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1.
A new approximation of the velocity-depth distribution in radially symmetric media is suggested. This approximation guarantees the continuity of velocity and its first and second derivatives, and does not generate false low-velocity layers. It removes false anomalies from the amplitude-distance curve and considerably increases its stability. The evaluation of ray integrals and ray amplitudes using this velocity-depth approximation does not require the computation of any transcendental function and is, therefore, very fast. Numerical examples are presented. 相似文献
2.
Summary Approximate expressions for the Hilbert transform of the functionf(t)=exp(-
0
2
t
2/2) cos(
0
t+v) are determined. This function, given a suitable choice of the three parameters 0, and v, approximates a wide class of seismic signals very well. The approximate expressions for the Hilbert transform enable very simple formulae to be given for the elementary seismograms of the individual seismic body waves (in the zero approximation of the ray theory). This accelerates the computation of ray theoretical seismograms considerably. 相似文献
3.
Vlastislav Červený 《Studia Geophysica et Geodaetica》2013,57(2):267-275
Recently, several expressions for the two-point paraxial travel time in laterally varying, isotropic or anisotropic layered media were derived. The two-point paraxial travel time gives the travel time from point S′ to point R′, both these points being situated close to a known reference ray Ω, along which the ray-propagator matrix was calculated by dynamic ray tracing. The reference ray and the position of points S′ and R′ are specified in Cartesian coordinates. Two such expressions for the two-point paraxial travel time play an important role. The first is based on the 4 × 4 ray propagator matrix, computed by dynamic ray tracing along the reference ray in ray-centred coordinates. The second requires the knowledge of the 6 × 6 ray propagator matrix computed by dynamic ray tracing along the reference ray in Cartesian coordinates. Both expressions were derived fully independently, using different methods, and are expressed in quite different forms. In this paper we prove that the two expressions are fully equivalent and can be transformed into each other. 相似文献
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Oldřich Novotný Vlastislav Červený L. A. Molotkov Reviewer I. Pšenčík 《Studia Geophysica et Geodaetica》1980,24(2):124-130
Summary The numerical properties of the low-frequency expansions for the reflection and transmission coefficients of SH-waves from transition layers, derived in [1], are studied. It is shown that the expansions are suitable for computations only when the thickness d of the transition layer is small in comparison with the wavelength of the incident wave (d0.5). For thicker transition layers, certain modifications of the method are suggested. 相似文献
8.
Jana Konopásková Vlastislav Červený Reviewer I. Pšenčik 《Studia Geophysica et Geodaetica》1984,28(2):113-128
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0
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0
. amu aa mu u aumu amu, a m mam n ¶rt; u L
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. u uu L
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0
auum. aumu amu, u L
0
um m uau m a uuu anum¶rt; u, mmmu a. uu L
0
, uuu nam. ma uam mumm mam ¶rt;a ¶rt;u naama am. uau ¶rt;m ma anum¶rt; u ma muna S, S u SS. 相似文献
9.
Summary The hybrid ray-reflectivity method is applied to the problem of the transmission of the reflected wave field through a thin high-velocity layer (or through a thin stack of high velocity layers), situated in the overburden of the reflector. In the hybrid ray-reflectivity method, the standard ray method is applied in the smooth parts of the model, and the reflectivity method is used locally at the thin high-velocity layer. With the exception of small epicentral distances, the standard ray method itself fails in such computations. The reason is that a considerable part of the energy for overcritical angles of incidence may be tunneled through the thin high-velocity layer along complex ray-paths, corresponding to inhomogeneous waves. The reflectivity method, applied locally at the thin high-velocity layer, automatically includes all inhomogeneous wave contributions. Thus, the hybrid ray-reflectivity method removes fully the limitations of the standard ray method, but still retains its main advantages, such as its applicability to 2-D and 3-D complex layered structures, flexibility, and low-cost computations. In the numerical examples, the hybrid ray-reflectivity synthetic seismograms are compared with standard ray synthetic seismograms and with full reflectivity computations. The numerical examples show that the hybrid ray-reflectivity method describes the tunneling of seismic energy through a thin high-velocity layer with sufficient accuracy. 相似文献
10.
Jana Konopásková Vlastislav Červený Reviewer I. Pšenčík 《Studia Geophysica et Geodaetica》1984,28(1):19-35
m¶rt;au n unm ¶rt; u ¶rt;uau uu n m nm ¶rt; ¶rt;. a uau ¶rt;m a ma m nau a¶rt;a, amu aa mu. au mu uu naam, m m¶rt;au n ¶rt;am ¶rt;mam m mam ¶rt;a u amu aa mu (. u. 9). aumu amu, uauau n ma nam ¶rt;a . ¶rt; amu m am ¶rt;m ¶rt;am mumm mam a naama am, an. aa uuau n, naama uauau n, um¶rt;. 相似文献