scholarly journals On supposed discontinuities in the mantle of the Earth

1931 ◽  
Vol 21 (3) ◽  
pp. 216-223 ◽  
Author(s):  
B. Gutenberg ◽  
C. F. Richter
Keyword(s):  
Travel Time ◽  
Glassy State ◽  
Time Curve ◽  
P Waves ◽  
S Waves ◽  
The Earth ◽  
Straight Line

Summary Investigations of the Mexican shocks of January 2, 15, and 17, 1931, as recorded at stations in California have shown that the travel-time curve of the P-waves at distances between 9° and 15° is nearly a straight line. At these distances the amplitudes of the P-waves are very small, as is to be expected from theory. At greater distances dt/dΔ decreases, and the amplitudes are larger. The data are not sufficient to decide whether the changes are abrupt or not. No S-waves could be found between 9° and 15°. The calculated velocities of the P-waves are near 8.2 kilometers per second at depths between 40 and 100 kilometers, increasing slightly with greater depths. It is possible that the velocity decreases very slightly at some depths between 40 and 80 kilometers, but there is no sign of any discontinuity at depths between 40 and more than 500 kilometers. The S-waves seem to be affected a little more at depths between 40 and 100 kilometers than the P-waves. It is not impossible that at some depth between 40 and 80 kilometers there is a transition from the crystalline to the glassy state.

scholarly journals Relative amplitudes of P and S waves as a mantle reconnaissance tool

1969 ◽  
Vol 59 (3) ◽  
pp. 1189-1200
Author(s):  
John R. McGinley ◽  
Don L. Anderson
Keyword(s):  
Travel Time ◽  
Upper Mantle ◽  
Poisson’S Ratio ◽  
Basin And Range ◽  
The Other ◽  
Poisson's Ratio ◽  
P Waves ◽  
S Waves ◽  
High Attenuation ◽  
Short Period

abstract The unified magnitude, the ratio of the amiplitudes of S to P waves, and travel-time residuals were compiled from published data for the five Seismological Observatories, TFO, UBO, BMO, WMO and CBO. Using one of the stations as a reference, a relative measure of the above quantities was calculated for each of the other stations for each of a number of earthquakes. The stations in the Basin and Range Province are consistent with a markedly higher attentuation of P waves and a high attenuation of S relative to P when compared to the other stations. This latter observation indicates a high Poisson's ratio in the mantle under the Basin and Range. The delay times to these stations are also consistent with the high Poisson's ratio and with a low-velocity upper mantle. The ratio of the amplitudes of long-period S waves to short-period P waves varies by a factor of 4 among these stations. BMO, in eastern Oregon, has a high S/P amplitude ratio compared to other stations and a travel-time residual that is comparable to the observatories in the mid-continent. This may be another example of a seismic “window” into the upper mantle that is generated by underthrusting of the oceanic lithosphere.

The Texas earthquake of August 16, 1931*

1934 ◽  
Vol 24 (2) ◽  
pp. 81-99
Author(s):  
Perry Byerly
Keyword(s):  
Travel Time ◽  
Travel Times ◽  
Time Curve ◽  
P Waves ◽  
First Order ◽  
First Motion ◽  
Order Discontinuity

Summary The travel-time curve of P for the Texas earthquake of August 16, 1931, shows that there is a definite break in the travel-time curve near Δ = 16°. This is interpreted as indicating a first-order discontinuity at a depth of about 300 kilometers. Another break in the travel-time curve at Δ = 25° is strongly suggested. Beyond Δ = 75° the curve has two branches, the lower following most existing curves, the upper following the Montana curve which latter seems to be a usual one for American earthquakes. This part of the curve is interpreted as indicating that the discontinuity at depth about 2,400 kilometers is a first-order one at which the speed of P waves drops discontinuously. From the direction of first motion on the records it is concluded that a sufficient source would have been motion on a fault of strike about N 35° W, the movement being up on the easterly side and down on the westerly side. The travel times of all waves read on the records are plotted on graphs. The scattering of all waves after P is marked.

scholarly journals Shear waves through the Earth's core

1935 ◽  
Vol 149 (866) ◽  
pp. 88-103 ◽  
Keyword(s):  
Magnetic Properties ◽  
P Wave ◽  
Time Data ◽  
P Waves ◽  
Nickel Iron ◽  
S Waves ◽  
The Core ◽  
The Earth ◽  
Travel Time Data ◽  
Core Depth

