Miroslav Novotny - Academia.edu (original) (raw)

Papers by Miroslav Novotny

Journal of Geosciences, 2018

Unlike standard ray-based tomographies, the Depth-Recursive Tomography on Grid (DRTG) method asse... more Unlike standard ray-based tomographies, the Depth-Recursive Tomography on Grid (DRTG) method assesses the travel-time fit at each model grid node using a regular network of refraction rays. This concept allows estimating the lateral resolution achieved in the velocity image that regards the chosen confidence levels and the strength of velocity anomalies. Recently, The DRTG has been applied to the S01 and CEL09 refraction profiles imaging major crustal structures of the Bohemian Massif in enhanced resolution. Now, similar enhanced velocity models are derived along the S04, S02 and S03 profiles mapping the Sudetic and Moldanubian regions. The S02 and S03 and the transverse CEL09 and S04 velocity sections particularly imaged the subsurface of the Moldanubian high-grade belts to the 15-20 km depth. Their common interpretation revealed the signatures of exhumation processes from upper-mantle depths assumed in this region. Particularly, the S02 and S03 sections map large volumes of high-grade metamorphic rocks forming low-velocity (LV) diapirs that are surrounded by 7000-6400 m/s high-velocity (HV) elevations. The S03 section images the coupled HV-LV-HV anomalies beneath the high-grade complexes of the Orlica-Śnieżnik Dome (OSD) and the Góry-Sowie Unit (GSU). The central gradient-free LV (5800-6000 m/s) cores of these triplets apparently correspond to the OSD or GSU felsic granulites/gneisses that ascended to supra-crustal levels. The Bouguer anomaly map suggests that the S02 and S03 profiles intersect the felsic sheets formed along the transverse Sudetic faults. Along the western belt of Moldanubian high-grade rocks, the S02 section revealed an extensive HV body shallowly emplaced beneath the high-grade Gföhl and Ostrong assemblages. Three mid-crustal HV elevations, correlating with local magnetic anomalies, obviously represent the deep sources of this HV mafic body and indicate its autochthonous nature. Finally, the DRTG also detected a shallowly emplaced HV layer beneath the Saxonian Granulite Massif at the S04 section. The mid-crustal HV-LV-HV diapiric triplets and shallowly emplaced HV bodies are likely typical of the high-grade terrains. The observed patterns resulted from contemporaneous intrusion of mafic and, more viscous, felsic magmas during continental collision. The inferred structural features of subduction-exhumation processes are suggested to further constrain their thermo-mechanic modeling.

Optica Acta: International Journal of Optics

Optica Acta: International Journal of Optics

A new series representation of the diffraction field G (u, v) due to the axially symmetrical filt... more A new series representation of the diffraction field G (u, v) due to the axially symmetrical filters is derived. The coefficients of the series are formed by certain scalar products of the pupil function and the Bernoulli polynomials. Unlike the previous representations of the Fresnel diffraction field containing the Lommel functions of two variables, this representation operates only with special functions of one variable. Applying the theory to the focal diffraction patterns G(4'1d1.L, v), L integer, due to the filters with transmissivities periodic with the squared distance from the axis, the previous result [3] directly follows: the focal patterns of any filter approach the Airy pattern if the number of the periods IVl increases. The series coefficients for the Fresnel diffraction fields of the ideal lens and also of the polynomial filter transmissivities are derived. The results are documented for the diffraction fields of the Fresnel and Gabor zone plates.

Surv Geophys, 2011

In the accompanying paper (Part A), depth-recursive tomography was applied to the CEL09 refractio... more In the accompanying paper (Part A), depth-recursive tomography was applied to the CEL09 refraction data. A deblurred P-wave velocity image was obtained down to a depth of 20 km. This paper (Part B) is devoted to the interpretation of the upper-and middle-crustal structures of the Bohemian Massif imaged in the CEL09 section. Because of inherent ambiguity of the refraction method in imaging low-velocity zones, other wellknown results based on other geophysical data sets are also used to independently verify the interpreted velocity features. Comparison with the density and velocity models previously obtained indicates that the presented P-wave velocity image has superior resolution revealing or verifying a number of geological features. The prominent lateral velocity changes encountered in the CEL09 pattern across the imaged crustal section were used to delineate the main terranes and deep regional fault zones such as the Krušné hory Fault, the SW continuation of the Litoměřice Fault Zone, the West and Central Bohemian Shear Zones, the Blanice-Rodl Fault, the Přibyslav-Vitis Fault and the Boskovice-Diendorf Fault. The 450-km-long CEL09 transect reveals seven major deeply rooted high-velocity (HV) anomalies identified as Variscan massifs intruded near or within these deep fault zones. They form buried ridges mostly parallel to the SW-NE trending Variscan strike. Their discovery allows new insights into a number of phenomena such as the West Bohemian earthquake swarms, the Saxothuringian paradox, the character of the Saxothuringian-Barrandian contact zone, the detachment surface due to the slab of the Saxothuringian crust subducting beneath the Teplá-Barrandian zone in the Devonian, the depth extent of the Mariánské-Lázně Complex (MLC) as an equivalent unit of the Zone Erbendorf-Vohenstrauss (ZEV), the subsidence of the Barrandian syncline, the root zones of the Central and South Bohemian Plutons, the accretionary wedge formed along the Moravo-Moldanubian suture and its link with the Gföhl terrane, the Carpathian foreland relief and the subsidence observed in the Vienna Basin.

