A theory for marine source arrays

Geophysics ◽  
1988 ◽  
Vol 53 (5) ◽  
pp. 650-658 ◽  
Author(s):  
Richard E. Duren
Keyword(s):  
Energy Density ◽  
Solid Angle ◽  
Large Element ◽  
Far Field ◽  
Linear Superposition ◽  
Frequency Spectra ◽  
Analysis And Design ◽  
Unit Solid Angle ◽  
Radiated Energy ◽  
Marine Source

General mathematical expressions for a marine source array’s (1) far‐field pulse spectrum, (2) radiated energy density, and (3) directivity are developed for both a source in an infinite homogeneous medium and a source operating near the ocean surface. These results, intended to assist the analysis and design of marine source arrays, apply to any marine source array when (1) individual elements radiate isotropically, (2) their individual waveforms are specified, and (3) the array geometry is specified. Arbitrary geometry and arbitrary isotropic waveforms are allowed. The theory assumes linear superposition of the individually specified waveforms, and is consistent with the “square law effect” for identical elements. For an array of small elements, expended energy agrees with the array’s radiated energy found using far‐field methods. Also, the energy radiated from an array with large element spacing is equal to the sum of the independently radiated energies. Two closely spaced identical elements radiate four times the energy contained in a single outgoing waveform over all space. The appropriate directivity definition for marine seismic sources is the ratio of the radiated energy density per unit solid angle in a particular direction to the average radiated energy density per unit solid angle. This definition allows directivity to be expressed explicitly in terms of the individual frequency spectra and geometry.

scholarly journals Sound radiation in turbulent channel flows

2003 ◽  
Vol 475 ◽  
pp. 269-302 ◽  
Author(s):  
ZHIWEI HU ◽  
CHRISTOPHER L. MORFEY ◽  
NEIL D. SANDHAM
Keyword(s):  
Mach Number ◽  
Sound Radiation ◽  
Fourth Power ◽  
Shear Stresses ◽  
Far Field ◽  
Good Resolution ◽  
Reynolds Stresses ◽  
Rigid Boundary ◽  
Frequency Spectra ◽  
Viscous Shear

Lighthill’s acoustic analogy is formulated for turbulent channel flow with pressure as the acoustic variable, and integrated over the channel width to produce a two-dimensional inhomogeneous wave equation. The equivalent sources consist of a dipole distribution related to the sum of the viscous shear stresses on the two walls, together with monopole and quadrupole distributions related to the unsteady turbulent dissipation and Reynolds stresses respectively. Using a rigid-boundary Green function, an expression is found for the power spectrum of the far-field pressure radiated per unit channel area. Direct numerical simulations (DNS) of turbulent plane Poiseuille and Couette flow have been performed in large computational domains in order to obtain good resolution of the low-wavenumber source behaviour. Analysis of the DNS databases for all sound radiation sources shows that their wavenumber–frequency spectra have non-zero limits at low wavenumber. The sound power per unit channel area radiated by the dipole distribution is proportional to Mach number squared, while the monopole and quadrupole contributions are proportional to the fourth power of Mach number. Below a particular Mach number determined by the frequency and radiation direction, the dipole radiation due to the wall shear stress dominates the far field. The quadrupole takes over at Mach numbers above about 0.1, while the monopole is always the smallest term. The resultant acoustic field at any point in the channel consists of a statistically diffuse assembly of plane waves, with spectrum limited by damping to a value that is independent of Mach number in the low-M limit.

