Showing papers on "Point source published in 1973"

Reflection and Transmission of Beams at a Dielectric Interface

Abstract: When complex values are assigned to the source coordinates in the expressions for the fields radiated by a line or point source in a homogeneous medium, the resulting fields have the form of a two- or three-dimensional Gaussian beam. This fact may be utilized to develop results for beam propagation and scattering in inhomogeneous regions from corresponding results for point or line source fields. After justifying the analytic continuation procedure to derive rigorous integral solutions for the (two-dimensional) beam fields reflected by and transmitted through a plane dielectric interface, asymptotic results are obtained by the saddle point method; it is found that the analytic continuation to complex source coordinates can be performed directly on the asymptotic expressions for reflected, refracted and lateral wave constituents of ordinary line source fields. Interpretation of the reflected fields reveals that they incorporate directly the lateral beam shift, a phenomenon usually regarded as a diffraction...

Maximum‐likelihood signal processing for a vertical array

Abstract: This paper presents the maximum‐likelihood signal processor for steering a vertical array in the vertical direction. The major application is to the estimation of the depth of a distant narrow‐band continuous point source in the waveguide. The eigenfunctions of the guide are used to match the array to the received signal The error of the depth estimate is derived as a function of the aperture and geometry of the array, the covariance function of the ambient noise received by the array, and the observation period; assuming that the source and medium are stationary during that period. The processing technique can be applied to any perfect waveguide in which a signal source is detected by an array of sensors.

Seismic waves due to a shear fault in a semi-infinite medium:part i: point source

Abstract: In order to clarify basic characteristics of seismic waves in the near-field as well as in the far-field, exact solutions for free surface displacements generated from a shear fault with an arbitrary orientation in a semi-infinite medium are obtained in a cylindrical coordinate system. First, taking the free surface effects into account, expressions for Laplace transforms of displacements with respect to time are derived, and secondly exact transient solutions are obtained by using the Cagniard's method which gives the inverse Laplace transforms in a very ingenious manner when the source time function is of the ramp type. In sections 2, 3 and 4, mathematical expressions are derived, and the results and interpretations of numerical computations for a point source are presented in section 5. Basic characteristics of each phase are summarized as follows: P pulse has basically a rectangular form. The initial pulse amplitudes in a semi-infinite medium are, even in rather near-field, close to those in an infinite medium with correction of surface effects due to plane wave incidence. SP pulse, which radiates from the source as S phase, is incident onto the free surface with a critical angle and then is propagated along the surface with the speed of P-wave velocity, has a relatively large amplitude in the near-field and cannot be neglected when the wave form on the free surface is discussed. This pulse is observed when the epicentral distance is greater than the critical distance. S pulse forms are quite different at epicentral distances less than and greater than the critical distance. S pulse beyond the critical distance has logarithmic infinities at the arrival time of S phase, tS, and tS+t0, t0 being the rise time of the source function. Therefore a plane-wave correction can-not be applied successfully as in the case of an onset of the P pulse. The Rayleigh pulse is well developed when the epicentral distance is about five to ten times as large as the focal depth and its form is not very much affected by the rise time of the source function. For surface focus, S pulse has no logarithmic infinity but the Rayleigh pulse has infinities at the arrival time tR and tR+t0. It is shown that the solutions for a moving source can be obtained by numerical integrations of the solutions for the point source. This case will be dealt with in a subsequent paper.