Mezinárodní seismické experimenty uskutečněné v posledních letech ve střední Evropě studují stavb... more Mezinárodní seismické experimenty uskutečněné v posledních letech ve střední Evropě studují stavbu zemské kůry a svrchního pláště pod touto oblastí. Pro studium hlubinné stavby se využívá seismická refrakční metoda, kdy se registrují seismické vlny generované odpaly a následně je zjišťována rychlost šíření vln v horninovém prostředí. Tyto údaje umožňují zpřesnit naše znalosti o vlastnostech svrchních partií litosféry do hloubek 50-60 km. Úvod V posledních letech se moderní geologicko-geofyzikální výzkum střední Evropy zaměřil mj. na studium zemské kůry a svrchního pláště. Nejvíce informací o hlubinné stavbě poskytuje metoda, založená na interpretaci seismických vln uměle vyvolaných odpaly na zemském povrchu a zaznamenaných pomocí seismických stanic. Sérii moderních seismických experimentů zahájil v devadesátých letech projekt POLONAISE'97, na který navázaly začátkem našeho tisíciletí projekty CELEBRATION 2000, ALP 2002 a SUDETES 2003. Za účasti více než 25 výzkumných institucí z mnoha zemí světa byla odměřena hustá síť seismických profilů, pokrývající střední Evropu (obr. 1). K registraci seismických vln bylo použito přes 1000 mobilních digitálních seismických stanic. Velikost náloží se zpravidla pohybovala od 200 do 400 kg, výjimečně bylo odpáleno 4000 kg i více; největší nálož v Bělorusku byla 15 000 kg. Seismické vlny vybuzené tímto mohutným odpalem bylo možné zaznamenat na sesimických stanicích vzdálených až 600 km. Časoprostorová koordinace experimentů byla zajištěna družicovou navigační službou GPS. Vlastní experiment sestává z odpálení náloží v odpalových bodech s rozestupy přibližně 30 km a následné registrace seismické energie pomocí digitálních stanic rozmístěných podél linií profilů s krokem 3 km. Nasazení velkého počtu stanic, nesrovnatelně většího než při kterémkoli refrakčním experimentu uskutečněném v minulosti v Evropě, umožnilo zásadní inovaci při koncipování terénní části experimentu. Stanice bylo možné rozmístit současně podél několika navzájem se křižujících profilů a tím zaznamenávat jak seismické vlny podél profilu s příslušným bodem odpalu, tak i vlny šířící se ke stanicím na profilech okolních. Tento přístup umožňuje nejen konstrukci standardních 2-D rychlostních řezů podél profilů, ale také 3-D interpretaci získaných dat. Podrobnosti o výše uvedených seismických projektech lze nalézt v [1-5].

In a laterally variable seismic medium, the slowness function s(x,z) can be derived from travel-t... more In a laterally variable seismic medium, the slowness function s(x,z) can be derived from travel-time curves of surface-to- surface refracted waves if the arrival times are interpreted in the form of a two-dimensional function. In the following article two methods are suggested for solving the inverse kinematic problem using a linearized formulation. The arrival times t(p,q) are arranged according to increasing epicentral distance q, and p represents the x-coordinate of the point midway between source and receiver. The first method is based on the Fourier transform of the time function t(p,q) in the variable p. This method can be applied to a system of travel-time curves with epicentral distances small in comparison to the length of the profile interval xp, i.e., q<<xp. The second, grid method interprets recursively the arrival times t(pj,qi)from the smallest epicentral distance to the largest one. The results of one interpretation step are the grid values of the slowness funct...

The interrelation between the Radon wave field extrapolation and integral solutions of boundary v... more The interrelation between the Radon wave field extrapolation and integral solutions of boundary value problems posed for scalar wave equation is studied. Using the stationary phase method it is found that the Radon extrapolator degenerates into the Rayleigh-Sommerfeld solution of the Dirichlet problem in the far-field zone. The derivations are done for the 3-D case, but the 2-D analogues are also mentioned. The practical consequences and advantages of slant-stack representation of space-under sampled noisy data are discussed.

Surveys in Geophysics, 2009

The refraction data from the SUDETES 2003 experiment were used for highresolution tomography alon... more The refraction data from the SUDETES 2003 experiment were used for highresolution tomography along the profile S01. The S01 profile crosses the zone Erbendorf-Vohenstrauss (ZEV) near the KTB site, then follows the SW-NE oriented Eger Rift in the middle part and continues toward the NE across the Elbe zone and the Sudetic structures as far as the Trans-European Suture Zone. To get the best resolution in the velocity image only the first arrivals of Pg waves with minimum picking errors were used. The previous depth-recursive tomographic method, based on Claerbout's imaging principle, has been adapted to perform the linearized inversions in iterative mode. This innovative DRTG method (Depth-Recursive Tomography on Grid) uses a regular system of refraction rays covering uniformly the mapped domain. The DRTG iterations yielded a fine-grid velocity model with a required level of RMS travel-time fit and the model roughness. The traveltime residuals, assessed at single depth levels, were used to derive the statistical lateral resolution of ''lens-shaped'' velocity anomalies. Thus, for the 95% confidence level and 5% anomalies, one can resolve their lateral sizes from 15 to 40 km at the depths from 0 to 20 km. The DRTG tomography succeeded in resolving a significant low-velocity zone (LVZ) bound to the Franconian lineament nearby the KTB site. It is shown that the next optimization of the model best updated during the DRTG iterations tends to a minimumfeature model with sweeping out any LVZs. The velocities derived by the depth-recursive tomography relate to the horizontal directions of wave propagation rather than to the vertical. This was proved at the KTB site where pronounced anisotropic behavior of a steeply tilted metamorphic rock complex of the ZEV unit has been previously determined. Involving a *7% anisotropy observed for the ''slow'' axis of symmetry oriented coincidentally in the horizontal SW-NE direction of the S01 profile, the DRTG velocity model agrees fairly well with the log velocities at the KTB site. Comparison with the reflectivity map obtained on the reflection seismic profile KTB8502 confirmed the validity of DRTG velocity model at maximum depths of *16 km. The DRTG tomography enabled us to follow the relationship of major geological units of Bohemian Massif as they manifested in the obtained P-wave velocity image down to 15 km. Although the contact of Saxothuringian and the Teplá-Barrandian Unit (TBU) is collateral with the S01 profile direction, several major tectonic zones are rather perpendicular to the Variscan strike and so fairly imaged in the S01 cross-section. They exhibit a weak velocity gradient of sub-horizontal directions within the middle crust. In particular, the Moldanubian and TBU contact beneath the Western Krušné hory/Erzgebirge Pluton, the buried contact of the Lusatia unit and the TBU within the Elbe fault zone were identified. The maxima on the 6,100 ms -1 isovelocity in the middle crust delimitated the known ultrabasic Erbendorf complex and implied also two next ultrabasic massifs beneath the Doupovské hory and the Č eské středohoří volcanic complexes. The intermediate mid-crustal P-wave velocity lows are interpreted as granitic bodies. The presented geological model is suggested in agreement with available gravity, aeromagnetic and petrophysical data.

