Development of computational methods

A new hybrid method for computation of the P-SV seismic motion in inhomogenous attenuating local structures with flat free surface has been developed (Zahradník & Moczo 1996). The two-step method combines the discrete-wavenumber (DW) and finite-difference (FD) methods. In the first step, the DW method is used to calculate the source radiation and wave propagation in the one-dimensional (1D) background medium that serves to model path between the source and local surface structure. The local surface structure itself is not included in the model in the first step. The DW method was chosen because it enables to calculate the radiated wavefield from dislocation sources accurately and efficiently. Principally, use of other suitable methods is possible. During the first step the complete wavefield (that is a superposition of the radiated wavefield plus wavefield reflected at the free surface) is recorded along two excitation lines that may create three sides of a rectangle that would surround the local inhomogeneity. In the second step, the FD method is used to compute wave motion in the local inhomogeneity. The computational region usually is smaller than that in the first step. The wavefield recorded during the first step is applied along the excitation lines. The source is not directly included in the second step (it is included in the recorded wavefield applied at the excitation lines).
     The hybrid method enables to compute seismic ground motion for such source-local structure configurations (e.g., the case of a distant source and complex surface sedimentary structure) that could not be computed by a single method due to very large computer time and memory requirements.

While the previous method is applicable to media with a flat free surface, the free-surface topography often should be included since it may have strong influence on seismic ground motion. Therefore, Moczo, Bystrický, Kristek, Carcione & Bouchon (1997) presented a generalization of the above method. Their hybrid approach combines the DW, FD and finite-element (FE) methods. It is designed for computation of the P-SV seismic motion in inhomogeneous attenuating local geologic structures with the free-surface topography. The role of the DW method is the same as in the above described DW-FD method. The difference is in the second step where, instead of the FD method, the combined FD-FE algorithm is used to compute seismic motion in local surface topographic/sedimentary structure. The FE method is used to cover fully or partially (e.g., in a narrow strip along the free surface) the topographic feature while the FD method is applied to a major part of the computational region. The FE method is applied along the free surface in order to eliminate principal problem of the FD method to satisfy the traction-free condition in a sufficiently accurate and stable manner. The FD method is applied to a major part of the model in order to avoid large computer time and memory that would be required by use of the FE method for the whole model.
     In developing the FD-FE algorithm for a viscoelastic medium the attenuation corresponding to rheology of two generalized Maxwell bodies was incorporated into the standard FE formulation. A time-integration scheme for the FD-FE algorithm was also developed.
     The FD-FE algorithm is general and can also be used without two-step hybrid procedure that includes the DW method if the wavefield excitation is solved within the FD-FE algorithm.
     A strip of finite elements was shown as a suitable transition zone between the h x h and 2h x 2h FD spatial grids.

Moczo, Kristek & Lucká (1998) and Moczo, Lucká, Kristek & Kristeková (1999) presented a 2^nd-order finite-difference scheme for modeling seismic wave propagation and seismic ground motion in three-dimensionally (3D) inhomogeneous media. The scheme is based on the displacement formulation. Contrary to the classical displacement FD schemes the presented scheme makes use of effective material parameters determined as harmonic averages between neighboring grid points. Such averaging was well-known and used for modeling the SH waves. Zahradník (1995) suggested a new approximation of the second mixed spatial derivative that is necessary in the P-SV and 3D displacement FD schemes. The presented 3D scheme makes use of Zahradník’s approximation.
     The scheme was shown to be very accurate in media with a /b < 2 and not very high velocity contrast. In such media, the scheme was shown capable to account for a position of an internal material discontinuity more accurately than recent velocity-stress and displacement-stress staggered-grid schemes. This again shows that none of the existing FD schemes is the best and universal scheme for all possible problem configurations.

A general optimization technique for the 3D FD modeling of seismic wave propagation and earthquake ground motion is presented. Applications of the 3D FD modeling to large sedimentary basins require very large computer memory if the modeling covers frequencies up to 1 Hz and larger. Usually, a required large memory is not available. Therefore, the FD algorithms and codes have to be memory-optimized.
     The combined memory optimization (CDMO) developed by Moczo, Kristek, Kristeková & Lucká (1998), Moczo, Kristek & Lucká (1998) and Moczo, Lucká, Kristek & Kristeková (1999) naturally comprises core memory optimization and disk memory optimization.
     Core memory optimization (presented recently by Graves 1996) is based on keeping only a limited number of grid planes in core memory at one time. For such a subset a maximum possible number of time updates is performed. The subset of planes repeatedly moves throughout the entire model space until a desired time window is computed. As the subset of planes repeatedly moves throughout the model space, displacement values (or, generally, wavefield characteristics) are successively (plane by plane) and periodically overwritten in disk memory. While the core memory optimization reduces problem with core memory, it may impose considerable problem with disk memory since this is used instead of core memory. In the case of realistic large-scale models the size of required disk space and number of the I/O operations can be too large. Large number of the I/O operations is a serious problem and creates a bottleneck of the computations. Moreover, subroutines performing the I/O operations cannot be parallelized, though a major part of the FD codes can be.
     Therefore, CDMO combines the core memory optimization with disk memory optimization. First, the discrete wavelet transform is applied to the two-dimensional array of the displacement (or particle velocity) - component values in a grid plane that is to be stored in disk. The wavelet transform decreases an information entropy of the array. A data compression is then applied to the set of the wavelet coefficients. Consequently, only relatively small streams of zeros and ones are written and stored in disk.
     The combined memory optimization significantly reduces memory requirements and allows for balanced use of core and disk memory. It is applicable to any explicit FD scheme on a conventional or staggered grid. It makes the FD modeling of large-scale problems and inclusion of a realistic attenuation more affordable. This was clearly demonstrated in the simulation of the Kobe 1995 mainshock (Kristek, Moczo, Irikura, Iwata & Sekiguchi 1998).