Interaction of waves with two-dimensional obstacles: a relation between the radiation and scattering problems

1975 ◽  
Vol 71 (2) ◽  
pp. 273-282 ◽  
Author(s):  
J. N. Newman
Keyword(s):  
Water Waves ◽  
The Body ◽  
Far Field ◽  
Linear Superposition ◽  
Scattering Problems ◽  
Simple Argument ◽  
Transmission Coefficients ◽  
Horizontal Symmetry ◽  
Phase Angles ◽  
Formal Application

A relation connecting the reflexion and transmission coefficients for scattering of water waves by a fixed body with the far-field radiated waves due to forced motions of the same body is derived. Two alternative derivations are given, including a simple argument based on the analysis of an appropriate linear superposition of the two problems, and a more formal application of Green's theorem to the two potentials. For bodies with horizontal symmetry, the transmission and reflexion coefficients are related to the phase angles of the far-field radiated waves associated with symmetric and antisymmetric forced motions of the body. Some general conclusions follow for arbitrary symmetric bodies, and these are verified in specific cases by comparison with existing solutions. The applicability of these relations to other types of wave problem is noted.

scholarly journals Laser generated plasma as a source for real time studies in X-ray crystal research: Part I: Fundamental remarks about source characteristics and requirements

1984 ◽  
Vol 2 (2) ◽  
pp. 167-185 ◽  
Author(s):  
E. Förster ◽  
K. Goetz ◽  
K. Schäfer ◽  
W. D. Zimmer
Keyword(s):  
Solid State ◽  
Real Time ◽  
Solid Angle ◽  
Wavelength Interval ◽  
Time Resolved ◽  
X Ray ◽  
Source Characteristics ◽  
Unit Solid Angle ◽  
State Research ◽  
Laser Plasmas

Because of the large number of X-ray photons which will be emitted per unit solid angle and wavelength interval, laser generated plasmas have good prospects as X-ray sources for time-resolved diffraction experiments in solid state research. Starting from this a modified two-crystal diffractometer will be described, which uses the particular advantages of laser plasmas as X-ray flash sources. Requirements for the source will be determined and discussed.

scholarly journals Strong Far-Field Vertical Excitation and Building Damage: A Systematic Review and Future Avenues

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Dipendra Gautam ◽  
Rewati Baruwal
Keyword(s):  
Systematic Review ◽  
Structural Analysis ◽  
Near Field ◽  
Building Damage ◽  
Far Field ◽  
Central Himalayas ◽  
Vertical Excitation ◽  
Analysis And Design ◽  
Himalayan Earthquakes

Strong vertical excitation may lead to detrimental consequences on structures and infrastructures. To date, the impacts of strong vertical shaking on structures and infrastructures are considered for near-field regions only. However, anomalies in terms of recorded evidence and damage occurrence in the central Himalayan earthquakes dragged the attention of the researchers to explore the possibility of strong vertical shaking in far-field regions as well. Systematic review approach is used to sum up the findings from scholastic works reported to date and juxtaposed the findings with the evidence from central Himalayan earthquakes. It is concluded that the strong vertical shaking in the far-field is undeniable, at least in the central Himalayas; thus, incorporation of strong far-field vertical shaking in structural analysis and design is required. This paper reports the evidence reported in the literature for strong vertical shaking and adds evidence from Nepal focusing on strong far-field vertical excitation.

Study on the Testing System of Far-Field Laser Energy Density Distribution

2012 ◽  
Vol 229-231 ◽  
pp. 1338-1342
Author(s):  
Xu Yang ◽  
Lu Song ◽  
Jin Duan
Keyword(s):  
Energy Density ◽  
Density Distribution ◽  
Measurement Errors ◽  
Laser Energy ◽  
Target Surface ◽  
Laser Spot ◽  
Laser Energy Density ◽  
Testing System ◽  
Far Field ◽  
Energy Density Distribution

This study designs and develops a set of far-field laser spot energy testing system based on energy density detecting array. Through installing energy density detectors on the characteristic location of energy density target, the practical value of laser’s energy could be adopted. Meanwhile, by the use of visible light image equipment, the energy density distribution image of laser spot with a wavelength of 532nm on target surface could be obtained. After that, the energy density of each spot on the target surface as well as the energy density distribution have been figured out by fusing the grey level of laser spot image with the practical energy value detected by laser energy probes. The result shows that this system, which is simple, reliable, and available for the far-field laser energy density measurement under all circumstances, is capable of precisely measuring the far-field laser energy distribution with more than 1km with few measurement errors.

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