Azimuth Radiation Pattern Research Articles

Theory of head waves for focal mechanism studies

Harskell's result for the displacement due to a single-couple source of arbitrary orientation in a homogeneous, isotropic, perfectly elastic infinite space has been used to obtain the P , SV and SH wave potentials in a cylindrical co-ordinate system ( r , ϕ , z ). Approximate, far field, solutions for the components of displacement of the free surface due to P 1 P 2 P 1, ( S 1 S 2 S 1)SV, ( S 1 S 2 S 1)SH head-wave arrivals for a single- and double-couple source in the upper medium of a layer over a half-space have been obtained. Equations of Nuttli, tan e = F h tan γ , tan e = F v tan δ may be used to obtain the polarization angle e from the observation of γ , angle between the horizontal component of the S -wave surface motion and the great circle path to the station, or from δ , angle between the vertical axis and the component of the S -wave surface motion in the plane transverse to the great circle path. In the present case F h and F v depend on the orientation of the forces of the couple, epicentral distance, azimuth of the observing station, wave period and the elastic properties of the earth model chosen for the study. Illustrative examples for the azimuthal radiation pattern for P 1 P 2 P 1 head wave and horizontal radial, cross-radial, and vertical S 1 S 2 S 1 head-wave dis-placement components for a suitably chosen single-layered earth model are given. Plots of the projection of the particle trajectory for the S waves in the horizontal and in the vertical cross-radial planes are given for different azimuths.

Body wave radiation patterns from elementary sources within a half space

abstract The known expressions for the polar radiation patterns due to a horizontal or a vertical force, applied at a point within a uniform half space, are used to obtain the body wave radiation patterns from several other elementary seismic sources. Polar radiation patterns from seven elementary line sources, i.e., horizontal and vertical double forces without moment, horizontal and vertical single couples, center of dilatation, center of ratation, and double couple without moment, are first derived. Similar point sources in the three-dimensional space are also considered and the corresponding polar as well as azimuthal radiation patterns are obtained for P, SV, and SH waves. The results obtained include the effect of finite depth of the source below the free surface. Some of the results of Burridge et al for double-couple type seismic sources near a free surface are reproduced in a simple manner. For the elementary point sources considered here, the azimuthal radiation patterns for a uniform half-space are found to be identical with those for an infinite homogeneous medium. However the polar radiation patterns appear to be profoundly affected by the proximity of the free surface.

Measurement of Underwater Sound Scattered from a Fluid Sphere

Experimental procedures and techniques are described for measuring, in an oceanographic tank, the scattering of underwater acoustical radiation from submerged, isolated liquid-filled spheres. Of interest are sphere diameters of the order of or larger than the acoustic wavelength and acoustic impedance contrasts of as much as 20%. A novel dual-hydrophone detecting scheme is presented which enables extraction of the scattered signal from the total (incident plus scattered) signal arriving at the receiver. Since the scattering sphere is mobile, azimuthal radiation patterns can be determined. A few typical scattering diagrams are displayed and are found to agree favorably with those derived from theoretical treatments available in the standard literature. Density and speed of sound variations (between the liquid within the sphere and the surrounding water medium) are obtained by employing various mixtures of liquids as the internal constituent. A brief survey is given of the results derived from scattering measurements with liquid spheres of various diameters and impedance contrasts.

The azimuthal and polar radiation patterns obtained from a horizontal stress applied at the surface of an elastic half space

Abstract The body waves and surface waves radiating from a horizontal stress applied at the free surface of an elastic half space are obtained. The SV wave suffers a phase shift of π at 45 degrees from the vertical. Also, a surface wave that is SH in character but travels with the Rayleigh velocity is shown to exist. This surface wave attenuates as r−3/2. For a value of Poisson's ratio of 0.25 or 0.33, the amplitude of the Rayleigh waves from a horizontal source should be smaller than the amplitude of the Rayleigh waves from a vertical source. The ratio of vertical to horizontal amplitude for the Rayleigh waves from the horizontal source is the same as the corresponding ratio for the vertical source for all values of Poisson's ratio.

RADIATION PATTERNS OF A DIELECTRIC-COATED AXIALLY-SLOTTED CYLINDER

The azimuthal radiation pattern of an axial slot in a dielectric-coated circular cylinder is derived. Some patterns are computed, and a comparison with experiment made.

A synthesis method for circular and cylindrical antennas composed of discrete elements

Antennas composed of discrete elements equally spaced in angle around a circle or circular cylinder are studied with the objective of designing such antennas to produce required azimuthal radiation patterns. Much has already been written upon this subject under the assumption that a continuous distribution of elementary sources will be an acceptable solution to the design problem or at least will form a step in the attainment of an acceptable solution. In the present writing, however, it is felt that something may be gained by analyzing the problem from the beginning on the basis of discrete elements. The question of how many elements are needed is discussed in detail and it is shown that the envelope of the excitation coefficients is not necessarily equivalent to the continuous solution available by other methods. Practical procedures for finding the envelope of the excitation coefficients, and hence the coefficients themselves, are outlined.