The correlation between the characteristics of seismic wave propagation in Western Caucasus and the geological–tectonic features of the region

The relationship between the characteristics of seismic waves in the Western Caucasus and the geological-tectonic structure of the region is studied for identifying the specificity of seismic propagation in the mountainous regions with a complicated geological structure and forecasting the characteristics of the propagation from the geological and tectonic data. The interpretation is presented for the estimates of the Q-factor of the medium (Q(f) ~ 55f^0.9 in the region of Sochi and Q(f) ~ 90f^0.7 in the region of Anapa), seismic wave enhancement in the upper crustal layers (A(f) ~ 1), and peak ground acceleration residuals, which were previously determined from the records of the local earthquakes and show the distributions of local variations in the parameters of seismic wave radiation and propagation. The obtained characteristics are interpreted in the context of the up-to-date information about the tectonic, geological, and deep structure of the epicentral zones in the Western Caucasus and neighboring territory of the Black Sea. The discrepancies revealed in the low-frequency behavior of the Q-factor in the vicinities of Sochi and Anapa is accounted for by the spatial scale and character of tectonic dislocations of the rocks in these regions. The local variations in the parameters of seismic radiation and propagation are probably related to the geological features of the region such as the fault structures, including the thrusts, shatter zones, oblique seismic boundaries, variations in the thickness and consolidation of the sedimentary cover, as well as the peculiarities in the structure and material composition of the basement.     

Features of Radiation and Propagation of Seismic Waves in the Northern Caucasus: Manifestations in Regional Coda

Based on the Anapa (ANN) seismic station records of ~40 earthquakes (M_W > 3.9) that occurred within ~300 km of the station since 2002 up to the present time, the source parameters and quality factor of the Earth’s crust (Q(f)) and upper mantle are estimated for the S-waves in the 1–8 Hz frequency band. The regional coda analysis techniques which allow separating the effects associated with seismic source (source effects) and with the propagation path of seismic waves (path effects) are employed. The Q-factor estimates are obtained in the form Q(f) = 90 × f 0.7 for the epicentral distances r < 120 km and in the form Q(f) = 90 × f1.0 for r > 120 km. The established Q(f) and source parameters are close to the estimates for Central Japan, which is probably due to the similar tectonic structure of the regions. The shapes of the source parameters are found to be independent of the magnitude of the earthquakes in the magnitude range 3.9–5.6; however, the radiation of the high-frequency components (f > 4–5 Hz) is enhanced with the depth of the source (down to h ~ 60 km). The estimates Q(f) of the quality factor determined from the records by the Sochi, Anapa, and Kislovodsk seismic stations allowed a more accurate determination of the seismic moments and magnitudes of the Caucasian earthquakes. The studies will be continued for obtaining the Q(f) estimates, geometrical spreading functions, and frequency-dependent amplification of seismic waves in the Earth’s crust in the other regions of the Northern Caucasus.     

The seismic wave absorption in the crust and upper mantle in the vicinity of the Kislovodsk seismic station

The Q-factor estimates of the Earth’s crust and upper mantle as the functions of frequency (Q(f)) are obtained for the seismic S-waves at frequencies up to ~35 Hz. The estimates are based on the data for ~40 earthquakes recorded by the Kislovodsk seismic station since 2000. The magnitudes of these events are M_W > 3.8, the sources are located in the depth interval from 1 to 165 km, and the epicentral distances range from ~100 to 300 km. The Q-factor estimates are obtained by the methods developed by Aki and Rautian et al., which employ the suppression of the effects of the source radiation spectrum and local site responses in the S-wave spectra by the coda waves measured at a fixed lapse time (time from the first arrival). The radiation pattern effects are cancelled by averaging over many events whose sources are distributed in a wide azimuthal sector centered at the receiving site. The geometrical spreading was specified in the form of a piecewise-continuous function of distance which behaves as 1/R at the distances from 1 to 50 km from the source, has a plateau at 1/50 in the interval from 50–70 km to 130–150 km, and decays as \({\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 {\sqrt R }}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{${\sqrt R }$}}\) beyond 130–150 km. For this geometrical spreading model and some of its modifications, the following Q-factor estimates are obtained: Q(f) ~ 85f^0.9 at the frequencies ranging from ~1 to 20 Hz and Q(f) ~ 75f^1.0 at the frequencies ranging from ~1 to 35 Hz.     

