**Progress report 2012**

http://geo.mff.cuni.cz/documents/research_12.pdf

http://geo.mff.cuni.cz/documents/publ_12.htm

Department
of Geophysics, belonging to the Faculty of Mathematics and Physics,

Research
project SW3D, *Seismic Waves in Complex 3-D Structures*, coordinated at
the Department of Geophysics since 1993, has continued successfully in 2012.
The project has been supported by 5 companies or research institutes (BP
America Inc., U.S.A.; Chevron U.S.A. Inc., U.S.A.; NORSAR, Norway; Petrobras,
Brazil; Schlumberger Cambridge Research Limited, U.K.) in the framework of the
international SW3D consortium. The project commisioned by ESA which aims to develop and test the
Swarm Level 2 processing facility started in October 2010. The Charles
University, as a member of the SMART consortium, is providing support in
development of the time-domain chain for inversion of Swarm data in terms of
3-D mantle conductivity.

Seismic station
PRA (created in

Operation of all
these stations is partly supported by the project CzechGeo/EPOS, see http://czechgeo.cz. Within this project the
department operates also the CzechGeo/EPOS Seismological Software Centre, see http://epos-eu.cz/ssc.

The Editors or Associated
Editors of international journals have been Vlastislav Červený (*Russian Geology and Geophysics*), Luděk
Klimeš (*Journal of Seismic Exploration*), Ctirad Matyska (*Journal of
Geophysical Research – Solid Earth; Studia Geophysica et Geodaetica*) and
Jiří Zahradník (*Journal of Seismology*). Ctirad Matyska has been
the member of the editorial board of the journal *Pokroky matematiky, fyziky
a astronomie,* which is devoted to popularization of mathematics, physics,
astronomy and education in these fields.

The master theses
written by David Einšpigel and Jiří
Vackář were defended at the Department in 2012.

As in previous
years, research at the Department was carried out in three directions:
Earthquake and structural studies, Theory of seismic waves, and
Geodynamics.

**Earthquake and
structural studies (reported by Jiří Zahradník)**

**Earthquake sources**

The following events were
studied (Mw denotes the moment magnitude): two earthquakes Mw > 5 Efpalio
2010 Greece; two Mw > 4.5 earthquakes of 2009 near Columbo volcano, Aegean
Sea, Greece; Mw 6.3 L’Aquila 2009 Italy; and Mw 7.1
Van 2011 Turkey. The two Efpalio mainshocks and the main part of the entire
2010 earthquake sequence in the Corinth Gulf were examined from several
viewpoints: (i) source location (Janský et al., 2012), (ii) crustal structure
(Novotný et al., 2012), and (iii) source properties (Sokos et al., 2012). The
two events from the Aegean Sea served for testing the resolvability of the
isotropic source component. The damaging earthquakes of L’Aquila (Gallovič and
Zahradník, 2012) and Van (two submitted papers) were investigated in terms of
source complexity. Practical consequences of the L’Aquila source model in the
high-frequency band of the engineering interest were treated by Ameri et al.
(2012), using the Hybrid Integral Composite method, developed at our department
in previous years by F. Gallovič and J. Brokešová.

A new method to calculate
the space-time slip distribution was developed by F. Gallovič (Gallovič and
Zahradník, 2012). The source model consists of Multiple Finite-Extent (MuFEx)
subsources. The slip amplitude, rupture velocity, rake and rise time are
assumed to be constant within each subsource. The size and location of the
MuFEx subsources have to be inferred independently from other methods, e.g.,
the truncated singular value decomposition, or the iterative multiple-point
source deconvolution (ISOLA). Each MuFEx subsource is characterized by an
individual set of trial nucleation points, rupture velocities and nucleation
times, which are grid-searched. For each combination of these parameters, the
subsources’ slip is determined by the least-squares approach. This procedure
provides not only the best-fitting model, but also a whole range of acceptable
models, allowing for the uncertainty analysis.