Numerical modeling of anomalous seismic ground motion

Numerical modeling of seismic response of the local geologic structure beneath the colosseum in Rome, Italy, (Moczo, Rovelli, Labák & Malagnini 1995 and Moczo, Rovelli & Labák 1995) indicated that a 2D resonance can develop in sedimentary valleys that do not satisfy Bard & Bouchon’s (1985) existence condition. Therefore, an extensive numerical investigation of a 2D antiplane resonance in certain types of surface geologic structures was carried out. The models included closed sediment-filled valleys in a homogeneous halfspace, closed valleys embedded in a horizontal surface layer, and trough at the bottom of the horizontal surface layer.
     It was found that a 2D resonance can arise in the valleys embedded in a medium with a horizontal surface layer (whose thickness is a half the maximum valley depth), even in the case when the valley-layer velocity contrast is well below Bard & Bouchon’s existence value.
     The fundamental and first higher modes are not much sensitive to the presence of the surface layer whose thickness is equal to or smaller than half the maximum valley depth and whose shear-wave velocity is larger than that in the valley and smaller the velocity in the basement.
     The differential motion due to the fundamental and first higher modes and the spectral amplification due to the first higher mode are more sensitive to the valley shape ratio and the shape of the valley than to the valley-basement velocity contrast if the contrast is high enough.
     Compared to the maximum spectral amplification, the maximum time-domain differential motion due to the fundamental mode is much less sensitive to the valley-basement velocity contrast. The twice smaller valley-basement contrast implies approximately twice smaller spectral amplification, at the corresponding resonant frequencies, but it affects only little the differential motion. This suggests that two valleys with very different levels of spectral amplification may be „comparably dangerous" due to close maximum time-domain differential motion.
     A simple trough at the bottom of the horizontal surface layer can give rise to the fundamental mode of a 2D resonance whose frequency, spectral amplification, and the maximum time-domain differential motion are very close to those in the closed sediment valley.
     The computations confirm that the resonant phenomena are to be expected in many configurations of sediment valleys and basins. The likelihood of the resonance is relatively high since the velocity contrast that determines the occurrence of the resonance seems to be the contrast between the sediments and the bedrock below the valley/basin.

Moczo, Bystrický, Kristek, Carcione & Bouchon (1997) and Kristek, Moczo & Bystrický (1998) numerically demonstrated an effect of a topography on seismic ground motion in a neighboring sedimentary valley. In most numerical studies the seismic ground motion in sedimentary valleys and basins has been studied without inclusion of neighboring topography. However, most of sedimentary valleys and basins is at least partly surrounded by mountain ranges or ridges.
     Numerical simulations of the seismic response of the sediment valley with and without neighboring ridge show that the valley response may be considerably affected by the presence of the ridge. This implies that an effect of the neighboring topography should be taken into account in both numerical simulations and interpretations of the observed earthquake ground motion across the sedimentary valley.

The January 17, 1995 Hyogoken-Nanbu (Kobe) earthquake of a moderate magnitude (M_s=6.8) has occurred. Despite its moderate size the earthquake was the most destructive in Japan since the 1923 Kanto earthquake. An interesting and dramatic feature of the damage distribution was a relatively narrow damage belt about 1 km from the fault. It is very likely that the coupling of the source-directivity effect and basin-edge effect caused a pronounced damage-pattern irregularity. While such a qualitative explanation is reasonable and acceptable a quantitative ground-motion simulations performed so far are unsatisfactory. Therefore, the Japanese working group on effects of surface geology organized Kobe simultaneous simulation experiment. The goals of the experiment were recognition of status for theoretical modeling of strong ground motion and understanding the strong ground motion characteristics. 19 teams from around the world participated in the experiment (Moczo & Irikura, in press).
     Kristek, Moczo, Irikura, Iwata & Sekiguchi (1998) presented finite-difference simulation of the ground motion. A model of the medium used for the simulation was that constructed by Iwata et al. (1998) on the basis of all available geophysical and geologic data. The three-dimensional model covers western part of the Osaka basin since the goal was to simulate motion for the Kobe region. Dimensions of the model are approximately 57, 13 and 27 km. The sedimentary basin is modeled by three layers with interfaces geometrically conformable with the sediment-basement interface. For simulation of the rupture process a new kinematic fault model by Sekiguchi et al. (1998) was used. The model has five segments with the total number of 310 subfaults. Each subfault was modeled by a point dislocation source. Slip velocity of each point source was modeled as a superposition of six time windows.
     A 4th-order displacement-stress FD scheme was used to perform simulation. Due to very large computer time and memory requirements it was necessary to use a discontinuous spatial grid and apply combined memory optimization.
     Simulated velocigrams do not match the recorded velocigrams. It is likely that uncertainties in the models of the basin edge and fault are responsible for disagreement.

ANALYSIS OF SEISMIC HAZARD

Seismic activity on the territory of Slovak Republic is not very high but certainly is not negligible in terms of seismic hazard. Need of seismic hazard analysis is underlined by the fact that nuclear power plants, large water structures and other important facilities are in operation.
     The research in the seismic hazard was focused on the following topics: investigation of historical earthquakes, analysis of macroseismic data, investigation of regional attenuation, seismic hazard analysis for the territory of Slovakia and for the Bohunice nuclear power plant site.

Investigation of historical earthquakes

Data on historical earthquakes is of crucial importance for the seismic hazard assessment in Slovakia. The June 5, 1443, May 25, 1443 and 1441 Central Slovakia and January 15, 1858 Žilina earthquakes were investigated. The 15^th century Central Slovakia earthquakes were candidates for the biggest earthquakes in the Western Carpathians (Western Carpathians cover the largest part of Slovakia). The January 15, 1858 Žilina earthquake is the first earthquake on the territory of Slovakia for which a systematic collection and analysis of the data was performed by earthquake contemporary researchers. However, epicentral and site intensities in the basic descriptive catalogues and in the Atlas of isoseismal maps for Central and Eastern Europe were inconsistent.
     The methods of historical science were used in the investigation of the earthquakes (see for example Stucchi 1993).
     The analysis of ten earthquake contemporary sources for the 15^th century Central Slovakia earthquakes has been performed by Labák, Broueek, Gutdeutsch & Hammerl (1996) and Labák (1996) in two steps: 1. the establishing of the family tree including the new sources found in the archives in Slovakia, Czech Republic and Austria, 2. transcription, source criticism and interpretation of the sources. It was found that the 1441 and May 25, 1443 events are fake earthquakes. All the estimated intensities of the June 5, 1443 event are less than 9⁰ EMS-92. The sources were good enough for a new intensity estimation only for nine localities. The nine intensity data points allowed only a poor determination of the epicenter for the June 5, 1443 earthquake.
     The analysis of the January 15, 1858 Žilina earthquake was performed by Labák & Hammerl (1997) and Labák, Hammerl & Gutdeutsch (1998). The family tree was established from the catalogue sources and from the retrieved Jeitteles’ collection (available in the Library of the Austrian Academy of Sciences), which contains 171 contemporary earthquake sources. The earthquake contemporary sources in the basic descriptive catalogues and the documents from the Jeitteles’ collection were analyzed. The supplementary character of the primary sources was found and more than 600 localities were identified. For damage estimation unique questionnaire data was used. The data was found in the Jeitelles´ collection. The EMS-98 scale was used for the estimation of the site intensities. Estimated site intensities were compared with the intensity estimations in the basic descriptive catalogues.

