Temporal change in scattering and attenuation associated with the earthquake occurrence—A review of recent studies on coda waves

The study of coda waves has recently attracted increasing attention from seismologists. This is due to the fact that it is viewed as a new means by which the stress accumulation stage preceding a large earthquake can be measured, since the scattering paths nearly uniformly cover a fairly large region around the focus and observation stations, compared with the direct ray paths. To date, we have had many reports on the temporal variation of the relation between coda duration and amplitude magnitude, and that of the coda attenuationQ _c ^–1 which is estimated from coda amplitude decay. Some of these have shown a precursor-like behavior; however, others seem to have shown a coseismic change. We have critically reviewed these reports, and discussed what these observational facts tell us about the change in the heterogeneous crust. We found significant temporal variations, not only in the mean but also in the scatter ofQ _c ^–1 , associated with the mainshock occurrence. The formation of new cracks, the reopening and growing of existing cracks, the interaction of these cracks, and the pore water movement through these cracks might correspond to such variations. In addition, we may expect an inhomogeneous distribution of crack clusters in a fairly large region, compared with the aftershock region. The gradual appearance of such crack clusters seems to be the most plausible mechanism by which coda decay gradients are caused to largely scatter in the stress accumulation stage.     

Scattering and anelastic attenuation of seismic energy in northern Greece

The relative contribution of scattering (Q _s ^–1 ) and intrinsic (Q _i ^–1 ) attenuation to the totalS-wave attenuation for the frequencies of 1.5, 3.0, 6.0 and 12.0 Hz has been studied by applying the radiative energy transfer theory, Data of local earthquakes which occurred in northern Greece and were recorded by the permanent telementered network of the Geophysical Laboratory of the University of Thessaloniki have been used. The results show that in this area the scattering attenuation is dominant over all frequencies while intrinsic attenuation is significantly lower. The estimatedQ _s ^–1 andQ _i ^–1 values have frequency dependences off ^–0.72 andf ^–0.45, respectively. The frequency dependence ofQ _s ^–1 is the same as that of the codaQ _c ^–1 , obtained by applying the single scattering model, which probably implies that the frequency dependence of the coda wave attenuation is attributed to the frequency dependence of the scattering attenuation.Q _c ^–1 values are very close to scattering attenuation for short lapse times, (10–20 sec), and intermediate between scattering and intrinsic attenuation for the longer lapse times, (50–100 sec). This difference is explained as the result of the depth-dependent attenuation properties and the multiple scattering effects.     

Frequency dependent characteristics of coda wave quality factor in central and southcentral Alaska

Coda wave quality factor (Q _c ) was investigated by using digital data (100 sample sec^–1) recorded by a vertical component short-period station installed for this study. The station was located in the greater Fairbanks area in central Alaska. From several hundred earthquakes recorded by this station in about a year, 27 earthquakes were selected for the above study; 7 of these selected earthquakes were located along the Alaska Wadati-Benioff zone (Pacific plate). The other 20 earthquakes were located in the area of intraplate seismicity (North American plate). The data was filtered using 9 pass-bands with center frequency varying from 1.5 Hz to 16 Hz with octave bandwidth. The values ofQ _c obtained from the coda amplitude decay rates measured on the filtered data after corrections due to the recording instrument and source-receiver separation show appreciable frequency dependence. The value ofQ _c varies in the range of 253 and 1190 corresponding to the frequency interval from 1.5 Hz to 16 Hz for the study area. This variation is close to that reported by others for the Kanto region of Japan. Moreover, the characteristics ofQ _c obtained in the present case seem to be independent of epicentral distance and hypocentral depth.     

CodaQ as a combination of scattering and intrinsic attenuation: Numerical simulations with the boundary integral method

Numerical modelling ofSH wave seismograms in media whose material properties are prescribed by a random distribution of many perfectly elastic cavities and by intrinsic absorption of seismic energy (anelasticity) demonstrates that the main characteristics of the coda waves, namely amplitude decay and duration, are well described by singly scattered waves in anelastic media rather than by multiply scattered waves in either elastic or anelastic media. We use the Boundary Integral scheme developed byBenites et al. (1992) to compute the complete wave field and measure the values of the direct waveQ and coda wavesQ in a wide range of frequencies, determining the spatial decay of the direct wave log-amplitude relation and the temporal decay of the coda envelope, respectively. The effects of both intrinsic absorption and pure scattering on the overall attenuation can be quantified separately by computing theQ values for corresponding models with (anelastic) and without (elastic) absorption. For the models considered in this study, the values of codaQ ^–1 in anelastic media are in good agreement with the sum of the corresponding scatteringQ ^–1 and intrinsicQ ^–1 values, as established by the single-scattering model ofAki andChouet (1975). Also, for the same random model with intrinsic absorption it appears that the singly scattered waves propagate without significant loss of energy as compared with the multiply scattered waves, which are strongly affected by absorption, suggesting its dominant role in the attenuation of coda waves.     

