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.

Travel-time errors in the laterally inhomogeneous earth

1971 ◽  
Vol 61 (6) ◽  
pp. 1639-1654 ◽  
Author(s):  
Cinna Lomnitz
Keyword(s):  
Travel Time ◽  
Root Mean Square ◽  
Time Estimation ◽  
Systematic Errors ◽  
Least Square ◽  
Travel Time Estimation ◽  
Mean Square ◽  
Travel Times ◽  
The Earth ◽  
Lateral Inhomogeneity

abstract Travel times from earthquakes or explosions contain both positive and negative systematic errors. Positive skews in travel-time residuals due to epicenter mislocation, and negative skews due to lateral inhomogeneity in the Earth, are analyzed. Methods for travel-time estimation are critically reviewed. Recent travel-time tables, including the J-B tables, are within the range of root-mean-square travel-time fluctuations; the J-B tables are systematically late but cannot be reliably improved by least-square methods. Effects of lateral inhomogeneity at teleseismic distances can be estimated by chronoidal methods independently of standard tables, but the available explosion data are insufficiently well-distributed in azimuth and distance for this purpose.

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 Magnitudes of great shallow earthquakes from 1904 to 1952

1977 ◽  
Vol 67 (3) ◽  
pp. 587-598 ◽  
Author(s):  
Robert J. Geller ◽  
Hiroo Kanamori
Keyword(s):  
Surface Wave ◽  
Seismic Moment ◽  
Body Wave ◽  
Magnitude Scale ◽  
Surface Wave Magnitude ◽  
Class A ◽  
The Earth ◽  
Shallow Earthquakes ◽  
The Moment

abstract The “revised magnitudes”, M, converted from Gutenberg's unified magnitude, m, and listed by Richter (1958) and Duda (1965) are systematically higher than the magnitudes listed by Gutenberg and Richter (1954) in Seismicity of the Earth. This difference is examined on the basis of Gutenberg and Richter's unpublished original worksheets for Seismicity of the Earth. It is concluded that (1) the magnitudes of most shallow “class a” earthquakes in Seismicity of the Earth are essentially equivalent to the 20-sec surface-wave magnitude, Ms; (2) the revised magnitudes, M, of most great shallow (less than 40 km) earthquakes listed in Richter (1958) (also used in Duda, 1965) heavily emphasize body-wave magnitudes, mb, and are given by M=14Ms+34(1.59mb−3.97). For earthquakes at depths of 40 to 60 km, M is given by M = (1.59 mb − 3.97). M and Ms are thus distinct and should not be confused. Because of the saturation of the surface-wave magnitude scale at Ms ≃ 8.0, use of empirical moment versus magnitude relations for estimating the seismic moment results in large errors. Use of the fault area, S, is suggested for estimating the moment.

Travel times and amplitudes of S waves from nuclear explosions in Nevada

1969 ◽  
Vol 59 (1) ◽  
pp. 385-398 ◽  
Author(s):  
Otto W. Nuttli
Keyword(s):  
Stress Field ◽  
Body Wave ◽  
P Wave ◽  
Travel Times ◽  
S Wave ◽  
Low Velocity ◽  
Time Curve ◽  
Regional Stress ◽  
S Waves ◽  
Regional Stress Field

Abstract The underground Nevada explosions HALF-BEAK and GREELEY were unique in creating relatively large amplitude and long-period body S waves which could be detected at teleseismic distances. Observations of the travel times of these S waves provide a surface focus travel-time curve which in its major features is similar to a curve calculated from the upper mantle velocity model of Ibrahim and Nuttli (1967). This model includes a low-velocity channel at a depth of 150 to 200 km and regions of rapidly increasing velocity beginning at depths of 400 and 750 km. Observations of the S wave amplitudes suggest that a discontinuous increase in velocity occurs at 400 km, whereas at 750 km the velocity is continuous but the velocity gradient discontinuous. Body wave magnitudes calculated from S amplitudes are 5.3 ± 0.2 for GREELEY and 4.9 ± 0.2 for HALF-BEAK. These are about one unit less than body wave magnitudes from P amplitudes as reported by others. The shape and orientation of the radiation pattern of SH for both explosions are consistent with the Rayleigh and P-wave amplitude distribution of BILBY as given by Toksoz and Clermont (1967). This suggests that the regional stress field is the same at all three sites, and that the direction of cracking as well as the strain energy release in the elastic zone outside the cavity is determined by the regional stress field.

scholarly journals A study of the Northwestern Pacific upper mantle

1965 ◽  
Vol 55 (5) ◽  
pp. 925-939
Author(s):  
Daniel A. Walker
Keyword(s):  
Upper Mantle ◽  
Fundamental Problem ◽  
Body Wave ◽  
Lower Boundary ◽  
P Wave ◽  
Northwestern Pacific ◽  
Travel Times ◽  
Low Velocity ◽  
S Waves ◽  
Wave Channel

abstract A fundamental problem of earthquake seismology is the occurrence of the upper mantle low-velocity channel. This study is intended to examine its existence in the upper mantle below the Northwestern Pacific on the basis of body-wave arrivals at a bottom-mounted hydrophone near Wake Island. A comparison of the observed travel times and the Jeffreys-Bullen travel times shows an extreme anomaly in the 21- to 33-degree range for both P and S waves. Assumed linear paths suggest a P-wave-channel upper boundary between 165 km and 185 km, and a lower boundary between 290 km and 542 km. Travel times for P and S waves indicate that the velocities in the channel remain constant at 8.1 km/sec and 4.65 km/sec respectively.