Analysis of macroseismic data

In 1998 a new version of the European Macroseismic Scale (EMS) was issued. Labák, Moczo, Kristek, Bystrický, Cipciar & Bednárik (1999) analyzed the consistency of the recently used Slovak and Czech macroseismic questionnaires with the scale and analyzed macroseismic data of several earthquakes using the EMS-98 scale.
     EMS-98 describes effects on humans, objects and nature, and damage to buildings in the form of a plain text for each intensity degree. It was pointed out that this form of the scale is not user-friendly either for the consistency analysis of the questionnaires or for the intensity estimation. Therefore, a new graphic form of the EMS-98 scale was developed. The arrangement of the graphic form of the scale and definition of the quantities is the same as in the original form of the scale. The effects on humans, objects and nature are displayed in the form of tables. The tables include the size of the effects for all intensities. The definition of damage to buildings is displayed in the form of the vulnerability class vs. damage grade table for each intensity degree.
     The graphic form of the EMS-98 scale was used for the intensity estimation for two recent earthquakes - the April 12, 1998 Slovenia and the September-October 1997 Umbria-Marche earthquakes. The Slovak and Czech questionnaire data was used for the Slovenian earthquake and the damage data collected by ESC WG Macroseismology was used for the Umbria-Marche earthquakes.
     The use of the proposed graphic form of the EMS-98 scale enabled to identify inconsistencies of the old Slovak questionnaire (originally proposed for the MSK-64 scale) with the new EMS-98 scale. A new Slovak macroseismic questionnaire was proposed. The new questionnaire is consistent with the EMS-98 scale. It consists of 24 questions clustered into 5 groups - place of the observation, earthquake shaking and sound, effects on people, effects on objects, nature or animals, and damage to buildings.

Investigation of regional attenuation

The macroseismic observations are the only data on moderate to strong earthquakes in the Western Carpathians. Bystrická & Labák (1996) and Bystrická, Labák & Campbell (1997) investigated the attenuation of macroseismic intensity. Macroseismic observations within 134 km from the epicenter were processed for 38 crustal earthquakes with epicentral intensities between 4 and 8-9° MSK-64. First, the coefficients in the attenuation relationship I-I₀ = c₁ + c₂ log(R) + c₃ R + e were determined (I₀ is the epicentral intensity, I intensity at the epicentral distance R, and e is a random error of regression analyses with mean of 0 and standard deviation of s ). The epicentral distance R was defined in three different ways: isoseismal radius determined in one of 12 directions, mean value of isoseismal radii, and epicentral distance of intensity data point. It was found that while the shapes of the attenuation curves for the first and third types of distances are the same (the only difference being in absolute values), they differ significantly from that for the second distance. In order to check the dependence of attenuation on I₀, R, and azimuth and thus the assumption of the above attenuation relationship, the distribution of residuals was analyzed. The analysis showed that the attenuation relationship I = c₁ + c₂ log(R) + c₃ R + + c₄I₀ + e , much better fits the observed data that the previous one. It predicts considerably different attenuation than the previous relationship. The difference may be as large as 1° MSK-64.
     It was pointed out that only the attenuation relationships with the same definitions of epicentral distances should be used in comparing attenuation relationships. It was found that the attenuation curves for the Western Carpathians have similar shapes as those for the San Andreas Province and Balkan region 1 and 3.

Seismic hazard analysis for the territory of Slovakia and Bohunice nuclear power plant site

First cross-border earthquake hazard maps for three Central European countries, the Czech Republic, Poland and the Slovak Republic within the Global Seismic Hazard Assessment Program (GSHAP) were prepared by Schenk, Schenková, Kottnauer, Guterch & Labák (1996a) and Schenková, Schenk, Kottnauer, Guterch & Labák (1997). These preliminary hazard maps were prepared in terms of macroseismic intensity for the 475- and 1000-year return periods. Final hazard maps for the three countries (Schenk, Schenková, Kottnauer, Guterch & Labák, 1998) were prepared in terms of peak ground acceleration and macroseismic intensity for the 475-year return period.

Seismic stations

Until January 1998, the Slovak national network operated by Geophysical Institute (GPI), Slovak Academy of Sciences, consisted of 7 seismic stations. Seismic stations Bratislava (ZST), Šrobárová (SRO), Hurbanovo (HRB) and Skalnaté Pleso (SPC) were registered in ISC. Three other stations, Modra (MOD), Vyhne (VYH) and Košice (KOS) have not been registered yet. In the period 1995-1998, most of the stations underwent a modernization. In June 1997, 3 broad-band channels were added to the existing 3 short-period channels in Bratislava (ZST). In November 1997, digital channels were established in Šrobárová (SRO) to work in parallel with the 3 analog registration channels until September 1998, when the analog registration was switched off. On the 13 January 1998, the vertical short-period component analog registration at the station Skalnaté Pleso (SPC) was terminated and the station was closed.
     On 1 December 1996, company Progseis in cooperation with GPI deployed three seismic stations of the new Mochovce NPP (EMO) local seismic network. During the first half of 1997, four stations were added to complete the local network. Since January 1998, the network of 7 stations is in regular operation.
     During the period 1995-1998, Progseis also operated 6 seismic stations of the Bohunice NPP (EBO) local seismic network.
     Currently, the Slovak national network includes 6 seismic stations: Bratislava (ZST), Šrobárová (SRO), Hurbanovo (HRB), Modra (MOD), Vyhne (VYH) and Košice (KOS). With the exception of the historic Hurbanovo (HRB) station, all of them are equipped with 3- component short-period velocimeters and digital registration. The only station with broad-band instruments is Bratislava (ZST). The EBO network consists of 6 stations with 3-component short-period velocimeters and digital registration. The EMO network consists of 7 stations with 3-component short-period velocimeters and digital registration.
     All the data supplied by the Slovak national network and selected data from the local networks is processed in the headquarters of GPI in Bratislava.
     The main interest of the GPI is to record and analyze earthquakes with epicenters and/or macroseismic effects on the territory of Slovak Republic. During the period 1995-1998, the Slovak national network recorded 27 such events. 6 of them were also observed macroseismically.