Dependence of coda attenuation on frequency and lapse time in central Greece

The dependence of coda attenuationQ _c on frequency and lapse time was studied. Data from small local earthquakes, recorded at three stations (VMR, VSI and VFI) of the VOLNET network operating in central Greece, were used.Q _c was estimated by applying the single scattering model to bandpass-filtered seismograms, over a frequency range of 1 to 12 Hz. Analysis was performed every 10 s until the end on overlapping time windows.Q _c is found to depend on frequencyf in Hz according to a power law,Q _c =Q ₀ f ⁿ . ObservedQ ₀ ranges from 30 to 100 and the powern ranges from 0.90 to 0.70.Q ₀ increases andn decreases with lapse time increasing. A strong dependence ofQ _c on lapse time was also found. In the frequency range of 1 to 8 Hz and at a short lapse time,Q _c values were found to be similar for all three stations. On the other hand, at the longest analyzed time window (50 s), the estimatedQ _c values show a discrepancy which is more obvious at a higher frequency band. The scattering coefficient around the central station VSI is found to range from 0.029 to 0.0041 km^–1.Q _c from the single scattering model andQ _s from the amplitude ratio of directS to coda waves for the VSI station are similar. We believe dependence of coda attenuationQ _c on frequency and lapse time is caused by a combination of geotectonic features and depth variation asQ _s .     

Estimation of frequency dependent coda wave attenuation structure at the vicinity of Cairo Metropolitan Area

Estimation of seismic wave attenuation in the shallow crust in terms of coda wave Q structure previously investigated in the vicinity of Cairo Metropolitan Area was improved using seismograms of local earthquakes recorded by the Egyptian National Seismic Network. The seismic wave attenuation was measured from the time decay of coda wave amplitudes on narrow bandpass filtered seismograms based on the single scattering theory. The frequency bands of interest are from 1.5 to 18 Hz. In general, the values obtained for various events recorded at El-Fayoum and Wadi Hagul stations are very similar for all frequency bands. A regional attenuation law Q _c = 85.66 f ^0.79 was obtained.     

Coda Q in the Kachchh Basin, Western India Using Aftershocks of the Bhuj Earthquake of January 26, 2001

Q_C-estimates of Kachchh Basin in western India have been obtained in a high frequency range from 1.5 to 24.0 Hz using the aftershock data of Bhuj earthquake of January 26, 2001 recorded within an epicentral distance of 80 km. The decay of coda waves of 30 sec window from 186 seismograms has been analysed in four lapse time windows, adopting the single backscattering model. The study shows that Q_c is a function of frequency and increases as frequency increases. The frequency dependent Q_c relations obtained for four lapse-time windows are: Q_c=82 f^1.17 (20–50 sec), Q_c=106 f^1.11 (30–60 sec), Q_c=126f^1.03 (40–70 sec) and Q_c=122f^1.02 (50–80 sec). These empirical relations represent the average attenuation properties of a zone covering the surface area of about 11,000, 20,000, 28,000 and 38,000 square km and a depth extent of about 60, 80, 95, 110 km, respectively. With increasing window length, the degree of frequency dependence, n, decreases marginally from 1.17 to 1.02, whereas Q₀ increases significantly from 82 to 122. At lower frequencies up to 6 Hz, Q_c⁻¹ of Kachchh Basin is in agreement with other regions of the world, whereas at higher frequencies from 12 to 24 Hz it is found to be low.     

Attenuation of coda waves and Q c value beneath the Chengdu telemetered seismic network

Based on the single scattering model of coda power spectrum analysis, digital waveform data of 50 events recorded by the real-time processing system of the Chengdu telemetry network are analyzed to estimate the Q _c values of earth medium beneath the Chengdu telemetry network for several specified frequencies. It is found that the Q _c shows the frequency dependency in the form of Q _c = Q ₀ f ⁿ in the range of 1.0 to 20.0Hz. Estimated Q ₀ ranges from 60.83 to 178.05, and n is found to be 0.713 to 1.159. The average value of Q ₀ and n are 117 and 0.978 respectively. This result indicates the strong frequency dependency of the attenuation of coda waves beneath the Chengdu telemetry network. Comparing with the results obtained in other regions of the world, it is found that Q ₀ ⁻¹ value and its change with frequency are similar to those in regions with strong tectonic activity. This subject is supported by the Ministry of Personnel, China for partly sponsoring.     