A new method to calculate uncertainty of the
strike, dip and rake of the earthquake source was proposed by Zahradník and
Custódio (2012). One of its possible applications demonstrated *ibid.*, is mapping the moment-tensor
uncertainty for a given station network, usable for a network design and/or its
improvement. The latter has found a practical application in the Irpinia
seismic network (diploma thesis by Magdalena Michele, Naples University
Federico II, supervised by A. Emolo and S. Custódio).
An
extension of the method to the non-linear case, where the source position and
time belong to the model parameters, was solved with a focus on the probability
density function of the isotropic source component. The latter was performed in
the framework of the PhD study of D. Křížová, supervised by J. Zahradník (a
paper accepted in BSSA, to appear in 2013).

Software ISOLA, developed
since

**New instruments**

A new six-degree-of
freedom (6-DOF) mechanical seismic sensor “Rotaphone” was developed and tested,
including the calibration, linearity, and cross-axis errors (Brokešová et al.,
2012a). The instrument records three translational and three rotational ground
motion velocity components. The device consists of standard geophones arranged
in parallel pairs to detect spatial gradients. The instrument operates in a
relatively high-frequency range, above 2 Hz. Its theoretical sensitivity limit
in this range is 10^{-9} m/s in ground velocity and 10^{-9}
rad/s in rotation rate. Small size and weight, and easy installation and
maintenance make the instrument useful for local-earthquake recording and
seismic prospecting.

The
calibration method, which is a key point of the Rotaphone development, is
explained in detail in Brokešová et al.
(2012b). The paper also includes a comparison with a
reference sensor (fiber optic gyroscope).

The prototype was
subjected to testing at the Albuquerque Seismological Laboratory, U.S.
Geological Survey using the rotational shaking table. It was also successfully
used to monitor the 6-DOF ground motions from shallow local microearthquakes in
various active regions (a seismic swarm area in the Czech Republic, the
vicinity of the salt-production factory of Provadia in Bulgaria, and the
Corinth Gulf rift zone in Greece).

**Structural studies**

The western part of the
Corinth Gulf was subjected to the investigation of the local 1D structural
model based on data of the Efpalio 2010 earthquake sequence. The model is based
on the minimization of travel-time residuals. A variant of the method of conjugate
gradients was used for this purpose. In comparison with several previous
models, the new model is characterized by higher velocities up to a depth of
about

The inversion of full
waveforms for the same purpose, i.e. construction of a 1D structural model, was
tested by V. Plicka (a paper under preparation). The method is based on a
combination of the Discrete Wavenumber forward solver of M. Bouchon and O.
Coutant, and the optimization Neighborhood Algorithm of M. Sambridge. Elevated
values of the Vp/Vs ~

Joint project of the
Charles University in Prague and the University in Patras, initiated in 1997,
has successfully continued. Current configuration of the jointly operated
seismic station is as follows: SERG (Sergoula), LTK (Loutraki), PYL (Pylos),
PDO (Prodromos), ZKS (Zakynthos), ANX (Ano Chora), PVO (Paravola) and FSK
(Fiskardo). For details, see http://seismo.geology.upatras.gr/heliplots/
Each site is equipped with a pair of the broad-band and strong-motion
instruments. All broad-band channels are continuously transmitted to the Patras
hub. The stations belong to the Hellenic Unified Seismic Network (HUSN), with
data sharing by three universities (Athens, Thessaloniki and Patras) and the
National Observatory of Athens. Data of LTK station are real-time transmitted
to the European data center ORFEUS. At the end of 2011 and in

**Free oscillations of the Earth**

Zábranová
et al. (2012, SGG) analysed synthetic seismograms for several source fast
solutions of the 2011 Tohoku earthquake obtained from surface waves and tested them
against the observed gravity data from the superconducting gravimeter installed
at the GOPE station. Zábranová et al.
(2012, GRL) studied radial modes excited by the 2010 Maule and 2011 Tohoku
earthquake, obtained new estimates of the quality factors of the modes _{0}S_{0}
and _{1}S_{0} and corresponding constraints to the M_{rr}
component of the seismic moment tensor.

