Results achieved at the Department of Geophysics in 2001

(reported in December, 2001)


We have tested the impact of lateral viscosity variations in the top 200 km of the mantle on the interpretation of Fennoscandian postglacial uplift data (Martinec, Cadek and Fleitout, 2001) and presented an analytical form of the layer propagator matrix for the response of a locally incompressible, layered, linear-viscoelastic sphere assuming that the initial density stratification is parametrized by Darwin's law (Martinec, Thoma and Wolf, 2001). We have also studied the numerical problems associated with the viscoelastic response of the Earth to external loads in the time domain by means of the method of lines, (Hanyk et al., in press).

We have continued in dealing with the geodetic boundary-value problems. We particularly discussed the effect of the planar and spherical terrain models (Vanicek et al, 2001., Novak et al. 2001) and the ellipsoidal model of the geoid (Ardestani and Martinec, 2001) on precise geoid determination. The satellite gradiometric mission GOCE (to be launched in 2004) motivated us to solve the spherical gradiometric boundary-value problems to find the external Earth's gravitational potential (Martinec, 2001).

We have simulated subduction of slabs and concentrated on the dynamic effect of slab weakening due to grain size reduction at the phase boundary under the presence of trench migration in Cizkova et al. (submitted).

We have developed novel approaches to electromagnetic induction modeling for axisymmetric 2-D models of electrical conductivity (Martinec, Everett and Velimsky, submitted), and fully 3-D models (Velimsky and Martinec, to be submitted till the end of 2001), based on direct integration in the time domain.

Classical Boussinesq approximation of thermal convection was used by Vecsey and Matyska (2001) to demonstrate the ability of wavelet spectra to reveal the multiscale temporal dynamics of convecting systems. We have also employed the extended-Boussinesq convection models to extract the Bullen parameter (Matyska and Yuen, 2001; Matyska and Yuen, in press), which revealed non-adiabaticity of plumes and similarities between the Bullen parameter magnitudes obtained from tomographic models and the values yielded by thermal convection. The effects of adiabatic heating/cooling and viscous dissipation on 3-D rapidly rotating thermal convection was studied by Mistr et al. (in press). The applicability of new multidimensional wavelet analysis to various geophysical fields was studied by Yuen et al. (2001, and the paper in press) and by Vecsey et al.(2001).

Ardestani, V. E. and Martinec, Z., Ellipsoidal Stokes boundary-value problem with ellipsoidal corrections in the boundary condition. Studia Geoph. et Geod., 45, 109-126, 2001.
Cizkova, H., van Hunen, J., van den Berg, A.P., and N.J. Vlaar, The influence of rheological weakening on the interaction of slabs with the 670-km discontinuity, Earth Planet. Sci. Lett., submitted.
Hanyk, L., Matyska, C. and Yuen, D.A., Determination of viscoelastic spectra by matrix eigenvalue analysis. In: Glacial Isostatic Adjustment and the Earth System: Sea-Level, Crustal Deformation, Gravity and Rotation, eds. J. X. Mitrovica and L. L. A. Vermeersen, AGU, in press (it should appear till the end of 2001).
Martinec, Z., 2001. Green's function solution to spherical gradiometric boundary-value problems. J. Geod., submitted.
Martinec, Z., 2001. Semi-analytical solution for the viscoelastic relaxation in spherical earth with an axisymmetric craton. Acta Geod. Geoph. Hungarica, submitted.
Martinec, Z., Cadek, O. and Fleitout, L., Can the 1D viscosity profiles inferred from postglacial rebound data be affected by lateral viscosity variations in the tectosphere? Geophys. Res. Lett., 28, 4403-4406, 2001.
Martinec, Z., Everett, M.E. and Velimsky, J., Time-domain, spectral-finite element approach to transient two-dimensional geomagnetic induction in a spherical heterogeneous earth. Geophys. J. Int., submitted.
Martinec, Z. and Grafarend, E. W., Separability conditions for the vector Helmholtz equation. Boll. Geod. Scien. Aff., in press, (it should appear in No. 1 or 2 in 2002).
Martinec, Z., Thoma, M. and Wolf, D., Material versus local incompressibility and its influence on glacial-isostatic adjustment, Geophys. J. Int., 144, 136-156, 2001.
Matyska, C. and Yuen, D.A., Are mantle plumes adiabatic? Earth Planet. Sci. Lett., 189, 165-176, 2001.
Matyska, C. and Yuen, D. A., Bullen's parameter eta: A link between seismology and geodynamical modelling, Earth Planet. Sci. Lett., revised version submitted.
Mistr, Z., Matyska, C. and Yuen, D.A., Modeling of rapidly rotating thermal convection at finite Prandtl number with vorticity, vector potential and temperature. Studia Geophys. et Geod., in press (it should appear in No. 1 in 2002).
Novak, P., Vanicek, P., Martinec, Z. and Veronneau, M., Effects of the spherical terrain on gravity and the geoid. J. Geod., 75, 491-504, 2001.
Vanicek, P., Novak, P. and Martinec, Z., Geoid, topography, and the Bouguer plate or shell. J. Geod., 75, 210-215, 2001.
Vecsey, L. and Matyska, C., Wavelet spectra and chaos in thermal convection modelling. Geophys. Res. Lett., Geophys. Res. Lett., 28, 395-398, 2001.
Vecsey, L., Hier, C., Yuen, D.A., and Sevre, E.O., Two dimensional wavelet analysis applied to geoid anomalies, mixing and high Rayleigh number mantle convection, Electronic Geosciences, Vol. 6, 2001.
Velimsky, J. and Martinec, Z, Initial value approach to three-dimensional electromagnetic induction in a spherical Earth, to be submitted to GJI till the end of 2001.
Yuen, D.A., Vincent, A.P., Vecsey, L. and Kido, M., Application of multidimensional wavelets for visualizing multiscale geophysical phenomena: geoid anomalies, mixing and high Rayleigh number convection, in APEC Cooperation for Earthquake Simulation: S2nd ACES Workshop Proceedings, Edited by M. Mastu'ura, K. Nakajima and P. Mora, pp. 517-524, ACES, Brisbane, 2001.
Yuen, D.A., Vincent, A.P., Kido, M, and Vecsey, L., Geophysical applications of multidimensional filtering using wavelets, Pure and Applied Geophysics, in press.