Lateral variations of coda Q and attenuation of seismic waves in Southwest Anatolia

The seismic quality factor (Q _c) and the attenuation coefficient (δ) in the earth’s crust in southwest (SW) Anatolia are estimated by using the coda wave method based on the decrease of coda wave amplitude by time on the seismogram. The quality factor Q _o, the value of Q _c at 1 Hz, and its frequency dependency η are determined from this method depending on the attenuation properties of scattered coda waves. δ is determined from the observations of amplitude variations of seismic waves. In applying the coda wave method, firstly, a type curve representing the average pattern of the individual coda decay curves for 0.75, 1.5, 3.0, 6.0, 12.0, and 24.0 Hz values was estimated. Secondly, lateral variation of coda Q and the attenuation coefficients for three main tectonic patterns are estimated. The shape of the type curve is controlled by the scattering and attenuation in the crustal volume sampled by the coda waves. The Q _o and η values vary from 30 to 180 and from 0.55 to 1.25, respectively for SW Anatolia. In SW Anatolia, coda Q–f relation is described by and δ = 0.008 km⁻¹. These results are expected to help in understanding the degree of tectonic complexity of the crust in SW Anatolia.     

Changes in the early part of the seismic coda due to localized scatterers: The estimation ofQ in a stope environment

A single scattering model was used to analyse the temporary changes in the mean density of scattered waves in a discrete random medium. The model of the mean energy density, originally proposed bySato (1977) for spherical radiation and isotropic scattering, has been modified and applied to a medium in which the scatterers are confined to a specified volume. The time variation of the early part of the mean energy density function for the different source durations was investigated. The dominant effect on the theoretical mean energy density is caused by the specified volume containing scatterers. The duration of the source pulse influences the early part of the coda fort/t ₀<1.2, wheret is the lapse time measured from the source origin time, andt ₀is arrival time of the body wave.The analysis of the coda signal of micro-events occurring immediately in front of the face enables us to estimate the size of the fracture zone induced by the stope. The model of the mean energy density of coda for a medium containing scatterers close to the seismic source was used to analyse a large number of events recorded close to an advancing mine face in a deep level gold mine in South Africa. The coda decay rate has two trends: the first, with a steep decay of coda, is produced by a larger deviation of rock parameters and/or larger size of the scatterers; the second trend, which decays more slowly, has the corresponding mean-free path ranging from 20 m to 200 m. The analysis indicates that the rock mass about 15–20 m from the stope contains a large proportion of fractured and blocked rock, which is the source of scattering. The scattering of theS-wave was much stronger and more stable, with the mean-free path varying from 11 m to 45 m. This is due to the shorter wavelength of theS wave in comparison with theP wave. The quality factor for theP coda wave varies from 30 to 100 in the fracture zone of stope and outside this zone it has a value of 300. The quality factor of theS wave varies from 20 to 78 in the equivalent volume. For rock surrounding the stope the ratioQ _sp ^–1 /Q _ss ^–1 varied from 0.31 to 0.69. This suggests that the radii of scatterers are smaller than 3.5 m.     

