Vaclav Vavrycuk - Academia.edu (original) (raw)

Papers by Vaclav Vavrycuk

Research paper thumbnail of Frequency‐Dependent Moment Tensors of Induced Microearthquakes

Geophysical Research Letters, Jun 20, 2019

Analysis of 984 induced microearthquakes from The Geysers geothermal reservoir in California reve... more Analysis of 984 induced microearthquakes from The Geysers geothermal reservoir in California reveals that the retrieved moment tensors depend on the frequency band of the inverted waveforms. The observed dependence is more significant for the percentages of the double-couple, compensated linear vector dipole, and isotropic (ISO) components than for the focal mechanisms. The average root-mean-square of the moment tensors obtained in different frequency bands is correlated with spectra of ambient noise. The percentages of double-couple and ISO components tend to decrease and increase with the upper cutoff frequency (f u), respectively. This suggests that shear rupture radiates energy preferentially in a lower frequency band and tensile rupture in a higher frequency band. Events displaying a strong increase of the ISO with f u are confined within the same depth interval as the injection points. This might be related to the strong thermoelastic effects in the vicinity of injection points that promote opening of small cracks adjacent to the main fractures. Plain Language Summary Moment tensor (MT) describes shear and tensile motions in the earthquake source. The components of MT are usually assumed to be independent of the frequency. However, this assumption may not satisfy the complex rupture process of induced microearthquakes. We use a novel approach to investigate 984 induced microearthquakes from The Geysers geothermal reservoir in California and find that the retrieved MTs depend on the frequency band of input waveforms. The observed dependence is more significant for the components of MT measuring the proportions of seismic energy than for the components determining fault geometry. The component of MT describing shear motion shows a different frequency dependence than that describing tensile motion, suggesting that these two motions occur on the structures with different spatial scales. A subset of seismic events is identified to have a distinct feature of frequency dependence. These events only occur in the layer where the cool water is injected into the hot reservoir and do not migrate downward as the other events. This might be related to the strong thermal effects in the vicinity of injection points that promote the opening of small cracks adjacent to the main fractures.

Research paper thumbnail of Moment tensor inversion of waveforms: a two-step time-frequency approach

Geophysical Journal International, Jul 30, 2012

We present a moment tensor inversion of waveforms, which is more robust and yields more stable an... more We present a moment tensor inversion of waveforms, which is more robust and yields more stable and more accurate results than standard approaches. The inversion is performed in two steps and combines inversions in time and frequency domains. First, the inversion for the source-time function is performed in the frequency domain using complex spectra. Second, the time-domain inversion for the moment tensor is performed using the source-time function calculated in the first step. In this way, we can consider a realistic, complex source-time function and still keep the final moment tensor inversion linear. Using numerical modelling, we compare the efficiency and accuracy of the proposed approach with standard waveform inversions. We study the sensitivity of the retrieved double-couple and non-double-couple components of the moment tensors to noise in the data, to inaccuracies of the location and of the velocity model, and to the type of the focal mechanism. Finally, the proposed moment tensor inversion is tested on real data observed in a complex 3-D inhomogeneous geological environment: a production blast and a rockburst in the Pyhäsalmi ore mine, Finland.

Research paper thumbnail of Detection of high-frequency tensile vibrations of a fault during shear rupturing: observations from the 2008 West Bohemia swarm

Geophysical Journal International, Jul 21, 2011

The analysis of 12 earthquakes of magnitudes between 1.7 and 3.7 that occurred in 2008 in West Bo... more The analysis of 12 earthquakes of magnitudes between 1.7 and 3.7 that occurred in 2008 in West Bohemia, Czech Republic reveals that shear rupturing along a fault is accompanied by weak tensile vibrations of the fault. The vibrations are of a narrow frequency band with frequencies distinctly higher than those of shear rupturing. The tensile vibrations decay slowly in time and often resemble resonant waves. They complicate the radiated P waveforms and the P-wave radiation pattern. The tensile vibrations can be observed in waveforms in directions near the nodal lines where the dominance of shear-faulting radiation is lost. The tensile vibrations are probably generated by opening of the fault during shear rupturing or by creating a wing tensile crack at the tip of the fault when shear fracturing stops.

Research paper thumbnail of Missing dust signature in the cosmic microwave background

Monthly Notices of the Royal Astronomical Society: Letters, May 6, 2017

I examine a possible spectral distortion of the cosmic microwave background (CMB) due to its abso... more I examine a possible spectral distortion of the cosmic microwave background (CMB) due to its absorption by galactic and intergalactic dust. I show that even subtle intergalactic opacity of 1 × 10 −7 mag h Gpc −1 at the CMB wavelengths in the local Universe causes non-negligible CMB absorption and decline of the CMB intensity because the opacity steeply increases with redshift. The CMB should be distorted even during the epoch of the Universe defined by redshifts z < 10. For this epoch, the maximum spectral distortion of the CMB is at least 20 × 10 −22 W m −2 Hz −1 sr −1 at 300 GHz, which is well above the sensitivity of the COBE/FIRAS, WMAP or Planck flux measurements. If dust mass is considered to be redshift dependent with noticeable dust abundance at redshifts 2-4, the predicted CMB distortion would be even higher. The CMB would also be distorted in a perfectly transparent universe due to dust in galaxies, but this effect is lower by one order than that due to intergalactic opacity. The fact that the distortion of the CMB by dust is not observed is intriguing and questions either opacity and extinction law measurements or validity of the current model of the Universe.

Research paper thumbnail of Universe opacity and EBL

Monthly Notices of the Royal Astronomical Society, Nov 3, 2016

The observed extragalactic background light (EBL) is affected by light attenuation due to absorpt... more The observed extragalactic background light (EBL) is affected by light attenuation due to absorption of light by galactic and intergalactic dust in the Universe. Even galactic opacity of 10-20 per cent and minute universe intergalactic opacity of 0.01 mag h Gpc −1 at the local Universe have a significant impact on the EBL because obscuration of galaxies and density of intergalactic dust increase with redshift as (1 + z) 3. Consequently, intergalactic opacity increases and the Universe becomes considerably opaque at z > 3. Adopting realistic values for galactic and intergalactic opacity, the estimates of the EBL for the expanding dusty universe are close to observations. The luminosity density evolution fits well measurements. The model reproduces a steep increase of the luminosity density at z < 2, its maximum at z = 2-3, and its decrease at higher redshifts. The increase of the luminosity density at low z is not produced by the evolution of the star formation rate but by the fact that the Universe occupied a smaller volume in previous epochs. The decline of the luminosity density at high z originates in the opacity of the Universe. The calculated bolometric EBL ranges from 100 to 200 nW m −2 sr −1 and is within the limits of 40 and 200 nW m −2 sr −1 of current EBL observations. The model predicts 98 per cent of the EBL coming from radiation of galaxies at z < 3.5. Accounting for light extinction by intergalactic dust implies that the Universe was probably more opaque than dark for z > 3.5.

