摘要:

Rotational splitting parameters for a large number of low‐order spheroidal and torsional free oscillations of the earth are computed. These results show that rotation introduces serious errors in estimates of density, Lamé parameters, and dissipation obtained from the free oscillations. Methods of correcting for these rotational effects are discuss

ISSN:8755-1209    

DOI:10.1029/RG003i001p00001

年代:1965

数据来源: WILEY

摘要:

A numerical scheme has been devised that permits calculation of the fit to seismic travel‐time data. The method involves the optimization of a multidimensional function of the parameters necessary to describe the segments of the curves used in the fit. In several examples it was found that (1) selective weights must be applied to avoid picking geophysically unreasonable solutions, and (2) many solutions exist. The results are in good agreement with those obtained by visual mean

ISSN:8755-1209    

DOI:10.1029/RG003i001p00011

年代:1965

数据来源: WILEY

摘要:

In this investigation we solve the problem of propagation of a compressional pulse in a solid half‐space which is overlain by a solid layer of different properties. The point source is situated at the depth ½H,Hdenoting the thickness of the layer. Theoretical seismograms of the vertical displacementwat the surface are evaluated out to rangesr= 20H. The solution is obtained by the exact ray theory. The displacementWodue to the source was assumed to have a shape which at large distances reduces to a sawtooth. The once‐reflected waves from the interface,PPandPS, are strongly marked. The Rayleigh wave is already recognizable atr= 5Hand is fully developed atr= 20H. The method of ‘ray theory’ was applied here far into the region where the normal mode theory converges well. The theoretical seismograms are illustrated. The properties assumed for the layer (1) and for the half‐space (2) are λ1= μ1μ2= 2μ1cs2≡c2= 1.1cs1≡

ISSN:8755-1209    

DOI:10.1029/RG003i001p00025

年代:1965

数据来源: WILEY

摘要:

If a harmonic surface source ofSHis applied to a homogeneous sphere, the body waves can be found by ray theory. Attention is focused on the body waves which undergo multiple reflections at shallow angles at the surface of the sphere. When the order of the reflections becomes large, these reflected waves interfere and are identified as surface waves. The surface waves can be computed from the body waves by an application of Watson's lemma and the saddle point method of integration. The extension to an inhomogeneous sphere is not difficult formally.

ISSN:8755-1209    

DOI:10.1029/RG003i001p00049

年代:1965

数据来源: WILEY

摘要:

An exact solution is obtained for the displacement of the surface of a uniform solid sphere of radiusadue to an impulsiveSH‐torque pulse from a point source situated at a distancebfrom the center. The duration of the source was varied from 0.05a/cto 0.5a/c, keeping the time variation of the torque such that the surface displacement stays finite when the time tends to infinity.cis the shear‐wave velocity. Theoretical seismograms have been computed at several distances from a surface source and from buried sources atb= 7a/8,a/2, 0.3a, and 0. Arrival times of reflected pulses coincide with arrival times of reflected rays, where the latter are obtained according to geometrical optics. The solution for buried sources reveals diffracted pulses. They are connected with the two cases in which reflected rays are disallowed by geometrical optics: (1) owing to distance of observer from source and (2) owing to depth of source. In these cases the arrival time as obtained from the ‘steepest descent’ analysis of Jeffreys and Lapwood is complex. The real part of the complex arrival times lies in the time interval during which diffracted pulses occur. There are no diffracted pulses for the surface

ISSN:8755-1209    

DOI:10.1029/RG003i001p00055

年代:1965

数据来源: WILEY

摘要:

Inferences that can be drawn about the structure of the upper mantle from observations of surface‐reflected longitudinal body phases are discussed. In particular, some aspects of previous observational, statistical, and theoretical work on the phasepPare reviewed. Recently, mathematical work has thrown more light on the properties of the cusps of the surface‐reflected longitudinal phases. Seismological experiments are discussed that are designed to determine the actual behavior of the wave pulses near the cusps. Some preliminary attention has been given to this problem using a seismic array with linear dimension about 10 times greater than the observed wavelength. Computer analysis of the pulses observed at the array elements leads to estimates of the gradients of the travel‐time curves. Weighting must be arranged to take into account the measured lateral refraction and crustal delays at each element. Analysis of the deep‐focus earthquake of April 2, 1963, is presented as an

ISSN:8755-1209    

DOI:10.1029/RG003i001p00083

年代:1965

数据来源: WILEY

摘要:

A Heaviside unit pulse is applied to a point on the surface of a half‐space. The refractive index of the medium varies in such a manner that the surface casts a shadow. By means of complex contour integral representations of the solution, it is shown how to obtain the pulse shape within the shadow zone at times near the arrival of the diffracted pulse. Two‐dimensional and axisymmetric distributions of refractive index are considered, but it can be shown that the form of the expression for the diffracted pulse shape is valid in more general situati

ISSN:8755-1209    

DOI:10.1029/RG003i001p00099

年代:1965

数据来源: WILEY

摘要:

Surface wave phase velocities for an inhomogeneous medium are usually given as eigenvalues of the wave equation. This is a differential equation (Love waves) or pair of differential equations (Rayleigh waves) of the second order. By means of a change of variable the problem is reducible to finding the zeros of a first‐order differential equation or pair of differential equations of first order. The solution can be obtained in any order of surface waves, and the eigenfunctions can be obtained as well by means of this transformation. The solution is thus amenable to computatio

ISSN:8755-1209    

DOI:10.1029/RG003i001p00105

年代:1965

数据来源: WILEY

摘要:

Inverse problems of seismology can be formulated as matrix inversion problems. If there are constraints on the system, such as the requirement that the parameters take positive values, and if the number of variables is large, statistical search methods become useful. A random search method is proposed which is superior to the usual gradient methods of search and which approaches the ‘ravine’ method if the interval of search is not changed by a ‘learning’ process during the

ISSN:8755-1209    

DOI:10.1029/RG003i001p00111

年代:1965

数据来源: WILEY

摘要:

Phase and group velocities are computed for several of the lowest modes of Love waves for a homogeneous spherical annulus overlying a homogeneous sphere. The solution is obtained by evaluating the contour integrals inpspace by a variety of asymptotic methods, each appropriate in a different range of frequency;pis the index of Bessel functions. Comparison is made with the corresponding solutions in a flat layer over a half‐space. Extension of the formalism is made to the case in which the inner sphere is inhomogeneou

ISSN:8755-1209    

DOI:10.1029/RG003i001p00115

年代:1965

数据来源: WILEY