<Emphasis Type="Italic">Q</Emphasis><Subscript>c</Subscript> and <Emphasis Type="Italic">Q</Emphasis><Subscript>S</Subscript> wave attenuation of South African earthquakes

Quality factor Q, which describes the attenuation of seismic waves with distance, was determined for South Africa using data recorded by the South African National Seismograph Network. Because of an objective paucity of seismicity in South Africa and modernisation of the seismograph network only in 2007, I carried out a coda wave decay analysis on only 13 tectonic earthquakes and 7 mine-related events for the magnitude range 3.6?≤?M _L ?≤?4.4. Up to five seismograph stations were utilised to determine Q _c for frequencies at 2, 4, 8 and 16 Hz resulting in 84 individual measurements. The constants Q ₀ and α were determined for the attenuation relation Q _c(f)?=?Q ₀ f ^α . The result was Q ₀?=?396?±?29 and α?=?0.72?±?0.04 for a lapse time of 1.9*(t _s???t ₀) (time from origin time t ₀ to the start of coda analysis window is 1.9 times the S-travel time, t _s) and a coda window length of 80 s. This lapse time and coda window length were found to fit the most individual frequencies for a signal-to-noise ratio of at least 3 and a minimum absolute correlation coefficient for the envelope of 0.5. For a positive correlation coefficient, the envelope amplitude increases with time and Q _c was not calculated. The derived Q _c was verified using the spectral ratio method on a smaller data set consisting of nine earthquakes and one mine-related event recorded by up to four seismograph stations. Since the spectral ratio method requires absolute amplitudes in its calculations, site response tests were performed to select four appropriate stations without soil amplification and/or signal distortion. The result obtained for Q _S was Q ₀?=?391?±?130 and α?=?0.60?±?0.16, which agrees well with the coda Q _c result.     

Attenuation coefficients of Rayleigh and <Emphasis Type="Italic">Lg</Emphasis> waves

Analysis of the frequency dependence of the attenuation coefficient leads to significant changes in interpretation of seismic attenuation data. Here, several published surface-wave attenuation studies are revisited from a uniform viewpoint of the temporal attenuation coefficient, denoted by χ. Theoretically, χ( f) is expected to be linear in frequency, with a generally non-zero intercept γ?=?χ(0) related to the variations of geometrical spreading, and slope dχ/df = π/Q _e caused by the effective attenuation of the medium. This phenomenological model allows a simple classification of χ( f) dependences as combinations of linear segments within several frequency bands. Such linear patterns are indeed observed for Rayleigh waves at 500–100-s and 100–10-s periods, and also for Lg from ~2 s to ~1.5 Hz. The Lg χ( f) branch overlaps with similar linear branches of body, Pn, and coda waves, which were described earlier and extend to ~100 Hz. For surface waves shorter than ~100 s, γ values recorded in areas of stable and active tectonics are separated by the levels of \(\gamma _{D} \approx 0.2 \times 10^{-3}\) s^???1 (for Rayleigh waves) and 8 ×10^???3 s^???1 (for Lg). The recently recognized discrepancy between the values of Q measured from long-period surface waves and normal-mode oscillations could also be explained by a slight positive bias in the geometrical spreading of surface waves. Similarly to the apparent χ, the corresponding linear variation with frequency is inferred for the intrinsic attenuation coefficient, χ _i , which combines the effects of geometrical spreading and dissipation within the medium. Frequency-dependent rheological or scattering Q is not required for explaining any of the attenuation observations considered in this study. The often-interpreted increase of Q with frequency may be apparent and caused by using the Q-based model of attenuation and following preferred Q( f) dependences while ignoring the true χ( f) trends within the individual frequency bands.     