Seismic waves due to a shear fault in a semi-infinite medium

Abstract: In order to clarify basic characteristics of seismic waves in the near-field as well as in the far-field, exact solutions for free surface displacements generated from a shear fault with an arbitrary orientation in a semi-infinite medium are obtained in a cylindrical coordinate system. First, taking the free surface effects into account, expressions for Laplace transforms of displacements with respect to time are derived, and secondly exact transient solutions are obtained by using the Cagniard's method which gives the inverse Laplace transforms in a very ingenious manner when the source time function is of the ramp type. In sections 2, 3 and 4, mathematical expressions are derived, and the results and interpretations of numerical computations for a point source are presented in section 5. Basic characteristics of each phase are summarized as follows: P pulse has basically a rectangular form. The initial pulse amplitudes in a semi-infinite medium are, even in rather near-field, close to those in an infinite medium with correction of surface effects due to plane wave incidence. SP pulse, which radiates from the source as S phase, is incident onto the free surface with a critical angle and then is propagated along the surface with the speed of P-wave velocity, has a relatively large amplitude in the near-field and cannot be neglected when the wave form on the free surface is discussed. This pulse is observed when the epicentral distance is greater than the critical distance. S pulse forms are quite different at epicentral distances less than and greater than the critical distance. S pulse beyond the critical distance has logarithmic infinities at the arrival time of S phase, tS, and tS+t0, t0 being the rise time of the source function. Therefore a plane-wave correction can-not be applied successfully as in the case of an onset of the P pulse. The Rayleigh pulse is well developed when the epicentral distance is about five to ten times as large as the focal depth and its form is not very much affected by the rise time of the source function. For surface focus, S pulse has no logarithmic infinity but the Rayleigh pulse has infinities at the arrival time tR and tR+t0. It is shown that the solutions for a moving source can be obtained by numerical integrations of the solutions for the point source. This case will be dealt with in a subsequent paper.

Method of hologram recording with reduced speckle noise

Abstract: A sampling mask having a regular array of light transmitting areas is superimposed by a phase mask having a random array of phase shifting areas. The superimposed sampling and phase masks are holographically recorded for producing a hologram which later acts as a beam splitter to provide object and reference beams. The hologram so prepared is illuminated with a spatially incoherent broad source of light and imaged through an optical system. The zero order diffracted wave serves as the reference beam and the first order diffracted wave is used to illuminate an object transparency which is placed in the focused beam of the first order wave. Each point source of light from the spatially incoherent broad light source produces a corresponding interference fringe pattern, and it is shown that the interference pattersn exactly overlaps one upon another so that sharply defined fringe contrast results. The size of the light source is determined only by the required degree of resolution which in turn is dependent on the sampling spacing. The use of the incoherent broad light source enables uniform illumination of the object transparency, resulting in high-quality holograms with reduced speckle noise.

Contributions to love-wave transformation theory: Earth-flattening transformation for love waves from a point source in a sphere

Abstract: By means of the Biswas-Knopoff (1970) transformation, programs for the computation of the Love-wave response to a point source in a flat structure can be modified, quite easily, to compute the response in a sphere.

Rapid Computation by Wave Theory of Propagation Loss in the Arctic Ocean

Abstract: : A rapid, accurate method was developed of computing propagation loss as a function of range in the ice covered Arctic Ocean. Input parameters to the propagation model are source and detector depth, wave frequency, ice roughness, bottom topography, and the velocity structure as a function of depth in the ice, water, and bottom. Computation is done by direct integration of the exact integral solution of the wave equation derived from a harmonic point source located in a multilayered, interbedded liquid-solid half space. The integration technique, introduced by H. W. Marsh, employs the Fast Fourier Transform for very rapid evaluation of the integral solution.

On the Nature of the Infrared Point Source in the Orion Nebula

Abstract: New photometric observations of the BN infrared source in the Orion Nebula eliminate the possibility that it is simply a highly reddened star, and undermine the conclusion that there are 80 mag of visual extinction to the source. We suggest that there is a generic relationship between it and the infrared source IRS 5 in the H II region W3.

Barrier‐wall attenuation with a finite‐sized source

Abstract: The computed attenuation afforded by an infinitely long barrier wall between a point source and a distant receiver has been extended to a source of finite size by considering it as a rectangular array of small equal closely spaced incoherent sub‐sources. While one axis of the array is assumed to be vertical, it may have any angular orientation relative to the receiver and to the axis of the wall. If the source and wall are parallel, the high‐frequency attenuation drops by 3 Db when the source‐to‐barrier spacing is doubled, and varies as 10 log (1 − h/H), where h is the source height and H is the height of the barrier.

Sound pressure in water from a source in air and vice versa

Abstract: Sound pressure level Lp at a depth d, in water, due to a point source in air at a distance h above the water surface, may be calculated from Lp = [Ls −7 + 20 log (cosθ)] −20 log(r/rs), where Ls, the source level, is the SPL in air at distance ra from the source; r is the straight‐line distance to the receiving hydrophone from a virtual sound source situated under the actual source at height h′ = (c1/c2) × h above the surface; c1 and c2 are the respective speeds of sound in air and water; θ is the angle between the vertical and the line of length r. Comparisons with various published results obtained by more sophisticated ray‐theory show agreement within 1 dB, except at shallow depths and far sidewise from the sound source; agreement within 2 dB is found for new experimental data here presented for sound bursts of frequency 500, 1000, and 2000 Hz, and h = 3.5 m. For sound originating in water at depth d below the surface, the SPL received in air is to be calculated from Lp = Ls −52 + 40 log(cosθ) −20 log(r...