Journal of GEOsciences, 2012

The P-wave velocity distribution, obtained recently by the depth-recursive tomography along the S... more The P-wave velocity distribution, obtained recently by the depth-recursive tomography along the S01 refraction profile of the SUDETES 2003 seismic experiment, correlated fairly well with other geophysical results known in the area of the KTB deep drilling site. The S01 velocity model also provided a reliable velocity image of the upper and middle-crustal structures along the Eger Graben. In the present paper we will use the results of the depth-recursive tomography applied to the crossing S04 profile to derive a 3-D picture of structures near the S04 and S01 intersection. The NW-SE trending S04 profile starts in the Saxonian Granulite Massif and intersects the Eger Graben in the region of Altenberg-Teplice Caldera. The depth-recursive tomography, applied to the S04 profile, also produced a velocity model allowing, together with the derived S01 velocities, a reliable 3-D interpretation down to the depths of 15-20 km. Besides the P-wave velocities, gravity, aeromagnetic and petrophysical data support the presented geological interpretation.

Surveys in Geophysics, 2011

In the accompanying paper (Part A), depth-recursive tomography was applied to the CEL09 refractio... more In the accompanying paper (Part A), depth-recursive tomography was applied to the CEL09 refraction data. A deblurred P-wave velocity image was obtained down to a depth of 20 km. This paper (Part B) is devoted to the interpretation of the upper-and middle-crustal structures of the Bohemian Massif imaged in the CEL09 section. Because of inherent ambiguity of the refraction method in imaging low-velocity zones, other wellknown results based on other geophysical data sets are also used to independently verify the interpreted velocity features. Comparison with the density and velocity models previously obtained indicates that the presented P-wave velocity image has superior resolution revealing or verifying a number of geological features. The prominent lateral velocity changes encountered in the CEL09 pattern across the imaged crustal section were used to delineate the main terranes and deep regional fault zones such as the Krušné hory Fault, the SW continuation of the Litoměřice Fault Zone, the West and Central Bohemian Shear Zones, the Blanice-Rodl Fault, the Přibyslav-Vitis Fault and the Boskovice-Diendorf Fault. The 450-km-long CEL09 transect reveals seven major deeply rooted high-velocity (HV) anomalies identified as Variscan massifs intruded near or within these deep fault zones. They form buried ridges mostly parallel to the SW-NE trending Variscan strike. Their discovery allows new insights into a number of phenomena such as the West Bohemian earthquake swarms, the Saxothuringian paradox, the character of the Saxothuringian-Barrandian contact zone, the detachment surface due to the slab of the Saxothuringian crust subducting beneath the Teplá-Barrandian zone in the Devonian, the depth extent of the Mariánské-Lázně Complex (MLC) as an equivalent unit of the Zone Erbendorf-Vohenstrauss (ZEV), the subsidence of the Barrandian syncline, the root zones of the Central and South Bohemian Plutons, the accretionary wedge formed along the Moravo-Moldanubian suture and its link with the Gföhl terrane, the Carpathian foreland relief and the subsidence observed in the Vienna Basin.

Surveys in Geophysics, 2013

The West Bohemia and adjacent Vogtland are well known for quasiperiodical earthquake swarms persi... more The West Bohemia and adjacent Vogtland are well known for quasiperiodical earthquake swarms persisting for centuries. The seismogenic area near Nový Kostel involved about 90% of overall earthquake activity clustered here in space and time. The latest major earthquake swarm took place in August-September 2011, two minor earthquake swarms appeared in another location, near Lazy. Recently, the depth-recursive tomography yielded a velocity image with an improved resolution along the CEL09 refraction profile passing between these swarm areas. The resolution, achieved in the velocity image and its agreement with the inverse gravity modeling along the collateral 9HR reflection profile, enabled us to reveal the key structural background of these West Bohemia earthquake swarms.

Surveys in Geophysics, 2013

Studia Geophysica et Geodaetica, 1985

S u m m a r y: The accuracy of wave field extrapolation is studied with respect to the diseretiza... more S u m m a r y: The accuracy of wave field extrapolation is studied with respect to the diseretization of field data and integral extrapolator. Assumin9 a far-field approximation of the Rayleigh-Sommerf eld sohttion for a two-dimensional sealar wave equation, the minimum and the maximum transmitted frequency are expressed as functions of the sampling intervals At, Ax, and the half-width x o and angle % of the migration aperture. The theoretical limitation of the transmitted frequency band is tested on numerical examples.

Studia Geophysica et Geodaetica, 2007

A series of kinematic inversions based on robust non-linear optimization approach were performed ... more A series of kinematic inversions based on robust non-linear optimization approach were performed using travel time data from a series of seismic refraction experiments: . These experiments were performed in Central Europe from 2000 were processed in this study. The goal of this work was to find seismic velocity models yielding travel times consistent with observed data.

Journal of Modern Optics - J MOD OPTIC, 1977

The form of the recently developed series representation of the axially symmetrical diffraction f... more The form of the recently developed series representation of the axially symmetrical diffraction fields enables us to establish the pupil function from the series coefficients γk(u). A new interpretation of the Strehl intensity ratio is given. It represents the ratio of the energy coming to the image focus and that coming to the other foci of the filter. Further, by the use of the three-term approximation, the transmissivity of the filter giving the desired two-point resolution and attaining the maximum value of the Strehl criterion is found and compared with the exact solution proposed by Luneberg. Finally, it is shown that the Luneberg filter transmissivity represents a common approximative solution of the apodization problems that utilize the integral criteria of apodization.

Geophysical Prospecting, 1990

ABSTRACT The slant-stack migration formula based on the Radon transform is studied with respect t... more ABSTRACT The slant-stack migration formula based on the Radon transform is studied with respect to the depth step Δz of wavefield extrapolation. It can be viewed as a generalized trace-interpolation procedure including wave extrapolation with an arbitrary step Δz. For Δz= 0 the formula yields the familiar plane-wave decomposition, while for Δz &gt; 0 it provides a robust tool for migration transformation of spatially undersampled wavefields. Using the stationary phase method, it is shown that the slant-stack migration formula degenerates into the Rayleigh-Sommerfeld integral in the far-field approximation. Consequently, even a narrow slant-stack gather applied before the diffraction stack can significantly improve the representation of noisy data in the wavefield extrapolation process. The theory is applied to synthetic and field data to perform trace interpolation and dip reject filtration. The data examples presented prove that the Radon interpolator works well in the dip range, including waves with mutual stepouts smaller than half the dominant period.

