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1.
Various techniques for estimating t1 (travel time/quality factor Q) from short-period seismic-array records of body waves have been investigated. Spectral analysis in the frequency domain seems to be more appropriate for this purpose than time domain methods, because of the relative ease with which source and instrument effects can be removed. Of the techniques available, those based on maximum likelihood and homomorphic deconvolution give estimates of relative power versus frequency which best represent the power contained in a time-domain wavelet of short duration. The latter technique seemed to have better noise-eliminating properties than the former. Therefore, homomorphic deconvolution was used to obtain estimates of t1 values from P, PcP, ScP and S phases recorded at the Warramunga array in the Northern Territory of Australia. The source regions for the event studied were the Sunda, Mariana, New Hebrides, Kermadec and Tonga trench zones.The short-period t1 estimates obtained using the above method were much smaller than estimates from published free-oscillation Q models, indicating that the values of Q for compressional and shear waves are frequently-dependent. It was found that short-period t1 values and free-oscillation Q models could be made consistent with one another by assuming Q = Q0(1+τω) where Q0 and τ are constants. The results of this investigation suggest another approach to how the Q structure of the mantle can be investigated.  相似文献   

2.
The fundamental mode Love and Rayleigh waves generated by ten earthquakes and recorded across the Tibet Plateau, at QUE, LAH, NDI, NIL, KBL, SHL, CHG, SNG and HKG are analysed. Love- and Rayleigh-wave attenuation coefficients are obtained at time periods of 5–120 s using the spectral amplitudes of these waves for 23 different paths. Love wave attenuation coefficient varies from 0.0021 km?1, at a period of 10 s, to 0.0002 km?1 at a period of 90 s, attaining two maxima at time periods of 10 and 115 s, and two minima at time periods of 25 and 90 s. The Rayleigh-wave attenuation coefficient also shows a similar trend. The very low value for the dissipation factor, Qβ, obtained in this study suggests high dissipation across the Tibetan paths. Backus-Gilbert inversion theory is applied to these surface wave attenuation data to obtain average Qβ?1 models for the crust and uppermost mantle beneath the Tibetan Plateau. Independent inversion of Love- and Rayleigh-wave attenuation data shows very high attenuation at a depth of ～50–120 km (Qβ ? 10). The simultaneous inversion of the Love and Rayleigh wave data yields a model which includes alternating regions of high and low Qβ?1 values. This model also shows a zone of high attenuating material at a depth of ～40–120 km. The very high inferred attenuation at a depth of ～40–120 km supports the hypothesis that the Tibetan Plateau was formed by horizontal compression, and that thickening occurred after the collision of the Indian and Eurasian plates.  相似文献   

3.
Deep earthquakes located in the Tonga-Kermadec region produce exceptionally clear and sharp short-period P, S, PcP, ScP, and ScS phases which are recorded at many stations at distances of less than 60°. The data used in this study are produced by short-period stations located in oceanic-type regions (Fiji and New Caledonia), a mobile continental region (eastern Australia) and a shield region (central Australia). Differential travel-time residuals of the above phases at these stations are investigated to determine the contribution to the differential residuals from: (1) the upper part of the mantle (S-P residuals); (2) the core-to-station portion of the mantle (ScS-ScP residuals); and (3) the hypocenter-to core portion of the mantle (ScP-PcP residuals). The use of differential travel-time residuals considerably reduces near-station effects and effects due to inaccurate determination of the source parameters, and hence the results can be interpreted as due to variations along the propagation paths. The results show that (S-P) residuals from phases traveling along event-to-station paths are about 7 s smaller at the shield station than at the oceanic stations. This correlation with surface tectonic environments is equally strong for the (ScS-ScP) residuals, with the shield/oceanic station difference being about 4 s. Moreover, the data suggest that this correlation between differential residuals and surface tectonic environments is caused by variations in shear velocity within the upper part of the mantle. However, the data cannot uniquely resolve the required depth of these variations within the mantle. For example, if the shear velocity variations extend to a depth of 400 km beneath the recording stations, then the average shear velocity difference between shield- and oceanic-type environments is about 4%. However, if the variations extend only to a depth of 200 km, this difference is more than 8%.(ScP-PcP) and (ScS-PcS) residuals vary from about +1 to about +4 s at the different stations, apparently because of compressional velocity variations in the mantle along the Pc path. If the variation in compressional velocity within the mantle below a depth of about 600 km is about 10% and occurs near the source region, these results suggest that, in the vicinity of deep earthquake zones, variations in compressional velocity extend to a depth of about 1000 km. However, these results can equally be explained by a 1% variation in compressional velocity, evenly distributed along the entire Pc path. An estimate of Q determined from the observed predominant frequency of ScS waves, as recorded at the shield station, suggests that the average 〈Qs〉 of the mantle beneath about 600 km is about 1050 at frequencies of about 1 Hz.  相似文献   