Research paper thumbnail of Stress Inversion of Regional Seismicity in the Sea of Marmara Region, Turkey

Pure and Applied Geophysics, Sep 3, 2018

In this study we derive the stress tensor and its local variations throughout the Marmara region,... more In this study we derive the stress tensor and its local variations throughout the Marmara region, Turkey. Based on a recently compiled 10-year earthquake catalogue, we directly invert first-motion polarity data and quantify confidence intervals for the principal stress orientations. We find a combined strike-slip and normal faulting stress field for the Marmara region generally reflecting the overall transtensional setting. However, the results clearly show moderate local variations of the stress field. The largest (r 1) and intermediate (r 2) principal stresses show an average regional trend of N125 E and locally varying plunges. The least principal stress (r 3) is well resolved in its confidence interval and consistent throughout the region with an average trend of $ N35 E and a subhorizontal plunge. The eastern Sea of Marmara shows local stress field orientations with pronounced strike-slip (northern part) and normal faulting (southern part) components. Along the central Marmara region, normal faulting tends to dominate, while a well resolved strike-slip stress regime is found in the western Sea of Marmara region. Regarding the faulting mechanism of an earthquake with magnitude up to 7.4 which is expected in this area in direct vicinity of the Istanbul metropolitan region, our results imply that neither strike-slip nor normal faulting kinematics can be excluded.

Research paper thumbnail of Inversion for parameters of tensile earthquakes

Journal of Geophysical Research, Aug 10, 2001

The tensile source model generalizes the shear source model by assuming that the slip vector can ... more The tensile source model generalizes the shear source model by assuming that the slip vector can be arbitrarily oriented with respect to the fault and is not constrained to lie within the fault plane. The proposed inversion for the parameters of tensile sources is based on the evaluation of the isotropic (ISO), compensated linear vector dipole (CLVD), and double-couple (DC) components in seismic moment tensors. The most significant parameters inverted are the /•//a ratio at the fault (denoted as the tc parameter) and the inclination a of the slip vector from the fault. The tc parameter is significant for discriminating noisy moment tensors of shear earthquakes from those of tensile earthquakes. The inclination a can be accurately determined from the DC component in the moment tensor because the DC component rapidly decreases with increasing a. For example, the inclination of 20 ø causes DC being-50-60% only. The inversion is applied to earthquakes which occurred in January 1997 in West Bohemia, Czech Republic. It is shown that some of these earthquakes display tensile faulting. The tc parameter is-0.1. The inclination of the slip from the fault attains values of up to 20 ø. This inclination is a result of tensile traction and reduced shear traction along the fault and high-fluid pressure in the region. 16,339 16,340 VAVRY(•UK: INVERSION FOR PARAMETERS OF TENSILE EARTHQUAKES 4 5 K-parameter 5 ß eo o' ß ß øø ß ß 4 2 '. ' 00 ' ß ß 000 • 00 ß • ß ß. '. .. ß. '. .

Research paper thumbnail of Varying speed of light in the conformal cosmology

Zenodo (CERN European Organization for Nuclear Research), Dec 22, 2022

The law of constancy of the velocity of light in vacuo, which constitutes one of the fundamental ... more The law of constancy of the velocity of light in vacuo, which constitutes one of the fundamental assumptions in the special theory of relativity and to which we have already frequently referred, cannot claim an unlimited validity.

Research paper thumbnail of Efficiency of Surface Monitoring Layouts for Retrieving Accurate Moment Tensors in Hydraulic Fracturing Experiments

Pure and Applied Geophysics, Aug 22, 2022

We study the sensor layouts of surface monitoring systems for injection areas in hydraulic fractu... more We study the sensor layouts of surface monitoring systems for injection areas in hydraulic fracturing experiments, which maximize the accuracy of retrieved moment tensors. The moment tensors (MTs) are determined using noisy synthetic P-wave amplitudes of microearthquakes with varying mechanisms. An optimum sensor layout is searched by minimizing a difference between the true and inverted MTs. First, we tested the efficiency of the circular networks. We focused on one-circle and two-circle layouts of various sizes and numbers of sensors on each circle and with their centre in the epicentral region. The results show that the optimal layout for events distributed within a circular epicentral area is characterized by: (1) one sensor fixed in the centre of the area; (2) about 1/10 of the total number of sensors gathered near the centre; and (3) the rest of sensors evenly distributed on a circle surrounding the area with the takeoff angle of 135°. In homogeneous media, this angle corresponds to the radius of the circle comparable with depth of microearthquakes. Second, we compared the efficiency of the circular layout with other layouts: regular-grid, star-shaped and uniform focal-sphere layouts. Taking 25 sensors and 81 sensors as examples, we show that the two-circle layout is always the best, which means that we can achieve more accurate MTs using the circular layout than with other layouts, if the number of sensors in the experiment is fixed. This contradicts a common opinion that networks, which cover the target area, work equally well irrespective of their layout.

Research paper thumbnail of Gravitational orbits in the expanding Universe revisited

Frontiers in Astronomy and Space Sciences, Feb 6, 2023

Modified Newtonian equations for gravitational orbits in the expanding Universe indicate that loc... more Modified Newtonian equations for gravitational orbits in the expanding Universe indicate that local gravitationally bounded systems like galaxies and planetary systems are unaffected by the expansion of the Universe. This result is derived for the space expansion described by the standard FLRW metric. In this paper, the modified Newtonian equations are derived for the space expansion described by the conformal cosmology (CC) metric. In this metric, the comoving and proper times are different similarly as the comoving and proper distances. As shown by Vavryčuk (Front. Phys. 2022), this metric is advantageous, because it properly predicts the cosmic time dilation, and fits the Type Ia supernova luminosity observations with no need to introduce dark energy. Surprisingly, the solution of the equations for gravitational orbits based on the CC metric behaves quite differently than that based on the FLRW metric. In contrast to the common opinion that local systems resist the space expansion, they expand according to the Hubble flow in the CC metric. The evolution of the local systems with cosmic time is exemplified on numerical modelling of spiral galaxies. The size of the spiral galaxies grows consistently with observations and a typical spiral pattern is well reproduced. The theory predicts flat rotation curves without an assumption of dark matter surrounding the galaxy. The theory resolves challenges to the ΛCDM model such as the problem of faint satellite galaxies, baryonic Tully-Fisher relation or the radial acceleration relation. Furthermore, puzzles in the solar system are successfully explained such as the Faint young Sun paradox or the Moon's and Titan's orbit anomalies.