Optica Acta: International Journal of Optics

A new series representation of the diffraction field G (u, v) due to the axially symmetrical filt... more A new series representation of the diffraction field G (u, v) due to the axially symmetrical filters is derived. The coefficients of the series are formed by certain scalar products of the pupil function and the Bernoulli polynomials. Unlike the previous representations of the Fresnel diffraction field containing the Lommel functions of two variables, this representation operates only with special functions of one variable. Applying the theory to the focal diffraction patterns G(4'1d1.L, v), L integer, due to the filters with transmissivities periodic with the squared distance from the axis, the previous result [3] directly follows: the focal patterns of any filter approach the Airy pattern if the number of the periods IVl increases. The series coefficients for the Fresnel diffraction fields of the ideal lens and also of the polynomial filter transmissivities are derived. The results are documented for the diffraction fields of the Fresnel and Gabor zone plates.

Surv Geophys, 2011

In the accompanying paper (Part A), depth-recursive tomography was applied to the CEL09 refractio... more In the accompanying paper (Part A), depth-recursive tomography was applied to the CEL09 refraction data. A deblurred P-wave velocity image was obtained down to a depth of 20 km. This paper (Part B) is devoted to the interpretation of the upper-and middle-crustal structures of the Bohemian Massif imaged in the CEL09 section. Because of inherent ambiguity of the refraction method in imaging low-velocity zones, other wellknown results based on other geophysical data sets are also used to independently verify the interpreted velocity features. Comparison with the density and velocity models previously obtained indicates that the presented P-wave velocity image has superior resolution revealing or verifying a number of geological features. The prominent lateral velocity changes encountered in the CEL09 pattern across the imaged crustal section were used to delineate the main terranes and deep regional fault zones such as the Krušné hory Fault, the SW continuation of the Litoměřice Fault Zone, the West and Central Bohemian Shear Zones, the Blanice-Rodl Fault, the Přibyslav-Vitis Fault and the Boskovice-Diendorf Fault. The 450-km-long CEL09 transect reveals seven major deeply rooted high-velocity (HV) anomalies identified as Variscan massifs intruded near or within these deep fault zones. They form buried ridges mostly parallel to the SW-NE trending Variscan strike. Their discovery allows new insights into a number of phenomena such as the West Bohemian earthquake swarms, the Saxothuringian paradox, the character of the Saxothuringian-Barrandian contact zone, the detachment surface due to the slab of the Saxothuringian crust subducting beneath the Teplá-Barrandian zone in the Devonian, the depth extent of the Mariánské-Lázně Complex (MLC) as an equivalent unit of the Zone Erbendorf-Vohenstrauss (ZEV), the subsidence of the Barrandian syncline, the root zones of the Central and South Bohemian Plutons, the accretionary wedge formed along the Moravo-Moldanubian suture and its link with the Gföhl terrane, the Carpathian foreland relief and the subsidence observed in the Vienna Basin.

Mezinárodní seismické experimenty uskutečněné v posledních letech ve střední Evropě studují stavb... more Mezinárodní seismické experimenty uskutečněné v posledních letech ve střední Evropě studují stavbu zemské kůry a svrchního pláště pod touto oblastí. Pro studium hlubinné stavby se využívá seismická refrakční metoda, kdy se registrují seismické vlny generované odpaly a následně je zjišťována rychlost šíření vln v horninovém prostředí. Tyto údaje umožňují zpřesnit naše znalosti o vlastnostech svrchních partií litosféry do hloubek 50-60 km. Úvod V posledních letech se moderní geologicko-geofyzikální výzkum střední Evropy zaměřil mj. na studium zemské kůry a svrchního pláště. Nejvíce informací o hlubinné stavbě poskytuje metoda, založená na interpretaci seismických vln uměle vyvolaných odpaly na zemském povrchu a zaznamenaných pomocí seismických stanic. Sérii moderních seismických experimentů zahájil v devadesátých letech projekt POLONAISE'97, na který navázaly začátkem našeho tisíciletí projekty CELEBRATION 2000, ALP 2002 a SUDETES 2003. Za účasti více než 25 výzkumných institucí z mnoha zemí světa byla odměřena hustá síť seismických profilů, pokrývající střední Evropu (obr. 1). K registraci seismických vln bylo použito přes 1000 mobilních digitálních seismických stanic. Velikost náloží se zpravidla pohybovala od 200 do 400 kg, výjimečně bylo odpáleno 4000 kg i více; největší nálož v Bělorusku byla 15 000 kg. Seismické vlny vybuzené tímto mohutným odpalem bylo možné zaznamenat na sesimických stanicích vzdálených až 600 km. Časoprostorová koordinace experimentů byla zajištěna družicovou navigační službou GPS. Vlastní experiment sestává z odpálení náloží v odpalových bodech s rozestupy přibližně 30 km a následné registrace seismické energie pomocí digitálních stanic rozmístěných podél linií profilů s krokem 3 km. Nasazení velkého počtu stanic, nesrovnatelně většího než při kterémkoli refrakčním experimentu uskutečněném v minulosti v Evropě, umožnilo zásadní inovaci při koncipování terénní části experimentu. Stanice bylo možné rozmístit současně podél několika navzájem se křižujících profilů a tím zaznamenávat jak seismické vlny podél profilu s příslušným bodem odpalu, tak i vlny šířící se ke stanicím na profilech okolních. Tento přístup umožňuje nejen konstrukci standardních 2-D rychlostních řezů podél profilů, ale také 3-D interpretaci získaných dat. Podrobnosti o výše uvedených seismických projektech lze nalézt v [1-5].

In a laterally variable seismic medium, the slowness function s(x,z) can be derived from travel-t... more In a laterally variable seismic medium, the slowness function s(x,z) can be derived from travel-time curves of surface-to- surface refracted waves if the arrival times are interpreted in the form of a two-dimensional function. In the following article two methods are suggested for solving the inverse kinematic problem using a linearized formulation. The arrival times t(p,q) are arranged according to increasing epicentral distance q, and p represents the x-coordinate of the point midway between source and receiver. The first method is based on the Fourier transform of the time function t(p,q) in the variable p. This method can be applied to a system of travel-time curves with epicentral distances small in comparison to the length of the profile interval xp, i.e., q<<xp. The second, grid method interprets recursively the arrival times t(pj,qi)from the smallest epicentral distance to the largest one. The results of one interpretation step are the grid values of the slowness funct...

