Papers by Vaclav Vavrycuk
Pure and Applied Geophysics, 2019
Due to an unfortunate technical error this article has not been published as Open Access. The ori... more Due to an unfortunate technical error this article has not been published as Open Access. The original has been updated. We apologise this error.
Pure and Applied Geophysics, Feb 9, 2018
We study two earthquake swarms that occurred in the Ubaye Valley, French Alps within the past dec... more We study two earthquake swarms that occurred in the Ubaye Valley, French Alps within the past decade: the 2003-2004 earthquake swarm with the strongest shock of magnitude ML = 2.7, and the 2012-2015 earthquake swarm with the strongest shock of magnitude ML = 4.8. The 2003-2004 seismic activity clustered along a 9-km-long rupture zone at depth between 3 and 8 km. The 2012-2015 activity occurred a few kilometres to the northwest from the previous one. We applied the iterative joint inversion for stress and fault orientations developed by Vavryčuk (2014) to focal mechanisms of 74 events of the 2003-2004 swarm and of 13 strongest events of the 2012-2015 swarm. The retrieved stress regime is consistent for both seismic activities. The r 3 principal axis is nearly horizontal with azimuth of * 103°. The r 1 and r 2 principal axes are inclined and their stress magnitudes are similar. The active faults are optimally oriented for shear faulting with respect to tectonic stress and differ from major fault systems known from geological mapping in the region. The estimated low value of friction coefficient at the faults 0.2-0.3 supports an idea of seismic activity triggered or strongly affected by presence of fluids.
Zenodo (CERN European Organization for Nuclear Research), Apr 12, 2023
We study a problem of energy and momentum of photons redshifted in a gravitational field. Based o... more We study a problem of energy and momentum of photons redshifted in a gravitational field. Based on the Einstein-Maxwell's equations for electromagnetic waves in curved spacetimes, we derive formulas for the speed, energy and momentum of photons in gravitational fields. The formulas are further specified for the Schwarzschild metric describing a local gravitational field around a massive body. It is shown that energy of photons is conserved in inertial (free-falling) as well as in non-inertial coordinate systems, and no energy is exchanged between photons and the gravitational field. The Planck energy-frequency relation valid in Special Relativity is modified to be applicable also to General Relativity. According to the new Planck relation, the photon energy depends not only on the frequency of photons but also on their speed. In a free-falling system, the photon energy is conserved, because no frequency shift and no change of the photon speed is detected. In non-inertial systems, the photon energy is also conserved, because the frequency shift due to gravity is compensated by the change of the photon speed.
Journal of Geophysical Research, 1999
Journal of Geophysical Research, 2001
International Journal of Rock Mechanics and Mining Sciences, 2013
GEOPHYSICS, 2008
Velocity, attenuation, and the quality [Formula: see text] factor of waves propagating in homogen... more Velocity, attenuation, and the quality [Formula: see text] factor of waves propagating in homogeneous media of arbitrary anisotropy and attenuation strength are calculated in high-frequency asymptotics using a stationary slowness vector, the vector evaluated at the stationary point of the slowness surface. This vector is generally complex-valued and inhomogeneous, meaning that the real and imaginary parts of the vector have different directions. The slowness vector can be determined by solving three coupled polynomial equations of the sixth order or by a nonlinear inversion. The procedure is simplified if perturbation theory is applied. The elastic medium is viewed as a background medium, and the attenuation effects are incorporated as perturbations. In the first-order approximation, the phase and ray velocities and their directions remain unchanged, being the same as those in the background elastic medium. The perturbation of the slowness vector is calculated by solving a system of...
GEOPHYSICS, 2007
Asymptotic wave quantities such as ray velocity and ray attenuation are calculated in anisotropic... more Asymptotic wave quantities such as ray velocity and ray attenuation are calculated in anisotropic viscoelastic media by using a stationary slowness vector. This vector generally is complex valued and inhomogeneous, and it predicts the complex energy velocity parallel to a ray. To compute the stationary slowness vector, one must find two independent, real-valued unit vectors that specify the directions of its real and imaginary parts. The slowness-vector inhomogeneity affects asymptotic wave quantities and complicates their computation. The critical quantities are attenuation and quality factor ([Formula: see text]-factor); these can vary significantly with the slowness-vector inhomogeneity. If the inhomogeneity is neglected, the attenuation and the [Formula: see text]-factor can be distorted distinctly by errors commensurate to the strength of the velocity anisotropy — as much as tens of percent for sedimentary rocks. The distortion applies to strongly as well as to weakly attenuati...
GEOPHYSICS, 1998
Approximate PP-wave reflection coefficients for weak contrast interfaces separating elastic, weak... more Approximate PP-wave reflection coefficients for weak contrast interfaces separating elastic, weakly transversely isotropic media have been derived recently by several authors. Application of these coefficients is limited because the axis of symmetry of transversely isotropic media must be either perpendicular or parallel to the reflector. In this paper, we remove this limitation by deriving a formula for the PP-wave reflection coefficient for weak contrast interfaces separating two weakly but arbitrarily anisotropic media. The formula is obtained by applying the first‐order perturbation theory. The approximate coefficient consists of a sum of the PP-wave reflection coefficient for a weak contrast interface separating two background isotropic half‐spaces and a perturbation attributable to the deviation of anisotropic half‐spaces from their isotropic backgrounds. The coefficient depends linearly on differences of weak anisotropy parameters across the interface. This simplifies studies...
Geophysics, 2012
The exact analytical solution of the complex eikonal equation describing P- and S-waves radiated ... more The exact analytical solution of the complex eikonal equation describing P- and S-waves radiated by a point source situated in a simple type of isotropic viscoelastic medium was ascertained. The velocity-attenuation model is smoothly inhomogeneous with a constant gradient of the square of the complex slowness. The resultant traveltime is complex; its real part describes the wave propagation and its imaginary part describes the attenuation effects. The solution was further used as a reference solution for numerical tests of the accuracy and robustness of two approximate ray-tracing approaches solving the complex eikonal equation: real elastic ray tracing and real viscoelastic ray tracing. Numerical modeling revealed that the real viscoelastic ray tracing method is unequivocally preferable to elastic ray tracing. It is more accurate and works even in situations when the elastic ray tracing fails. Also, the ray fields calculated by the real viscoelastic ray tracing are excellently repr...
GEOPHYSICS, 2009
Velocity anisotropy and attenuation in weakly anisotropic and weakly attenuating structures can b... more Velocity anisotropy and attenuation in weakly anisotropic and weakly attenuating structures can be treated uniformly using weak anisotropy-attenuation (WAA) parameters. The WAA parameters are constructed in a way analogous to weak anisotropy (WA) parameters designed for weak elastic anisotropy. The WAA parameters generalize WA parameters by incorporating attenuation effects. They can be represented alternatively by one set of complex values or by two sets of real values. Assuming high-frequency waves and using the first-order perturbation theory, all basic wave quantities such as the slowness vector, the polarization vector, propagation velocity, attenuation, and the quality factor are linear functions of WAA parameters. Numerical modeling shows that perturbation equations have different accuracy for different wave quantities. The propagation velocity usually is calculated with high accuracy. However, the attenuation and quality factor can be reproduced with appreciably lower accura...
Geophysical Prospecting, 2007
Geophysical Journal International, 2013
Geophysical Journal International, 1992
Geophysical Journal International, 2010
Geophysical Journal International, 1995
Geophysical Journal International, 2005
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Papers by Vaclav Vavrycuk