4.
Based on the long period surface wave data recorded by the China Digital Seismograph Network (CDSN), theQ R of fundamental mode Rayleigh wave with periods from 10 s to 146 s is determined for the eastern Sino-Korean paraplatform in this paper. TheQ β models of the crust and upper mantle are respectively obtained for the 4 paths, with the aid of stochastic inverse method. It shows that in the eastern Sino-Korean paraplatform, the average crustalQ β is about 200, and that there exists a weak attenuation layer in the middle crust (about 10–20 km deep) which is possibly related to earthquake-prone layer. A strong attenuation layer (lowQ) of 70 km thick extensively exists in the uppermost mantle, with the buried depth about 80 km. The averageQ R of fundamental mode Rayleigh wave is between the value of stable tectonic region and that of active tectonic region, and much close to the latter.  相似文献   

5.
Free oscillation and body wave data are used to construct average Q models for the earth. The data set includes fundamental and overtone observations of the radial, spheroidal and toroidal modes, ScS observations and amplitudes of body waves as a function of distance. The preferred model includes a low-Q zone at both the top and the bottom of the mantle. In these regions the seismic velocities are likely to be frequency dependent in the “seismic” band. Absorption in the mantle is predominantly due to losses in shear. Compressional absorption may be important in the inner core.A grain-boundary relaxation model is proposed that explains the dominance of shear over compressional dissipation, the roughly frequency independent average values for Q and the variation of Q with depth. In the high-Q regions, the lithosphere and the midmantle (200–2000 km), Q is predicted to be frequency dependent. However, the low-Q regions of the earth, where Q is roughly frequency independent, dominate the observations of attenuation.  相似文献   

6.
—?The digital data acquired by 16 short-period seismic stations of the Friuli-Venezia-Giulia seismic network for 56 earthquakes of magnitude 2.3–4.7 which occurred in and near NE Italy have been used to estimate the coda attenuation Q c and seismic source parameters. The entire area under study has been divided into five smaller regions, following a criterion of homogeneity in the geological characteristics and the constrains imposed by the distribution of available events. Standard IASPEI routines for coda Q c determination have been used for the analysis of attenuation in the different regions showing a marked anomaly in the values measured across the NE border between Friuli and Austria for Q 0 value. A large variation exists in the coda attenuation Q c for different regions, indicating the presence of great heterogeneities in the crust and upper mantle of the region. The mean value of Q c (f) increases from 154–203 at 1.5?Hz to 1947–2907 at 48?Hz frequency band with large standard deviation estimates.¶Using the same earthquake data, the seismic-moment, M 0, source radius, r and stress-drop, Δσ for 54 earthquakes have been estimated from P- and S-wave spectra using the Brune's seismic source model. The earthquakes with higher stress-drop (greater than 1?Kbar) occur at depths ranging from 8 to 14?km.  相似文献   

7.
The availability of accelerometric data for the Montenegro earthquake of 15th April 1979 makes it possible to investigate seismic Q of the lithosphere in that region, in particular, its dependence on frequency, on the depth reached by seismic waves, and on the length of time windows in which signals are processed. Two different spectral methods, S phase energy ratio and coda envelope decay, are applied, respectively, to direct and scattered shear waves. Similar results are obtained using different portions of the recordings, i.e., coda waves for the envelope decay fit and the S wave train, with a significant duration of ～ 10 s, for the energy ratios. The same apparent Q (Q ～ 40 f, where f is the frequency expressed in Hz) that is found for other neighbouring central Mediterranean regions (e.g., Ancona, on the central Italian Adriatic coast; Valnerina, in the central Apennines; Irpinia, in the southern Apennines) is also found for the southern Yugoslavian coast, in the band 1–25 Hz up to a maximum range of ～ 120 km from the focus. This strong frequency dependence is probably connected with the type of small-scale heterogeneity and the same geological age and level of tectonic activity peculiar to all these seismotectonic areas.In order to compare the apparent Q of the whole S wave train, ～ 10 s long, with the (intrinsic) apparent Q of the single direct S wave (usually 1 s or less), the maximum entropy method is applied in the energy spectrum computation for shorter wave trains. The use of shorter time windows does not reveal any significant variation in the tendency of Q to increase linearly with frequency as the length of the time window containing the sample of the S waves decreases. This seems to indicate that scattering-dependent Q is generally inseparable from intrinsic Q in the lithosphere when estimates based on variations with distance of the seismic signal spectrum are used. While the type of linear growth with frequency does not seem to undergo any variations (it remains of the Q = qf type), the data show there are a considerable decrease in the coefficient of proportionality Q with decreasing duration of the window of S waves analysed, probably as a result of variations in seismic attenuation with depth.  相似文献   