Detection capability of selected seismic stations in Central Europe

Kristeková & Skáeiková (1997) determined the 50% and 90% P-wave detection thresholds of 3 Austrian (KMR, OGA, VKA), 2 Czech (KHC, PRU), 5 German (BRG, CLL, HOF, MOX, WET), 1 Hungarian (BUD) and 3 Slovak (SPC, SRO, ZST) seismic stations for four intervals of epicentral distances by a direct method using the maximum likelihood technique. The USGS-NEIC Earthquake Data Reports covering the period from January 1990 to November 1994 were used as the reference system. The differences in both the 50% detection threshold MB50 and 90% detection threshold MB90 between the best and the worst seismic stations are about one m_b magnitude unit for all investigated intervals of epicentral distances. The sequences of seismic stations according to MB50 differ from those according to MB90. MB50 was found more suitable for comparing the detectability of the seismic stations using the direct method. The detection thresholds estimated using direct method are less accurate for seismic stations with lower detection capability. Seismic stations Kašperské Hory (KHC, Czech Republic) and Collmberg (CLL, Germany) are the stations with the best detection capabilities. Hungarian seismic station BUD as well as Austrian stations are among the stations with lower detection capabilities. The group of German seismic stations displays a large scatter in quality. The Czech seismic stations belong to the best stations. The Slovak seismic stations rank among those with better-than-average detectability.

Theory of thin elastic plate (Karner & Watts 1983) was applied for study of the lithospheric flexure (regional isostasy) beneath the outer Western Carpathians (Bielik 1995a). Comparison of calculated, theoretical deflection curves and the topographic profiles passing across the Western Carpathian belt showed that the lithosphere behaves elastically and the flexural bulge of topography can be described in terms of the vertical force and bending moment. The reason of the flexure of the subducted European platform lithosphere is the weight of the thrust sheets and nappes within the central Western Carpathian belt. It provides genetic relationship between the emplacement of the thrust sheets (nappes) during Alpine orogenesis and the synchronous development of the outer Western Carpathian foredeep from external to active part of the belt.
     Bielik & Ursíny (1997) and Ursíny & Bielik (1997) numerically and analytically demonstrated the influence of the shape and position of a load acting on the elastic plate both freely supported at its ends and embedded at its end into the wall. Bielik (1995d) also calculated the gravitational effect over the model representing collision orogens, which was suggested by Royden (1993). The model is characterized by a asymmetric gravity low and high. This positive - negative gravity anomaly couple is associated with deep - seated anomalous zones: elevation of the upper mantle beneath the flexural bulge and crustal root beneath the collision orogen.

Gravity and local isostasy

Calculation of a simple density model in local isostatic equilibrium provides a clue to analysis of observed gravity anomaly (Lillie 1991; Lillie, Bielik, Babuška & Plomerová 1994). The method is capable to offer and show the contributions of main anomalous layers (zones) to the free-air and Bouguer anomalies. Based on this approach the long - wavelength gravity anomalies over the different types of continental lithosphere in Europe were studied (Bielik 1995c; Bielik, Dyrelius & Lillie 1995, 1996; Bielik 1998a,b; Ádám & Bielik 1998). The Western and Eastern Carpathians, the Eastern Alps and the Scandinavian Caledonides represented continental collision regions and the Pannonian basin and its the Békés subbasin characterized extensional type of continental lithosphere. In spite of different evolution of the lithosphere in studied areas all results indicated clearly that configuration of the lithosphere - asthenosphere boundary is an important component of the observed long-wavelength gravity anomalies. It means that the lithosphere - asthenosphere boundary beneath the European continent is also evidenced as density boundary. Density contrast of -0.03 g cm^-3 between asthenosphere and lower lithosphere was determined. The gravity effect of the asthenosphere must be taken into account in modelling long - wavelength gravity anomalies. Especially in the regions where the relief of this boundary is large. Based on density modelling in local isostasy in the Scandinavian Caledonides (Bielik, Dyrelius & Lillie 1995, 1996) the fundamental contradiction between gravity and seismic data was removed. Incorporation the lithosphere - asthenosphere boundary allowed to explain the Scandinavian Caledonian gravity low without an existence of prominent Moho root beneath the mountain elevation, as primarily inferred from seismic data along the Blue Road profile.

Density models in the Carpatho - Pannonian region

Understanding the major contributions for a local isostatic situation helped us to analyze the problems of mass lithospheric distribution and strength in terms of deviation from local isostasy. 2 1/2 D and 3D density modelling was applied for calculation of the lithospheric density distribution in the Western Carpathians (Bielik 1995b; Bielik 1998a), the Eastern Carpathians (Bielik & Mocanu 1998) and the Békés basin (Bielik 1998b).

Integrated application of geophysical and geological studies

Ádám A., Bielik M., 1998. The crustal and upper-mantle geophysical signature of narrow continental rifts in the Pannonian basin. Geophys. J. Int., 134, 157-171.

Bard P.-Y., Bouchon M., 1985. The two-dimensional resonance of sediment-filled valleys. Bull. Seism. Soc. Am., 75, 519-541.

Bezák V., Šefara J., Bielik M., Kubeš P., 1995. Structure of the lithosphere of the Western Carpathians: geophysical interpretation. Mineralia Slovaca, 27, 169-178 (in Slovak).

