scholarly journals Longitudinal waves through the Earth's Core*

1952 ◽  
Vol 42 (2) ◽  
pp. 119-134
Author(s):  
M. E. Denson
Keyword(s):  
Velocity Distribution ◽  
Travel Time ◽  
Focal Point ◽  
Epicentral Distance ◽  
Outer Core ◽  
Travel Times ◽  
Time Curve ◽  
Longitudinal Waves ◽  
The Core ◽  
The Waves

Abstract Amplitudes, periods, and travel times of the longitudinal P′ or PKP core waves have been investigated. Results indicate that the epicentral distance of the main focal point and the travel time of P′ phases vary with the periods of the waves. This variation would seem reasonably explained in terms of dispersion. The point of reversal in the travel-time curve of the waves through the outer core is believed to lie near 157°. Data suggest a discontinuity between 120° and 125° rather than 110°. Anomalies existing in energy, period, and travel-time relationships of the P′ phases indicate that current concepts of velocity distribution and of propagation paths within the core are in need of modification.

On focal points of SKS*

1938 ◽  
Vol 28 (3) ◽  
pp. 197-200
Author(s):  
B. Gutenberg
Keyword(s):  
Travel Time ◽  
Extreme Values ◽  
Focal Point ◽  
Epicentral Distance ◽  
Outer Part ◽  
Focal Points ◽  
Time Curve ◽  
Longitudinal Waves ◽  
The Core ◽  
Preliminary Study

Summary The travel-time curve of the first section of SKS depends much on the velocity in the outer part of the core. It begins on the travel-time curve of ScS at an epicentral distance somewhere between 65° and 90°, depending on the velocity of longitudinal waves just below the surface of the core. The extreme values correspond to velocities there of approximately 8.0 and 7.4 km/sec., respectively. If the distance where SKS begins is relatively large, its first section extends to decreasing distances and is convex towards the axis of distance, and SKS must have an odd number of cusps with focal points (at least one) where it reverses in direction and changes from convex to concave or vice versa. If SKS begins at a relatively short distance, its first segment extends to increasing distances and is concave towards the axis of distance; in this case the number of cusps is even (possibly zero). In an intermediate case, SKS begins with a focal point. In any case, the first segment of the travel-time curve of SKS is below the travel-time curve of ScS. Similar conclusions are correct for SKS. A preliminary study of the observations seems to indicate a focal point of SKS at a distance between 70° and 80°. More detailed investigations which are under way may be used to draw conclusions respecting the velocity of longitudinal waves in the outer part of the core.

The velocities in the outer core

1971 ◽  
Vol 61 (4) ◽  
pp. 1051-1059
Author(s):  
A. L. Hales ◽  
J. L. Roberts
Keyword(s):  
Velocity Distribution ◽  
Lower Limit ◽  
Outer Core ◽  
Time Of Arrival ◽  
Travel Times ◽  
Mantle Boundary ◽  
Core Mantle Boundary ◽  
The Core ◽  
Arc Distance ◽  
The Difference

abstract Earlier studies of the velocity distribution in the outer core have been based on the travel times of SKS.SKS arrivals can only be observed satisfactorily for arc distances at the surface greater than 85°. This lower limit of observation of SKS corresponds to an arc distance of 40.2° within the core. Thus the velocities in the outermost 250 km of the core are based upon an extrapolation. We have used observations of the difference in time of arrival of SKKS and SKS to obtain core travel times extending the range of observation down to a Δ within the core of about 14°. The velocity distribution thus found is significantly lower than those of Jeffreys (Bullen, 1963) and Randall (in press) near the core mantle boundary.

The fine structure of the Earth's core

1964 ◽  
Vol 54 (5A) ◽  
pp. 1299-1313 ◽  
Author(s):  
R. D. Adams ◽  
M. J. Randall
Keyword(s):  
Fine Structure ◽  
Travel Time ◽  
Velocity Gradient ◽  
Inner Core ◽  
Outer Core ◽  
Earth’S Core ◽  
Time Curve ◽  
Earth's Core ◽  
The Core

Abstract Detailed study of arrivals from accurately fixed earthquakes has revealed additional complexity in the travel-time curve for PKP. A notation is introduced in which observations are denoted by P′ with a two-letter suffix indicating the branch to which they belong, namely P′AB, P′IJ, P′GH and P′DF. A new velocity solution for the Earth's core has been derived from these observations. This velocity solution differs from those previously suggested in having three discontinuous increases in velocity between the outer and inner core, at levels corresponding to 0.570, 0.455 and 0.362 times the radius of the core. This implies two shells, each between 300 and 400 km thick, surrounding the inner core; in each shell there is a small negative velocity gradient. The outer discontinuity is sufficiently shallow to prevent rays in the outer core from forming a caustic.

