 ◽  
Author(s):  
P. B. Dillon
Keyword(s):  
Wave Equation ◽  
Wave Field ◽  
Near Field ◽  
Synthetic Data ◽  
Real Data ◽  
Seismic Profile ◽  
Processing Strategies ◽  
Receiver Array ◽  
Vsp Data ◽  
Kirchhoff Integral

Wave‐equation migration can form an accurate image of the subsurface from suitable VSP data. The image’s extent and resolution are determined by the receiver array dimensions and the source location(s). Experiments with synthetic and real data show that the region of reliable image extent is defined by the specular “zone of illumination.” Migration is achieved through wave‐field extrapolation, subject to an imaging procedure. Wave‐field extrapolation is based upon the scalar wave equation and, for VSP data, is conveniently handled by the Kirchhoff integral. The migration of VSP data calls for imaging very close to the borehole, as well as imaging in the far field. This dual requirement is met by retaining the near‐field term of the integral. The complete integral solution is readily controlled by various weighting devices and processing strategies, whose worth is demonstrated on real and synthetic data.

Three-dimensional inverse scattering for the wave equation with variable speed: near-field formulae using point sources

1989 ◽  
Vol 5 (1) ◽  
pp. 1-6 ◽  
Author(s):  
M Cheney ◽  
G Beylkin ◽  
E Somersalo ◽  
R Burridge
Keyword(s):  
Wave Equation ◽  
Inverse Scattering ◽  
Near Field ◽  
Three Dimensional ◽  
Point Sources ◽  
Variable Speed

NUMERICAL SOLUTION OF THE ACOUSTIC WAVE EQUATION AT THE LIMIT BETWEEN NEAR AND FAR FIELD PROPAGATION

2001 ◽  
Vol 12 (10) ◽  
pp. 1497-1507 ◽  
Author(s):  
ERICH STOLL ◽  
STEFAN DANGEL
Keyword(s):  
Wave Equation ◽  
Acoustic Wave ◽  
Seismic Waves ◽  
Near Field ◽  
Three Dimensional ◽  
Low Frequency ◽  
Far Field ◽  
Acoustic Wave Equation ◽  
Sound Sources ◽  
Continuous Waves

The acoustic wave equation is solved numerically for two and three-dimensional systems at the limit between near and far field propagation. Our results show that for large sound velocities, corresponding to wavelengths larger than the system, near field properties are dominant. When the near field conditions are no longer satisfied, standing waves close to the sound emitters and interference patterns between the near field and far field solutions appear. Our procedure is applied to sound sources, which broadcast coherent and continuous waves as well as to sources emitting bursts of incoherent and uncorrelated waves. Both cases can be used to simulate the spreading of low frequency seismic waves observed close to volcanoes and hydrocarbon reservoirs.

Radiation from turbulence near a composite flexible boundary

1970 ◽  
Vol 314 (1517) ◽  
pp. 153-173 ◽  
Keyword(s):  
Boundary Layer ◽  
Wave Equation ◽  
Pressure Field ◽  
Near Field ◽  
Singular Integral Equations ◽  
Acoustic Power ◽  
Fluid Loading ◽  
Homogeneous Surface ◽  
Turbulent Pressure ◽  
Effect Of Surface

The effect of surface inhomogeneities on the sound radiated by nearby turbulence is examined in a particular case. The surface considered consists of two semi-infinite flexible planes which have different elastic and inertia constants, and a turbulent boundary layer is formed on this composite boundary. Lighthill’s wave equation is converted into a pair of singular integral equations for this problem, and the equations are solved to obtain the farfield radiation. The solution shows how the propagating components of the turbulent pressure field are reflected and diffracted by the surface, but these effects do not basically augment the radiation. It is also shown, however, that the discontinuity in surface properties acts as a ‘wavenumber converter’, scattering the turbulence near-field into propagating sound. The scattered acoustic power varies as U 4 when fluid loading on the surface is negligible (aeronautical applications), and as U 6 when fluid loading is appreciable (underwater applications), U being a typical flow velocity. These results are interpreted in terms of the radiation from a homogeneous surface under the action of a point force, and show that scattering by surface inhomogeneities should be a very important feature of the noise fields found in practice.

The near-field singularity predicted by the spiral Green’s function in acoustics and electrodynamics

1991 ◽  
Vol 433 (1888) ◽  
pp. 451-459 ◽  
Keyword(s):  
Wave Equation ◽  
Point Source ◽  
Wave Speed ◽  
Near Field ◽  
Radial Component ◽  
Extended Source ◽  
Ill Posed ◽  
Field Singularity ◽  
Theory Of Generalized Functions ◽  
Well Posed

The retarded solution of the wave equation for a point source in circular motion, whose speed exceeds the wave speed, is singular on a spiralling tube-like surface that is at rest in the rest frame of the point source. When solving the wave equation for a corresponding extended source, therefore, we are faced with integrals over the volume of the source which are improper and need to be handled either with the aid of the theory of generalized functions or by Hadamard’s method of finite parts. In this paper, after isolating the finite part of the gradient of the retarded potential due to a rotating extended source, we calculate the asymptotic values of the coefficients in its Fourier representation and show that the radial component of this gradient does not remain finite at those points within the source which move with the wave speed, and so lie on the boundary of the domain of hyperbolicity of the equation of the mixed type to which the wave equation in this case reduces. This latter singularity arises because the problem in question, though well posed physically, is in fact mathematically ill posed.