Bezák V., Šefara J., Bielik M., Kubeš P., 1998. Models of the Western Carpathian Lithosphere. In: Geological evolution of the Western Carpathians. Mineralia Slovaca, Corporation-Geocomplex, a.s., Geofy-zika Bratislava and Geological Survey of Slovak Republic, Bratislava, pp. 25-34.

Bielik M., 1995a. Estimation of the effective elastic thickness and flexure rigidity in the Western Carpathians. Contr. Geophys. Instit. Slov. Acad. Sci., 25, 81-93.

Bielik M., 1995b. Continental convergence in the Carpathian region by density modelling. Geologica Carpathica, 46, 3-12.

Bielik M., 1995c. Importance of the lithosphere-asthenosphere boundary in gravity modelling lithosphere structure. In: Proc. of the 1^st Slovak Geo-physical Conference. Geoph. Inst. Slov. Acad. Sci., Bratislava, 16-20.

Bielik M., 1995d. Creation of foredeep basins by flexural loading of the foreland lithosphere - analysis of the gravity field. In: Proc. of the 1^st Slovak Geophysical Conference, May 31, 1995, Geoph. Inst. Slov. Acad. Sci., Bratislava, 12-15.

Bielik M., 1998a. Analysis of the gravity field in the Western and Eastern Carpathian junction area: density modelling. Geologica Carpathica, 49, 75-83.

Bielik M., 1998b. 3D interpretation of the gravity field in the Békés basin. Contr. Geoph.& Geod., 28, 1-8.

Bielik M., Dyrelius D., Lillie R. J., 1995. Caledonian lithosphere - gravity structure and comparison with Carpathian lithosphere. Contr. Geophys. Inst. Slov. Acad. Sci., 26, 72-84.

Bielik M., Dyrelius D., Lillie R. J., 1996. Interpretation of long-wavelength gravity anomalies mainly in the Western Carpathians and partly in the Scandinavian Caledonides and the Eastern Alps. Österreeichische Beiträge zu Meteorologie und Geophysik, 14, 13-27.

Bielik M., Kohút I., Kostecký P., 1998. Preliminary results of the stress field calculation for extensioanl basins: pure shear model. Contr. Geoph. & Geod., 28, 139-146.

Bielik M., Mocanu V., 1998. Deep lithosphere structure of the Eastern Carpathians: density modelling. Contr. Geoph. & Geod., 28, 95-100.

Bielik M., Šefara J., Bezák V., Kubeš P., 1995. Deep-seated models of the Western Carpathians. In: Proc. of the 1^st Slovak Geophysical Confe-rence, May 31, 1995, Geoph. Inst. Slov. Acad. Sci., Bratislava,
7-11.

Bielik M., Ursíny M., 1997. Flexure of the elastic plate. Contr. Geophys. Inst. Slov. Acad. Sci., 27, 81-93.

Bystrická A., Labák P., 1996. Attenuation relationships for Western Carpathians determined from macroseismic data. In: Data analysis in seismology and engineering geophysics, Kaláb, Z., (ed.), Institute of Geonics AS CR, Ostrava-Poruba, pp. 34-43. (in Slovak)

Bystrická A., Labák P., Campbell K. W., 1997. Intensity attenuation relationships for Western Carpathians and their comparison with other regional relationships. In: Proc. of the 29th General Assembly of the IASPEI, Aug. 18-28, 1997, Thessaloniki, Greece, p. 40. (abstract)

Debski W., Guterch B., Labák P., Lewandowska H., 1997. Earthquake sequences in the Krynica region, Western Carpathians. 1992 & 1993. Acta Geophysica Polonica, 45, pp. 255-290.

Hrušecký I., Bielik M., Šefara J., Kúšik D., 1998. Slovak part of the Danube basin from geological structure to lithospheric dynamics - defined from seismic profiles. Contr. Geoph. & Geod., 28, 205-226.

Iwata T., Sekiguchi H., Pitarka A., Kamae K., Irikura K., 1998. Evaluation of strong ground motions in the source area during the 1995 Hyogoken-Nanbu (Kobe) earthquake. In: Proc. 10^th Japan Earthq. Eng. Symposium (in press).

Karner G. R., Watts A. B., 1983. Gravity anomalies and flexure of the lithosphere at mountain ranges. J. Geophys. Res., 88, 10449-10477.

Kováe M., Bielik M., Lexa J., Pereszlényi M., Šefara J., Túnyi I., Vass D. 1998. The Western Carpathian intramountane basins. In: Geological evolution of the Western Carpathians. Mineralia Slovaca Corporation-Geocomplex, a.s., Geofyzika Bratislava and Geological Survey of Slovak Republic, Bratislava, pp. 43-64.

Kristek J., Moczo P., Bystrický E., 1998. Effect of neighboring topography on seismic motion in the sediment valley. Contr. Geoph. & Geod., 28, 45-51.

Kristek J., Moczo P., Irikura K., Iwata T., Sekiguchi H., 1998. The 1995 Hyogo-ken Nambu, Japan, earthquake simulated by the 3D finite-difference method. In: Special Volume on Simultaneous Simulation for Kobe, Second International Symposium on The Effect of Surface Geology on Seismic Motion, December 1-3, 1998, Yokohama, Japan, pp. 67-74.

Kristek, J., Moczo, P., Irikura, K., Iwata, T., Sekiguchi, H.: The 1995 Kobe mainshock simulated by the 3D finite differences. In: Irikura, K. et al. (Eds.), The Effects of Surface Geology on Seismic Motion, Vol. 3, Balkema, Rotterdam (in press).

Kristeková M., Labák P., (Eds.), 1996. Bulletin of the Slovak seismological stations for the year 1991. Geophysical Institute, Slovak Academy of Sciences, Bratislava, 201 pp.

Kristeková M., Skáeiková I., 1996. Detection thresholds MB50 and MB90 for selected Central European seismic stations. In: Data analysis in seismology and engineering geophysics, Kaláb, Z., (Ed.), Institute of Geonics AS CR, Ostrava-Poruba, pp. 54-62. (in Slovak).

Kristeková M., Skáeiková I., 1997. Detection capability of selected seismic stations in Central Europe. Studia geoph. et geod., 41, 149-163.