A method of obtaining P and S travel-time curves within a “Stripped Earth”*

1952 ◽  
Vol 42 (4) ◽  
pp. 313-314
Author(s):  
V. C. Stechschulte
Keyword(s):  
Travel Time ◽  
Depth Distribution ◽  
Epicentral Distance ◽  
Travel Times ◽  
Depth Of Focus ◽  
Distance Curve ◽  
Simple Method ◽  
Time Distance ◽  
Deep Focus

Abstract A simple method is outlined for obtaining from a time-distance curve of a deep-focus earthquake a table of travel times within an earth “stripped” to the depth h, the depth of focus. The method depends on the fact that such a curve for a deep-focus earthquake has a point of inflection and therefore has the same slope at two different values of epicentral distance. The Herglotz-Wiechert method may then be applied to these travel times to obtain a velocity-depth distribution.

scholarly journals Wave velocities in the earth's core

1958 ◽  
Vol 48 (4) ◽  
pp. 301-314
Author(s):  
B. Gutenberg
Keyword(s):  
Travel Time ◽  
Transition Zone ◽  
Southern California ◽  
Inner Core ◽  
Travel Times ◽  
Earth’S Core ◽  
Earth's Core ◽  
The Core ◽  
Wave Velocities

Abstract More than 700 seismograms of 39 shocks recorded mainly in southern California at epicentral distances between 105 and 140 degrees are used to investigate records of phases which have penetrated the earth's core. Properties of PKIKP, SKP, SKIKP, PKS, and PKIKS are discussed. Portions of travel-time curves of these phases are revised. Travel times of waves starting and ending at the surface of the core, and wave velocities in the core, are recalculated. Between about 1,500 and 1,200 km. from the earth's center in the transition zone from the liquid outer to the probably solid inner core, waves having lengths of the order of 10 km. travel faster than longer waves. This is probably caused by a rather rapid increase in viscosity toward the earth's center in this transition zone.

Transverse plasma waves and their instability

1962 ◽  
Vol 14 (3) ◽  
pp. 321-335 ◽  
Author(s):  
F. D. Kahn
Keyword(s):  
Magnetic Field ◽  
Velocity Distribution ◽  
Plasma Waves ◽  
Practical Case ◽  
Transverse Waves ◽  
Longitudinal Waves ◽  
Linearized Equations ◽  
The Waves

Linearized equations are derived for disturbances in an infinite plasma without an imposed magnetic field. It is shown that besides the electrostatic, or longitudinal, waves which are usually considered, there can also exist electromagnetic, or transverse, waves. The two sets of waves are generally coupled, but one can nevertheless classify the waves as either mainly longitudinal or mainly transverse. It turns out that a plasma which is stable to longitudinal waves will be unstable to transverse waves unless the velocity distribution of its particles satisfies some rather stringent conditions. In a practical case these conditions would require the distribution to be isotropic.

The velocity of seismic waves near the earth's center

1964 ◽  
Vol 54 (1) ◽  
pp. 191-208
Author(s):  
Bruce A. Bolt
Keyword(s):  
Travel Time ◽  
Seismic Waves ◽  
Inner Core ◽  
Earth’S Core ◽  
Time Curve ◽  
Earth's Core ◽  
The Core ◽  
Earth Models ◽  
Velocity Jump

abstract A double velocity jump in the Earth's core entails a PKP travel-time curve with two lengthy branches extending back from 143°. The later branch is associated with the PKIKP phase. The earlier branch arises from waves, here designated PKHKP, which are refracted through the intermediate shell. Theoretical travel-time curves for PKP and SKS in possible Earth models with tripartite cores are presented. It is shown that the PKHKP branch provides an explanation for precursors to PKIKP observed at epicentral distances between 123° and 140°. Observations of waves predicted by the portion of this branch from 148° to 156° have been also reported. The SKS curve is examined in the light of some 550 SKS observations in the range 85° < Δ < 145°. The study provides evidence that there is in the core a discrete shell with thickness of order 420 kms and with a mean P velocity near 10.31 km/sec. This shell surrounds the inner core having mean radius 1220 kms and mean P velocity 11.22 km/sec, approximately. The material of the intermediate shell is not likely to have marked rigidity. The inner core is likely to be solid; published times for PKJKP waves may be, however, too small by several minutes.