Research paper thumbnail of Cosmological Redshift and Cosmic Time Dilation in the FLRW Metric

Frontiers in Physics, May 23, 2022

The paper shows that the commonly used Friedmann-Lemaitre-Robertson-Walker (FLRW) metric describi... more The paper shows that the commonly used Friedmann-Lemaitre-Robertson-Walker (FLRW) metric describing the expanding Universe must be modified to properly predict the cosmological redshift. It is proved that the change in the frequency of redshifted photons is always connected with time dilation, similarly as for the gravitational redshift. Therefore, the cosmic time runs differently at high redshifts than at present. Consequently, the cosmological time must be identified with the conformal time and the standard FLRW metric must be substituted by its conformal version. The correctness of the proposed conformal metric is convincingly confirmed by Type Ia supernovae (SNe Ia) observations. The standard FLRW metric produces essential discrepancy with the SNe Ia observations called the 'supernova dimming', and dark energy has to be introduced to comply theoretical predictions with data. By contrast, the conformal FLRW metric fits data well with no need to introduce any new free parameter. Hence, the discovery of the supernova dimming actually revealed a failure of the FLRW metric and introducing dark energy was just an unsuccessful attempt to cope with the problem within this false metric. Obviously, adopting the conformal FLRW metric for describing the evolution of the Universe has many fundamental cosmological consequences.

Research paper thumbnail of Universe opacity and CMB

Monthly Notices of the Royal Astronomical Society, Apr 18, 2018

A cosmological model, in which the cosmic microwave background (CMB) is a thermal radiation of in... more A cosmological model, in which the cosmic microwave background (CMB) is a thermal radiation of intergalactic dust instead of a relic radiation of the big bang, is revived and revisited. The model suggests that a virtually transparent local Universe becomes considerably opaque at redshifts z > 2-3. Such opacity is hardly to be detected in the Type Ia supernova data, but confirmed using quasar data. The opacity steeply increases with redshift because of a high proper density of intergalactic dust in the previous epochs. The temperature of intergalactic dust increases as (1 + z) and exactly compensates the change of wavelengths due to redshift, so that the dust radiation looks apparently like the radiation of the blackbody with a single temperature. The predicted dust temperature is T D = 2.776 K, which differs from the CMB temperature by 1.9 per cent only, and the predicted ratio between the total CMB and extragalactic background light (EBL) intensities is 13.4 which is close to 12.5 obtained from observations. The CMB temperature fluctuations are caused by EBL fluctuations produced by galaxy clusters and voids in the Universe. The polarization anomalies of the CMB correlated with temperature anisotropies are caused by the polarized thermal emission of needle-shaped conducting dust grains aligned by large-scale magnetic fields around clusters and voids. A strong decline of the luminosity density for z > 4 is interpreted as the result of high opacity of the Universe rather than of a decline of the global stellar mass density at high redshifts.

Research paper thumbnail of Universe opacity and Type Ia supernova dimming

Monthly Notices of the Royal Astronomical Society: Letters, Aug 19, 2019

In this paper, I revoke a debate about an origin of Type Ia supernova (SN Ia) dimming. I argue th... more In this paper, I revoke a debate about an origin of Type Ia supernova (SN Ia) dimming. I argue that except for a commonly accepted accelerating expansion of the Universe, a conceivable alternative for explaining this observation is universe opacity caused by light extinction by intergalactic dust, even though it is commonly assumed that this effect is negligible. Using data of the Union2.1 SN Ia compilation, I find that the standard cold dark matter (CDM) model and the opaque universe model fit the SN Ia measurements at redshifts z < 1.4 comparably well. The optimum solution for the opaque universe model is characterized by the B-band intergalactic opacity λ B = 0.10 ± 0.03 Gpc −1 and the Hubble constant H 0 = 68.0 ± 2.5 km s −1 Mpc −1. The intergalactic opacity is higher than that obtained from independent observations but still within acceptable limits. This result emphasizes that the issue of the accelerating expansion of the Universe as the origin of the SN Ia dimming is not yet definitely resolved. Obviously, the opaque universe model as an alternative to the CDM model is attractive, because it avoids puzzles and controversies associated with dark energy and the accelerating expansion.

Research paper thumbnail of Impact of galactic and intergalactic dust on the stellar EBL

Astrophysics and Space Science, May 25, 2016

Current theories assume that the low intensity of the stellar extragalactic background light (ste... more Current theories assume that the low intensity of the stellar extragalactic background light (stellar EBL) is caused by finite age of the Universe because the finite-age factor limits the number of photons that have been pumped into the space by galaxies and thus the sky is dark in the night. We oppose this opinion and show that two main factors are responsible for the extremely low intensity of the observed stellar EBL. The first factor is a low mean surface brightness of galaxies, which causes a low luminosity density in the local Universe. The second factor is light extinction due to absorption by galactic and intergalactic dust. Dust produces a partial opacity of galaxies and of the Universe. The galactic opacity reduces the intensity of light from more distant background galaxies obscured by foreground galaxies. The inclination-averaged values of the effective extinction A V for light passing through a galaxy is about 0.2 mag. This causes that distant background galaxies become apparently faint and do not contribute to the EBL significantly. In addition, light of distant galaxies is dimmed due to absorption by intergalactic dust. Even a minute intergalactic opacity of 1 × 10 −2 mag per Gpc is high enough to produce significant effects on the EBL. As a consequence, the EBL is comparable with or lower than the mean surface brightness of galaxies. Comparing both extinction effects, the impact of the intergalactic opacity on the EBL is more significant than the obscuration of distant galaxies by partially opaque foreground galaxies by factor of 10 or more. The absorbed starlight heats up the galactic and intergalactic dust and is further re-radiated at IR, FIR and microwave spectrum. Assuming static infinite universe with no galactic B V. Vavryčuk

Research paper thumbnail of Non-double-couple earthquakes of 1997 January in West Bohemia, Czech Republic: evidence of tensile faulting