Near-source attenuation of high-frequency body waves beneath the New Madrid Seismic Zone

Attenuation characteristics in the New Madrid Seismic Zone (NMSZ) are estimated from 157 local seismograph recordings out of 46 earthquakes of 2.6?≤?M?≤?4.1 with hypocentral distances up to 60 km and focal depths down to 25 km. Digital waveform seismograms were obtained from local earthquakes in the NMSZ recorded by the Center for Earthquake Research and Information (CERI) at the University of Memphis. Using the coda normalization method, we tried to determine Q values and geometrical spreading exponents at 13 center frequencies. The scatter of the data and trade-off between the geometrical spreading and the quality factor did not allow us to simultaneously derive both these parameters from inversion. Assuming 1/R ^1.0 as the geometrical spreading function in the NMSZ, the Q _P and Q _S estimates increase with increasing frequency from 354 and 426 at 4 Hz to 729 and 1091 at 24 Hz, respectively. Fitting a power law equation to the Q estimates, we found the attenuation models for the P waves and S waves in the frequency range of 4 to 24 Hz as Q _P?=?(115.80?±?1.36) f ^{(0.495?±?0.129)} and Q _S?=?(161.34?±?1.73) f ^{(0.613?±?0.067)}, respectively. We did not consider Q estimates from the coda normalization method for frequencies less than 4 Hz in the regression analysis since the decay of coda amplitude was not observed at most bandpass filtered seismograms for these frequencies. Q _S/Q _P?>?1, for 4?≤?f?≤?24 Hz as well as strong intrinsic attenuation, suggest that the crust beneath the NMSZ is partially fluid-saturated. Further, high scattering attenuation indicates the presence of a high level of small-scale heterogeneities inside the crust in this region.     

Investigation on regional attenuation of Vrancea (Romania) intermediate-depth earthquakes

This paper aims at investigating possible regional attenuation patterns in the case of Vrancea(Romania) intermediate-depth earthquakes.Almost 500 pairs of horizontal components recorded during 13 intermediate-depth Vrancea earthquakes are employed in order to evaluate the regional attenuation patterns.The recordings are grouped according to the azimuth with regard to the Vrancea seismic source and subsequently,Q models are computed for each azimuthal zone assuming similar geometrical spreading.Moreover,the local soil amplification which was disregarded in a previous analysis performed for Vrancea intermediate-depth earthquakes is now clearly evaluated.The results show minor differences between the four regions situated in front of the Carpathian Mountains and considerable differences in attenuation of seismic waves between the forearc and backarc regions(with regard to the Carpathian Mountains).Consequently,an average Q model of the type Q(f) = 115×f~(1.25) is obtained for the four forearc regions,while a separate Q model of the type Q(f) = 70×f~(0.90) is computed for the backarc region.These results highlight the need to evaluate the seismic hazard of Romania by using ground motion models which take into account the different attenuation between the forearc/backarc regions.     

Body wave attenuation characteristics in the crust of Alborz region and North Central Iran

Attenuation of P and S waves has been investigated in Alborz and north central part of Iran using the data recorded by two permanent and one temporary networks during October 20, 2009, to December 22, 2010. The dataset consists of 14,000 waveforms from 380 local earthquakes (2 < M _L < 5.6). The extended coda normalization method (CNM) was used to estimate quality factor of P (Q _P) and S waves (Q _S) at seven frequency bands (0.375, 0.75, 1.5, 3, 6, 12, 24 Hz). The Q _P and Q _S values have been estimated at lapse times from 40 to 100 s. It has been observed that the estimated values of Q _P and Q _S are time independent; therefore, the mean values of Q _P and Q _S at different lapse times have been considered. The frequency dependence of quality factor was determined by using a power-law relationship. The frequency-dependent relationship for Q _P was estimated in the form of (62 ± 7)f ^{(1.03 ± 0.07)} and (48 ± 5)f ^{(0.95 ± 0.07)} in Alborz region and North Central Iran, respectively. These relations for Q _S for Alborz region and North Central Iran have estimated as (83 ± 8)f ^{(0.99 ± 0.07)} and (68 ± 5)f ^{(0.96 ± 0.05)}, respectively. The observed low Q values could be the results of thermoelastic effects and/or existing fracture. The estimated frequency-dependent relationships are comparable with tectonically active regions.     