Estimation of PcP travel times and the depth to the core

1968 ◽  
Vol 58 (4) ◽  
pp. 1293-1303 ◽  
Author(s):  
James Taggart ◽  
E. R. Engdahl
Keyword(s):  
Velocity Distribution ◽  
Core Radius ◽  
Travel Times ◽  
Nuclear Explosions ◽  
Velocity Models ◽  
The Core

Abstract Based on a new P velocity distribution and observed PcP travel times from nuclear explosions, the core is estimated to have a mean radius = 3477 ± 2.0 km (depth = 2894 ± 2.0 km). Five velocity models were tested for the lower-most 90 km of the mantle. The PcP data suggest that the P velocity increases slightly with depth in this region. Tables of PcP travel times have been computed for the preferred model and a core radius of 3477 km.

Influence of Mantle Structures on Measurements of Anisotropy in the Inner Core

2020 ◽  
Author(s):  
Sandra Beiers ◽  
Christine Thomas
Keyword(s):  
Seismic Anisotropy ◽  
Inner Core ◽  
Incidence Angle ◽  
Outer Core ◽  
Western Hemisphere ◽  
Travel Times ◽  
Array Seismology ◽  
Two Parameters ◽  
The Waves ◽  
Ray Paths

<p>The seismological exploration of the Earth’s inner core has revealed some structural complexities such as seismic anisotropy and hemispherical separation. Investigating the travel times of PKP waves from at least two different ray paths, a polar and an equatorial one, is one of the commonly used methods to probe the inner core’s anisotropy. Since the waves are traversing anomalous structures in the lowermost mantle before entering the core, these heterogeneities have to be taken into account when investigating anisotropy in the inner core.</p><p>In this study we use data from an equatorial path with events from Indonesia recorded in Morocco and a nearly polar one with earthquakes in New Zealand recorded in England. The two waves used in our study, PKPdf and PKPab, both propagate through mantle and outer core and PKPab additionally traverses the inner core. Within this work, we do not only analyse the travel times of the waves but rather investigate their deviations from the originally assumed path along with their incidence angle. This is done with the methods of array seismology, mainly its two parameters slowness and backazimuth.</p><p>The results of this study reveal opposite deviations of slowness and backazimuth of the polar in contrast to the equatorial path. While the polar waves travel shallower and closer to North, the equatorial waves propagate deeper and farther from North than predicted by ak135. Additionally we observe hemispherical differences between waves that sample the eastern and the ones that sample the western hemisphere for both ray paths, PKPdf and PKPab, which leads us to the assumption that the deviations are not caused by the inner core but are rather due to mantle structures.</p>

scholarly journals Occurrence of “precursors” of PKP-waves in the layered radial-symmetric Earth

2019 ◽  
Vol 489 (1) ◽  
pp. 84-88
Author(s):  
A. G. Fatyanov ◽  
V. Yu. Burmin
Keyword(s):  
Analytical Solution ◽  
Wave Field ◽  
Travel Time ◽  
High Frequency ◽  
Spherical Model ◽  
Outer Core ◽  
Small Scale ◽  
Longitudinal Waves ◽  
High Frequency Oscillations ◽  
The Earth

It is generally accepted that PKP‑waves precursors, which are observed on a real data ahead of PKP‑waves, are explained by scattering on small-scale inhomogeneities in the lower mantle. In this paper, a stable analytical solution (without interference) was obtained for the wave field of longitudinal waves in a layered (discrete) ball of planetary size. The calculations of the total wave field, rays and travel-time curves of longitudinal waves for the spherical model of the Earth AK135 with a carrier frequency of 1 hertz are presented. The analytical solution showed that at angles smaller than 145 degrees ahead of the PKP‑waves, low-amplitude waves appear, with a higher frequency of about 1,3 hertz. Indeed, these high-frequency oscillations have the form characteristic for waves scattered at a certain object. The ray pattern and the travel-time graph show that these high-frequency oscillations are due to exclusively to the spherical geometry of the Earth. This could be explained by the interference of refracted and reflected longitudinal waves in the bottom of a discrete outer core. This field propagates even further towards smaller angles due to the interference of diffraction waves.

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