Seismological evidence of a central core to the earth was first pointed out by Oldham in 1906. From his analysis of travel-time data regarding longitudinal (P) and transverse (S) waves observed at great distances from earthquake epicentres, he concluded that at a depth equal to about three-fifths of the radius there occurs a transition to material possessing radically different physical properties from that external to this boundary. With the aid of more extensive data assembled by Turner and others, the problem was later re-examined independently by Knott and by Gutenberg. The latte concluded that at a depth of 2900 km the velocity of P waves suddenly decreases from over 13 km per sec to about 8 1/2. The theory involves the appearance of a delayed P wave at epicentral distances beyond 143º, and the chief characteristics predicted for this wave have been amply verified by Gutenberg, by Macelwane and by Lehmann. Also Wadati has lately confirmed the earlier estimates of the core depth from observation on S c S. Mean density considerations suggest that this core is metallic; and the magnetic properties of the earth are consistent with a nickel-iron composition resembling that found in many meteors.

scholarly journals Travel times, apparent velocities and amplitudes of body waves

1968 ◽  
Vol 58 (1) ◽  
pp. 339-366
Author(s):  
Bruce R. Julian ◽  
Don L. Anderson
Keyword(s):  
Surface Wave ◽  
Travel Time ◽  
Velocity Gradient ◽  
Body Wave ◽  
Travel Times ◽  
S Waves ◽  
The Earth ◽  
Geometric Spreading ◽  
First Arrival ◽  
Wave Models

abstract Surface wave studies have shown that the transition region of the upper mantle, Bullen's Region C, is not spread uniformly over some 600 km but contains two relatively thin zones in which the velocity gradient is extremely high. In addition to these transition regions which start at depths near 350 and 650 km, there is another region of high velocity gradient which terminates the lowvelocity zone near 160 km. Theoretical body wave travel time and amplitude calculations for the surface wave model CIT11GB predict two prominent regions of triplication in the travel-time curves between about 15° and 40° for both P and S waves, with large amplitude later arrivals. These large later arivals provide an explanation for the scatter of travel time data in this region, as well as the varied interpretations of the “20° discontinuity.” Travel times, apparent velocities and amplitudes of P waves are calculated for the Earth models of Gutenberg, Lehmann, Jeffreys and Lukk and Nersesov. These quantities are calculated for both P and S waves for model CIT11GB. Although the first arrival travel times are similar for all the models except that of Lukk and Nersesov, the times of the later arrivals differ greatly. The neglect of later arrivals is one reason for the discrepancies among the body wave models and between the surface wave and body wave models. The amplitude calculations take into account both geometric spreading and anelasticity. Geometric spreading produces large variations in the amplitude with distance, and is an extremely sensitive function of the model parameters, providing a potentially powerful tool for studying details of the Earth's structure. The effect of attenuation on the amplitudes varies much less with distance than does the geometric spreading effect. Its main effect is to reduce the amplitude at higher frequencies, particularly for S waves, which may accunt for their observed low frequency character. Data along a profile to the northeast of the Nevada Test Site clearly show a later branch similar to the one predicted for model CIT11GB, beginning at about 12° with very large amplitudes and becoming a first arrival at about 18°. Strong later arrivals occur in the entire distance range of the data shown, 1112°. to 21°. Two models are presented which fit these data. They differ only slightly and confirm the existence of discontinuities near 400 and 600 kilometers. A method is described for predicting the effect on travel times of small changes in the Earth structure.

The Alaskan earthquake of July 22, 1937*

1940 ◽  
Vol 30 (4) ◽  
pp. 353-376
Author(s):  
John N. Adkins
Keyword(s):  
Travel Time ◽  
Epicentral Distance ◽  
Time Interval ◽  
Time Curve ◽  
Arrival Times ◽  
The Earth ◽  
Geographical Latitude ◽  
The World ◽  
First Motion ◽  
First Arrival