Region-specific <Emphasis Type="Italic">S</Emphasis>-wave attenuation for earthquakes in northwestern Iran

In this study, continuous wavelet transform is applied to estimate the frequency-dependent quality factor of shear waves, Q _S , in northwestern Iran. The dataset used in this study includes velocigrams of more than 50 events with magnitudes between 4.0 and 6.5, which have occurred in the study area. The CWT-based method shows a high-resolution technique for the estimation of S-wave frequency-dependent attenuation. The quality factor values are determined in the form of a power law as Q _S (f)?=?(147?±?16)f ^0.71?±?0.02 and (126?±?12)f ^0.73?±?0.02 for vertical and horizontal components, respectively, where f is between 0.9 and 12 Hz. Furthermore, in order to verify the reliability of the suggested Q _S estimator method, an additional test is performed by using accelerograms of Ahar-Varzaghan dual earthquakes on August 11, 2012, of moment magnitudes 6.4 and 6.3 and their aftershocks. Results indicate that the estimated Q _S values from CWT-based method are not very sensitive to the numbers and types of waveforms used (velocity or acceleration).     

The coda attenuation of the Yao’an area in Yunnan Province

An earthquake withM=6.5 happened on January 15, 2000 in Yao’an of Yunnan Province. After the earthquake, a temporary digital network with 6 detectors around the epicenter area was set up. 402 aftershocks were located more precisely. According to coda short recording observed, the coda averaging quality factor has been acquired via Sato’s single scattering model analyses,Q _c(f)=49f ^0.95,f=1.5～20.0 Hz, which has the attenuation characteristics of high structural active region.     

A study of Guptkashi,Uttarakhand earthquake of 6 February 2017 (<Emphasis Type="Italic">M</Emphasis><Subscript><Emphasis Type="Italic">w</Emphasis></Subscript>5.3) in the Himalayan arc and implications for ground motion estimation

The 2017 Guptkashi earthquake occurred in a segment of the Himalayan arc with high potential for a strong earthquake in the near future. In this context, a careful analysis of the earthquake is important as it may shed light on source and ground motion characteristics during future earthquakes. Using the earthquake recording on a single broadband strong-motion seismograph installed at the epicenter, we estimate the earthquake’s location (30.546° N, 79.063° E), depth (H?=?19 km), the seismic moment (M₀?=?1.12×10¹⁷ Nm, M _w 5.3), the focal mechanism (φ?=?280°, δ?=?14°, λ?=?84°), the source radius (a?=?1.3 km), and the static stress drop (Δσ _s ~22 MPa). The event occurred just above the Main Himalayan Thrust. S-wave spectra of the earthquake at hard sites in the arc are well approximated (assuming ω^?2 source model) by attenuation parameters Q(f)?=?500f^0.9, κ?=?0.04 s, and f_max?=?infinite, and a stress drop of Δσ?=?70 MPa. Observed and computed peak ground motions, using stochastic method along with parameters inferred from spectral analysis, agree well with each other. These attenuation parameters are also reasonable for the observed spectra and/or peak ground motion parameters in the arc at distances ≤?200 km during five other earthquakes in the region (4.6?≤?M _w ?≤?6.9). The estimated stress drop of the six events ranges from 20 to 120 MPa. Our analysis suggests that attenuation parameters given above may be used for ground motion estimation at hard sites in the Himalayan arc via the stochastic method.     