**Theory of seismic
waves (reported by L. Klimeš)**

**Paraxial ray methods and Gaussian beams
in anisotropic media**

The
two-point travel times represent the travel times between two points. Assuming that these points are chosen in a
paraxial vicinity of the reference ray, Červený, Iversen & Pšenčík (2012:
Two-point paraxial traveltimes in an inhomogeneous anisotropic medium, Geophys.
J. int., 189, 1597-1610) derived the equations for the paraxial approximation
of two-point travel times in heterogeneous anisotropic media.

Waheed,
Červený, Iversen & Pšenčík (2012: Tests of two-point paraxial traveltime
formula in inhomogeneous anisotropic media, In: Seismic Waves in Complex 3-D
Structures, Report 22, Dep. Geophys., Charles Univ., Prague, pp. 113-127), Waheed,
Červený, Iversen & Pšenčík (2012: Tests of efficiency of two-point paraxial
traveltime formula in inhomogeneous anisotropic media, In: The 15th
International Workshop on Seismic Anisotropy (Bahrain), Dhahran Geoscience
Society, Dhahran, pp. 82-85), Waheed, Alkhalifah, Pšenčík, Červený &
Iversen (2012: Two-point paraxial traveltime in inhomogeneous
isotropic/anisotropic media -- tests of accuracy, In: Extended Abstracts of
74th EAGE Conference (Copenhagen), Eur. Assoc. Geoscientists & Engr.,
Houten, P282), and Pšenčík, Waheed & Červený (2012: Two-point paraxial
travel time approximation, In: Kolman, Berezovski, Okrouhlik & Plesek:
Advanced Modelling of Wave Propagation in Solids, Institute of Thermodynamics ASCR,
Prague, Czech Republic, pp. 109-110) tested efficiency and accuracy of the
two-point paraxial travel time approximation in smoothly varying isotropic and
also anisotropic velocity models. They
demonstrated that, for sufficiently distant points in the studied models, the
approximation yields accurate results to a great distance from the reference
ray. Application of the approximation to the problem of perturbation of the
source and receivers solved recently by the method based on numerical solution
of the eikonal equation leads to increased efficiency and accuracy.

Červený,
Iversen & Pšenčík (2012: Two-point paraxial travel times using dynamic ray
tracing in wavefront orthonormal coordinates, In: Seismic Waves in Complex 3-D
Structures, Report 22, Dep. Geophys., Charles Univ., Prague, pp. 129-137)
generalized the above mentioned equations for the two-point paraxial travel
times to the situation in which the paraxial ray propagator matrix is computed
along the reference ray by dynamic ray tracing in wavefront orthonormal coordinates.

**Anisotropic ray theory**

Klimeš
(2012: Zero-order ray-theory Green tensor in a heterogeneous anisotropic
elastic medium, Stud. geophys. geod., 56, 373-382) simplified the derivation of
the zero-order ray-theory Green tensor in a heterogeneous anisotropic medium.

**Coupling ray theory for S waves**

The
coupling ray theory is necessary for calculating S waves in heterogeneous
weakly anisotropic elastic media by ray-based methods. After many years of their effort, Klimeš
& Bulant (2012: Single-frequency approximation of the coupling ray theory, In:
Seismic Waves in Complex 3-D Structures, Report 22, Dep. Geophys., Charles
Univ., Prague, pp. 143-167) proposed the approximation of the
coupling-ray-theory Green tensor by two S waves described by the
coupling-ray-theory travel times and the coupling-ray-theory amplitudes. This
approximation enables to interpolate the coupling ray theory results within ray
cells and to use the coupling ray theory in all applications where we have used
the standard ray theory up to now.