Regional coda Q in Costa Rica, Central America

Regional seismic apparent attenuation was estimated for Costa Rica, Central America, by using a time domain single scattering model of the shear wave coda decay of local earthquakes. The sensitivity of coda Q (Q_c) measurements with respect to geological differences in the crust is demonstrated in eight sub-regions with a large variety of tectonic and geologic properties. The Q_c estimations were performed for 96 selected local earthquakes recorded at 13 sites during a period of three months. In order to model the scattering as a weak process and to avoid short distance nonlinear effects, we made use of the S-wave coda data only from events within a hypocentral distance of 12 to 106 km with a lapse time between 9 and 53 s. Seismograms were also divided into groups with three different focal depths d, namely d<21 km, 21 kmc values are frequency dependent in the range 1–9 Hz, and are approximated by a least-squares fit to the power law Q_c(f) = Q₀(f/f₀)ⁿ. The estimated parameters of the power-law dependence of Q_c for the whole region, including all depths and possible wave paths, are Q₀ = 91 (± 8.4) and n = 0.72 (±0.071). Differences in the parameter of Q_c for different depths intervals are small, ranging from Q₀ = 90 (±0.7) and n = 0.70 (±0.006) for the uppermost group, with focal depths less than 21 km, to Q₀ = 97 (±0.7) and n = 0.79 (±0.005) for the deepest group with focal depths larger than 43 km. The regional differences in Q_c for the eight sub-regions are significantly larger when compared with the differences between the three focal depth groups. An attempt is made to interpret the variation of Q_c in terms of spatial variations in the geologic and tectonic properties of the crust. Other authors have found that the frequency exponent n might be larger in active tectonic areas and smaller in more stable regions. In the northern region of the Pacific coast we obtain a value of n = 0.52 (±0.011), which might indicate a lower level of tectonic activity when compared with n = 0.85 (±0.015) and 0.83 (±0.031), respectively, for the central and southern sub-regions along the Pacific coast. The latter two sub-regions are located closer to the active area near the Cocos ridge. We obtain the frequency exponent n = 0.72 (±0.052) along a major shear zone in central Costa Rica characterized by high volcanic activity and large geologic complexity. Values of n along the Panamean border are 0.62 (±0.029) in the north and 0.86 (±0.009) and 0.83 (±0.031) in two regions adjacent to the subduction zone and the Cocos Ridge, respectively.     

Attenuation characteristics of Garwhal–Kumaun Himalayas from analysis of coda of local earthquakes

Coda of local earthquakes that occurred during 2006–2007 are used to study the attenuation characteristics of the Garhwal–Kumaun Himalayas. The coda attenuation characteristics are represented in terms of coda Q or Q _c . It is observed that Q _c increases with frequency. Q _c also varies with increase in lapse time of coda waves. Q _c increases up to an 85-s average lapse time. This is similar to observations around the world reported by many workers who have interpreted this as a manifestation of the fact that heterogeneity decreases with depth. However, around a 90-s average lapse time Q _c is lower than its values for lower and higher average lapse times. This is interpreted as an indication of possible presence of a fluid-filled medium or a medium having partial melts at around a 160-km depth. Q ₀, i.e., Q _c at 1 Hz, increases, and frequency parameter n decreases with increasing lapse time, barring around a 90-s lapse time. This again shows that in general, heterogeneity decreases with increasing depth. The Q ₀ and n values for smaller lapse times are similar to those for tectonically active areas. By comparing Q _c values obtained in this study with those obtained by us using the 1999 Chamoli earthquake aftershocks, it is concluded that the crust is turbid and the mantle is more transparent. However, whether the variation in Q _c values between 1999 and 2006–2007 is temporal or not cannot be definitely established from the available data set.     

Coda wave attenuation in the Parecis Basin,Amazon Craton,Brazil: sensitivity to basement depth

Small local earthquakes from two aftershock sequences in Porto dos Gaúchos, Amazon craton—Brazil, were used to estimate the coda wave attenuation in the frequency band of 1 to 24 Hz. The time-domain coda-decay method of a single backscattering model is employed to estimate frequency dependence of the quality factor (Q _c) of coda waves modeled using Q_c = Q₀ f^hQ_{\rm c} =Q_{\rm 0} f^\eta , where Q ₀ is the coda quality factor at frequency of 1 Hz and η is the frequency parameter. We also used the independent frequency model approach (Morozov, Geophys J Int, 175:239–252, 2008), based in the temporal attenuation coefficient, χ(f) instead of Q(f), given by the equation c(f)=g+\fracpfQ_e \chi (f)\!=\!\gamma \!+\!\frac{\pi f}{Q_{\rm e} }, for the calculation of the geometrical attenuation (γ) and effective attenuation (Q_e^-1 )(Q_{\rm e}^{-1} ). Q _c values have been computed at central frequencies (and band) of 1.5 (1–2), 3.0 (2–4), 6.0 (4–8), 9.0 (6–12), 12 (8–16), and 18 (12–24) Hz for five different datasets selected according to the geotectonic environment as well as the ability to sample shallow or deeper structures, particularly the sediments of the Parecis basin and the crystalline basement of the Amazon craton. For the Parecis basin Q_c = (98±12)f^(1.14±0.08)Q_{\rm c} =(98\pm 12)f^{(1.14\pm 0.08)}, for the surrounding shield Q_c = (167±46)f^(1.03±0.04)Q_{\rm c} =(167\pm 46)f^{(1.03\pm 0.04)}, and for the whole region of Porto dos Gaúchos Q_c = (99±19)f^(1.17±0.02)Q_{\rm c} =(99\pm 19)f^{(1.17\pm 0.02)}. Using the independent frequency model, we found: for the cratonic zone, γ = 0.014 s^− 1, Q_e^-1 = 0.0001Q_{\rm e}^{-1} =0.0001, ν ≈ 1.12; for the basin zone with sediments of ~500 m, γ = 0.031 s^− 1, Q_e^-1 = 0.0003Q_{\rm e}^{-1} =0.0003, ν ≈ 1.27; and for the Parecis basin with sediments of ~1,000 m, γ = 0.047 s^− 1, Q_e^-1 = 0.0005Q_{\rm e}^{-1} =0.0005, ν ≈ 1.42. Analysis of the attenuation factor (Q _c) for different values of the geometrical spreading parameter (ν) indicated that an increase of ν generally causes an increase in Q _c, both in the basin as well as in the craton. But the differences in the attenuation between different geological environments are maintained for different models of geometrical spreading. It was shown that the energy of coda waves is attenuated more strongly in the sediments, Q_c = (78±23)f^(1.17±0.14)Q_{\rm c} =(78\pm 23)f^{(1.17\pm 0.14)} (in the deepest part of the basin), than in the basement, Q_c = (167±46)f^(1.03±0.04)Q_{\rm c} =(167\pm 46)f^{(1.03\pm 0.04)} (in the craton). Thus, the coda wave analysis can contribute to studies of geological structures in the upper crust, as the average coda quality factor is dependent on the thickness of sedimentary layer.     