Journal of Geosciences, 2018

Unlike standard ray-based tomographies, the Depth-Recursive Tomography on Grid (DRTG) method asse... more Unlike standard ray-based tomographies, the Depth-Recursive Tomography on Grid (DRTG) method assesses the travel-time fit at each model grid node using a regular network of refraction rays. This concept allows estimating the lateral resolution achieved in the velocity image that regards the chosen confidence levels and the strength of velocity anomalies. Recently, The DRTG has been applied to the S01 and CEL09 refraction profiles imaging major crustal structures of the Bohemian Massif in enhanced resolution. Now, similar enhanced velocity models are derived along the S04, S02 and S03 profiles mapping the Sudetic and Moldanubian regions. The S02 and S03 and the transverse CEL09 and S04 velocity sections particularly imaged the subsurface of the Moldanubian high-grade belts to the 15-20 km depth. Their common interpretation revealed the signatures of exhumation processes from upper-mantle depths assumed in this region. Particularly, the S02 and S03 sections map large volumes of high-grade metamorphic rocks forming low-velocity (LV) diapirs that are surrounded by 7000-6400 m/s high-velocity (HV) elevations. The S03 section images the coupled HV-LV-HV anomalies beneath the high-grade complexes of the Orlica-Śnieżnik Dome (OSD) and the Góry-Sowie Unit (GSU). The central gradient-free LV (5800-6000 m/s) cores of these triplets apparently correspond to the OSD or GSU felsic granulites/gneisses that ascended to supra-crustal levels. The Bouguer anomaly map suggests that the S02 and S03 profiles intersect the felsic sheets formed along the transverse Sudetic faults. Along the western belt of Moldanubian high-grade rocks, the S02 section revealed an extensive HV body shallowly emplaced beneath the high-grade Gföhl and Ostrong assemblages. Three mid-crustal HV elevations, correlating with local magnetic anomalies, obviously represent the deep sources of this HV mafic body and indicate its autochthonous nature. Finally, the DRTG also detected a shallowly emplaced HV layer beneath the Saxonian Granulite Massif at the S04 section. The mid-crustal HV-LV-HV diapiric triplets and shallowly emplaced HV bodies are likely typical of the high-grade terrains. The observed patterns resulted from contemporaneous intrusion of mafic and, more viscous, felsic magmas during continental collision. The inferred structural features of subduction-exhumation processes are suggested to further constrain their thermo-mechanic modeling.

Optica Acta: International Journal of Optics

Optica Acta: International Journal of Optics

A new series representation of the diffraction field G (u, v) due to the axially symmetrical filt... more A new series representation of the diffraction field G (u, v) due to the axially symmetrical filters is derived. The coefficients of the series are formed by certain scalar products of the pupil function and the Bernoulli polynomials. Unlike the previous representations of the Fresnel diffraction field containing the Lommel functions of two variables, this representation operates only with special functions of one variable. Applying the theory to the focal diffraction patterns G(4'1d1.L, v), L integer, due to the filters with transmissivities periodic with the squared distance from the axis, the previous result [3] directly follows: the focal patterns of any filter approach the Airy pattern if the number of the periods IVl increases. The series coefficients for the Fresnel diffraction fields of the ideal lens and also of the polynomial filter transmissivities are derived. The results are documented for the diffraction fields of the Fresnel and Gabor zone plates.

Surv Geophys, 2011

In the accompanying paper (Part A), depth-recursive tomography was applied to the CEL09 refractio... more In the accompanying paper (Part A), depth-recursive tomography was applied to the CEL09 refraction data. A deblurred P-wave velocity image was obtained down to a depth of 20 km. This paper (Part B) is devoted to the interpretation of the upper-and middle-crustal structures of the Bohemian Massif imaged in the CEL09 section. Because of inherent ambiguity of the refraction method in imaging low-velocity zones, other wellknown results based on other geophysical data sets are also used to independently verify the interpreted velocity features. Comparison with the density and velocity models previously obtained indicates that the presented P-wave velocity image has superior resolution revealing or verifying a number of geological features. The prominent lateral velocity changes encountered in the CEL09 pattern across the imaged crustal section were used to delineate the main terranes and deep regional fault zones such as the Krušné hory Fault, the SW continuation of the Litoměřice Fault Zone, the West and Central Bohemian Shear Zones, the Blanice-Rodl Fault, the Přibyslav-Vitis Fault and the Boskovice-Diendorf Fault. The 450-km-long CEL09 transect reveals seven major deeply rooted high-velocity (HV) anomalies identified as Variscan massifs intruded near or within these deep fault zones. They form buried ridges mostly parallel to the SW-NE trending Variscan strike. Their discovery allows new insights into a number of phenomena such as the West Bohemian earthquake swarms, the Saxothuringian paradox, the character of the Saxothuringian-Barrandian contact zone, the detachment surface due to the slab of the Saxothuringian crust subducting beneath the Teplá-Barrandian zone in the Devonian, the depth extent of the Mariánské-Lázně Complex (MLC) as an equivalent unit of the Zone Erbendorf-Vohenstrauss (ZEV), the subsidence of the Barrandian syncline, the root zones of the Central and South Bohemian Plutons, the accretionary wedge formed along the Moravo-Moldanubian suture and its link with the Gföhl terrane, the Carpathian foreland relief and the subsidence observed in the Vienna Basin.