Estimating seismic moments and Lg <Emphasis Type="Italic">Q</Emphasis> using Lg spectra

A multi-event and multi-station inverse method is presented in the paper to simultaneously estimate the seismic moments (M ₀) and source corner frequencies (f _c) of several Jiashi (Xinjiang, China) earthquakes, as well as the apparent Lg Q models for the paths from Jiashi to eight seismic stations (WMQ, AAK, TLG, MAKZ, KUR, VOS, ZRN and CHK) in Central Asia. The resultant seismic moments correlate well with the M ₀ values obtained by Harvard University using the centroid moment tensor (CMT) inversion and the surface-wave magnitudes as well. After the correction by a typical value of average radiation coefficient for regional SV waves, the M ₀ values from Lg spectral inversion are still close to the corresponding values obtained from CMT inversion. The obtained apparent Q _0Lg values (Lg Q at 1 Hz) are consistent with the tectonic features of corresponding propagation paths. The Q _0Lg values are 351±87, 349±86 and 300±27 for the paths from Jiashi to AAK, TLG and MAKZ, respectively. They are smaller than Q _0Lg values for the paths to KUR, VOS, ZRN and CHK, which are 553±72, 569±58, 550±57 and 603±65, respectively. These results agree with the condition that the paths to AAK, TLG and MAKZ mainly propagate through the mountainous Tianshan area where relatively strong seismic activities and large variations of topography are exhibited, while the paths to KUR, VOS, ZRN and CHK mainly propagate through the stable area of Kazak platform. The Q _0Lg value for the path to WMQ is 462±56. This is also in agreement with the condition that the path to WMQ is basically along the border area between Tianshan Mountain and Tarim Basin, and along this path the variations of topography and crustal thickness are moderate in comparison with that along the path to MAKZ.     

Characteristics of radiation and propagation of seismic waves in the Baikal Rift Zone estimated by simulations of acceleration time histories of the recorded earthquakes

The regularities in the radiation and propagation of seismic waves within the Baikal Rift Zone in Buryatia are studied to estimate the ground motion parameters from the probable future strong earthquakes. The regional parameters of seismic radiation and propagation are estimated by the stochastic simulation (which provides the closest agreement between the calculations and observations) of the acceleration time histories of the earthquakes recorded by the Ulan-Ude seismic station. The acceleration time histories of the strongest earthquakes (M _W ~ 3.4–4.8) that occurred in 2006–2011 at the epicentral distances of ~96–125 km and had source depths of ~8–12 km have been modeled. The calculations are conducted with estimates of the Q-factor which were previously obtained for the region. The frequency-dependent attenuation and geometrical spreading are estimated from the data on the deep structure of the crust and upper mantle (velocity sections) in the Ulan-Ude region, and the parameters determining the wave forms and duration of acceleration time histories are found by fitting. These parameters fairly well describe all the considered earthquakes. The Ulan-Ude station can be considered as the reference bedrock station with minimum local effects. The obtained estimates for the parameters of seismic radiation and propagation can be used for forecasting the ground motion from the future strong earthquakes and for constructing the seismic zoning maps for Buryatia.     

G: Fracture energy,friction and dissipation in earthquakes

Recent estimates of fracture energy G ^′ in earthquakes show a power-law dependence with slip u which can be summarized as G ^′ ∝ u ^a where a is a positive real slightly larger than one. For cracks with sliding friction, fracture energy can be equated to G _f : the post-failure integral of the dynamic weakening curve. If the dominant dissipative process in earthquakes is friction, G ^′ and G _f should be comparable and show a similar scaling with slip. We test this hypothesis by analyzing experiments performed on various cohesive and non-cohesive rock types, under wet and dry conditions, with imposed deformation typical of seismic slip (normal stress of tens of MPa, target slip velocity > 1 m/s and fast accelerations ≈ 6.5 m/s²). The resulting fracture energy G _f is similar to the seismological estimates, with G _f and G ^′ being comparable over most of the slip range. However, G _f appears to saturate after several meters of slip, while in most of the reported earthquake sequences, G ^′ appears to increase further and surpasses G _f at large magnitudes. We analyze several possible causes of such discrepancy, in particular, additional off-fault damage in large natural earthquakes.     