Attenuation of P- and S-waves in the Chamoli Region, Himalaya, India

The attenuation properties of the crust in the Chamoli region of Himalaya have been examined by estimating the frequency-dependent relationships of quality factors for P waves (Q_α) and for S waves (Q_β) in the frequency range 1.5–24 Hz. The extended coda normalization method has been applied on the waveforms of 25 aftershocks of the 1999 Chamoli earthquake (M 6.4) recorded at five stations. The average value of Q_α is found to be varied from 68 at 1.5 Hz to 588 at 24 Hz while it varies from 126 at 1.5 Hz to 868 at 24 Hz for Q_β. The estimated frequency-dependent relations for quality factors are Q_α = (44 ± 1)f^(0.82±.04) and Q_β = (87 ± 3)f^(0.71±.03). The rate of increase of Q(f) for P and S waves in the Chamoli region is comparable with the other regions of the world. The ratio Q_β/Q_α is greater than one in the region which along with the frequency dependence of quality factors indicates that scattering is an important factor contributing to the attenuation of body waves in the region. A comparison of attenuation relation for S wave estimated here (Q_β = 87f^0.71) with that of coda waves (Q_c = 30f^1.21) obtained by Mandal et al. (2001) for the same region shows that Q_c > Q_β for higher frequencies (>8 Hz) in the region. This indicates a possible high frequency coda enrichment which suggests that the scattering attenuation significantly influences the attenuation of S waves at frequencies >8 Hz. This observation may be further investigated using multiple scattering models. The attenuation relations for quality factors obtained here may be used for the estimation of source parameters and near-source simulation of earthquake ground motion of the earthquakes, which in turn are required for the assessment of seismic hazard in the region.     

Lapse time and frequency-dependent attenuation characteristics of coda waves in the Northwestern Himalayas

We analyzed the local earthquakes waveform recorded on a broadband seismic network in the northwestern Himalayan Region to compute lapse time and frequency dependence of coda Q (Q _c). The observed Q _c values increase with increasing lapse time at all frequency bands. The increase in Q _c values with lapse time is attributed to an increase in Q _c with depth. This implies that attenuation decreases with increasing depth. The approximate radius of medium contributing to coda generation varies from 55 to 130 km. By comparing the Q _c values with those from other regions of the world, we find that they are similar to those obtained from tectonically active regions. The estimated Q _c values show a frequency-dependent relationship, Q _c = Q ₀ f ⁿ , where Q ₀ is Q _c at 1 Hz and n represents degree of frequency dependence. They represent the level of heterogeneity and tectonic activity in an area. Our results show that northwest Himalayas are highly heterogeneous and tectonically very active. Q ₀ increases from 113 ± 7 to 243 ± 10 and n decreases from 1.01 ± 0.05 to 0.85 ± 0.03 when lapse time increases from 30 to 70 s. As larger time window sees the effect of deeper part of the Earth, it is concluded that Q ₀ increases and n decreases with increasing depth; i.e., heterogeneity decreases with depth in the study area.     