Geophysical Journal International, May 1, 2002

A mixed family of double-couple (DC) and non-double-couple (non-DC) earthquakes was observed duri... more A mixed family of double-couple (DC) and non-double-couple (non-DC) earthquakes was observed during the 1997 January earthquake swarm in West Bohemia, which is a geothermal region typical for the occurrence of earthquakes swarms. The DC and non-DC earthquakes occurred within a small area of less than 1 km 3 on faults of different orientations. The stress in the area is determined from focal mechanisms and attains values (plunge/azimuth): σ 1 = 33 • /156 • , σ 2 = 48 • /20 • , σ 3 = 23 • /262 • , with a shape ratio of R = 0.69 ± 0.15. The error in the stress directions (plunge/azimuth) is up to ∼5 • /10 •. The absolute stress values were estimated to be σ 1 = 350 MPa, σ 2 = 220 MPa and σ 3 = 162 MPa. The lithostatic stress is 250 MPa. The stress analysis shows that the DC earthquakes occurred on optimally oriented faults (with high shear traction) but the non-DC earthquakes occurred on misoriented faults (with low shear traction). The percentage of the DC in earthquakes clearly correlates with the magnitude of shear traction: high/low DC is associated with high/low shear traction. This indicates that the type of faulting is probably controlled by tectonic stress and that the non-DC earthquakes are not related to pure shear faulting but may combine shear and tensile faulting. The tensile faulting is manifested by positive isotropic and compensated linear vector dipole components. The tensile faulting is conditioned by high pore fluid pressure, which was estimated to be approximately 244 MPa. The fluid pressure is less than the lithostatic stress by ∼5 MPa. The ratio of the fluid pressure to the maximum compressive stress is 0.7.

Research paper thumbnail of Contact of the Samoan Plume with the Tonga Subduction from Intermediate and Deep-Focus Earthquakes

Surveys in Geophysics, 2021

The Tonga subduction zone in the south-west Pacific is the fastest convergent plate boundary in t... more The Tonga subduction zone in the south-west Pacific is the fastest convergent plate boundary in the world with the most active mantle seismicity. This zone shows unique tectonic features including Samoan volcanic lineament of plume-driven origin near the northern rim of the Tonga subducting slab. The proximity of the Samoa hotspot to the slab is enigmatic and invokes debates on interactions between the Samoa plume and the Tonga subduction. Based on long-term observations of intermediate and deep-focus Tonga earthquakes reported in the Global Centroid Moment Tensor (CMT) catalog, we provide novel detailed imaging of this region. Accurate traveltime residua of the P- and S-waves recorded at two nearby seismic stations of the Global Seismographic Network are inverted for the P- and S-wave velocities and their ratio and reveal their pronounced lateral variations. In particular, they differ for the southern and northern parts of the Tonga subduction region. While no distinct anomalies ar...

Research paper thumbnail of Traveltime Calculations for qP, qSV, and qSH Waves in Two‐Dimensional Tilted Transversely Isotropic Media

Journal of Geophysical Research: Solid Earth, 2020

This is the author manuscript accepted for publication and has undergone full peer review but has... more This is the author manuscript accepted for publication and has undergone full peer review but has not been through the copyediting, typesetting, pagination and proofreading process, which may lead to differences between this version and the Version of Record. Please cite this article as

Research paper thumbnail of Non-double-couple earthquakes in 2017 swarm in Reykjanes Peninsula, SW Iceland: Sensitive indicator of volcano-tectonic movements at slow-spreading rift

Earth and Planetary Science Letters, 2021

The analysis of the 2017 earthquake swarm along the obliquely divergent Reykjanes Peninsula plate... more The analysis of the 2017 earthquake swarm along the obliquely divergent Reykjanes Peninsula plate boundary revealed the most frequent focal mechanisms corresponding to main activated fault, which relates to transform faulting of the North Atlantic Rift in Iceland. Detailed double-difference locations, focal mechanisms and non-double-couple (non-DC) volumetric components of seismic moment tensors indicate an activation of three fault segments suggesting continuous interactions between tectonic and magmatic processes. They are related to inflation/deflation of a vertical magmatic dike and comprise: (1) shearing at strike-slip transform fault with left lateral motion; (2) collapses at normal faulting with negative volumetric components due to magma/fluid escape, and (3) shear-tensile opening at oblique strike-slip faulting with positive volumetric components connected to flow of trapped overpressurized fluids. The identification of three regimes of complex volcano-tectonic evolution in divergent plate movement proves an enormous capability of the non-DC volumetric components to map tectonic processes in such settings.

Research paper thumbnail of The failure of testing for cosmic opacity via the distance-duality relation

Monthly Notices of the Royal Astronomical Society, 2020

The distance-duality relation (DDR) between the luminosity distance DL and the angular diameter d... more The distance-duality relation (DDR) between the luminosity distance DL and the angular diameter distance DA is viewed as a powerful tool for testing for the opacity of the Universe, being independent of any cosmological model. It was applied by many authors, who mostly confirm its validity and report a negligible opacity of the Universe. Nevertheless, a thorough analysis reveals that applying the DDR in cosmic opacity tests is tricky. Its applicability is strongly limited because of a non-unique interpretation of the DL data in terms of cosmic opacity and a rather low accuracy and deficient extent of currently available DA data. Moreover, authors usually assume that cosmic opacity is frequency independent and parametrize it in their tests by a prescribed phenomenological function. In this way, they only prove that cosmic opacity does not follow their assumptions. As a consequence, no convincing evidence of transparency of the universe using the DDR has so far been presented.

Research paper thumbnail of Non‐Double‐Couple Moment Tensors of Earthquakes Calculated Using Empirical Green’s Functions

Seismological Research Letters, 2019

We present a joint inversion for empirical Green’s functions (EGFs) and high‐resolution non‐doubl... more We present a joint inversion for empirical Green’s functions (EGFs) and high‐resolution non‐double‐couple (non‐DC) moment tensors. First, the EGFs are constructed using known moment tensors of earthquakes occurring in a small focal zone. Second, the estimated EGFs are applied to refine the original moment tensors used for constructing the EGFs. Because the EGFs describe the velocity model better than the standard GFs, the refined moment tensors are more accurate. The method is applied to real observations of earthquakes of the 2008 swarm in West Bohemia, Czech Republic, where tiny details in fracturing in the focal zone are revealed. Refined moment tensors indicate fault closing caused by compaction of fault gouge during fracturing process related to fault weakening by fluids in the focal zone. The application of the proposed inversion can improve moment tensors reported in existing local, regional, or global catalogs for areas with a concentrated seismicity.