8.
—Northeastern Venezuela has been studied in terms of coda wave attenuation using seismograms from local earthquakes recorded by a temporary short-period seismic network. The studied area has been separated into two subregions in order to investigate lateral variations in the attenuation parameters. Coda-Q ?1 (Q c ?1) has been obtained using the single-scattering theory. The contribution of the intrinsic absorption (Q i ?1) and scattering (Q s ?1) to total attenuation (Q t ?1) has been estimated by means of a multiple lapse time window method, based on the hypothesis of multiple isotropic scattering with uniform distribution of scatterers. Results show significant spatial variations of attenuation the estimates for intermediate depth events and for shallow events present major differences. This fact may be related to different tectonic characteristics that may be due to the presence of the Lesser Antilles subduction zone, because the intermediate depth seismic zone may be coincident with the southern continuation of the subducting slab under the arc.  相似文献   

9.
—Investigations of the spectral characteristics of teleseismic body waves revealed that the spectral falloff rate between 1 Hz and 10 Hz is primarily controlled by anelastic attenuation along the path. In addition, the amount of high-frequency energy in teleseismic body waves is far above the level expected on the basis of Q estimates at low frequencies, thus leading to the idea of frequency dependence in Q. Q variations in the earth’s mantle can be investigated by mapping out the variations of high frequency (4 - 10 Hz) energy relative to the low frequency (1 - 3 Hz) energy in teleseismic P waves, and similar ratios at lower frequencies in teleseismic S waves. Because of the extreme sensitivity of spectral content of short-period body waves to Q variations, large uncertainties in other factors affecting spectral content can be tolerated in such studies. With the increasing number and density of broadband seismic stations recording at high sampling rates, tomographic studies of Q at high frequencies become possible.  相似文献   

10.
The phenomenon of the seismic coda, which is composed of seismic energy delayed by scattering, is seen on both the Earth and the Moon. On the Moon the scattered coda is very large relative to body wave arrivals with a delay of the time of maximum energy, whereas on Earth scattered codas are relatively small and show no delay of the energy maximum. In both cases the form of the coda is controlled by three distance scales, the mean free path L, which is the average distance seismic energy travels before it is scattered, the attenuation distance x1, which is the average distance seismic energy travels before it is attenuated, and the source-receiver distance R. Two coda models are discussed based on these parameters; a strong scattering (diffusion) model, and a weak scattering (single scattering) model. A discussion of the diffusion scattering model indicates that if x1/L ? 1, diffusion scattering is an appropriate model, but if x1/L ? 1, single scattering is the appropriate model, within the appropriate range of R. A survey of the literature indicates that for the frequency range 0.5–10 Hz, diffusion scattering is important in lunar codas, but for the frequency range 1–25 Hz single scattering is important in terrestrial codas. Another important effect of attenuation is the elimination of scattering paths much longer than x1. On the Moon, this means that seismic energy in the coda can only propagate directly in the near-surface strong scattering zone between surface sources and the seismometer for source-seismometer separations of the order of (x1L)12; otherwise, scattering is limited to regions near the source and the receiver. On Earth, this effect probably prevents multiple scattering.  相似文献   