Labák P., (Ed.), 1995. Bulletin of the Slovak seismological stations for the year 1990. Geophysical Institute, Slovak Academy of Sciences, Bratislava. 193 pp.

Labák P., 1996. Reinterpretation of the June 5, 1443 Central Slovakia. In: Data analysis in seismology and engineering geophysics, Kaláb, Z., (Ed.), Institute of Geonics AS CR, Ostrava-Poruba, pp. 83-93 (in Slovak).

Labák P., Alivizatos G., 1995. Azimuthally dependent local travel times for the seismic station Železná studnieka. In: Proc. of the 1^st Slovak Geophy-sical Conference, Geophysical Institute, Slovak Academy of Sciences, Bratislava, pp. 185-191.

Labák P., Broueek I., Gutdeutsch R., Hammerl C., 1996. The June 5, 1443 Central Slovakia earthquake. In: Proc. of the ESC XXV General Assembly, Sep. 9-14, 1996, Reyjkjavík, p. 141. (abstract).

Labák P., Bystrická A., Moczo P., Campbell K. W., Rosenberg L., 1998. Preliminary probabilistic seismic hazard assessment for the Nuclear Power Plant Bohunice (Slovakia) site. In.: Bisch, P. et al., Proc. of the 11^th ECEE, Balkema, Rotterdam. (CD-ROM)

Labák P., Hammerl Ch., 1997. Source study of the January 15, 1858 Žilina (Slovakia) earthquake. Annales Geophysicae, 15, Supplement I, Part I, C 179. (abstract).

Labák P., Hammerl Ch., Gutdeutsch R., 1998. Source study of the January 15th 1858 Žilina (Slovakia) earthquake. In: Seismotectonic seminar, May 12th 1998, Geocenter Vienna. (abstract)

Labák P., Kristek J., 1995. Some aspects of compilation of seismological database for the determination of the seismic hazard of a nuclear power plant site. In: New knowledge in seismology and engineering geophysics, Kaláb, Z., (ed.), Institute of Geonics AS CR, Ostrava, pp. 92-97. (in Slovak)

Labák P., Moczo P., Kristek J., Bystrický E., Cipciar A., Bednárik M., 1999. New Slovak macroseismic questionnaire and data analysis using the EMS-98 scale. Contr. Geoph. & Geod., 29, 123. (abstract)

Lillie R. J., 1991. Evolution of gravity anomalies across collisional mountain belts: dues to the amount of continental convergence and underthrusting. Tectonics, 10, 672-687.

Lillie R. J., Bielik M., Babuška V., Plomerová J., 1994. Gravity modelling of the lithosphere in the Eastern Alpine - Western Carpathian - Pannonian Basin region. Tectonophysics, 231, 215-235.

Moczo P., 1998: Introduction to Modeling Seismic Wave Propagation by the Finite-Difference Method. Lecture Notes. Kyoto University, 108 pp.

Moczo P., Bystrický E., Kristek J., 1998. A hybrid method for computation of P-SV seismic motion at topographic structures. Contr. Geoph. & Geod., 28, 52-58.

Moczo P., Bystrický E., Kristek J., Carcione J. M., Bouchon M., 1997. Hybrid modeling of P-SV seismic motion at inhomogeneous viscoelastic topographic structures. Bull. Seism. Soc. Am., 87, 1305-1323.

Moczo P., Irikura K. The Northridge and Kobe simultaneous simulation experiments. In: Irikura, K. et al. (Eds.), The Effects of Surface Geology on Seismic Motion, Vol. 3, Balkema, Rotterdam, (in press).

Moczo P., Kristek J., 1995. Simple finite-difference algorithm on a combined rectangular grid for SH waves. In: Proc. of the 1^st Slovak Geophysical Conference, Bratislava, May 31, 1995, pp. 179 - 184, Geophysical Institute, Slovak Academy of Sciences, Bratislava.

Moczo P., Kristek J., Kristeková M., Lucká M., 1998. Efficient technique for 3D modeling of earthquake ground motion based on the finite-difference method. In.: Bisch, P. et al., Proc. of the 11^th ECEE, Balkema, Rotterdam. (CD-ROM)

Moczo P., Kristek J., Lucká M., 1998. 3D FD modeling of site effects with a combined memory optimization. In: Irikura, K. et al. (Eds.), The Effects of Surface Geology on Seismic Motion, Vol. 2, Balkema, Rotterdam, pp. 939-946.

Moczo P., Labák P., Kristek J., 1995. Spectral amplification and differential seismic motion in surface sedimentary structures. In: New knowledge in seismology and engineering geophysics, Kaláb, Z., (Ed.), Institute of Geonics AS CR, Ostrava, pp. 65-73. (in Slovak)

Moczo P., Labák P., Kristek J., Hron F., 1996. Amplification and differential motion due to an antiplane 2D resonance in the sediment valleys embedded in a layer over the halfspace. Bull. Seism. Soc. Am., 86, 1434-1446.

Moczo P., Lucká M., 1997. Efficient numerical 3-D simulation of seismic wave propagation in complex geological structures. In: Proc. of the International Workshop 'Parallel Numerics 97', pp. 112-117, Zakopane, Poland, September 5-7, 1997.

Moczo P., Lucká M., Kristek J., Kristeková M., 1999. 3D displacement finite differences and a combined memory optimization. Bull. Seism. Soc. Am., 89, 69-79.

Moczo P., Rovelli A., Labák P., 1995. Effects of the lateral heterogeneity beneath Roman Colosseum on seismic ground motion. In: Proc. of the 10^th ECEE, August 28 - September 2, 1994, Vienna, Vol. 1, Duma, G., ed., pp. 377-383. Balkema, Rotterdam.

Moczo P., Rovelli A., Labák P., Malagnini L., 1995. Seismic response of the geologic structure underlying Roman Colosseum and a 2-D resonance of a sediment valley. Annali di Geofisica, 38, 939-956.

Royden L. H., 1993. The tectonic expression stab pull at continental conver-gent boundaries. Tectonics, 12, 303-325.