The
review of the coupling ray theory for S waves was presented by Bulant &
Klimeš (2012: S-wave coupling in heterogeneous anisotropic media, In: Kolman,
Berezovski, Okrouhlík & Plešek: Advanced Modelling of Wave Propagation in
Solids, Institute of Thermodynamics ASCR, Prague, Czech Republic, pp. 35-36).

**Ray-based Born approximation**

Šachl
(2012: Effect of caustics on the ray-based Born approximation, In: Seismic
Waves in Complex 3-D Structures, Report 22, Dep. Geophys., Charles Univ.,
Prague, pp. 55-82) continued his work on the ray-based first-order Born
approximation, studied the problems with caustics corresponding to the incident
ray-theory wave field or to the ray-theory Green tensor from a receiver, and
demonstrated the considerable improvement of the accuracy of the reflected wave
containing a caustic if the reflected wave is calculated by the Born
approximation. Šachl (2012: Born and ray-theory seismograms in 2D heterogeneous
isotropic models, In: Seismic Waves in Complex 3-D Structures, Report 22, Dep.
Geophys., Charles Univ., Prague, pp. 83-112) then presented his final P-P Born
scattering seismograms.

**Structural seismology**

It
was determined how the perturbations of a generally heterogeneous isotropic or
anisotropic structure manifest themselves in the wave field, and which
perturbations can be detected within a limited aperture and a limited frequency
band (Klimeš, 2012: Sensitivity of seismic waves to structure, Stud. geophys.
geod., 56, 483-520). Perturbations of
elastic moduli and density may be decomposed into Gabor functions. The wave field scattered by the perturbations
is then composed of waves scattered by individual Gabor functions. If a short-duration broad-band incident wave
field with a smooth frequency spectrum is considered, the wave scattered by one
Gabor function is composed of only several Gaussian packets with uniquely
defined frequencies and directions of propagation. We can thus evaluate to which properties of
the structure the recorded wave field is sensitive. The derived approximate solution of the
forward scattering problem may be utilized in designing the migration algorithm
based on true linearized inversion of the complete set of seismograms recorded
for all shots.

The
theory describing the sensitivity of seismic waves to the geological structure
together with a numerical example were demonstrated by Klimeš (2012:
Sensitivity Gaussian packets, In: Kolman, Berezovski, Okrouhlík & Plešek:
Advanced Modelling of Wave Propagation in Solids, Institute of Thermodynamics
ASCR, Prague, Czech Republic, pp. 71-72).

Jechumtálová
& Bulant (2012: Effects of 1-D versus 3-D velocity models on moment tensor
inversion in the Dobra Voda locality at the Male Karpaty region, Slovakia, In:
Seismic Waves in Complex 3-D Structures, Report 22, Dep. Geophys., Charles
Univ., Prague, pp. 17-27) presented their results obtained during the
cooperation with Slovak industrial partner ProgSeis within the framework of the
European Commission's FP7 project "Advanced Industrial Microseismic
Monitoring". They applied the software
developed within the SW3D Consortium to smoothing 1-D and 3-D velocity models
of the Dobrá Voda locality, and to the calculation of ray-theory amplitudes
which they then use within the moment tensor inversion using the software
developed by the group lead by Jan Šílený at the Institute of Geophysics,
Academy of Sciences of the Czech Republic. Klimeš (2012: Resolution of prestack
depth migration, Stud. geophys. geod., 56, 457-482) derived that, for a given
source, the migrated section is the convolution of the reflectivity function
with the corresponding local resolution function, or the convolution of the
spatial distribution of the weak-contrast displacement reflection-transmission
coefficient with the corresponding local resolution function.

Bucha
(2012: Kirchhoff prestack depth migration in 3-D simple models: comparison of
triclinic anisotropy with simpler anisotropies, Stud. geophys. geod., 56,
533-552) demonstrated the behaviour of the 3-D Kirchhoff prestack depth
migration in the presence of triclinic anisotropy. He then studied the effects of simplified or
incorrectly estimated anisotropy upon the migrated image.