Mezinárodní seismické experimenty uskutečněné v posledních letech ve střední Evropě studují stavb... more Mezinárodní seismické experimenty uskutečněné v posledních letech ve střední Evropě studují stavbu zemské kůry a svrchního pláště pod touto oblastí. Pro studium hlubinné stavby se využívá seismická refrakční metoda, kdy se registrují seismické vlny generované odpaly a následně je zjišťována rychlost šíření vln v horninovém prostředí. Tyto údaje umožňují zpřesnit naše znalosti o vlastnostech svrchních partií litosféry do hloubek 50-60 km. Úvod V posledních letech se moderní geologicko-geofyzikální výzkum střední Evropy zaměřil mj. na studium zemské kůry a svrchního pláště. Nejvíce informací o hlubinné stavbě poskytuje metoda, založená na interpretaci seismických vln uměle vyvolaných odpaly na zemském povrchu a zaznamenaných pomocí seismických stanic. Sérii moderních seismických experimentů zahájil v devadesátých letech projekt POLONAISE'97, na který navázaly začátkem našeho tisíciletí projekty CELEBRATION 2000, ALP 2002 a SUDETES 2003. Za účasti více než 25 výzkumných institucí z mnoha zemí světa byla odměřena hustá síť seismických profilů, pokrývající střední Evropu (obr. 1). K registraci seismických vln bylo použito přes 1000 mobilních digitálních seismických stanic. Velikost náloží se zpravidla pohybovala od 200 do 400 kg, výjimečně bylo odpáleno 4000 kg i více; největší nálož v Bělorusku byla 15 000 kg. Seismické vlny vybuzené tímto mohutným odpalem bylo možné zaznamenat na sesimických stanicích vzdálených až 600 km. Časoprostorová koordinace experimentů byla zajištěna družicovou navigační službou GPS. Vlastní experiment sestává z odpálení náloží v odpalových bodech s rozestupy přibližně 30 km a následné registrace seismické energie pomocí digitálních stanic rozmístěných podél linií profilů s krokem 3 km. Nasazení velkého počtu stanic, nesrovnatelně většího než při kterémkoli refrakčním experimentu uskutečněném v minulosti v Evropě, umožnilo zásadní inovaci při koncipování terénní části experimentu. Stanice bylo možné rozmístit současně podél několika navzájem se křižujících profilů a tím zaznamenávat jak seismické vlny podél profilu s příslušným bodem odpalu, tak i vlny šířící se ke stanicím na profilech okolních. Tento přístup umožňuje nejen konstrukci standardních 2-D rychlostních řezů podél profilů, ale také 3-D interpretaci získaných dat. Podrobnosti o výše uvedených seismických projektech lze nalézt v [1-5].

In a laterally variable seismic medium, the slowness function s(x,z) can be derived from travel-t... more In a laterally variable seismic medium, the slowness function s(x,z) can be derived from travel-time curves of surface-to- surface refracted waves if the arrival times are interpreted in the form of a two-dimensional function. In the following article two methods are suggested for solving the inverse kinematic problem using a linearized formulation. The arrival times t(p,q) are arranged according to increasing epicentral distance q, and p represents the x-coordinate of the point midway between source and receiver. The first method is based on the Fourier transform of the time function t(p,q) in the variable p. This method can be applied to a system of travel-time curves with epicentral distances small in comparison to the length of the profile interval xp, i.e., q<<xp. The second, grid method interprets recursively the arrival times t(pj,qi)from the smallest epicentral distance to the largest one. The results of one interpretation step are the grid values of the slowness funct...

The interrelation between the Radon wave field extrapolation and integral solutions of boundary v... more The interrelation between the Radon wave field extrapolation and integral solutions of boundary value problems posed for scalar wave equation is studied. Using the stationary phase method it is found that the Radon extrapolator degenerates into the Rayleigh-Sommerfeld solution of the Dirichlet problem in the far-field zone. The derivations are done for the 3-D case, but the 2-D analogues are also mentioned. The practical consequences and advantages of slant-stack representation of space-under sampled noisy data are discussed.

Surveys in Geophysics, 2009

The refraction data from the SUDETES 2003 experiment were used for highresolution tomography alon... more The refraction data from the SUDETES 2003 experiment were used for highresolution tomography along the profile S01. The S01 profile crosses the zone Erbendorf-Vohenstrauss (ZEV) near the KTB site, then follows the SW-NE oriented Eger Rift in the middle part and continues toward the NE across the Elbe zone and the Sudetic structures as far as the Trans-European Suture Zone. To get the best resolution in the velocity image only the first arrivals of Pg waves with minimum picking errors were used. The previous depth-recursive tomographic method, based on Claerbout's imaging principle, has been adapted to perform the linearized inversions in iterative mode. This innovative DRTG method (Depth-Recursive Tomography on Grid) uses a regular system of refraction rays covering uniformly the mapped domain. The DRTG iterations yielded a fine-grid velocity model with a required level of RMS travel-time fit and the model roughness. The traveltime residuals, assessed at single depth levels, were used to derive the statistical lateral resolution of ''lens-shaped'' velocity anomalies. Thus, for the 95% confidence level and 5% anomalies, one can resolve their lateral sizes from 15 to 40 km at the depths from 0 to 20 km. The DRTG tomography succeeded in resolving a significant low-velocity zone (LVZ) bound to the Franconian lineament nearby the KTB site. It is shown that the next optimization of the model best updated during the DRTG iterations tends to a minimumfeature model with sweeping out any LVZs. The velocities derived by the depth-recursive tomography relate to the horizontal directions of wave propagation rather than to the vertical. This was proved at the KTB site where pronounced anisotropic behavior of a steeply tilted metamorphic rock complex of the ZEV unit has been previously determined. Involving a *7% anisotropy observed for the ''slow'' axis of symmetry oriented coincidentally in the horizontal SW-NE direction of the S01 profile, the DRTG velocity model agrees fairly well with the log velocities at the KTB site. Comparison with the reflectivity map obtained on the reflection seismic profile KTB8502 confirmed the validity of DRTG velocity model at maximum depths of *16 km. The DRTG tomography enabled us to follow the relationship of major geological units of Bohemian Massif as they manifested in the obtained P-wave velocity image down to 15 km. Although the contact of Saxothuringian and the Teplá-Barrandian Unit (TBU) is collateral with the S01 profile direction, several major tectonic zones are rather perpendicular to the Variscan strike and so fairly imaged in the S01 cross-section. They exhibit a weak velocity gradient of sub-horizontal directions within the middle crust. In particular, the Moldanubian and TBU contact beneath the Western Krušné hory/Erzgebirge Pluton, the buried contact of the Lusatia unit and the TBU within the Elbe fault zone were identified. The maxima on the 6,100 ms -1 isovelocity in the middle crust delimitated the known ultrabasic Erbendorf complex and implied also two next ultrabasic massifs beneath the Doupovské hory and the Č eské středohoří volcanic complexes. The intermediate mid-crustal P-wave velocity lows are interpreted as granitic bodies. The presented geological model is suggested in agreement with available gravity, aeromagnetic and petrophysical data.

