Showing papers on "Point source published in 1971"

Approximate Treatment of Elastic Body Waves in Media with Spherical Symmetry

Abstract: Summary An Earth-flattening approximation for body waves is given which transforms a spherically symmetrical Earth into a vertically inhomogeneous half-space. This approximation includes a depth transformation and a transformation of the velocities of compressional and shear waves. It is an optimum approximation in the sense that the displacement amplitudes of corresponding seismic rays, i.e. of rays leaving a point source in the Earth and the image source in the half-space under the same radiation angle, show maximum agreement in their geometrical optics approximation. The epicentral distances of these rays are identical, and likewise the travel times provided that source and receiver are at the same depth. The amplitude difference is 10 (20,30) per cent at the epicentral distance 60° (82°, 96°). The main field of application of this Earth-flattening approximation is the computation of theoretical body wave seismograms with methods originally devised for half-spaces with plane layers. Theoretical P wave seismograms are given for the upper mantle models of Jeffreys, Gutenberg, Lehmann, Johnson and Mayer-Rosa. The method of calculation is an extension of the ray-theoretical method which was developed in a previous paper. Even without wave front approximations, it permits rather fast computations. Finally, the Earth-flattening approximation is applied to vertical reflections from a spherically symmetrical medium, and a method is briefly described which accounts for the Earth's curvature in computations of crustal and mantle transfer functions, respectively.

Mode Coupling in First-Order Optics

Abstract: A simple procedure is described to obtain the modes of propagation in square-law lens-like media. This procedure consists of evaluating the geometrical-optics field created by a point source at the input plane of an optical system (called mode-generating system) with nonuniform losses. An expansion of the field in power series of the coordinates of the point source gives the modes of propagation. In the case of optical resonators, the mode-generating system is described by the modal matrix of the resonator round-trip ray matrix. This representation of modes by point sources allows the coupling factor between two modes with different parameters (beam radii, wave-front curvatures, and axes) to be evaluated without integration. Only matrix algebra is used. In the general three-dimensional case, the coupling factor is expressed as a product of Gauss functions and Hermite polynomials in four complex variables. The quantities introduced are generalized ray invariants.

Two-dimensional anisotropic elastic waves emanating from a point source

Abstract: A two (spatial) dimensional initially strained elastic body is excited by a point impulse. Expressions are found for the various displacement components in a form which is readily evaluated by residues. The solid itself is characterized by three parameters which depend on the material properties and the initial deformation. For the case when two of these parameters are equated, explicit expressions for the displacements are given along the Cartesian axes passing through the origin of the point impulse. Wave front singularities and lacunas are identified and discussed. Some typical numerical results are given.

The Analysis of Surface Wave Spectra Using a Reciprocity Theorem for Surface Waves

Abstract: Summary By the use of a reciprocity theorem for surface waves, the mathematical expression for the spectrum of surface waves from a point source in a plane layered solid medium can be factorized into a component involving the transmission path and a component involving the source mechanism and depth. This second component can be easily constructed from expressions for the displacement and stress in a propagating surface wave. The factorization has been used to study the effect of source mechanism and depth on the magnitude of the surface waves generated from point sources. In particular this study shows how holes may appear in the surface wave spectra due to the principle that it is impossible to excite a mode of oscillation by action at a node; it also throws doubt on the applicability of the depth correction terms currently used in the formula for Ms.

Physical Sciences: Two New Point Sources of High Energy Cosmic Gamma Rays

Abstract: MORRISON1 was the first to suggest that certain astronomical objects might emit a measurable flux of γ-rays. By the middle of the last decade much theoretical work had been done on the flux to be expected from neutral pion decay, inverse Compton collisions and bremsstrahlung2–6. Evidence for the detection of such a point source of cosmic γ-rays above 50 MeV, Sgr γ-1, was reported by the CWRU–Melbourne collaboration7 and Fazio8 reviewed high energy γ-ray astronomy in early 1970, but as far as we know, no other observation of this source has been made at γ-ray, X-ray or longer wavelengths. The identification of Sgr γ-1 was based on preliminary analysis of spark chamber data from two high altitude flights in Australia and a third flight has confirmed this source. The combined data from the three flights make possible the identification of two other point sources of high energy γ-rays which agree in position with known hard X-ray sources. We find no evidence on any flight for a diffuse line source along the galactic plane.

Electric potential near a spherical body in a conducting half-space

Abstract: An extensive summary of classical potential solutions has been given recently by Van Nostrand and Cook (1966). This note presents a solution for the potential due to a point source of electric current placed on the earth’s surface in the vicinity of a buried spherical body of arbitrary resistivity. The analysis follows the procedure suggested by Van Nostrand and Cook and is similar to that used recently by Merkel (1969, 1971).

Moiré Patterns and Hologram Interferometry

Abstract: A DOUBLE exposure hologram can be produced if an object (C) is illuminated by a spherical coherent wavefront originating from a point source (A). Observations can be made from another point (B), at a distance L from A and a photographic plate (P) between C and B can be used to record all the optical information from C. P also must be illuminated by a reference beam1–6.