11.
Multi-phase long-period t* measurements are among the key evidences for the frequency-dependent mantle attenuation factor, Q. However, similarly to Q, poorly constrained variations of Earth’s structure may cause spurious frequency-dependent effects in the observed t*. By using an attenuation-coefficient approach which incorporates measurements of geometric spreading (GS), such effects can be isolated and removed. The results show that the well-known increase of body P-wave t* from ~0.2 s at short periods to ~1–2 s at long periods may be caused by a small and positive bias in the underlying GS, which is measured by a dimensionless parameter γ*?≈?0.06. Similarly to the nearly constant t* at teleseismic distances, this GS bias is practically range-independent and interpreted as caused by velocity heterogeneity within the crust and uppermost mantle. This bias is accumulated within a relatively thin upper part of the lithosphere and may be closely related to the crustal body-wave GS parameter γ?~?4–60 mHz reported earlier. After a correction for γ, P-wave t P * becomes equal ~0.18 s at all frequencies. By using conventional dispersion relations, this value also accounts for ~40 % of the dispersion-related delay in long-period travel times. For inner-core attenuation, the attenuation coefficient shows a distinctly different increase with frequency, which is remarkably similar to that of fluid-saturated porous rock. As a general conclusion, after the GS is accounted for, no absorption-band type or frequency-dependent upper-mantle Q is required for explaining the available t* and velocity dispersion observations. The meaning of this Q is also clarified as the frequency-dependent part of the attenuation coefficient. At the same time, physically justified theories of elastic-wave attenuation within the Earth are still needed. These conclusions agree with recent re-interpretations of several surface, body and coda-wave attenuation datasets within a broad range of frequencies.  相似文献   

12.
Based on the Anapa (ANN) seismic station records of ~40 earthquakes (MW > 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.  相似文献   

13.
We employ a niching genetic algorithm to invert ∼30,000 differential ScS/S attenuation values for a new spherically symmetric radial model of shear quality factor (Qμ) with high sensitivity to the lower mantle. The new radial Qμ model, QLM9, possesses greater sensitivity to Qμ at large mantle depths than previous studies. On average, lower mantle Qμ increases with depth, which supports models of increasing viscosity with depth [B.M. Steinberger, A.R. Calderwood. Mineral physics constraints on viscous flow models of mantle flow, J. Conf. Abs., 6, 2001., 2001.]. There are two higher-Qμ regions at ∼1000 and ∼2500 km depth, which roughly correspond to high-viscosity regions observed by Forte and Mitrovica [A.M. Forte and J.X. Mitrovica, Deep-mantle high-viscosity flow and thermochemical structure inferred from seismic and geodynamic data, Nature 410, 1049–1056, 2001.]. There is a lower-Qμ layer at the core–mantle boundary and a relatively low-Qμ region in the mid-lower mantle. With several caveats, we infer a divergence of the solidus and geotherm in the lower mantle and a convergence within Dʺ by relating Qμ to homologous temperature.  相似文献   

14.
We inverted for laterally varying attenuation, absolute site terms, moments and apparent stress using over 460,000 Lg amplitudes recorded by the USArray for frequencies between 0.5 and 16 Hz. Corner frequencies of Wells, Nevada, aftershocks, obtained by independent analysis of coda spectral ratios, controlled the tradeoff between attenuation and stress, while independently determined moments from St. Louis University and the University of California constrained absolute levels. The quality factor, Q, was low for coastal regions and interior volcanic and tectonic areas, and high for stable regions such as the Great Plains, and Colorado and Columbia Plateaus. Q increased with frequency, and the rate of increase correlated inversely with 1-Hz Q, with highest rates in low-Q tectonic regions, and lowest rates in high-Q stable areas. Moments matched independently determined moments with a scatter of 0.2 NM. Apparent stress ranged from below 0.01 to above 1 MPa, with means of 0.1 MPa for smaller events, and 0.3 MPa for larger events. Stress was observed to be spatially coherent in some areas; for example, stress was lower along the San Andreas fault through central and northern California, and higher in the Walker Lane, and for isolated sequences such as Wells. Variance reduction relative to 1-D models ranged from 50 to 90 % depending on band and inversion method. Parameterizing frequency dependent Q as a power law produced little misfit relative to a collection of independent, multi-band Q models, and performed better than the omega-square source parameterization in that sense. Amplitude residuals showed modest, but regionally coherent patterns that varied from event to event, even between those with similar source mechanisms, indicating a combination of focal mechanism, and near source propagation effects played a role. An exception was the Wells mainshock, which produced dramatic amplitude patterns due to its directivity, and was thus excluded from the inversions. The 2-D Q plus absolute site models can be used for high accuracy, broad area source spectra, magnitude and yield estimation, and, in combination with models for all regional phases, can be used to improve discrimination, in particular for intermediate bands that allow coverage to be extended beyond that available for high frequency P-to-S discriminants.  相似文献   