Journal of GEOsciences, 2012

The P-wave velocity distribution, obtained recently by the depth-recursive tomography along the S... more The P-wave velocity distribution, obtained recently by the depth-recursive tomography along the S01 refraction profile of the SUDETES 2003 seismic experiment, correlated fairly well with other geophysical results known in the area of the KTB deep drilling site. The S01 velocity model also provided a reliable velocity image of the upper and middle-crustal structures along the Eger Graben. In the present paper we will use the results of the depth-recursive tomography applied to the crossing S04 profile to derive a 3-D picture of structures near the S04 and S01 intersection. The NW-SE trending S04 profile starts in the Saxonian Granulite Massif and intersects the Eger Graben in the region of Altenberg-Teplice Caldera. The depth-recursive tomography, applied to the S04 profile, also produced a velocity model allowing, together with the derived S01 velocities, a reliable 3-D interpretation down to the depths of 15-20 km. Besides the P-wave velocities, gravity, aeromagnetic and petrophysical data support the presented geological interpretation.

Surveys in Geophysics, 2011

In the accompanying paper (Part A), depth-recursive tomography was applied to the CEL09 refractio... more In the accompanying paper (Part A), depth-recursive tomography was applied to the CEL09 refraction data. A deblurred P-wave velocity image was obtained down to a depth of 20 km. This paper (Part B) is devoted to the interpretation of the upper-and middle-crustal structures of the Bohemian Massif imaged in the CEL09 section. Because of inherent ambiguity of the refraction method in imaging low-velocity zones, other wellknown results based on other geophysical data sets are also used to independently verify the interpreted velocity features. Comparison with the density and velocity models previously obtained indicates that the presented P-wave velocity image has superior resolution revealing or verifying a number of geological features. The prominent lateral velocity changes encountered in the CEL09 pattern across the imaged crustal section were used to delineate the main terranes and deep regional fault zones such as the Krušné hory Fault, the SW continuation of the Litoměřice Fault Zone, the West and Central Bohemian Shear Zones, the Blanice-Rodl Fault, the Přibyslav-Vitis Fault and the Boskovice-Diendorf Fault. The 450-km-long CEL09 transect reveals seven major deeply rooted high-velocity (HV) anomalies identified as Variscan massifs intruded near or within these deep fault zones. They form buried ridges mostly parallel to the SW-NE trending Variscan strike. Their discovery allows new insights into a number of phenomena such as the West Bohemian earthquake swarms, the Saxothuringian paradox, the character of the Saxothuringian-Barrandian contact zone, the detachment surface due to the slab of the Saxothuringian crust subducting beneath the Teplá-Barrandian zone in the Devonian, the depth extent of the Mariánské-Lázně Complex (MLC) as an equivalent unit of the Zone Erbendorf-Vohenstrauss (ZEV), the subsidence of the Barrandian syncline, the root zones of the Central and South Bohemian Plutons, the accretionary wedge formed along the Moravo-Moldanubian suture and its link with the Gföhl terrane, the Carpathian foreland relief and the subsidence observed in the Vienna Basin.

Surveys in Geophysics, 2013

The West Bohemia and adjacent Vogtland are well known for quasiperiodical earthquake swarms persi... more The West Bohemia and adjacent Vogtland are well known for quasiperiodical earthquake swarms persisting for centuries. The seismogenic area near Nový Kostel involved about 90% of overall earthquake activity clustered here in space and time. The latest major earthquake swarm took place in August-September 2011, two minor earthquake swarms appeared in another location, near Lazy. Recently, the depth-recursive tomography yielded a velocity image with an improved resolution along the CEL09 refraction profile passing between these swarm areas. The resolution, achieved in the velocity image and its agreement with the inverse gravity modeling along the collateral 9HR reflection profile, enabled us to reveal the key structural background of these West Bohemia earthquake swarms.

Surveys in Geophysics, 2013

Studia Geophysica et Geodaetica, 1985

S u m m a r y: The accuracy of wave field extrapolation is studied with respect to the diseretiza... more S u m m a r y: The accuracy of wave field extrapolation is studied with respect to the diseretization of field data and integral extrapolator. Assumin9 a far-field approximation of the Rayleigh-Sommerf eld sohttion for a two-dimensional sealar wave equation, the minimum and the maximum transmitted frequency are expressed as functions of the sampling intervals At, Ax, and the half-width x o and angle % of the migration aperture. The theoretical limitation of the transmitted frequency band is tested on numerical examples.

Studia Geophysica et Geodaetica, 2007

A series of kinematic inversions based on robust non-linear optimization approach were performed ... more A series of kinematic inversions based on robust non-linear optimization approach were performed using travel time data from a series of seismic refraction experiments: . These experiments were performed in Central Europe from 2000 were processed in this study. The goal of this work was to find seismic velocity models yielding travel times consistent with observed data.

Journal of Modern Optics - J MOD OPTIC, 1977

The form of the recently developed series representation of the axially symmetrical diffraction f... more The form of the recently developed series representation of the axially symmetrical diffraction fields enables us to establish the pupil function from the series coefficients γk(u). A new interpretation of the Strehl intensity ratio is given. It represents the ratio of the energy coming to the image focus and that coming to the other foci of the filter. Further, by the use of the three-term approximation, the transmissivity of the filter giving the desired two-point resolution and attaining the maximum value of the Strehl criterion is found and compared with the exact solution proposed by Luneberg. Finally, it is shown that the Luneberg filter transmissivity represents a common approximative solution of the apodization problems that utilize the integral criteria of apodization.

Geophysical Prospecting, 1990

ABSTRACT The slant-stack migration formula based on the Radon transform is studied with respect t... more ABSTRACT The slant-stack migration formula based on the Radon transform is studied with respect to the depth step Δz of wavefield extrapolation. It can be viewed as a generalized trace-interpolation procedure including wave extrapolation with an arbitrary step Δz. For Δz= 0 the formula yields the familiar plane-wave decomposition, while for Δz &gt; 0 it provides a robust tool for migration transformation of spatially undersampled wavefields. Using the stationary phase method, it is shown that the slant-stack migration formula degenerates into the Rayleigh-Sommerfeld integral in the far-field approximation. Consequently, even a narrow slant-stack gather applied before the diffraction stack can significantly improve the representation of noisy data in the wavefield extrapolation process. The theory is applied to synthetic and field data to perform trace interpolation and dip reject filtration. The data examples presented prove that the Radon interpolator works well in the dip range, including waves with mutual stepouts smaller than half the dominant period.