The reflexion of an acoustic pulse by a plane vortex sheet

Abstract: This paper deals with the influence of a vortex sheet separating two fluids in relative motion on the radiation from a point source of sound. Both the harmonic and impulsive sources are considered and it is found that waves due to Helmholtz instability must be included in order to ensure that there is no field before the source is excited. The instability wave is confined to a finite region and dominates other disturbances in that region. It is suggested that the instabifity wave is initiated by the unrestricted growth of the specularly reflected wave.

A note on the application of a radiation condition for a source in a rotating stratified fluid

Abstract: The motion due to an oscillatory point source in a rotating stratified fluid has been studied by Sarma & Naidu (1972) by using threefold Fourier transforms. The solution obtained by them in the hyperbolic case is wrong since they did not make use of any radiation condition, which is always necessary to get the correct solution. Whenever the motion is created by a source, the condition of radiation is that the sources must remain sources, not sinks of energy and no energy may be radiated from infinity into the prescribed singularities of the field. The purpose of the present note is to explain how Lighthill's (1960) radiation condition can be applied in the hyperbolic case to pick the correct solution. Further, the solution thus obtained is reiterated by an alternative procedure using Sommerfeld's (1964) radiation condition.

Short-wave asumptotic behaviour of Green's function in the problem of diffraction at a plane layer

Abstract: The saddle-point method is used to obtain asymptotic estimates for the function of a point source, in the two-dimensional problem of diffraction at a layer which is bounded by two planes and located in free spaces.

Seismic waves due to a dislocation source model in a multi-layered medium part ii. numerical calculations for a point source

Abstract: Expressions for surface displacements due to a fault in a multi-layered medium were derived in Part I of this paper. In Part II, numerical approach to calculate theoretical seismograms in the near field is prsented with some examples. Further extension of the problem for a two-dimensional moving fault will be studied in the forthcoming paper.

Mariner 9 star photography.

Abstract: Successful photography of stars by the Mariner 9 spacecraft has confirmed both mathematical prediction of point source response by vidicons and preflight calibration results. Camera-B limiting magnitude and integrated image data are presented to provide information relevant to absolute photometric reduction. These data appear consistent to better than 15% and suggest a good calibration source. Decalibration of Mars picture information, however, requires precise knowledge of Mars spectral radiance and camera point spread function. The effect of image motion on star detection thresholds is also discussed.

Point-Source Artifacts in Fresnel Zone Plate Imaging

Abstract: When a Fresnel zone plate is used as a coded aperture to image large-area sources of X-rays or gamma rays, it is necessary to use a half-tone screen. It is shown here that small-area sources, with such a system, will always produce strong ghost images or artifacts.

A Numerical Solution of the Integral Equation Describing a Photometric Integrating Sphere.

Abstract: A photometric integrating sphere containing a single disk-shaped baffle and a point source with an arbitrary angular intensity distribution is described by an integral equation. Numerical solutions of this equation are presented for several different source distributions. The errors involved in comparing the various sources are evaluated as a function of baffle size and position.

Identification of Free Oscillations Spectral Peaks using the Excitation Criterion

Abstract: A new method for identification of free oscillations spectral peaks was developed. It requires observations of free oscillations at many stations and the knowledge of the source mechanism. It consists of the following steps: First the theoretical amplitude and phase of the mode that we want to identify, let us say 5s26, is computed for each of the observing stations. A laterally homogeneous Earth mode, a double-couple point source and a step function as source time function are assumed. The source mechanism is derived from the fist motion of P wave. A factor of n is then added to the observed spectra of those stations where the theoretical phase of 5536 is n, leaving the spectra of the remaining stations unchanged (the theoretical phase of a spectral peak with respect to the origin time can only be 0 or n). In this way the phase of the 5326 peaks at all stations becomes the same (zero). For all other modes the phase will be zero at some stations and Zat others. Finally the spectra are vectorially summed. Through this summation, the peaks of all modes other than 5s26 cancel each other. If properly excited, &6 will clearly dominate the spectrum resulting from summation. This method was applied to the free oscillations excited by the deep shock which occurred on 1972 July 31, in Colombia, South America. Fundamental and higher modes were uniquely identified. An example of identification of 5 s modes on the colatitudinal component is shown in Fig. 1. Observations from 60 stations were used in this case. The excitation criterion renders identifications unbiased by personal judgement; it is not critically dependent on the assumed Earth model; it can be applied to short length records; and it has made it possible to identify peaks even at periods below 100 s and for modes with low Q.