Field due to a Point Source in an Inhomogeneous Elastic Medium

Abstract: Wave propagation in an inhomogeneous elastic half‐space is investigated. Integral expressions for vertical and horizontal displacement due to a point source have been obtained in terms of reflection coefficients for a medium in which compressional‐ and shear‐wave velocities increase monotonically with depth. These expressions are further shown to reduce to known expressions in the case of homogeneous solid and stratified liquid.

A model for analysis of the temperature field downstream of a heated jet injected into an isothermal crossflow at an angle of 90 deg

Abstract: The temperature distribution downstream of a heated jet entering an isothermal crossflow at an angle of 90 deg is predicted using two conduction models with energy sources above the point of injection, in one case a point source and in the second a line source. The models use effective turbulent diffusivities that are determined empirically from previous measurements. Temperatures predicted by the models are compared to experimental results.

On the relativistic ejection of a particle by radiation pressure

Abstract: The Poynting-Robertson formulae are used to evaluate the motion and terminal velocity of a particle ejected from rest in a powerful radiation field due to a point source, generalizing the results of Chandrasekhar (1934) to the relativistic case.

Exact design of an array of dipole antennas giving the prescribed radiation patterns

Abstract: The exact method of designing an array of dipole antennas with the prescribed radiation patterns in the magnetic plane is described. The integral of the current distribution, which is expressed according to the improved circuit theory, is set equal to the magnitude of the point source, which is given by the conventional synthesis method. The current distributions and the correct set of driving voltages or currents are sought to the prescribed radiation pattern simultaneously by the present method.

Reflected and head waves from a linear transition layer in a fluid medium

Abstract: Reflected and head waves from a linear transition layer between two homogeneous media are studied in the frequency domain. A point source is located in the upper fluid of lower velocity, and the velocity structure is considered to be continuous throughout. Exact solutions are derived by numerical evaluation of the contour integrals in the complex wave-number plane. These are compared with approximate solutions obtained by the saddle point method. It was found that the approximate solutions for head and reflected waves beyond the critical distance may be regarded as the asymptotic ones for large values of r /2 h . Similarly, the approximate solutions for reflected waves inside the critical distance are the asymptotic ones for large values of H /2 h , where H is the sum of vertical distances of the source and a receiver from the transition layer of thickness 2 h , and r is the horizontal distance of a receiver from the source. At high frequencies, the spectral amplitudes of reflected waves inside the critical distance are proportional to ω −1 , while head-wave amplitudes are proportional to ω −2/3 , (ω being the angular frequency). Numerical calculations also show that contributions from complex poles are significant near the critical distance if the transition layer is thick. In this region, the amplitude variations of the sum of the reflected and secondary waves are similar to those from a sharp discontinuity, although the maximum amplitude for a wave of narrow-frequency band width occurs at greater distances for thicker transition layers.

Wave Propagation In A Layered Model Due To Point Source Loading In A High-impedance Medium

Abstract: Dynamic photoelastic techniques were used to study the incident, reflected, and refracted waves in a layered model. The model, consisting of two birefringent layers with an impedance ratio of 2.2:1, was subjected to point source explosive loading in the high‐impedance medium. The isochromatic fringe patterns were photographed with a Cranz‐Schardin multiple spark camera operating at a rate of 200,000 frames per second. Propagation and attenuation characteristics of waves in both layers were studied.

Power Output of a Point Source Exciting a Single Cartesian Mode

Abstract: When a point source radiates steadily in a rectangular enclosure and excites one mode only, its power output W depends strongly on its position. Distribution functions for W are found when the source is positioned randomly, and an axial, tangential, or oblique mode is excited. The functions for these three cases form a consistent family of curves, whose shapes are controlled by the mode shapes. The space‐averaged value of W, i.e., the average for all source positions in the enclosure, does not equal the free‐field value W0, but depends on the modal damping. The value of W0 can be derived from sound‐pressure measurements, however. The results are derived theoretically, and checked by a Monte Carlo procedure. Some experimental data which confirm the theoretical results are given for a small source driving an axial mode in a reverberation chamber. The work has application to standard methods of measuring the sound power output of a source.

Sound Pressure in Water from Source in Air

Abstract: Sound pressure in the water under a point source overhead in air is shown by theory and experiment to propagate as from a virtual source situated (c1/c2) times the actual source height above the water and emitting unit‐distance sound pressure that is (2c1/c2) times the actual unit‐distance sound pressure, where c1 and c2 are the speeds of sound in air and water, respectively.

Analysis of Ground Wave Propagation in Layered Media.

Abstract: : The propagation of elastic waves in a multilayered geological environment is analyzed based on the theory of generalized-rays and the method of Lamb-Cagniard-Pekeris. The waves are generated by an underground explosion which is approximated by a point source. Velocity responses at receivers at ranges about one to three times the thickness of the source layer are calculated with a new computer code. The results are exact within the framework of the theory of elastic waves. Comparisons of the calculated results with the observations made at the Nevada Test Site in 1966 show considerable discrepencies. (Author)

Linear Energy Transfer Distributions for Neutrons about a 252Cf Point Source in Tissue1

Abstract: Linear energy transfer distributions for neutrons about a 252Cf point source have been calculated using Monte Carlo techniques. The results show that the distribution is not altered appreciably for depths less than 5.0 cm from the source.

