Gradients of travel‐time curves from deep‐focus earthquakes

Bolt, Bruce A.

doi:10.1029/rg003i001p00083

Cited by 3 publications

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References 21 publications

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“…7,10,13 and 17 show that both reflected and diffracted phases are small compared with the Rayleigh wave due to a source at 1 km depth. The relevance of diffracted phases in determination of travel-time curves, and seismological experiments designed to determine the actual behaviour of the wave pulses near the cusps, have been discussed recently by Bolt (1965).…”

Section: Alterman and F Abramovicimentioning

confidence: 99%

Effect of Depth of a Point Source on the Motion of the Surface of an Elastic Solid Sphere

Alterman

Abramovici

1966

Geophys J Int

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An exact solution, obtained previously for the displacement of the surface of a uniform elastic solid sphere due to an impulsive compressional pulse from a point-source situated at depth d below the surface of a sphere of radius a is applied here to the problem of propagation from a source at d = aJ32 and a16400 and compared with results for d = aJ8. Theoretical seismograms, radial and angular component, are given at distances 0 < 6 < 7c from the source.Rayleigh waves are found due to all sources. In the high frequency limit they have the velocity of Rayleigh waves in a homogeneous half space. There is dispersion towards higher velocities. The Rayleigh waves from the shallow source have amplitudes more than ten times the amplitude of body waves. In the seismograms from the medium and deep sources their amplitude is smaller, they have less high-frequency components and show more dispersion. The amplitude of Rayleigh waves has a minimum at 90" and 270". At 180" and 360" the radial component has a maximum of ten, seventeen and forty times the radial component at 90" for the deep, medium and shallow sources respectively. The ratio of angular to radial amplitude is largest at 90" and 270", decreasing to zero at 180" and 360". The Rayleigh waves show phase shift, almost elliptical retrograde particle motion, change in form of ellipses with depth of source and deviations of the direction of the major axis from the vertical direction similar to results in observed seismograms. Higher modes of surface waves are found and their connection with groups of reflected pulses of mixed types given. As in several observed seismograms the second mode is especially predominant in the angular component. Whereas diffracted pulses connected with p times reflected P, are encountered mainly in deep-focus events, diffraction phenomena connected with the transformed phases P,S, are found here at all depths and have in several cases amplitudes comparable to, or larger than, the reflected pulses.

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Section: Alterman and F Abramovicimentioning

confidence: 99%

Effect of Depth of a Point Source on the Motion of the Surface of an Elastic Solid Sphere

Alterman

Abramovici

1966

Geophys J Int

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Azimuth and slowness anomalies of seismic waves measured on the central California seismographic array. Part I. Observations

Otsuka

1966

Bulletin of the Seismological Society of America

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Arrays of seismographs are usually considered to be detectors which give enhanced signals from distant earthquakes. They also provide, however, a new way of learning more about the structure of the crust and upper mantle. The deviation of the seismic-wave surface from its expected configuration may be regarded as a consequence of non-homogeneous and anisotropic conditions in the earth. The operations of the University of California network of telemetry stations in the Coast Ranges of California provides an opportunity to discover the practicality of this approach. The situation of this network near the continental margin gives the study particular interest. The differences in arrival-times between array elements of coherent peaks or troughs of P and pP phases from 28 teleseisms in the period of 1963-1964 were read from the telemetry records of the central California seismographic array. The direction of approach and velocities of the wave fronts were then determined and compared with the great circle azimuths and with the apparent velocities calculated from the Jeffreys-Bullen tables. The observed anomalies in direction of approach and apparent velocites are found to be cyclic functions of the direction of the source. The amplitudes of these functions are almost 10 degrees in azimuth anomaly and 1.0 sec/deg in slowness anomaly. Error analyses show that the anomaly functions cannot be attributed to the measurement errors. The derived anomaly functions provide a powerful means of examining crustal and upper mantle structure under the array and perhaps at the source. Variations between subsets of the array indicate significant differences in structure between portions of the Coast Ranges to the north and to the south of Hollister.

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A new analytical method for finding the upper mantle velocity structure from P and S wave travel times of deep earthquakes

Kaila

1969

Bulletin of the Seismological Society of America

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A new analytical method for the determination of velocity at the hypocenter of a deep earthquake has been developed making use of P- and S-wave travel times. Unlike Gutenberg's method which is graphical in nature, the present method makes use of the least square technique and as such it yields more quantitative estimates of the velocities at depth. The essential features of this method are the determination from the travel times of a deep-focus earthquake the lower and upper limits Δ1 and Δ2 respectively of the epicentral distance between which p = (dT/dΔ) in the neighborhood of inflection point can be considered stationary so that the travel-time curve there can be approximated to a straight line T = pΔ + a. From p = (1/v*) determined from the straight line least-square fit made on the travel-time observation points between Δ1 and Δ2 for various focal depths, upper-mantle velocity structure can be obtained by making use of the well known relation v = v*(r0 − h)/r0, h being the focal depth of the earthquake, r0 the radius of the Earth, v* the apparent velocity at the point of inflection and v the true velocity at that depth. This method not only gives an accurate estimate of p, at the same time it also yields quite accurate value of a which is a function of focal depth. Calibration curves can be drawn between a and the focal depth h for various regions of the Earth where deep focus earthquakes occur, and these calibration curves can then be used with advantage to determine the focal depths of deep earthquakes in those areas.

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Gradients of travel‐time curves from deep‐focus earthquakes

Cited by 3 publications

References 21 publications

Effect of Depth of a Point Source on the Motion of the Surface of an Elastic Solid Sphere

Effect of Depth of a Point Source on the Motion of the Surface of an Elastic Solid Sphere

Azimuth and slowness anomalies of seismic waves measured on the central California seismographic array. Part I. Observations

A new analytical method for finding the upper mantle velocity structure from P and S wave travel times of deep earthquakes

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