15.
To better understand (and correct for) the factors affecting the estimation of attenuation (Q), we simulate subsurface wave propagation with the Weyl/Sommerfeld integral. The complete spherical wavefield emanating from a P‐wave point source surrounded by a homogeneous, isotropic and attenuative medium is thus computed. In a resulting synthetic vertical seismic profile, we observe near‐field and far‐field responses and a 90° phase rotation between them. Depth dependence of the magnitude spectra in these two depth regions is distinctly different. The logarithm of the magnitude spectra shows a linear dependence on frequency in the far‐field but not in those depth regions where the near‐field becomes significant. Near‐field effects are one possible explanation for large positive and even negative Q‐factors in the shallow section that may be estimated from real vertical seismic profile data when applying the spectral ratio method. We outline a near‐field compensation technique that can reduce errors in the resultant Q estimates.  相似文献   

16.
—Observed velocities and attenuation of fundamental-mode Rayleigh waves in the period range 7–82 sec were inverted for shear-wave velocity and shear-wave Q structure in the Middle East using a two-station method. Additional information on Q structure variation within each region was obtained by studying amplitude spectra of fundamental-mode and higher-mode Rayleigh waves. We obtained models for the Turkish and Iranian Plateaus (Region 1), areas surrounding and including the Black and Caspian Seas (Region 2), and the Arabian Peninsula (Region 3). The effect of continent-ocean boundaries and mixed paths in Region 2 may lead to unrealistic features in the models obtained there. At lower crustal and upper-mantle depths, shear velocities are similar in all three regions. Shear velocities vary significantly in the uppermost 10 km of the crust, being 3.21, 2.85, and 3.39 km/s for Regions 1, 2, and 3, respectively. Q models obtained from an inversion of interstation attenuation data show that crustal shear-wave Q is highest in Region 3 and lowest in Region 1. Q’s for the upper 10 km of the crust are 63, 71, and 201 for Regions 1, 2, and 3, respectively. Crustal Q’s at 30 km depth for the three regions are about 51, 71, and 134. The lower crustal Q values contrast sharply with results from stable continental regions where shear-wave Q may reach one thousand or more. These low values may indicate that fluids reside in faults, cracks, and permeable rock at lower crustal, as well as upper crustal depths due to convergence and intense deformation at all depths in the Middle Eastern crust.  相似文献   

17.
By treating the lithosphere as a diffusive boundary layer to mantle convection, the convective speed or mantle creep rate, ??, can be related to the mantle-derived heat flux, Q?. If cell size is independent of Q?2 then ?? ∝ Q?. (If cell size varies with Q?, then a different power law prevails, but the essential conclusions are unaffected.) Then the factthat for constant thermodynamic efficiency of mantle convection, the mechanical power dissipation is proportionalto Q?, gives convective stress σ ∝ Q??1, i.e. the stress increases as the convection slows. This means an increasing viscosityor stiffness of the mantle which can be identified with a cooling rate in terms of a temperature-dependent creep law. If we suppose that the mantle was at or close to its melting point within 1 or 2 × 108 years of accretionof the Earth, the whole scale of cooling is fixed. The present rate of cooling is estimated to be about 4.6 × 10?8 deg y?1 for the average mantle temperature, assumed to be 2500 K, but this very slow cooling rate represents a loss ofresidual mantle heat of 7 × 1012 W, about 30% of the total mantle-derived heat flux. This conclusion requires theEarth to be deficient in radioactive heat, relative to carbonaceous chondrites. A consideration of mantle outgassing and atmospheric argon leads to the conclusion that the deficiency is due to depletion of potassium, and that the K/U ratio of the mantle is only about 2500, much less than either the crustal or carbonaceous chondritic values. Thetotal terrestrial potassium is estimated to be about 6 × 1020 kg. Acceptance of the cooling of the Earth removes the necessity for potassium in the core.  相似文献   

18.
    