Theory of seismic waves

Development of the algorithms for two-point ray tracing and travel-time interpolation in 3-D continued. The equations derived for the estimation of the average Lyapunov exponents, describing the ray chaos due to heterogeneities in the velocity model, have been applied to the construction of velocity models suitable for ray tracing and other high-frequency asymptotic methods. The designed algorithm of constructing velocity models have been tested on various 2-D and 3-D synthetic structures. Particular attention have been devoted to the resolution of seismic inversion techniques, model fitting, conversion and smoothing with the application of medium correlation functions and Sobolev scalar products.

The equations for calculation of the third and higher partial derivatives of travel time in both isotropic and anisotropic media have been derived. The equations for the linear paraxial approximation of the polarization vectors and for the variation of the polarization vectors with a velocity perturbation have been derived. Fermat's variational principle for anisotropic inhomogeneous media and its relation to the Finslerian metric and Hamiltonian have been studied.

Explicit equations for approximate linearized reflection/transmission coefficients at a generally oriented weak-contrast interface separating generally anisotropic media have been derived. A comparison of the reflection/transmission coefficients for dissipative and nondissipative media has been also performed. Various kinds of the coupling ray theory for weakly anisotropic models have been studied and compared with the exact solution derived for the "twisted crystal" model.

A new algorithm of the optimization of the shape of Gaussian beams and packets for prestack migrations in complex models have been designed, including smoothing of the beam parameters over the Hamiltonian hypersurface in the phase space.

The contemporary state of the seismic ray theory has been described by V. Cerveny in his monograph. Professor V. Cerveny received the Ernst Mach Award from the Academy of Sciences of the Czech Republic. K. Zacek received the Award of the Minister of Education, Youth and Sports, awarded annually to the five best university students in the Czech Republic.

P. Bulant: Sobolev scalar products in the construction of velocity models - application to model Hess and to SEG/EAGE Salt Model. Pure and appl. Geophys., 159 (2002), in press.
P. Bulant: Constructing the SEG/EAGE 3-D Salt Model for ray tracing using Sobolev scalar products. Geophys. Prospecting, submitted 2001. PS
P. Bulant & L. Klimes: Numerical algorithm of the coupling ray theory in weakly anisotropic media. Pure and appl. Geophys., 159 (2002), in press.
V. Cerveny: Seismic Ray Theory. Cambridge Univ. Press, New York, 2001 (713 pp).
J. Brokesova: Reflection/transmission coefficients at a plane interface in dissipative and nondissipative isotropic media: a comparison. J. Comput. Acoustics 9 (2001), 623-641.
L. Klimes: Perturbation of the polarization vectors in the isotropic ray theory. Pure and appl. Geophys., 159 (2002), in press.
L. Klimes: Lyapunov exponents for 2-D ray tracing without interfaces. Pure and appl. Geophys., 159 (2002), in press.
L. Klimes: Application of the medium covariance functions to travel-time tomography. Pure and appl. Geophys., 159 (2002), in press.
L. Klimes: Calculation of the third and higher derivatives of travel time in isotropic and anisotropic media. Geophys. J. int., submitted.
L. Klimes: Weak-contrast reflection/transmission coefficients in a generally anisotropic background. Geophysics, submitted.
L. Klimes: Correlation functions of random media. Pure and appl. Geophys., 159 (2002), in press.
L. Klimes: Estimating the correlation function of a self-affine random medium. Pure and appl. Geophys., 159 (2002), in press.
K. Zacek: Optimization of the shape of Gaussian beams. Geophys. Prospecting, submitted 2001.
K. Zacek: Smoothing the Marmousi model. Pure and appl. Geophys., 159 (2002), in press.