Research paper thumbnail of Frequency‐Dependent Moment Tensors of Induced Microearthquakes

Geophysical Research Letters, Jun 20, 2019

Analysis of 984 induced microearthquakes from The Geysers geothermal reservoir in California reve... more Analysis of 984 induced microearthquakes from The Geysers geothermal reservoir in California reveals that the retrieved moment tensors depend on the frequency band of the inverted waveforms. The observed dependence is more significant for the percentages of the double-couple, compensated linear vector dipole, and isotropic (ISO) components than for the focal mechanisms. The average root-mean-square of the moment tensors obtained in different frequency bands is correlated with spectra of ambient noise. The percentages of double-couple and ISO components tend to decrease and increase with the upper cutoff frequency (f u), respectively. This suggests that shear rupture radiates energy preferentially in a lower frequency band and tensile rupture in a higher frequency band. Events displaying a strong increase of the ISO with f u are confined within the same depth interval as the injection points. This might be related to the strong thermoelastic effects in the vicinity of injection points that promote opening of small cracks adjacent to the main fractures. Plain Language Summary Moment tensor (MT) describes shear and tensile motions in the earthquake source. The components of MT are usually assumed to be independent of the frequency. However, this assumption may not satisfy the complex rupture process of induced microearthquakes. We use a novel approach to investigate 984 induced microearthquakes from The Geysers geothermal reservoir in California and find that the retrieved MTs depend on the frequency band of input waveforms. The observed dependence is more significant for the components of MT measuring the proportions of seismic energy than for the components determining fault geometry. The component of MT describing shear motion shows a different frequency dependence than that describing tensile motion, suggesting that these two motions occur on the structures with different spatial scales. A subset of seismic events is identified to have a distinct feature of frequency dependence. These events only occur in the layer where the cool water is injected into the hot reservoir and do not migrate downward as the other events. This might be related to the strong thermal effects in the vicinity of injection points that promote the opening of small cracks adjacent to the main fractures.

Research paper thumbnail of Moment tensor inversion of waveforms: a two-step time-frequency approach

Geophysical Journal International, Jul 30, 2012

We present a moment tensor inversion of waveforms, which is more robust and yields more stable an... more We present a moment tensor inversion of waveforms, which is more robust and yields more stable and more accurate results than standard approaches. The inversion is performed in two steps and combines inversions in time and frequency domains. First, the inversion for the source-time function is performed in the frequency domain using complex spectra. Second, the time-domain inversion for the moment tensor is performed using the source-time function calculated in the first step. In this way, we can consider a realistic, complex source-time function and still keep the final moment tensor inversion linear. Using numerical modelling, we compare the efficiency and accuracy of the proposed approach with standard waveform inversions. We study the sensitivity of the retrieved double-couple and non-double-couple components of the moment tensors to noise in the data, to inaccuracies of the location and of the velocity model, and to the type of the focal mechanism. Finally, the proposed moment tensor inversion is tested on real data observed in a complex 3-D inhomogeneous geological environment: a production blast and a rockburst in the Pyhäsalmi ore mine, Finland.

Research paper thumbnail of Detection of high-frequency tensile vibrations of a fault during shear rupturing: observations from the 2008 West Bohemia swarm

Geophysical Journal International, Jul 21, 2011

The analysis of 12 earthquakes of magnitudes between 1.7 and 3.7 that occurred in 2008 in West Bo... more The analysis of 12 earthquakes of magnitudes between 1.7 and 3.7 that occurred in 2008 in West Bohemia, Czech Republic reveals that shear rupturing along a fault is accompanied by weak tensile vibrations of the fault. The vibrations are of a narrow frequency band with frequencies distinctly higher than those of shear rupturing. The tensile vibrations decay slowly in time and often resemble resonant waves. They complicate the radiated P waveforms and the P-wave radiation pattern. The tensile vibrations can be observed in waveforms in directions near the nodal lines where the dominance of shear-faulting radiation is lost. The tensile vibrations are probably generated by opening of the fault during shear rupturing or by creating a wing tensile crack at the tip of the fault when shear fracturing stops.

Research paper thumbnail of Missing dust signature in the cosmic microwave background

Monthly Notices of the Royal Astronomical Society: Letters, May 6, 2017

I examine a possible spectral distortion of the cosmic microwave background (CMB) due to its abso... more I examine a possible spectral distortion of the cosmic microwave background (CMB) due to its absorption by galactic and intergalactic dust. I show that even subtle intergalactic opacity of 1 × 10 −7 mag h Gpc −1 at the CMB wavelengths in the local Universe causes non-negligible CMB absorption and decline of the CMB intensity because the opacity steeply increases with redshift. The CMB should be distorted even during the epoch of the Universe defined by redshifts z < 10. For this epoch, the maximum spectral distortion of the CMB is at least 20 × 10 −22 W m −2 Hz −1 sr −1 at 300 GHz, which is well above the sensitivity of the COBE/FIRAS, WMAP or Planck flux measurements. If dust mass is considered to be redshift dependent with noticeable dust abundance at redshifts 2-4, the predicted CMB distortion would be even higher. The CMB would also be distorted in a perfectly transparent universe due to dust in galaxies, but this effect is lower by one order than that due to intergalactic opacity. The fact that the distortion of the CMB by dust is not observed is intriguing and questions either opacity and extinction law measurements or validity of the current model of the Universe.

Research paper thumbnail of Universe opacity and EBL

Monthly Notices of the Royal Astronomical Society, Nov 3, 2016

The observed extragalactic background light (EBL) is affected by light attenuation due to absorpt... more The observed extragalactic background light (EBL) is affected by light attenuation due to absorption of light by galactic and intergalactic dust in the Universe. Even galactic opacity of 10-20 per cent and minute universe intergalactic opacity of 0.01 mag h Gpc −1 at the local Universe have a significant impact on the EBL because obscuration of galaxies and density of intergalactic dust increase with redshift as (1 + z) 3. Consequently, intergalactic opacity increases and the Universe becomes considerably opaque at z > 3. Adopting realistic values for galactic and intergalactic opacity, the estimates of the EBL for the expanding dusty universe are close to observations. The luminosity density evolution fits well measurements. The model reproduces a steep increase of the luminosity density at z < 2, its maximum at z = 2-3, and its decrease at higher redshifts. The increase of the luminosity density at low z is not produced by the evolution of the star formation rate but by the fact that the Universe occupied a smaller volume in previous epochs. The decline of the luminosity density at high z originates in the opacity of the Universe. The calculated bolometric EBL ranges from 100 to 200 nW m −2 sr −1 and is within the limits of 40 and 200 nW m −2 sr −1 of current EBL observations. The model predicts 98 per cent of the EBL coming from radiation of galaxies at z < 3.5. Accounting for light extinction by intergalactic dust implies that the Universe was probably more opaque than dark for z > 3.5.

