Body waves and ray theory – travel times

2021 ◽  
pp. 339-362
Author(s):  
Charles J. Ammon ◽  
Aaron A. Velasco ◽  
Thorne Lay ◽  
Terry C. Wallace
Keyword(s):  
Body Waves ◽  
Ray Theory ◽  
Travel Times

scholarly journals Asymptotic analysis for dispersion relations and travel times in noise cross-correlations: spherically symmetric case

2018 ◽  
Vol 474 (2218) ◽  
pp. 20180382
Author(s):  
Tianshi Liu ◽  
Haiming Zhang
Keyword(s):  
Asymptotic Analysis ◽  
Surface Waves ◽  
Green's Functions ◽  
Green’S Functions ◽  
Dispersion Relations ◽  
Body Waves ◽  
Spherically Symmetric ◽  
Travel Times ◽  
Cross Correlations ◽  
The Cross

The cross-correlations of ambient noise or earthquake codas are massively used in seismic tomography to measure the dispersion curves of surface waves and the travel times of body waves. Such measurements are based on the assumption that these kinematic parameters in the cross-correlations of noise coincide with those in Green's functions. However, the relation between the cross-correlations of noise and Green's functions deserves to be studied more precisely. In this paper, we use the asymptotic analysis to study the dispersion relations of surface waves and the travel times of body waves, and come to the conclusion that for the spherically symmetric Earth model, when the distribution of noise sources is laterally uniform, the dispersion relations of surface waves and the travel times of SH body-wave phases in noise correlations should be exactly the same as those in Green's functions.

A study of the Earth's crust and upper mantle using travel times and spectrum characteristics of body waves

1970 ◽  
Vol 60 (6) ◽  
pp. 1921-1935
Author(s):  
B. M. Gurbuz
Keyword(s):  
Upper Mantle ◽  
Body Waves ◽  
Earth’S Crust ◽  
Travel Times ◽  
Time Data ◽  
Crust And Upper Mantle ◽  
Contour Maps ◽  
Spectrum Characteristics ◽  
Earth's Crust ◽  
Early Rise

Abstract The aim of this paper is to investigate the velocity distribution and structure of the Earth's crust and upper mantle from the close collaboration of theory and experimental results of travel times and spectrum characteristics of body waves. The interpretation was based on 38 seismic records which were obtained from the “Project Early Rise” experiment during July 1966. The results refer to the area bounded by latitudes 49°W and 51°30′ and longitudes 93°W and 98°W. A least-squares analysis of the travel-time data was made and the uncertainties of the slopes, intercept times, and corresponding velocities were determined. The observed wide-angle reflections were used to calculate the root mean square velocities applying the T2 - X2 method. Depth calculations for the velocity discontinuities and seismic depth contour maps were made. A model was constructed, and the validity of the proposed new model was tested by comparing the observed travel times, spectrum-amplitude ratios, and relative phase shifts of body waves with theoretically expected values. Evidence is given for three discontinuities in the Earth's crust with velocities of 6.11 ± 0.01 km/sec, 6.8 ± 0.08 km/sec, and 7.10 ± 0.04 km/sec at average depths 18 ± 2 km and 25.5 ± 0.9 km. Velocities in the uppermost part of the mantle were determined as 7.90 ± 0.05 km/sec and 8.48 ± 0.05 km/sec with interfaces at the average depths of 34 ± 1 km, and 47 ± 1 km, respectively.

P-wave amplitudes and magnitudes between 10° and 35°

1974 ◽  
Vol 64 (6) ◽  
pp. 1887-1899
Author(s):  
George A. McMechan ◽  
Warren G. Workman
Keyword(s):  
Upper Mantle ◽  
Epicentral Distance ◽  
Maximum Amplitude ◽  
Body Waves ◽  
P Wave ◽  
Ray Theory ◽  
Mantle Structure ◽  
Upper Mantle Structure ◽  
Wave Trains ◽  
Theory Technique

abstract The observed behavior of P-wave relative amplitudes, as a function of epicentral distance, between 10° and 35°, is controlled primarily by the velocity-depth structure of the upper mantle. P-wave synthetic seismograms calculated by the new quantized ray theory technique are used to determine theoretical log (A/T) versus log Δ curves from a number of upper mantle models. Maximum amplitude arrivals show less model dependence than the first arrivals in the same wave trains, and hence are more consistent magnitude indicators for regions where the upper mantle structure is poorly known. Log (A/T) versus log Δ curves vary considerably, but predictably, from model to model. This model-dependent variation can account for a major part of the large standard deviations usually associated with the calculation of magnitudes from body waves.

Body-waves and ray theory – amplitudes

2021 ◽  
pp. 363-390
Author(s):  
Charles J. Ammon ◽  
Aaron A. Velasco ◽  
Thorne Lay ◽  
Terry C. Wallace
Keyword(s):  
Body Waves ◽  
Ray Theory

Ray theory: Travel times

2012 ◽  
pp. 65-102
Author(s):  
Peter M. Shearer
Keyword(s):  
Ray Theory ◽  
Travel Times

Investigation of a method for determining stress accumulation at depth—II

1969 ◽  
Vol 59 (1) ◽  
pp. 43-58
Author(s):  
Joseph D. Eisler
Keyword(s):  
Field Experiments ◽  
San Andreas Fault ◽  
Body Waves ◽  
Travel Times ◽  
Compressional Waves ◽  
San Andreas ◽  
Path Lengths ◽  
Stress Accumulation

Abstract The second of two seismic field experiments designed to study the precision with which the arrival of compressional body waves could be timed over paths up to 42 km in length was performed seven months after the first at the same location in the Gabilan Range near Salinas, California. Results of the second experiment show that the timing of the compressional waves could be carried out to the same order of precision as in the first experiment, i.e., to ±1 msec. In addition, the travel times over certain path lengths increased by about 6 msec within the intervening period. This observation is discussed in terms of the possible release of stress at depth in the region adjacent to the San Andreas Fault.

scholarly journals Towards a Wave Theory Interpretation of Time-Distance Helioseismology Data

2001 ◽  
Vol 203 ◽  
pp. 180-182
Author(s):  
A. C. Birch ◽  
A. G. Kosovichev
Keyword(s):  
Spatial Scale ◽  
Born Approximation ◽  
Acoustic Waves ◽  
Sound Speed ◽  
Large Scale ◽  
Small Scale ◽  
Ray Theory ◽  
Travel Times ◽  
Large Spatial Scale ◽  
Time Distance

Time-distance helioseismology, which measures the time for acoustic waves to travel between points on the solar surface, has been used to study small-scale three-dimensional features in the sun, for example active regions, as well as large-scale features, such as meridional flow, that are not accessible by standard global helioseismology. Traditionally, travel times have been interpreted using geometrical ray theory, which is not always a good approximation. In order to develop a wave interpretation of time-distance data we employ the first Born approximation, which takes into account finite-wavelength effects and is expected to provide more accurate inversion results. In the Born approximation, in contrast with ray theory, travel times are sensitive to perturbations to sound speed which are located off the ray path. In an example calculation of travel time perturbations due to sound speed perturbations that are functions only of depth, we see that that the Born and ray approximations agree when applied to perturbations with large spatial scale and that the ray approximation fails when applied to perturbations with small spatial scale.

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