Based on the long period surface wave data recorded by the China Digital Seismograph Network (CDSN), theQ R of fundamental mode Rayleigh wave with periods from 10 s to 146 s is determined for the eastern Sino-Korean paraplatform in this paper. TheQ β models of the crust and upper mantle are respectively obtained for the 4 paths, with the aid of stochastic inverse method. It shows that in the eastern Sino-Korean paraplatform, the average crustalQ β is about 200, and that there exists a weak attenuation layer in the middle crust (about 10–20 km deep) which is possibly related to earthquake-prone layer. A strong attenuation layer (lowQ) of 70 km thick extensively exists in the uppermost mantle, with the buried depth about 80 km. The averageQ R of fundamental mode Rayleigh wave is between the value of stable tectonic region and that of active tectonic region, and much close to the latter. Contribution No. 96A0001, Institute of Geophysics, SSB, China. Funded by the Chinese Joint Seismological Science Foundation.  相似文献   

19.
—Teleseismic broadband recordings of intermediate and deep focus earthquakes are used to quantify both compression (Q and shear(Q ) wave attenuation within the Lau backarc basin. A spectral-ratio method is employed to measure differential attenuation (t*) between the depth phases sS, pP, and sP and the direct S and P phases over the frequency band 0.05 and 0.5 Hz. We use a stacking algorithm to combine the spectra of several phase pairs from a single event, having similar azimuth and range, to obtain more robust t* measurements; these estimates are then used to compute the average Q above the focal depth. Q and Q are measured directly from the sS-S and pP-P phase pairs respectively, however, the interpretation of t* measured from sP-P requires assumptions about the ratio Q ?/Q . We find an empirical ratio of Q ?/Q = 1.93 for this region and use it to compute Q and Q from the Q sP observations. We observe lateral and depth variations in both Q β and Q >alpha< beneath the tectonically active Lau Basin and the geologically older, inactive Lau Ridge and Fiji Plateau. The upper 200 km beneath the Central and Northern Lau Basin show a Q of 45–57 and a Q of 102–121, and Q appears to increase rapidly with depth. The upper 600 km beneath the Lau backarc basin has a Q of 118–138, while over the same depth interval we observe a higher Q of 139–161 beneath the Lau Ridge and Fiji Plateau. We also find Q of 235–303 beneath the northern Lau Basin and a higher Q of 292–316 beneath the Fiji Plateau and the Lau Ridge measured directly from pP-P phase pairs. These geographic trends in the broadband Q measurements correlate with our previous long-period estimates of Q in this region, however, the broadband measurements themselves are higher by about a factor of two. These observations suggest substantial frequency dependence of Q in the upper mantle, beginning at frequencies less than 1.0 Hz and consistent with the power-law form Q∝ωα with between -0.1 and -0.3.  相似文献   

20.
The parameters of S-wave attenuation (the total effect of absorption and scattering) near the Petropavlovsk (PET) station in Kamchatka were estimated by means of the spectral method through an original procedure. The spectral method typically analyzes the changes with distance of the shape of spectra of the acceleration records assuming that the acceleration spectrum at the earthquake source is flat. In reality, this assumption is violated: the source acceleration spectra often have a high-frequency cutoff (the source-controlled fmax) which limits the spectral working bandwidth. Ignoring this phenomenon not only leads to a broad scatter of the individual estimates but also causes systematic errors in the form of overestimation of losses. In the approach applied in the present study, we primarily estimated the frequency of the mentioned high-frequency cutoff and then constructed the loss estimates only within the frequency range where the source spectrum is approximately flat. The shape of the source spectrum was preliminarily assessed by the approximate loss compensation technique. For this purpose, we used the tentative attenuation estimates which are close to the final ones. The difference in the logarithms of the spectral amplitudes at the edges of the working bandwidth is the input for calculating the attenuation. We used the digital accelerograms from the PET station, with 80 samples per second digitization rate, and based on them, we calculated the averaged spectrum of the S-waves as the root mean square along two horizontal components. Our analysis incorporates 384 spectra from the local earthquakes with M = 4–6.5 at the hypocentral distances ranging from 80 to 220 km. By applying the nonlinear least-square method, we found the following parameters of the loss model: the Q-factor Q0 = 156 ± 33 at frequency f = 1 Hz for the distance interval r = 0–100 km; the exponent in the power-law relationship describing the growth of the Q-factor with frequency, γ = 0.56 ± 0.08; and the loss parameter beneath the station κ0 = 0.03 ± 0.005 s. The actual accuracy of the estimates can probably be somewhat lower than the cited formal accuracy. It is also established (with a confidence level of 10%) that the losses decrease with distance.  相似文献   

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