Research paper thumbnail of Stress Inversion of Regional Seismicity in the Sea of Marmara Region, Turkey

Pure and Applied Geophysics, Sep 3, 2018

In this study we derive the stress tensor and its local variations throughout the Marmara region,... more In this study we derive the stress tensor and its local variations throughout the Marmara region, Turkey. Based on a recently compiled 10-year earthquake catalogue, we directly invert first-motion polarity data and quantify confidence intervals for the principal stress orientations. We find a combined strike-slip and normal faulting stress field for the Marmara region generally reflecting the overall transtensional setting. However, the results clearly show moderate local variations of the stress field. The largest (r 1) and intermediate (r 2) principal stresses show an average regional trend of N125 E and locally varying plunges. The least principal stress (r 3) is well resolved in its confidence interval and consistent throughout the region with an average trend of $ N35 E and a subhorizontal plunge. The eastern Sea of Marmara shows local stress field orientations with pronounced strike-slip (northern part) and normal faulting (southern part) components. Along the central Marmara region, normal faulting tends to dominate, while a well resolved strike-slip stress regime is found in the western Sea of Marmara region. Regarding the faulting mechanism of an earthquake with magnitude up to 7.4 which is expected in this area in direct vicinity of the Istanbul metropolitan region, our results imply that neither strike-slip nor normal faulting kinematics can be excluded.

Research paper thumbnail of Inversion for parameters of tensile earthquakes

Journal of Geophysical Research, Aug 10, 2001

The tensile source model generalizes the shear source model by assuming that the slip vector can ... more The tensile source model generalizes the shear source model by assuming that the slip vector can be arbitrarily oriented with respect to the fault and is not constrained to lie within the fault plane. The proposed inversion for the parameters of tensile sources is based on the evaluation of the isotropic (ISO), compensated linear vector dipole (CLVD), and double-couple (DC) components in seismic moment tensors. The most significant parameters inverted are the /•//a ratio at the fault (denoted as the tc parameter) and the inclination a of the slip vector from the fault. The tc parameter is significant for discriminating noisy moment tensors of shear earthquakes from those of tensile earthquakes. The inclination a can be accurately determined from the DC component in the moment tensor because the DC component rapidly decreases with increasing a. For example, the inclination of 20 ø causes DC being-50-60% only. The inversion is applied to earthquakes which occurred in January 1997 in West Bohemia, Czech Republic. It is shown that some of these earthquakes display tensile faulting. The tc parameter is-0.1. The inclination of the slip from the fault attains values of up to 20 ø. This inclination is a result of tensile traction and reduced shear traction along the fault and high-fluid pressure in the region. 16,339 16,340 VAVRY(•UK: INVERSION FOR PARAMETERS OF TENSILE EARTHQUAKES 4 5 K-parameter 5 ß eo o' ß ß øø ß ß 4 2 '. ' 00 ' ß ß 000 • 00 ß • ß ß. '. .. ß. '. .

Research paper thumbnail of Varying speed of light in the conformal cosmology

Zenodo (CERN European Organization for Nuclear Research), Dec 22, 2022

The law of constancy of the velocity of light in vacuo, which constitutes one of the fundamental ... more The law of constancy of the velocity of light in vacuo, which constitutes one of the fundamental assumptions in the special theory of relativity and to which we have already frequently referred, cannot claim an unlimited validity.

Research paper thumbnail of Efficiency of Surface Monitoring Layouts for Retrieving Accurate Moment Tensors in Hydraulic Fracturing Experiments

Pure and Applied Geophysics, Aug 22, 2022

We study the sensor layouts of surface monitoring systems for injection areas in hydraulic fractu... more We study the sensor layouts of surface monitoring systems for injection areas in hydraulic fracturing experiments, which maximize the accuracy of retrieved moment tensors. The moment tensors (MTs) are determined using noisy synthetic P-wave amplitudes of microearthquakes with varying mechanisms. An optimum sensor layout is searched by minimizing a difference between the true and inverted MTs. First, we tested the efficiency of the circular networks. We focused on one-circle and two-circle layouts of various sizes and numbers of sensors on each circle and with their centre in the epicentral region. The results show that the optimal layout for events distributed within a circular epicentral area is characterized by: (1) one sensor fixed in the centre of the area; (2) about 1/10 of the total number of sensors gathered near the centre; and (3) the rest of sensors evenly distributed on a circle surrounding the area with the takeoff angle of 135°. In homogeneous media, this angle corresponds to the radius of the circle comparable with depth of microearthquakes. Second, we compared the efficiency of the circular layout with other layouts: regular-grid, star-shaped and uniform focal-sphere layouts. Taking 25 sensors and 81 sensors as examples, we show that the two-circle layout is always the best, which means that we can achieve more accurate MTs using the circular layout than with other layouts, if the number of sensors in the experiment is fixed. This contradicts a common opinion that networks, which cover the target area, work equally well irrespective of their layout.

Research paper thumbnail of Gravitational orbits in the expanding Universe revisited

Frontiers in Astronomy and Space Sciences, Feb 6, 2023

Modified Newtonian equations for gravitational orbits in the expanding Universe indicate that loc... more Modified Newtonian equations for gravitational orbits in the expanding Universe indicate that local gravitationally bounded systems like galaxies and planetary systems are unaffected by the expansion of the Universe. This result is derived for the space expansion described by the standard FLRW metric. In this paper, the modified Newtonian equations are derived for the space expansion described by the conformal cosmology (CC) metric. In this metric, the comoving and proper times are different similarly as the comoving and proper distances. As shown by Vavryčuk (Front. Phys. 2022), this metric is advantageous, because it properly predicts the cosmic time dilation, and fits the Type Ia supernova luminosity observations with no need to introduce dark energy. Surprisingly, the solution of the equations for gravitational orbits based on the CC metric behaves quite differently than that based on the FLRW metric. In contrast to the common opinion that local systems resist the space expansion, they expand according to the Hubble flow in the CC metric. The evolution of the local systems with cosmic time is exemplified on numerical modelling of spiral galaxies. The size of the spiral galaxies grows consistently with observations and a typical spiral pattern is well reproduced. The theory predicts flat rotation curves without an assumption of dark matter surrounding the galaxy. The theory resolves challenges to the ΛCDM model such as the problem of faint satellite galaxies, baryonic Tully-Fisher relation or the radial acceleration relation. Furthermore, puzzles in the solar system are successfully explained such as the Faint young Sun paradox or the Moon's and Titan's orbit anomalies.