The study of the radiation characteristics and propagation of seismic waves in the North Caucasus by modeling the accelerograms of the recorded earthquakes

For evaluating the parameters of the vibrations of the Earth’s surface in the case of strong earthquakes, which are possible in the future, the regular patterns of the emission and propagation of seismic waves in the North Caucasus regions are investigated. The regional parameters of emission and propagation of seismic waves are evaluated by solution of the inverse problems of stochastic modeling of the accelerograms of the earthquakes, recorded by the seismic station in Sochi. The horizontal components of the strongest earthquakes (M _w ～ 3.9?5.6), that occurred in 2002–2006 within a radius of ～300 km from the seismic station, with source depths up to 60 km are modeled. For calculations of accelerograms, estimates of the quality are used, obtained earlier for this region in the form: Q(f) ～ 80 ～ f ^0.9. The parameter settings are carried out, which determine the shapes of the source spectra, the amplification of the seismic waves in the Earth’s crust, the weakening of the waves at high frequencies (κ), the parameters that determine the shape and duration of accelerograms, etc. Sufficiently good agreement of the calculated and recorded accelerograms is obtained, the regional characteristics of emission and propagation of seismic waves, which can be used for prediction of the parameters of strong motions in the North Caucasus, are evaluated; however, in the future these characteristics should be studied in more detail.     

<Emphasis Type="Italic">M</Emphasis>9 Tohoku Earthquake Hydro- and Seismic Response in the Caucasus and North Turkey

Presently, there are a lot of observations on the significant impact of strong remote earthquakes on underground water and local seismicity. Teleseismic wave trains of strong earthquakes give rise to several hydraulic effects in boreholes, namely permanent water level changes and water level oscillations, which closely mimic the seismograms (hydro-seismograms). Clear identical anomalies in the deep borehole water levels have been observed on a large part of the territory of Georgia during passing of the S and Love–Rayleigh teleseismic waves (including also multiple surface Rayleigh waves) of the 2011 Tohoku M9 earthquake. The analysis carried out in order to find dynamically triggered events (non-volcanic tremors) of the Tohoku earthquake by the accepted methodology has not revealed a clear tremor signature in the test area: the Caucasus and North Turkey. The possible mechanisms of some seismic signals of unknown origin observed during passage of teleseismic waves of Tohoku earthquake are discussed.     

Characteristics of seismic wave attenuation in the crust and upper mantle of the Northern Caucasus

The quality factor Q as a function of frequency in an S wave range of 1–8 Hz is estimated from records of ～60 earthquakes (M _w > 3.9 and source depths of 1–60 km) obtained at the Sochi seismic station at epicentral distances of less than ～300 km. Methods of Q estimation used in the paper were developed in works by Aki, Rautian, and others; they are based on the suppression of source-related and local effects in S wave spectra with the help of coda waves measured at a fixed time from the first arrival. To compensate for directivity effects, averaging was performed over the set of events whose sources were located in a wide range of back azimuths. The geometric divergence is represented as a three-segment function: 1/R, 1, and 1/√R at epicentral distances of 1/50–1/70 to 50–70 km, 50–70 to 130–150 km, and greater than 130–150 km, respectively. The geometric divergences in this model yielded the following estimates of the quality factor: Q(f) ～ 80f ^0.9 with a base of 35–280 km and Q(f) ～ 110f ^0.8 with a base of 60–280 km. The resulting combinations of the propagation path effects (Q and the geometric divergence) can be used for predicting strong motion parameters in the Northern Caucasus.     

FCaZm intelligent recognition system for locating areas prone to strong earthquakes in the Andean and Caucasian mountain belts

The fuzzy clustering and zoning method (FCAZm) of systems analysis is suggested for recognizing the areas of the probable generation of the epicenters of significant, strong, and the strongest earthquakes. FCAZm is a modified version of the previous FCAZ algorithmic system, which is advanced by the creation of the blocks of artificial intelligence that develop the system-forming algorithms. FCAZm has been applied for recognizing areas where the epicenters of the strongest (M ≥ 7³/4) earthquakes within the Andes mountain belt in the South America and significant earthquakes (M ≥ 5) in the Caucasus can emerge. The reliability of the obtained results was assessed by the seismic-history type control experiments. The recognized highly seismic zones were compared with the ones previously recognized by the EPA method and by the initial version of the FCAZ system. The modified FCAZm system enabled us to pass from simple pattern recognition in the problem of recognizing the locations of the probable emergence of strong earthquakes to systems analysis. In particular, using FCAZm we managed to uniquely recognize a subsystem of highly seismically active zones from the nonempty complement using the exact boundary.     