Bucha
(2012: Kirchhoff prestack depth migration in velocity models with and without
gradients: Comparison of triclinic anisotropy with simpler anisotropies, In:
Seismic Waves in Complex 3-D Structures, Report 22, Dep. Geophys., Charles
Univ., Prague, pp. 29-40) demonstrated the behaviour of the 3-D Kirchhoff
prestack depth migration in the presence of triclinic anisotropy and vertical or
horizontal velocity gradients, and studied the effects of incorrectly estimated
anisotropy and of simple heterogeneity upon the migrated image.

**CD-ROM with SW3D software, data and
papers**

Compact
disk SW3D-CD-16 (Bucha & Bulant, 2012: SW3D-CD-16, In: Seismic Waves in
Complex 3-D Structures, Report 22, Dep. Geophys., Charles Univ., Prague, pp.
183-184) contains the revised and updated versions of the software developed
within the consortium research project "Seismic Waves in Complex 3-D Structures"
(SW3D), together with input data used in various calculations. Compact disk SW3D-CD-16 also contains over 430
complete papers from journals and from the SW3D consortium research reports,
and 3 books by V. Červený. The software and papers from compact disk SW3D-CD-16
can be found at "http://sw3d.cz".

**Geodynamics (reported by Ondřej
Čadek)**

**Planetology**

In the field of
planetology, attention has been paid to icy satellites with special emphasis on
thermal stability of Enceladus. Using a fully consistent 3d spherical model of
thermal convection driven by tidal heating, Běhounková et al. (2012)
demonstrated that the present day tidal heat production on Enceladus is not
sufficient to explain the heat flux observed at the south pole of the body.
They suggested that the present day activity is a consequence of enhanced
eccentricity in the past which led to intense melting and disruption of the lid
due to volumetric changes in the ice. Kalousová et al. (2012) carefully tested different membrane approximations used to
simulate elastic deformation of single-plate terrestrial planets. Besides the
shells of constant thickness, traditionally used in planetology studies, they
also considered models with uneven thickness and they demonstrated the limits
of various thin shell approximations. The role of elastic lithosphere on Mars
was also studied in the paper by Golle et al. (2012) where the 3d spherical
convection simulations were combined with elastic lithosphere deformation to
estimate the dynamic topography of the planet.

Benešová and Čížková (2012) studied the geoid and
topography of Venus generated by various models of thermal convection to
determine possible viscosity structure of the Venus mantle. They found that the
profile proposed by Pauer et al. (2006) is still acceptable and no thick
lithosphere is needed to explain the topography and geoid data.

**Tectonophysical modeling**

Maierová et al.
(2012a) examined the influence of variable thermal properties on the thermal
state of a subducting slab in the top

**Electromagnetic induction research**

In the area of EM
induction modeling, Velímský et al. (2012) concluded the study of detectability
of large lateral variations of conductivity in D" by means of time-domain

**Earth’s lower mantle dynamics**

Čížková et al.
2012 used the lower-mantle sinking speed of lithosphere subduction remnants as
a unique internal constraint on modeling the viscosity profile. Performing a
series of elaborate dynamic subduction calculations spanning a range of
viscosity profiles, they selected such profiles that predict the inferred
sinking speed of 12 ± 3 mm/yr. This modeling showed that sinking speed is very
sensitive to lower mantle viscosity. Good predictions of sinking speed were
obtained for nearly constant lower mantle viscosity of about 3-4×10^{22}
Pa s. Viscosity profiles incorporating a viscosity maximum in the deep lower
mantle only lead to a good prediction in combination with a weak postperovskite
layer at the bottom of the lower mantle, and only for a depth average viscosity
of 5×10^{22} Pa s.

Androvičová and
Čížková (Studia Geoph. Geod., accepted) studied the processes within subduction
zones and their influence on the plate dynamics. Besides control parameters
related to the upper mantle describing the composite rheology including
diffusion creep, dislocation creep and stress limiter or Peierls creep, they
also considered the effect of viscosity contrast across the