Atmospheric Transmission from a 4-pi Light Source to a 2-pi Receiver.

Abstract: This survey report points out the progress and insufficiencies in the assessment and prediction of atmospheric effects on thermal radiation from an effective point source in the troposphere to a 2-π sr receiver at the ground. Major findings of investigators during the past two decades are summarized, which also provide additional conclusions. Complicated transmission problems can, futhermore, be treated theoretically by assuming model type atmospheres and solving the radiation transfer equation by an available technique such as the Monte Carlo method. Some of the major results of this method are also presented.

Potential Induced by a Point Source of Current inside an Infinite Cylindrical Cell

Abstract: : The potential is determined everywhere inside an infinitely long cylindrical cell, for a point source of current at an arbitrary location in the cell interior. The mathematical techniques used are applicable to a wide variety of physical problems with mixed boundary conditions in cylindrical geometry in which a small parameter appears in the boundary condition. The model for the cell consists of a cylinder of radius a, with an interior of conductivity (sigma sub i), surrounded by a thin membrane of conductivity (sigma sub m) and thickness delta. The cell is bathed in a highly conducting external medium which maintains the outer membrane surface at zero potential. The potential in terms of the small parameter epsilon = (sigma sub m)a/(sigma sub i) delta. One (inner or near-field) expansion is valid in a region including the point source, and a second (outer or far-field) expansion is valid in a region away from the source. (Author Modified Abstract)

Melting of a semiinfinitely large body by an internal point source of heat

Abstract: The propagation of the melt front in a semiinfinitely large solid body with an internal point source of heat is analyzed.

Waves in an Elastic Medium Generated by a Point Source Moving in an Overlying Fluid Medium

Abstract: Elastic waves coupled to atmospheric compressional waves radiated from a supersonic moving point source are considered. The point source has the form. $$\operatorname{Re} [(vt - z\cos \alpha )^2 - r^2 \sin ^2 \alpha ]^{ - 1/2} fort > zcos\alpha /v,0< \alpha \leqslant \frac{\pi }{2},$$ describing a conic shock wave whose vertex is moving uniformly with a velocity δ, δ=v/cosα>v. An exact expression is derived for the motion of an elastic half-space excited by the moving point source in an overlying fluid half-space.

Point-source position estimation in under-sampled optical systems*

Abstract: This paper presents a new technique for measuring the location of point images in an image-sampling system. Primary attention is given to the situation in which the image is under sampled. Such under sampling could be the result of data-storage or bandwidth limitations, and would introduce errors into standard methods of image location. The new technique is valid for under-sampled as well as adequately sampled images, and consists of a linear-filtering procedure of the same complexity required by standard location-measurement techniques. The problem is formulated as one of statistical-estimation theory, the optimum-location procedures being derived for an additive-gaussian-noise environment, and for conditions of known and unknown image irradiance.

Scale model experiments on noise reduction scale model experiments on noise reduction scale model experiments on noise reduction scale model experiments on noise reduction scale model experiments on noise reduction by acoustic barrier of a straight line source by acoustic barrier of a straight line source by acoustic barrier of a straight line source by acoustic barrier of a straight line source by acoustic barrier of a straight line source

Abstract: SUMMARY Noise reduction by an acoustic barrier of a straight line source is examined with the aid of scale model experiments The line source used in these experiments is an incoherent line source mechanically radiating broad band noise From the experimental results a curve can be deduced which shows a relation between sound attenuation and Fresnel number N This curve shows values lower than those of Maekawa's data by 3 ～ 5 dB, which are presented for a point source On the other hand, it agrees fairly well with Rathe's experimental results, measured near the tracks of a railway line, and also shows a similar tendency to the curve calculated by Kurze and Anderson for an incoherent line source