Structural seismology and earthquake modeling

Records of several Turkey earthquakes of 1999, obtained at broad-band seismic stations jointly operated by the Charles University and Patras University since 1997 in the Corinth Gulf, Greece, have been used to study dispersion of Love and Rayleigh waves. As compared with previous structural models for the territory of Greece, the dispersion data require significantly lower velocities in the uppermost crust, and smaller crustal thickness (Novotny et al., 2001).

In conjunction with an active litospheric structural experiment in Europe, CELEBRATION, four additional short profiles (of about 50 km long) were measured and interpreted, with a special emphasis on the upper-crustal structure in the earthquake swarm region of Western Bohemia (Malek et al., in press-a). The previously gathered controlled-source data (1989-91), and microearthquake data (1996-99) from Western Bohemia were re-interpreted with the aim to reveal anisotropy of the upper crust (Malek et al., in press-b). Methodical and practical aspects of the hypocentral location by deterministic grid search were solved (Jansky, 2000).

Focal mechanism retrieval based on amplitude spectra of complete waveforms and first-motion polarities, ASPO (Zahradnik et al., 2001), has been successfully validated on the 1999 Athens and the 2001 Skyros, Greece earthquakes (Zahradnik, submitted-a,b). Classical method of empirical Green's functions has been generalized for the practically important case of unequal focal mechanisms of the mainshock and aftershock, and the innovated method has been applied to inversion of the rupture nucleation point of the Athens 1999 earthquake (Plicka and Zahradnik, submitted). The finite-extent model of the Athens earthquake was then used to synthesize strong-ground motions by the newly developed combined deterministic-stochastic method, PEXT; the modeling results have been found in agreement with the observed peak acceleration values and empirical attenuation relations (Zahradnik and Tselentis, submitted).

A new 3D finite-difference code for the elastic wavefield modeling on spatially irregular (rectangular) grids was written and successfully tested. Attention was focused on efficiency; to that aim, the source- and path-effects are treated separately of the site effects by means of a hybrid fully 3D approach (Oprsal and Zahradnik, in press).

Jansky, J, 2000. Grid search hypocentral location method in simple 1-D media. Acta Montana IRSM AS CR, Series A No. 16(118), 71-84.
Malek, J., Broz, M., Fisher, T., Horalek, J., Hrubcova, P., Jansky, J., Novotny, O., Ruzek, B., and the CELEBRATION working group: Seismic measurements along short profiles in Western Bohemia during the CELEBRATION 2000 experiment. Acta Montana IRSM, CR in press-a.
Malek, J., Horalek, J., Jansky, J.: One-dimensional qP-wave velocity model of the upper crust for the West Bohemia/Vogtland earthquake swarm region. Studia geoph. et geod., in press-b.
Novotny, O., Zahradnik, J., and Tselentis, G-A., 2001. North-western Turkey earthquakes and the crustal structure inferred from surface waves observed in the Corinth Gulf, Greece. Bull. Seism. Soc. Am. 91, 875-879.
Oprsal, I., Zahradnik, J. 3D finite-difference method and hybrid modeling of earthquake ground motion, J. Geophys. Res., in press.
Plicka V., and Zahradnik, J., Inversion of rupture nucleation from regional records by eGf method for unequal focal mechanisms of the mainshock and aftershock: The Athens 1999 earthquake, Tectonophysics (submitted).
Zahradnik, J., Focal mechanism of the Athens 1999 earthquake by ASPO method, Tectonophysics (submitted-a).
Zahradnik, J., Modeling the Skyros island, Aegean Sea Mw=6.5 earthquake of July 26, 2001. Studia geoph. et geod. (submitted-b).
Zahradnik, J., and Tselentis, G.-A., Modeling strong-motion accelerograms by PEXT method, application to the Athens 1999 earthquake, Bull. Seism. Soc. Am. (submitted).
Zahradnik, J., Jansky, J., Papatsimpa, N., 2001. Focal mechanisms of weak earthquakes from amplitude spectra and polarities. Pure and Appl. Geophys., 158, 647-665.