Optica Acta: International Journal of Optics

A new series representation of the diffraction field G (u, v) due to the axially symmetrical filt... more A new series representation of the diffraction field G (u, v) due to the axially symmetrical filters is derived. The coefficients of the series are formed by certain scalar products of the pupil function and the Bernoulli polynomials. Unlike the previous representations of the Fresnel diffraction field containing the Lommel functions of two variables, this representation operates only with special functions of one variable. Applying the theory to the focal diffraction patterns G(4'1d1.L, v), L integer, due to the filters with transmissivities periodic with the squared distance from the axis, the previous result [3] directly follows: the focal patterns of any filter approach the Airy pattern if the number of the periods IVl increases. The series coefficients for the Fresnel diffraction fields of the ideal lens and also of the polynomial filter transmissivities are derived. The results are documented for the diffraction fields of the Fresnel and Gabor zone plates.

Surv Geophys, 2011

In the accompanying paper (Part A), depth-recursive tomography was applied to the CEL09 refractio... more In the accompanying paper (Part A), depth-recursive tomography was applied to the CEL09 refraction data. A deblurred P-wave velocity image was obtained down to a depth of 20 km. This paper (Part B) is devoted to the interpretation of the upper-and middle-crustal structures of the Bohemian Massif imaged in the CEL09 section. Because of inherent ambiguity of the refraction method in imaging low-velocity zones, other wellknown results based on other geophysical data sets are also used to independently verify the interpreted velocity features. Comparison with the density and velocity models previously obtained indicates that the presented P-wave velocity image has superior resolution revealing or verifying a number of geological features. The prominent lateral velocity changes encountered in the CEL09 pattern across the imaged crustal section were used to delineate the main terranes and deep regional fault zones such as the Krušné hory Fault, the SW continuation of the Litoměřice Fault Zone, the West and Central Bohemian Shear Zones, the Blanice-Rodl Fault, the Přibyslav-Vitis Fault and the Boskovice-Diendorf Fault. The 450-km-long CEL09 transect reveals seven major deeply rooted high-velocity (HV) anomalies identified as Variscan massifs intruded near or within these deep fault zones. They form buried ridges mostly parallel to the SW-NE trending Variscan strike. Their discovery allows new insights into a number of phenomena such as the West Bohemian earthquake swarms, the Saxothuringian paradox, the character of the Saxothuringian-Barrandian contact zone, the detachment surface due to the slab of the Saxothuringian crust subducting beneath the Teplá-Barrandian zone in the Devonian, the depth extent of the Mariánské-Lázně Complex (MLC) as an equivalent unit of the Zone Erbendorf-Vohenstrauss (ZEV), the subsidence of the Barrandian syncline, the root zones of the Central and South Bohemian Plutons, the accretionary wedge formed along the Moravo-Moldanubian suture and its link with the Gföhl terrane, the Carpathian foreland relief and the subsidence observed in the Vienna Basin.

Mezinárodní seismické experimenty uskutečněné v posledních letech ve střední Evropě studují stavb... more Mezinárodní seismické experimenty uskutečněné v posledních letech ve střední Evropě studují stavbu zemské kůry a svrchního pláště pod touto oblastí. Pro studium hlubinné stavby se využívá seismická refrakční metoda, kdy se registrují seismické vlny generované odpaly a následně je zjišťována rychlost šíření vln v horninovém prostředí. Tyto údaje umožňují zpřesnit naše znalosti o vlastnostech svrchních partií litosféry do hloubek 50-60 km. Úvod V posledních letech se moderní geologicko-geofyzikální výzkum střední Evropy zaměřil mj. na studium zemské kůry a svrchního pláště. Nejvíce informací o hlubinné stavbě poskytuje metoda, založená na interpretaci seismických vln uměle vyvolaných odpaly na zemském povrchu a zaznamenaných pomocí seismických stanic. Sérii moderních seismických experimentů zahájil v devadesátých letech projekt POLONAISE'97, na který navázaly začátkem našeho tisíciletí projekty CELEBRATION 2000, ALP 2002 a SUDETES 2003. Za účasti více než 25 výzkumných institucí z mnoha zemí světa byla odměřena hustá síť seismických profilů, pokrývající střední Evropu (obr. 1). K registraci seismických vln bylo použito přes 1000 mobilních digitálních seismických stanic. Velikost náloží se zpravidla pohybovala od 200 do 400 kg, výjimečně bylo odpáleno 4000 kg i více; největší nálož v Bělorusku byla 15 000 kg. Seismické vlny vybuzené tímto mohutným odpalem bylo možné zaznamenat na sesimických stanicích vzdálených až 600 km. Časoprostorová koordinace experimentů byla zajištěna družicovou navigační službou GPS. Vlastní experiment sestává z odpálení náloží v odpalových bodech s rozestupy přibližně 30 km a následné registrace seismické energie pomocí digitálních stanic rozmístěných podél linií profilů s krokem 3 km. Nasazení velkého počtu stanic, nesrovnatelně většího než při kterémkoli refrakčním experimentu uskutečněném v minulosti v Evropě, umožnilo zásadní inovaci při koncipování terénní části experimentu. Stanice bylo možné rozmístit současně podél několika navzájem se křižujících profilů a tím zaznamenávat jak seismické vlny podél profilu s příslušným bodem odpalu, tak i vlny šířící se ke stanicím na profilech okolních. Tento přístup umožňuje nejen konstrukci standardních 2-D rychlostních řezů podél profilů, ale také 3-D interpretaci získaných dat. Podrobnosti o výše uvedených seismických projektech lze nalézt v [1-5].

In a laterally variable seismic medium, the slowness function s(x,z) can be derived from travel-t... more In a laterally variable seismic medium, the slowness function s(x,z) can be derived from travel-time curves of surface-to- surface refracted waves if the arrival times are interpreted in the form of a two-dimensional function. In the following article two methods are suggested for solving the inverse kinematic problem using a linearized formulation. The arrival times t(p,q) are arranged according to increasing epicentral distance q, and p represents the x-coordinate of the point midway between source and receiver. The first method is based on the Fourier transform of the time function t(p,q) in the variable p. This method can be applied to a system of travel-time curves with epicentral distances small in comparison to the length of the profile interval xp, i.e., q<<xp. The second, grid method interprets recursively the arrival times t(pj,qi)from the smallest epicentral distance to the largest one. The results of one interpretation step are the grid values of the slowness funct...