Summary The study of the Alaskan earthquake of July 22, 1937, is based on the examination of original seismograms and photographic copies from seismological observatories throughout the world. The arrival times of P at 71 stations were used in locating the epicenter. By Geiger's method and the use of Jeffreys' travel times, the position of the epicenter was found to be: geographical latitude, 64.67±.04° N, longitude, 146.58±.12° W, and the time of occurrence to be 17h 9m 30.0±.25s, U.T. The epicenter lies in the Yukon-Tanana upland in central Alaska, which is not a region of frequent major earthquakes. The disagreement caused by the apparently early arrivals at College and Sitka was reduced by replacing the standard travel-time curve of P by a linear travel-time curve in the interval of epicentral distance 0° to 16° and by interpreting the first arrival at College as P. It was possible to determine the direction of the first motion of P for 51 stations. The observed distribution of first motion and the geological trends in the region of the epicenter are consistent with the earthquake's having been caused by movement along a fault with strike between N 30° E and N 37° E, and dip between 64° and 71° to the southeast, in which the southeast side of the fault was displaced relatively northeastward with the line of movement pitching between 12° and 16° northeast. A wave designated F (for “false S”) was found to precede S on the records by 20 to 55 seconds, depending on the epicentral distance. The wave is longitudinal in type and the arrival times define a linear travel-time curve. It is suggested that this wave may be a longitudinal surface wave, of the type proposed by Nakano, produced at the surface of the earth by the arrival of a transverse wave which has been reflected at a surface of discontinuity within the earth. The records show two impulses near the time when S is expected. The average time interval between the two impulses is 11.3 sec. The first, called S1, has a plane of vibration intermediate in direction between the plane of propagation and the normal thereto. The second impulse, called S2, is nearly pure SH movement. The writer wishes to express his indebtedness to Professor Perry Byerly for invaluable suggestions and criticism during the course of the investigation.

scholarly journals Wave velocities at depths between 50 and 600 kilometers†

1953 ◽  
Vol 43 (3) ◽  
pp. 223-232
Author(s):  
B. Gutenberg
Keyword(s):  
Travel Time ◽  
New Method ◽  
Depth Interval ◽  
Time Curve ◽  
Earth’S Mantle ◽  
Wave Velocities ◽  
The Earth

abstract Wave velocities in the interior of the earth are usually calculated by means of the Wiechert-Herglotz method. Incorrect interpretation of the form of the travel time curve for a certain distance interval then leads to errors not only in results concerning the corresponding depth interval but (in decreasing amounts) also for all greater depths. A new method is described and applied to that portion of the earth's mantle in which earthquake foci exist. Values obtained with this method for velocities at various depths are independent of each other.

3. Seismology and the Earth’s internal structure

2018 ◽  
pp. 22-46
Author(s):  
William Lowrie
Keyword(s):  
Internal Structure ◽  
Seismic Waves ◽  
The Body ◽  
Body Waves ◽  
Seismic Behaviour ◽  
P Waves ◽  
S Waves ◽  
The Earth ◽  
Rayleigh And Love Waves ◽  
The Relationship

Seismology is the most powerful geophysical tool for understanding the structure of the Earth. It is concerned with how the Earth vibrates. Physically, seismic behaviour depends on the relationship between stress and strain in the Earth. ‘Seismology and the Earth’s internal structure’ explains compressional and shear elastic deformation and the four types of seismic waves caused by earthquakes: P-waves and S-waves that travel through the body of the Earth, and Rayleigh and Love waves that spread out at and near the Earth’s surface. It describes the reflection, refraction, and diffraction of body waves and how their observation and measurement by seismometers can be used to understand the internal structure of core, mantle, and crust.

https://urvak.ru/articles/compu-8014-vypusk-3-analiz-obshchego-uravneniya-po/

2020 ◽  
Vol 7 (3) ◽  
pp. 57-61
Author(s):  
RUSTAM RAKHIMOV ◽  
◽  
MMATMATISA JALILOV ◽  
ASATULLA MAKHSUDOV ◽  
Keyword(s):  
Mathematical Modeling ◽  
Three Dimensional ◽  
Mathematical Concept ◽  
P Waves ◽  
Normal Loading ◽  
Tectonic Plates ◽  
S Waves ◽  
The Earth ◽  
General Dynamics ◽  
Definition Of