Research paper thumbnail of Cosmological Redshift and Cosmic Time Dilation in the FLRW Metric

Frontiers in Physics, May 23, 2022

The paper shows that the commonly used Friedmann-Lemaitre-Robertson-Walker (FLRW) metric describi... more The paper shows that the commonly used Friedmann-Lemaitre-Robertson-Walker (FLRW) metric describing the expanding Universe must be modified to properly predict the cosmological redshift. It is proved that the change in the frequency of redshifted photons is always connected with time dilation, similarly as for the gravitational redshift. Therefore, the cosmic time runs differently at high redshifts than at present. Consequently, the cosmological time must be identified with the conformal time and the standard FLRW metric must be substituted by its conformal version. The correctness of the proposed conformal metric is convincingly confirmed by Type Ia supernovae (SNe Ia) observations. The standard FLRW metric produces essential discrepancy with the SNe Ia observations called the 'supernova dimming', and dark energy has to be introduced to comply theoretical predictions with data. By contrast, the conformal FLRW metric fits data well with no need to introduce any new free parameter. Hence, the discovery of the supernova dimming actually revealed a failure of the FLRW metric and introducing dark energy was just an unsuccessful attempt to cope with the problem within this false metric. Obviously, adopting the conformal FLRW metric for describing the evolution of the Universe has many fundamental cosmological consequences.

Research paper thumbnail of Universe opacity and CMB

Monthly Notices of the Royal Astronomical Society, Apr 18, 2018

A cosmological model, in which the cosmic microwave background (CMB) is a thermal radiation of in... more A cosmological model, in which the cosmic microwave background (CMB) is a thermal radiation of intergalactic dust instead of a relic radiation of the big bang, is revived and revisited. The model suggests that a virtually transparent local Universe becomes considerably opaque at redshifts z > 2-3. Such opacity is hardly to be detected in the Type Ia supernova data, but confirmed using quasar data. The opacity steeply increases with redshift because of a high proper density of intergalactic dust in the previous epochs. The temperature of intergalactic dust increases as (1 + z) and exactly compensates the change of wavelengths due to redshift, so that the dust radiation looks apparently like the radiation of the blackbody with a single temperature. The predicted dust temperature is T D = 2.776 K, which differs from the CMB temperature by 1.9 per cent only, and the predicted ratio between the total CMB and extragalactic background light (EBL) intensities is 13.4 which is close to 12.5 obtained from observations. The CMB temperature fluctuations are caused by EBL fluctuations produced by galaxy clusters and voids in the Universe. The polarization anomalies of the CMB correlated with temperature anisotropies are caused by the polarized thermal emission of needle-shaped conducting dust grains aligned by large-scale magnetic fields around clusters and voids. A strong decline of the luminosity density for z > 4 is interpreted as the result of high opacity of the Universe rather than of a decline of the global stellar mass density at high redshifts.

Research paper thumbnail of Universe opacity and Type Ia supernova dimming

Monthly Notices of the Royal Astronomical Society: Letters, Aug 19, 2019

In this paper, I revoke a debate about an origin of Type Ia supernova (SN Ia) dimming. I argue th... more In this paper, I revoke a debate about an origin of Type Ia supernova (SN Ia) dimming. I argue that except for a commonly accepted accelerating expansion of the Universe, a conceivable alternative for explaining this observation is universe opacity caused by light extinction by intergalactic dust, even though it is commonly assumed that this effect is negligible. Using data of the Union2.1 SN Ia compilation, I find that the standard cold dark matter (CDM) model and the opaque universe model fit the SN Ia measurements at redshifts z < 1.4 comparably well. The optimum solution for the opaque universe model is characterized by the B-band intergalactic opacity λ B = 0.10 ± 0.03 Gpc −1 and the Hubble constant H 0 = 68.0 ± 2.5 km s −1 Mpc −1. The intergalactic opacity is higher than that obtained from independent observations but still within acceptable limits. This result emphasizes that the issue of the accelerating expansion of the Universe as the origin of the SN Ia dimming is not yet definitely resolved. Obviously, the opaque universe model as an alternative to the CDM model is attractive, because it avoids puzzles and controversies associated with dark energy and the accelerating expansion.

Research paper thumbnail of Impact of galactic and intergalactic dust on the stellar EBL

Astrophysics and Space Science, May 25, 2016

Current theories assume that the low intensity of the stellar extragalactic background light (ste... more Current theories assume that the low intensity of the stellar extragalactic background light (stellar EBL) is caused by finite age of the Universe because the finite-age factor limits the number of photons that have been pumped into the space by galaxies and thus the sky is dark in the night. We oppose this opinion and show that two main factors are responsible for the extremely low intensity of the observed stellar EBL. The first factor is a low mean surface brightness of galaxies, which causes a low luminosity density in the local Universe. The second factor is light extinction due to absorption by galactic and intergalactic dust. Dust produces a partial opacity of galaxies and of the Universe. The galactic opacity reduces the intensity of light from more distant background galaxies obscured by foreground galaxies. The inclination-averaged values of the effective extinction A V for light passing through a galaxy is about 0.2 mag. This causes that distant background galaxies become apparently faint and do not contribute to the EBL significantly. In addition, light of distant galaxies is dimmed due to absorption by intergalactic dust. Even a minute intergalactic opacity of 1 × 10 −2 mag per Gpc is high enough to produce significant effects on the EBL. As a consequence, the EBL is comparable with or lower than the mean surface brightness of galaxies. Comparing both extinction effects, the impact of the intergalactic opacity on the EBL is more significant than the obscuration of distant galaxies by partially opaque foreground galaxies by factor of 10 or more. The absorbed starlight heats up the galactic and intergalactic dust and is further re-radiated at IR, FIR and microwave spectrum. Assuming static infinite universe with no galactic B V. Vavryčuk

Research paper thumbnail of Non-double-couple earthquakes of 1997 January in West Bohemia, Czech Republic: evidence of tensile faulting