Propagation of Elastic Waves Caused by an Impulsive Source in a Half Space with a Corrugated Surface

Abstract: Summary The motion caused by a point source and a source of finite extent in an elastic half space with corrugated boundary is obtained and compared with the motion in a flat half space. The method of solution is based upon a combination of a perturbation theory and a finite difference method. The effect of corrugation on body and surface waves is investigated.

Radio continuum observations of Maffei 2.

Abstract: WE have mapped the area containing the suspected galaxies Maffei 1 and 2 at a wavelength of 11 cm with half-power beam-width 5′.0 using the 300 foot transit telescope of the National Radio Astronomy Observatory at Green Bank, West Virginia, from January 28 to 31, 1971. A three-feed system with four receivers was used; the centre feed provided independent right-and left-hand circularly polarized beams at the same point in the sky, and two outrigger beams (2′ north and 2′ south of the centre beam) each received right hand circularly polarized radiation. Several transits with the telescope set at different declinations provided full mapping of an area between right ascensions 02 h 25 m and 02 h 43 m (1950.0) and between declinations + 59° 15′ and 59° 33′ (1950.0). The output of the radiometers was recorded every 4 s. With the parametric amplifiers used, the lower flux density limit was set by confusion rather than by system noise. We estimate that the lower flux density limit for detection of a point source is 0.06 f.u.

Synthetic seismograms for a long spread of seismometer stations

Abstract: The assumption that the earth is made up of plane-parallel, homogeneous, elastic layers, which can exhibit transverse isotropy and moderate constant-Q attenuation, leads to an effective method of modeling the response from a point source into a long spread of seismometer stations. Most of the computations are carried out in the complex frequency and complex horizontal wavenumber domains. Minimum sampling criteria are based on an algorithm that suppresses time and distance aliasing at the expense of the large dynamic range available on the digital computer. Other artifacts can be identified and are removed by additional wavenumber filtering. Computational effort is almost independent of the number of detectors and their nature. The structure and symmetry properties of the propagator matrices describing the response are the same for isotropic and transversely isotropic layers. Synthetic seismic panels for a regional model of a west Texas well site exhibit strong, shot-generated surface waves. A very simple model, based on a south Texas well site, shows the effects of transverse isotropy and the reverberatory nature of converted signals generated by a surface P-wave.

Method for locating the position of members relative to each other

Abstract: Energy from a point source is directed through a plurality of non-visible structures having known dimensions in a given plane. Variations in the density of the material traversed by the energy vary the intensity of the energy reaching a photographic film. Within the plane including the energy source and the film, the distance from the source to each of the structures determines the lateral dimensions and the relative position of the structure''s image on the film. Given the distance between the source and the film, the lateral dimensions of the structures and the lateral position, size and intensity of the image cast by each of the structures on the film, the relative location of all such structures with respect to the known position of a reference structure may be determined either graphically or mathematically. The device employed in the practice of the present invention includes a source of radio active energy carried in a camera housing which supports the source at a known, fixed distance from the reference structure. A film holder mounts the film behind the non-visible structures so that energy emitted from the source travels through the structures before striking the film. A small aperture in the camera housing focuses the energy causing it to radiate from a point. In use, the housing is flooded with water, lowered below the water surface and positioned about a subsurface well structure. The water in the housing is replaced with air after the housing is in place to reduce energy attenuation caused by the water.

Prediction of Sound Attenuation by Barriers

Abstract: A simple analytical approximation for the sound attenuation by barriers is derived on the basis of prior theoretical and experimental results. The approximation takes into account oblique sound incidence at the barrier and also applies for the transition region between the “bright” zone and the shadow zone behind the barrier. Results for a point source are compared with those for a line source parallel to the edge of the barrier. Engineering estimates are given for the aspect angle of an incoherent line source, for which the barrier attenuation can be calculated by considering only a single diffracted ray. Predictions of the sound attenuation by a barrier parallel to a number of incoherent line sources agree well with experimental results reported for an acoustical model of a multilane highway. The length of a barrier along a highway required for efficient sound attenuation is calculated in terms of the angle at the observer that encompasses the barrier. [These studies were carried out in part under Contr. No. DOT‐OS‐A9‐018, under subcontract with Serendipity, Inc., Arlington, Virginia.]

Remarks on the restoration of occultation observations.

Abstract: If the limb of the Moon can be regarded as a straight edge, then the diffraction pattern of a point source which it produces at the distance of the Earth is the well known Fresnel diffraction pattern. Observations of stellar occultations reveal the variation of intensity with time as the diffraction pattern passes across the detector due to the orbital motion of the Moon and the rotation of the Earth. The linear scale of the diffraction pattern in monochromatic light depends on both the wavelength of observation, λ, and on the distance of the Moon,D, so that the scale is proportional to (λ)1/2.