In article occurrence of earthquakes and mountain blows and their communication by volcanic processes occurring in a kernel is analyzed. Mathematical modeling is resulted, uniting occurring processes in a kernel, occurrence Р-longitudinal shock waves and the S-intensity before earthquakes. In the given work it is considered, how by means of mathematical modeling it is possible to create model of occurring events and to untangle communication of seismic signatures of pushes arising from seismic processes. Such method of modeling will allow to create the three dimensional image of earth crust and to show in interaction of tectonic plates as the forces creating and pushing the formed break change in due course. For this purpose it is necessary to enter the seismic given districts that the model corresponded to supervision of how the plate is deformed to and during time, and after earthquake. It will help to draw conclusions on what forces operate on plate border - plates and as it is deformed, handing over the fluctuation information outside and as in things in common one plate dives into a hot viscous cloak of the Earth. In it to a floor the fused layer firm breeds exude and behave in the unexpected image, therefore the understanding of general dynamics of a status of a kernel can help to define communication between pressure along a break before earthquake. The problem of influence of mobile loadings on layers arises from a kernel of the earth a striking power of boiling magma, a surface top a piecewise homogeneous two-layer plate-plate the running wave along a x axis with constant speed V0 normal loading extends. The blows which are starting with a kernel of the Earth from an event volcanism, creating running waves in earth crust it is described by the total formula (17). The mathematical concept of interpretation can be applied to concept of occurring events of a kernel of definition of striking power P-waves, intensity S-waves and places at forecasting of natural accidents for the Earth.

The Hebgen Lake, Montana, earthquake of August 18, 1959: P waves

1962 ◽  
Vol 52 (2) ◽  
pp. 235-271
Author(s):  
Alan Ryall
Keyword(s):  
Travel Time ◽  
Sierra Nevada ◽  
Fault Plane ◽  
Time Curve ◽  
P Waves ◽  
Arrival Times ◽  
The Pacific ◽  
First Motion ◽  
Plane Solution ◽  
The Pacific Ocean

ABSTRACT The instrumental epicenter of the Hebgen Lake earthquake is found to lie within the region of surface faulting. The depth of focus had a maximum value of 25 kilometers. Times of P are studied in detail for epicentral distances less than 13 degrees. The apparent scatter of arrival times from 700 to 1400 kilometers can be explained by variations of the velocity of Pn between the physiographic provinces of the western United States. A comparison of observations for the Hebgen Lake earthquake with published times for blasts in Nevada and Utah indicates that the velocity of Pn in the central and eastern Basin and Range is about 7.5 km/sec, and that the crust in that region thickens toward the east and thins toward the south. A comparison of apparent velocities in northern California, in directions parallel and transverse to the structure, indicates that the crust thins by about 19 kilometers, from the edge of the Sierra Nevada to the Pacific Ocean. A discontinuity is observed in the travel-time curve at a distance of 24–25 degrees. Arrivals of P waves in the range 65–128 degrees fall on two parallel travel-time branches; this multiplicity in the travel-time curve may be related to repeated motion at the source. Travel-times of PKIKP appear to deviate from published curves. The fault-plane solution for the Hebgen Lake earthquake, together with a consideration of the first motion at Bozeman, Montana, indicates a focal mechanism of the dipole, or fault, type. The strike and dip of the instrumental fault plane agree well with observed ruptures at the surface.

Earthquakes off the coast of northern California*

1937 ◽  
Vol 27 (2) ◽  
pp. 73-96 ◽  
Author(s):  
Perry Byerly
Keyword(s):  
Travel Time ◽  
Smooth Curve ◽  
Least Square ◽  
The Other ◽  
Time Curve ◽  
Humboldt County ◽  
San Andreas ◽  
Straight Line ◽  
Mendocino County ◽  
Better Than

Summary The epicenters as located for the earthquakes of July 6, 1934, January 2, 1935, and June 3, 1936, indicate that earthquakes centering off the coast of Humboldt County do not originate on a linear extension of the San Andreas fault in Mendocino County. Figure 1 shows the epicenters of these shocks as located by two methods, and also the epicenter of the earthquake of January 31, 1922, as located by Professor Macelwane. On the basis of least square residuals alone, the epicenters located by assuming a straight-line travel-time curve for Pn to Δ=18° are better than those located by the Jeffreys-Bullen curves. But for the shock of June 3, 1935, the epicenter located by the first method is inconsistent with the S-P interval at Ferndale, whereas that obtained by the second method is consistent. For the other two shocks the epicenters located by the two methods are little different in position. Whereas the July 6 shock shows a definite Sn travel-time curve with an intercept approximately equal to that of the Pn curve, the other two earthquakes show a marked wave preceding Sn and almost masking it at the coastal stations south of the epicenter. The travel-time curve of this wave has an intercept about 15 seconds below that of Pn. This wave is longitudinal and has a period of 4.35 km/sec. It is suggested that it is P in the sedimentary layer, although objections to such an interpretation are cited. The travel-time curve of P for the July 6 shock between 26° and 40° indicates that it is composed of two nearly straight branches rather than the more smooth curve of Jeffreys and Bullen.

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