Geophysical Journal International, May 1, 2002

A mixed family of double-couple (DC) and non-double-couple (non-DC) earthquakes was observed duri... more A mixed family of double-couple (DC) and non-double-couple (non-DC) earthquakes was observed during the 1997 January earthquake swarm in West Bohemia, which is a geothermal region typical for the occurrence of earthquakes swarms. The DC and non-DC earthquakes occurred within a small area of less than 1 km 3 on faults of different orientations. The stress in the area is determined from focal mechanisms and attains values (plunge/azimuth): σ 1 = 33 • /156 • , σ 2 = 48 • /20 • , σ 3 = 23 • /262 • , with a shape ratio of R = 0.69 ± 0.15. The error in the stress directions (plunge/azimuth) is up to ∼5 • /10 •. The absolute stress values were estimated to be σ 1 = 350 MPa, σ 2 = 220 MPa and σ 3 = 162 MPa. The lithostatic stress is 250 MPa. The stress analysis shows that the DC earthquakes occurred on optimally oriented faults (with high shear traction) but the non-DC earthquakes occurred on misoriented faults (with low shear traction). The percentage of the DC in earthquakes clearly correlates with the magnitude of shear traction: high/low DC is associated with high/low shear traction. This indicates that the type of faulting is probably controlled by tectonic stress and that the non-DC earthquakes are not related to pure shear faulting but may combine shear and tensile faulting. The tensile faulting is manifested by positive isotropic and compensated linear vector dipole components. The tensile faulting is conditioned by high pore fluid pressure, which was estimated to be approximately 244 MPa. The fluid pressure is less than the lithostatic stress by ∼5 MPa. The ratio of the fluid pressure to the maximum compressive stress is 0.7.

Research paper thumbnail of Contact of the Samoan Plume with the Tonga Subduction from Intermediate and Deep-Focus Earthquakes

Surveys in Geophysics, 2021

The Tonga subduction zone in the south-west Pacific is the fastest convergent plate boundary in t... more The Tonga subduction zone in the south-west Pacific is the fastest convergent plate boundary in the world with the most active mantle seismicity. This zone shows unique tectonic features including Samoan volcanic lineament of plume-driven origin near the northern rim of the Tonga subducting slab. The proximity of the Samoa hotspot to the slab is enigmatic and invokes debates on interactions between the Samoa plume and the Tonga subduction. Based on long-term observations of intermediate and deep-focus Tonga earthquakes reported in the Global Centroid Moment Tensor (CMT) catalog, we provide novel detailed imaging of this region. Accurate traveltime residua of the P- and S-waves recorded at two nearby seismic stations of the Global Seismographic Network are inverted for the P- and S-wave velocities and their ratio and reveal their pronounced lateral variations. In particular, they differ for the southern and northern parts of the Tonga subduction region. While no distinct anomalies ar...

Research paper thumbnail of Traveltime Calculations for qP, qSV, and qSH Waves in Two‐Dimensional Tilted Transversely Isotropic Media

Journal of Geophysical Research: Solid Earth, 2020

This is the author manuscript accepted for publication and has undergone full peer review but has... more This is the author manuscript accepted for publication and has undergone full peer review but has not been through the copyediting, typesetting, pagination and proofreading process, which may lead to differences between this version and the Version of Record. Please cite this article as

Research paper thumbnail of Non-double-couple earthquakes in 2017 swarm in Reykjanes Peninsula, SW Iceland: Sensitive indicator of volcano-tectonic movements at slow-spreading rift

Earth and Planetary Science Letters, 2021

The analysis of the 2017 earthquake swarm along the obliquely divergent Reykjanes Peninsula plate... more The analysis of the 2017 earthquake swarm along the obliquely divergent Reykjanes Peninsula plate boundary revealed the most frequent focal mechanisms corresponding to main activated fault, which relates to transform faulting of the North Atlantic Rift in Iceland. Detailed double-difference locations, focal mechanisms and non-double-couple (non-DC) volumetric components of seismic moment tensors indicate an activation of three fault segments suggesting continuous interactions between tectonic and magmatic processes. They are related to inflation/deflation of a vertical magmatic dike and comprise: (1) shearing at strike-slip transform fault with left lateral motion; (2) collapses at normal faulting with negative volumetric components due to magma/fluid escape, and (3) shear-tensile opening at oblique strike-slip faulting with positive volumetric components connected to flow of trapped overpressurized fluids. The identification of three regimes of complex volcano-tectonic evolution in divergent plate movement proves an enormous capability of the non-DC volumetric components to map tectonic processes in such settings.

Research paper thumbnail of The failure of testing for cosmic opacity via the distance-duality relation

Monthly Notices of the Royal Astronomical Society, 2020

The distance-duality relation (DDR) between the luminosity distance DL and the angular diameter d... more The distance-duality relation (DDR) between the luminosity distance DL and the angular diameter distance DA is viewed as a powerful tool for testing for the opacity of the Universe, being independent of any cosmological model. It was applied by many authors, who mostly confirm its validity and report a negligible opacity of the Universe. Nevertheless, a thorough analysis reveals that applying the DDR in cosmic opacity tests is tricky. Its applicability is strongly limited because of a non-unique interpretation of the DL data in terms of cosmic opacity and a rather low accuracy and deficient extent of currently available DA data. Moreover, authors usually assume that cosmic opacity is frequency independent and parametrize it in their tests by a prescribed phenomenological function. In this way, they only prove that cosmic opacity does not follow their assumptions. As a consequence, no convincing evidence of transparency of the universe using the DDR has so far been presented.

Research paper thumbnail of Non‐Double‐Couple Moment Tensors of Earthquakes Calculated Using Empirical Green’s Functions

Seismological Research Letters, 2019

We present a joint inversion for empirical Green’s functions (EGFs) and high‐resolution non‐doubl... more We present a joint inversion for empirical Green’s functions (EGFs) and high‐resolution non‐double‐couple (non‐DC) moment tensors. First, the EGFs are constructed using known moment tensors of earthquakes occurring in a small focal zone. Second, the estimated EGFs are applied to refine the original moment tensors used for constructing the EGFs. Because the EGFs describe the velocity model better than the standard GFs, the refined moment tensors are more accurate. The method is applied to real observations of earthquakes of the 2008 swarm in West Bohemia, Czech Republic, where tiny details in fracturing in the focal zone are revealed. Refined moment tensors indicate fault closing caused by compaction of fault gouge during fracturing process related to fault weakening by fluids in the focal zone. The application of the proposed inversion can improve moment tensors reported in existing local, regional, or global catalogs for areas with a concentrated seismicity.