COMPUTATION OF THE FLOW AND NEAR SOUND FIELDS OF A FREE SURFACE PIERCING CYLINDER

2009 ◽  
Vol 17 (04) ◽  
pp. 365-382 ◽  
Author(s):  
ELDAD J. AVITAL ◽  
GUANGXU YU ◽  
JOHN WILLIAMS
Keyword(s):  
Wave Equation ◽  
Free Surface ◽  
Sound Wave ◽  
Near Field ◽  
Low Frequency ◽  
Sound Field ◽  
Frequency Component ◽  
Sound Fields ◽  
Pressure Surface ◽  
Interface Surface

The near sound field generated due to a vertically mounted circular cylinder piercing a free surface in shallow water, is studied computationally using the Large Eddy Simulation (LES) approach and the sound wave equation. The flow is simulated in both the air and water phases. The interface surface is allowed to move and is simulated using the Volume of Fluid technique. The pressure distribution over the cylinder is fed back into the sound wave equation to calculate the near field. The interface surface is modeled as a zero pressure surface in the acoustic calculation and the bottom is taken as having infinite impedence modeling the case of a rigid floor. Two of acoustic calculations methods are used. In the first method, the interface surface is assumed to be fixed and the wave equation is solved in the frequency domain in a post-processing stage. In the second method, the evolution of the interface surface is taken into account and the wave equation is simulated simultaneously with the LES. Both solutions are analyzed and compared to show that the interface surface acts as a strong damper to the low frequency sound by damping the vortex Von Karman rollers as well as causing the low frequency component to be nonradiative. The variation of the near sound field with the water depth and Froude number is investigated and the propagation and damping characteristics are analyzed.

scholarly journals Spherical One-Way Wave Equation

Acoustics ◽  
2021 ◽  
Vol 3 (2) ◽  
pp. 309-315
Author(s):  
Oskar Bschorr ◽  
Hans-Joachim Raida
Keyword(s):  
Wave Equation ◽  
Asymptotic Approximation ◽  
Bessel Functions ◽  
Near Field ◽  
Far Field ◽  
Spherical Coordinates ◽  
Nabla Operator ◽  
Spherical Waves ◽  
New Variant ◽  
Amplitude Decrease

The coordinate-free one-way wave equation is transferred in spherical coordinates. Therefore it is necessary to achieve consistency between gradient, divergence and Laplace operators and to establish, beside the conventional radial Nabla operator ∂Φ/∂r, a new variant ∂rΦ/r∂r. The two Nabla operator variants differ in the near field term Φ/r whereas in the far field r≫0 there is asymptotic approximation. Surprisingly, the more complicated gradient ∂rΦ/r∂r results in unexpected simplifications for – and only for – spherical waves with the 1/r amplitude decrease. Thus the calculation always remains elementary without the wattless imaginary near fields, and the spherical Bessel functions are obsolete.

scholarly journals Microphone array beamforming with near‐field correlated sources.

2009 ◽  
Vol 125 (4) ◽  
pp. 2545-2545
Author(s):  
Jonathan L. Odom ◽  
Jeffery Krolik
Keyword(s):  
Microphone Array ◽  
Near Field ◽  
Correlated Sources ◽  
Array Beamforming

Near-field scanning optical microscopy

1986 ◽  
Vol 44 ◽  
pp. 642-643
Author(s):  
E. Betzig ◽  
A. Harootunian ◽  
M. Isaacson ◽  
A. Lewis
Keyword(s):  
Near Field ◽  
Optical Microscope ◽  
Visible Radiation ◽  
Field Methods ◽  
Optical Elements ◽  
Optical Region ◽  
Order Of Magnitude ◽  
Nondestructive Imaging ◽  
Scanning Optical Microscopy ◽  
Near Field Scanning

In general, conventional methods of optical imaging are limited in spatial resolution by either the wavelength of the radiation used or by the aberrations of the optical elements. This is true whether one uses a scanning probe or a fixed beam method. The reason for the wavelength limit of resolution is due to the far field methods of producing or detecting the radiation. If one resorts to restricting our probes to the near field optical region, then the possibility exists of obtaining spatial resolutions more than an order of magnitude smaller than the optical wavelength of the radiation used. In this paper, we will describe the principles underlying such "near field" imaging and present some preliminary results from a near field scanning optical microscope (NS0M) that uses visible radiation and is capable of resolutions comparable to an SEM. The advantage of such a technique is the possibility of completely nondestructive imaging in air at spatial resolutions of about 50nm.

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