Schenk V., Schenková Z., Kottnauer P., Guterch B., Labák P., 1996a. Earthquake hazard assessment for the Czech Republic, Poland and Slovakia. In: Proc. of the ESC XXV General Assembly, Sep. 9-14, 1996, Reyjkjavík, p. 81. (abstract)

Schenk V., Schenková Z., Kottnauer P., Guterch B., Labák P., 1996b. Third level seismogeographical regionalisation of the Czech Republic, Poland and Slovakia. Version September 1996. In: Data analysis in seismology and engineering geophysics, Kaláb, Z., (Ed.), Institute of Geonics AS CR, Ostrava-Poruba, pp. 15-21.

Schenková Z., Schenk V., Kottnauer P., Guterch B., Labák P., 1998. Earthquake hazard for the Czech republic, Poland and Slovakia. Contribution to the ILC/IASPEI Global Seismic Hazard Assessment Program. In: Recent Trends in Seismology and Engineering Geophysics, Kaláb, Z., (Ed.) 1998, Institute of Geonics AS CR, April 21-22, 1998, Ostrava-Poruba, Czech Republic, pp. 121-125.

Schenková Z., Schenk V., Kottnauer P., Guterch B., Labák P. Earthquake catalogue for the Czech Republic, Poland and Slovakia. Acta Montana, ser. A (in press).

Sekiguchi H., Irikura K., Iwata T., 1998. Detailed source process of the 1995 Hyogo-ken Nanbu (Kobe) earthquake using near-field strong ground motion data. In: Proc. 10^th Japan Earthq. Eng. Symposium. (in press)

Stucchi M., (Ed.), 1993. Historical investigation of European earthquakes. Part 1. CNR - Istituto di Ricerca sul Rischio Sismico, Milan.

Šefara J., Bielik M., Koneený P., Bezák V., Hurai V., 1996. The latest stage of development of the Western Carpathian Lithosphere and its interaction with the astenosphere. Geologica Carpathica, 47, 1-9.

Ursíny M., Bielik M. 1997. Analytical solution of the flexure of an elastic plate for point and planar loads. Contr. Geophys. Inst. Slov. Acad. Sci., 27, 94-102.

Zahradník J., Moczo P., 1996. Hybrid seismic modeling based on discrete - wavenumber and finite - difference methods. PAGEOPH, 148, 21-38.

Zahradník J., 1995. Simple elastic finite-difference scheme. Bull. Seism. Soc. Am., 85, 1879-1887.

 

Bezák V., Šefara J., Bielik M., Kubeš P. Evolution of the lithosphere in the Western Carpathians. 8^th EUG, March 23-27, 1995, Strassbourg, France.

Bezák V., Šefara J., Bielik M. Complex geophysical - geological study of the lithosphere in the Western Carpathians. New trends in low-frequency geodynamics, October 2-6, 1995, Smolenice, Slovak Rebuplic.

Bezák V., Šefara J., Bielik M. Structure of the crust and Lithosphere in the Western Carpathians. Europrobe Workoshops - PANCARDI, October 21-25, 1995, Stará Lesná, Slovak Republic.

Bielik M., Dyrelius D., Lillie R. J. Gravity effects of the lithosphere in the Carpathian - Pannonian region and Scandinavian Caledonides. EGS XX General Assembly, April 3-7, 1995, Hamburg, Germany.

Bielik M., Šefara J., Tomek E. Geophysical picture of the Western Carpathians. Europrobe Workoshop - PANCARDI, October 21-25, 1995, Stará Lesná, Slovak Republic.

Bielik M., Karner G. Preliminary results of the flexure lithosphere in the Carpathians. New trends in low-frequency geodynamics, October 2-6, 1995, Smolenice, Slovak Rebuplic.

Bielik M. Density models of the continental lithosphere and tectonics in the Western Carpathians. EGS XXI General Assembly, May 6-10, 1996, The Hague, The Netherlands.

Bielik M., Dyrelius D., Lillie R. J. Interpretation of long-wavelength gravity anomalies mainly in the Western Carpathians and partly in the Scandinavian Caledonides and the Eastern Alps. 7. Alpengravimetrie - kolloqium, April 11-12, 1996, Vienna, Austria.

Bielik M., Mocanu V., Ádám A., Corneliu D., Lillie R. J. A preliminary study of gravity field in the Eastern and Southern Carpathians and the narrow continental rifts in the Pannonian Basin. Europrobe Workshop - PANCARDI, September 23-27, 1996, Lindabrunn, Austria.

Bielik M., Mocanu V., Ádám A. Gravity field and its relationship to the crustal and lithospheric structure in the Carpathian Pannonian region. EGS XX General Assembly, April 21-25, Vienna, Austria.

Bielik M. The gravity field of the Eastern part of the Western Carpathians and its geodynamic implications. Europrobe Workshop - PANCARDI, October 20-26, 1997, Krakow - Zakopane, Poland.

Bielik M., Hrušecký I., Kohút I., Kostecký P. Lithosphere structure of the sedimentary basins in the Carpatho - Pannonian region as inferred from interpretation of geophysical data. EGS XXII General Assembly, April 20-24, 1998, Nice, France.

Bielik M., Šefara J., Bezák V., Mocanu V. Correlation of the Western and Eastern Carpathian lithospheric structures. XVI. CBGA Conress, August 30 - September 2, Vienna, Austria.

Bielik M., Zeyen H. Determination of the 2D thermal structure of the lithosphere in the Western Carpathians combining heat flow, Bouguer anomaly and local isostatic elevation. XVI. CBGA Conress, August 30 - September 2, Vienna, Austria.

Bystrická A., Labák P. Attenuation relationships for Western Carpathians determined from macroseismic data. Data analysis in seismology and engineering geophysics, October 8, 1996, Ostrava, Czech Republic.

Bystrická A., Labák P., Campbell K. W. Intensity attenuation relationships for Western Carpathians and their comparison with other regional relationships. 29th General Assembly of the IASPEI, August 18-28, 1997, Thessaloniki, Greece.

Kristek J., Moczo P., Bystrický E. Effect of neighboring topography on seismic motion in the sediment valley. 2^nd Slovak Geophysical Confe-rence, June 18, 1997, Bratislava, Slovak Republic

Kristek J., Moczo P., Irikura K., Iwata T., Sekiguchi H. The 1995 Hyogo-ken Nambu, Japan, earthquake simulated by the 3D finite-difference method. Second International Symposium on The Effect of Surface Geology on Seismic Motion, December 1-3, 1998, Yokohama, Japan.