Rays and travel times in a spherical anisotropic earth

1969 ◽  
Vol 59 (3) ◽  
pp. 1051-1060
Author(s):  
N. J. Vlaar
Keyword(s):  
Travel Time ◽  
Body Wave ◽  
Travel Times ◽  
Isotropic Model ◽  
Wave Fronts ◽  
Spherical Medium ◽  
Radially Inhomogeneous ◽  
Special Case ◽  
Ray Paths

abstract A study is made of the propagation of stress discontinuities (wave fronts) in a radially inhomogeneous, tangentially isotropic model of an anisotropic spherical medium. The results are given in the form of integrals for the ray paths and the travel times for the several body-wave phases. A special case of anisotropy dealt with in Section 2.2 (3) gives rise to considerable simplifications. This case in particular appears to be useful for the construction of travel-time tables for an Earth in which anisotropy occurs.

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.

Travel-time monitoring with vibroseis

1981 ◽  
Vol 71 (6) ◽  
pp. 1903-1927
Author(s):  
R. W. Clymer ◽  
T. V. McEvilly
Keyword(s):  
Travel Time ◽  
Single Channel ◽  
Travel Times ◽  
Near Surface ◽  
First Arrival Travel Times ◽  
First Arrival ◽  
Time Variations ◽  
Time Changes ◽  
Time Accuracy ◽  
A Site

Abstract The general failure of searches for precursory seismic travel-time variations associated with strike-slip earthquakes in California has led to this investigation into the feasibility of using a controlled-source seismic method to improve significantly the precision of travel-time measurements, and to investigate the nature of any detected travel-time changes. Travel times have been measured over a period of several years at sites south of Hollister, California, along the seismically active creeping zone of the San Andreas fault, using a single-channel VIBROSEIS system with real-time on-site data processing. At a site near Bear Valley, 7 km from the fault, no variations in the travel time of a deep crustal reflection were observed that could be associated with local earthquakes. However, significant variations (0.5 to 2.5 msec) of first arrival travel times observed near the Cienega Winery may have been associated with a series of nearby earthquakes and with a creep event. Major sources of measurement error have been identified in source variations and in rainfall-induced variations in near-surface properties. The former limits the precision of the deep reflection measurements to about 0.05 per cent of the travel time and the first arrival measurements to about 0.1 per cent of the travel time. The second effect is apparent as seasonal oscillations in travel time of as much as 15 to 20 msec, and also in wavelet amplitude and waveform, giving an implied travel-time accuracy of about 0.2 per cent for the deep reflection measurements and about 1 per cent for first arrivals. While these noise levels are disappointing, they can be reduced significantly by improved field procedures. Ongoing experiments are testing such procedures.

Travel times, variational parameters, and Love numbers for Moon models

1970 ◽  
Vol 60 (3) ◽  
pp. 697-716
Author(s):  
John S. Derr
Keyword(s):  
Surface Wave ◽  
Travel Time ◽  
Free Oscillation ◽  
Travel Times ◽  
Phase Velocities ◽  
Wave Phase ◽  
Solid Models ◽  
Love Numbers

Abstract Travel time graphs are given for previously defined Moon models for phases P, pP, PP, sS, SS, L, and R for focal depths 5, 50, 100, 200, 400, 600, and 1000 km. The teleseismic travel times for most models are significantly different. Variational parameters are graphed and tabulated to allow inversion of surface wave phase velocities and free oscillation periods. Love numbers are computed for all models and found to be essentially invariant for reasonable solid models.

The agreement of proposed earth models with observed body-wave travel times

1968 ◽  
Vol 58 (3) ◽  
pp. 1059-1069
Author(s):  
Daniel A. Walker ◽  
George H. Sutton
Keyword(s):  
Computer Program ◽  
Travel Time ◽  
Body Wave ◽  
Travel Times ◽  
Low Velocity ◽  
Velocity Models ◽  
Earth’S Mantle ◽  
Earth Models ◽  
Wave Travel

abstract A computer program was used to evolve a model of compressional and shearwave velocity for the earth's mantle which would be consistent with the travel times given in the Jeffreys-Bullen (J-B) tables. The sensitivity shown by our computed travel times to changes in layer velocities suggests that models containing low-velocity channels would produce travel times different from those given in the tables. Travel times associated with velocity models proposed by others were also computed. The significance of travel-time residuals depends primarily on the reliability of observed travel times for those epicentral distances at which the model fails.

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