Tomographic inversion of near-surface <Emphasis Type="Italic">Q</Emphasis> factor by combining surface and cross-hole seismic surveys

The estimation of the quality factor Q plays a fundamental role in enhancing seismic resolution via absorption compensation in the near-surface layer. We present a new geometry that can be used to acquire field data by combining surface and cross-hole surveys to decrease the effect of geophone coupling on Q estimation. In this study, we drilled number of receiver holes around the source hole, each hole has different depth and each geophone is placed geophones into the bottom of each receiver hole to avoid the effect of geophone coupling with the borehole wall on Q estimation in conventional cross-hole seismic surveys. We also propose a novel tomographic inversion of the Q factor without the effect of the source signature, and examine its stability and reliability using synthetic data. We estimate the Q factors of the near-surface layer in two different frequency bands using field data acquired in the Dagang Oilfield. The results show that seismic absorption in the near-surface layer is much greater than that in the subsurface strata. Thus, it is of critical practical importance to enhance the seismic solution by compensating for near-surface absorption. In addition, we derive different Q factors from two frequency bands, which can be treated, to some extent, as evidence of a frequency-dependent Q.     

Detailed Study of Time Variations in the Gutenberg–Richter <Emphasis Type="Italic">b</Emphasis>-value Based on Highly Accurate Seismic Observations at the Garm Prognostic Site,Tajikistan

The time variations in the Gutenberg–Richter b-value are minutely studied based on the data of highly accurate seismological observations at the Garm prognostic site, Tajikistan, where a stationary network of seismic stations of the Complex Seismological Expedition (CSE) of Schmidt Institute of Physics of the Earth (IPE) of the USSR (Russian) Academy of Sciences was in operation from 1955 to 1992. A total of 93035 local earthquakes ranging from 0.0 to 6.3 in the Ml magnitudes are considered. The spatiotemporal fluctuations in the minimal magnitude of completeness of the earthquakes, Mc, are analyzed. The study considers a 25-year interval of the observations at the center of the observation system within which Mc = 0.9. It is shown that in most cases, the b-value and log₁₀E^2/3 experience characteristic time variations before the earthquakes with magnitudes higher than the minimal magnitude of the predicted earthquake (MPE). The 6-year anomaly in the parameters’ b-value, log₁₀E^2/3, and log₁₀N associated with the single strongest earthquake with M = 6.3 that occurred in the observation region on October 26, 1984 is revealed. The inversely proportional relationship is established between the time variations in the b-value and the time variations in the velocities of seismic waves Vp and Vp/Vs. It is shown that the exponent p in the power function which links the time variations of the b-value and log₁₀E^2/3 is higher in the zones of crustal compression than in the zones of extension. It is simultaneously confirmed that the average b-value in the zones of compression is lower than in the zones of extension. It is established that in the case of earthquakes with M ≥ 2.6, the time series of seismic activity log₁₀N_i and the time series of the b-value are highly cross correlated with a coefficient of r ≈ 0.75, whereas in the case of earthquakes with M ≥ 0.9, the coefficient of cross correlation between these time series is close to zero (r ≈ 0.06). The law of variations in the slope of the lines approximating the relationship between the log₁₀N_i time series in the different magnitude ranges (M ≥ Mc_i) and b-value time series is obtained. It is hypothesized that the seismic activity of the earthquakes with high magnitudes can be estimated provided that the parameters of the time series of the b-value and time series of the number of earthquakes logN(ΔM_i) in the range of low magnitudes are known. It is concluded that using the parameter log₁₀N for prognostic estimates of the strong earthquakes only makes sense for earthquakes having moderate and large magnitudes. It is inferred that the time variations in the b-value are predominantly contributed by the time variations of the earthquakes with relatively large magnitudes.