Kristeková M., Skáeiková I. Detection thresholds MB50 and MB90 for selected Central European seismic stations. Data analysis in seismology and engineering geophysics, October 8, 1996, Ostrava, Czech Republic.

Labák P., Alivizatos G. Azimuthally dependent local travel times for the seismic station Železná studnieka. 1^st Slovak Geophysical Conference, May 31, 1995, Bratislava, Slovak Republic.

Labák P., Kristek J. Some aspects of compilation of seismological database for the determination of the seismic hazard of a nuclear power plant site. New knowledge in seismology and engineering geophysics, April 20, 1995, Ostrava, Czech Republic.

Labák P. Reinterpretation of the June 5, 1443 Central Slovakia. Data analysis in seismology and engineering geophysics, October 8, 1996, Ostrava, Czech Republic.

Labák P., Broueek I., Gutdeutsch R., Hammerl C. The June 5, 1443 Central Slovakia earthquake. ESC XXV General Assembly, September 9-14, 1996, Reyjkjavík.

Labák P., Bystrická A., Moczo P., Campbell K.W., Rosenberg L. Preliminary probabilistic seismic hazard assessment for the Nuclear Power Plant Bohunice (Slovakia) site. 11^th ECEE, September 6-11, 1998, Paris, France.

Labák P., Hammerl Ch. Source study of the January 15, 1858 Žilina (Slovakia) earthquake. XXII EGS General Assembly, April 21-25, 1997, Vienna, Austria.

Labák P., Hammerl Ch., Gutdeutsch R. Source study of the January 15th 1858 Žilina (Slovakia) earthquake. Seismotectonic seminar, May 12th 1998, Geocenter Vienna.

Lankreijer A., Bielik M., Zoetemeijer R., Majcin D. Rheological variation in the Carpathian Lithosphere: Implication for basin evolution. 9^th EUG, March 23-27, 1997, Strassbourg, France.

Lankreijer A., Bielik M. Investigation of Rheology of the lithosphere in the Pancardi system. Europrobe Workshop - PANCARDI, October 20-26, 1997, Krakow - Zakopane, Poland.

Moczo P., Labák P., Kristek J. Spectral amplification and differential seismic motion in surface sedimentary structures. New knowledge in seismology and engineering geophysics, April 20, 1995, Ostrava, Czech Republic.

Moczo P., Labák P., Hron F. Amplification and differential motion due to a 2D resonance in the sediment valleys embedded in a heterogeneous medium. IUGG XXI General Assembly, July 2-14, 1995, Boulder, Colorado, USA.

Moczo P., Kristek J. Simple finite-difference algorithm on a combined rectangular grid for SH waves. 1st Slovak Geophysical Conference, Bratislava, May 31, 1995, Bratislava, Slovak Republic.

Moczo P., Bystrický E., Kristek J.. A hybrid method for computation of P-SV seismic motion at topographic structures. 2^nd Slovak Geophysical Conference, June 18, 1997, Bratislava, Slovak Republic.

Moczo P., Bystrický E., Kristek J., Bouchon M. A hybrid method of computing the P-SV seismic motion at inhomogeneous topographic structures. ESC XXV General Assembly, September 9-14, 1996, Reykjavík, Island.

Moczo P., Bystrický E., Kristek J., Carcione J.M., Bouchon M. P-SV seismic response of topographic/sedimentary structures by hybrid DW-FD-FE method. IASPEI 29th General Assembly, August 18-28, 1997, Thessaloniki, Greece.

Moczo P., Lucká M. Efficient numerical 3-D simulation of seismic wave propagation in complex geological structures. International Workshop 'Parallel Numerics 97', September 5-7, 1997, Zakopane, Poland.

Moczo P., Kristek J., Kristeková M., Lucká M. Efficient technique for 3D modeling of earthquake ground motion based on the finite-difference method. 11th ECEE, September 6-11, 1998, Paris, France.

Moczo P., Kristek J., Lucká M. 3D FD modeling of site effects with a combined memory optimization. The Effects of Surface Geology on Seismic Motion, December 1-3, 1998, Yokohama, Japan.

Schenk V., Schenková Z., Kottnauer P., Guterch B., Labák P. Third level seismogeographical regionalization for the Czech Republic, Poland and Slovakia. ESC 26th General Assembly, Aug. 23-28, 1998, Tel Aviv - Holon, Israel.

Schenk V., Schenková Z., Kottnauer P., Guterch B., Labák P. Earthquake hazard for the Czech republic, Poland and Slovakia. Contribution to the Global Seismic Hazard Assessment Program. 7th International Conference on Natural & Man-Made Hazards: Hazards-’98, May 17-22, 1998, Chania, Crete Isl., Greece.

Schenk V., Schenková Z., Kottnauer P., Guterch B., Labák P. Third level seismogeographical regionalisation of the Czech Republic, Poland and Slovakia. Version September 1996. Data analysis in seismology and engineering geophysics, October 8, 1996, Ostrava, Czech Republic.

Schenková Z., Schenk V., Kottnauer P., Guterch B., Labák P. Final version of the GSHAP map for the Czech Republic, Poland and Slovakia. ESC 26th General Assembly, Aug. 23-28, 1998, Tel Aviv - Holon, Israel.

Schenková Z., Schenk V., Kottnauer P., Guterch B., Labák P. Earthquake hazard for the Czech republic, Poland and Slovakia. Contribution to the ILC/IASPEI Global Seismic Hazard Assessment Program. Recent Trends in Seismology and Engineering Geophysics, April 21-22, 1998, Ostrava, Czech Republic.

Tomek E., Bielik M., Sitárová A. Kolárovo gravity high and its relationship to the Miocene-recent extension of the Danube Basin. 9^th EUG, March 23-27, 1997, Strassbourg, France.

Zeyen H., Bielik M. Integrated lithospheric modelling in the Western Carpathians. EGS XXIII General Assembly, April 20-24, 1998, Nice, France.