Amplitude of Body Waves in a Heterogeneous Sphere Comparison of Wave Theory and Ray Theory

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.

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Body-waves and ray theory – amplitudes

Foundations of Modern Global Seismology ◽

10.1016/b978-0-12-815679-7.00021-5 ◽

2021 ◽

pp. 363-390

Author(s):

Charles J. Ammon ◽

Aaron A. Velasco ◽

Thorne Lay ◽

Terry C. Wallace

Keyword(s):

Body Waves ◽

Ray Theory

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Photodeflection signal formation in photothermal measurements: comparison of the complex ray theory, the ray theory, the wave theory, and experimental results

Applied Optics ◽

10.1364/ao.46.005216 ◽

2007 ◽

Vol 46 (22) ◽

pp. 5216 ◽

Cited By ~ 9

Author(s):

Dorota Korte Kobylińska ◽

Roman J. Bukowski ◽

Boguslaw Burak ◽

Jerzy Bodzenta ◽

Stanislaw Kochowski

Keyword(s):

Wave Theory ◽

Experimental Results ◽

Ray Theory ◽

Complex Ray

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The Fresnel volume and transmitted waves

Geophysics ◽

10.1190/1.1759451 ◽

2004 ◽

Vol 69 (3) ◽

pp. 653-663 ◽

Cited By ~ 120

Author(s):

Jesper Spetzler ◽

Roel Snieder

Keyword(s):

Wave Equation ◽

Fresnel Zone ◽

Wave Theory ◽

Three Dimensions ◽

Ray Theory ◽

Finite Frequency ◽

Frequency Wave ◽

Reflected Waves ◽

Band Limited ◽

Propagation Of Waves

In seismic imaging experiments, it is common to use a geometric ray theory that is an asymptotic solution of the wave equation in the high‐frequency limit. Consequently, it is assumed that waves propagate along infinitely narrow lines through space, called rays, that join the source and receiver. In reality, recorded waves have a finite‐frequency content. The band limitation of waves implies that the propagation of waves is extended to a finite volume of space around the geometrical ray path. This volume is called the Fresnel volume. In this tutorial, we introduce the physics of the Fresnel volume and we present a solution of the wave equation that accounts for the band limitation of waves. The finite‐frequency wave theory specifies sensitivity kernels that linearly relate the traveltime and amplitude of band‐limited transmitted and reflected waves to slowness variations in the earth. The Fresnel zone and the finite‐frequency sensitivity kernels are closely connected through the concept of constructive interference of waves. The finite‐frequency wave theory leads to the counterintuitive result that a pointlike velocity perturbation placed on the geometric ray in three dimensions does not cause a perturbation of the phase of the wavefield. Also, it turns out that Fermat's theorem in the context of geometric ray theory is a special case of the finite‐frequency wave theory in the limit of infinite frequency. Last, we address the misconception that the width of the Fresnel volume limits the resolution in imaging experiments.

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A procedure for source studies from spectrums of long-period seismic body waves

Bulletin of the Seismological Society of America ◽

10.1785/bssa0550020203 ◽

1965 ◽

Vol 55 (2) ◽

pp. 203-235 ◽

Cited By ~ 5

Author(s):

Ari Ben-Menahem ◽

Stewart W. Smith ◽

Ta-Liang Teng

Keyword(s):

Body Wave ◽

Source Parameters ◽

Wave Theory ◽

Body Waves ◽

Spectral Window ◽

Earthquake Sources ◽

Source Studies ◽

New Ideas ◽

Intermediate Earthquake ◽

Set Up

Abstract The well-known first motion method of Nakano and Byerly is extended, generalized and combined with recent new ideas in body wave theory in order to set up a routine procedure for extracting source parameters from spectral analysis of isolated P and S pulses recorded at a net of standardized stations around a non-shallow source. The method consists of compensating the observed spectrums for instrumental and propagational effects. A combined study of the resulting radiation patterns, initial phases, and the initial amplitudes will render information regarding the spatial and temporal nature of deep and intermediate earthquake sources as seen through the spectral window of 10-100 seconds. The shorter periods can be used for source studies only if an accurate station correction is available.

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Estimates of short-period Q values and seismic moments from coda waves for earthquakes of the Beijing and Yun-nan regions of China

Bulletin of the Seismological Society of America ◽

10.1785/bssa0740041189 ◽

1984 ◽

Vol 74 (4) ◽

pp. 1189-1207

Author(s):

Peishan Chen ◽

Otto W. Nuttli ◽

Wenhua Ye ◽

Jiazheng Qin

Keyword(s):

Wave Theory ◽

Seismic Intensity ◽

Body Waves ◽

Wave Frequency ◽

Coda Waves ◽

Coda Wave ◽

Master Curves ◽

Beijing Area ◽

Short Period ◽

Simple Equations

Abstract Coda waves are used to determine the Q value of short-period waves in the Beijing area and in Yun-nan Province, China, and the seismic moments of the earthquakes studied. For the Beijing area the Q0, or 1-Hz value, is found to be approximately 400, with little or no indication of frequency dependence of Q for frequencies near 1 Hz in that region. For Yun-nan Province, the Q0 value is about 180, and the data suggest that Q(f) = Q0f0.2, where f is wave frequency. These values are in fairly good agreement with short-period Q estimates made for those regions by Chen and Nuttli (1984), on the basis of attenuation of seismic intensity values. Hermann's (1980) application of Aki's (1969) coda wave theory is extended, to provide simple equations for calculating master curves for coda wave studies. Two types of master curves provide independent estimates of Q0 and of the dependency of Q on wave frequency. For the data analyzed the two methods gave similar results. A third type of master curves gives estimates of the seismic moments of the earthquakes studied. The moments obtained by this means agree with values obtained by the conventional methods of analysis that use the spectrum of body waves or surface waves.

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Reflexion levels and coupling regions in a horizontally stratified ionosphere

Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences ◽

10.1098/rsta.1959.0014 ◽

1959 ◽

Vol 252 (1004) ◽

pp. 53-68 ◽

Cited By ~ 18

Keyword(s):

Collision Frequency ◽

Plasma Frequency ◽

Wave Theory ◽

Electron Collision ◽

Ray Theory ◽

Radio Waves ◽

Quartic Equation ◽

Full Wave ◽

Electron Collision Frequency ◽

Full Solution

The propagation of radio waves through a horizontally stratified and slowly varying ionosphere is governed, in the case of oblique incidence, by a quartic equation (Booker 1938). Ray theory breaks down when two roots of this quartic are equal, for then coupling occurs between the characteristic waves, and full wave theory must be used. This paper is concerned with determining the conditions under which the two roots are equal; it is not concerned with the full wave theory. Values of the plasma frequency, and electron collision frequency, which lead to equal roots, are determined, and are exhibited in a set of curves. A full solution of the ‘Booker’ quartic is also given for a case of special interest. It is pointed out that the electric wave-field is unlikely to become very large in a slowly varying ionosphere, so that, if the ionosphere were irregular, scattering cannot be unduly enhanced by a plasma resonance.

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