Temporal and spatial variation on codaQ −1 associated with the North Palm Springs earthquake of July 8, 1986

A temporal and spatial change of codaQ ^–1 associated with the occurrence of the North Palm Springs earthquake of July 8, 1986 was studied by using 242 small local earthquakes in the vicinity of the mainshock. We found that the codaQ ^–1 of earthquakes which occurred before the mainshock was significantly higher than that of the aftershocks in the mainshock area while the codaQ ^–1 for the surrounding area remained almost constant throughout 1986. CodaQ ^–1 was determined separately for the lapse time windows of 10 to 20 sec. and 15 to 40 sec. for the period from 1981 to 1987. The result for the time window 10 to 20 sec. showed a peak in codaQ ^–1 before the time of mainshock at all frequencies. The peak appeared earlier at lower frequencies. There was no significant change in codaQ ^–1 for the time window 15 to 40 sec., probably because the change was restricted to a small area.     

Characteristics of the seismic attenuation in two tectonically active zones of Southern Europe

The seismic energy attenuation in the frequency range of 1–18 Hz was studied in the two tectonically active zones of Irno Valley (Southern Italy) and Granada Basin (South-East Spain). Data were recorded by short period vertical components seismographs for low-magnitude local earthquakes. The method of coda waves, assuming singleS toS scattering approximation, was used to calculate the quality factorQ from the two data set. Results show a quality factor increasing with frequency, following the empirical lawQ=Q _o f ⁿ .Q _o andn are lower for the Irno Valley than for Granada. This result is interpreted in terms of different scattering environments present in the two investigated areas.     

Comparison of Sesimic Body Wave and Coda Wave Measures of Q

—Measurements of seismic attenuation (Q ^?1) can vary considerably when made from different parts of seismograms or using different techniques, particularly at high frequencies. These discrepancies may be methodological, or may reflect earth processes. To investigate this problem, we compare body wave with coda Q ^?1 results utilizing three common techniques i) parametric fit to spectral decay, ii) coda normalization of S waves, and iii) coda amplitude decay with lapse time. Q ^?1 is measured from both body and coda waves beneath two mountain ranges and one platform, from recordings made at seismic arrays in the Caucasus and Kopet Dagh over paths ≤ 4° long. If Q is assumed frequency independent, spectral decay fits show Q _s and Q _coda near 700–800 for both mountain paths and near 2100–2200 for platform paths. Similar values are determined with the coda normalization technique. However, frequency-dependent parameterizations fit the data significantly better, with Q _s ?(1 Hz) and Q _coda?(1 Hz) near 200–300 for mountain paths and near 500–600 for platform paths. Lapse decay measurements are close to the frequency-dependent values, showing that both spectral and lapse decay methods can give similar results when Q has comparable parameterizations. Above 6 Hz, coda measurements suggest some enrichment relative to body waves, perhaps due to scattering, but intrinsic absorption appears to dominate at lower frequencies. All approaches show sharp path differences between the Eurasian platform and adjacent mountains, and all are capable of resolving spatial variations in Q.     

Estimation of codaQ using the maximum likelihood method

A seismic coda wave from local earthquakes is an indication of heterogeneity in the crust and upper mantle, and codaQ (Q _c ) is the parameter defining the temporal decay of the coda wave. ButQ _c estimates obtained with the conventional least-square method are not based on any solid statistical background, assuming the Gaussian distributiona priori. In this study, we propose a statistically reliable estimation method of estimatingQ _c using the maximum likelihood method, and show its validity and usefulness with the data from the 1986 Joint Seismological Research in the western Nagano Prefecture. We found first that theQ _c estimation with the maximum likelihood method is statistically valid and its reliability can be checked with the -square test. Next,Q _c around Ohtaki village, within the studied area, is estimated using the maximum likelihood method. The averageQ _c value at low frequencies (up to 2 Hz) is one of the lowest in the world, which is in harmony with the geological setting of the site condition directly above an active fault.     

Attenuation in Southeastern Sicily (Italy) by applying different coda methods

The attenuation in Southeastern Sicily has been investigated using 40aftershocks of the December 13 1990, earthquake. The quality factor ofcoda waves (Q_c) was estimated in the frequency range 1.5–24 Hz,applying three different methods in time and frequency domains. On thewhole, a clear dependence of Q_c on frequency was observed,according to the general law Q = Q₀(f/f₀)ⁿ . Thefrequency dependence relationships obtained from the analysis of codawaves at three lapse time windows (10, 20 and 30 seconds) show that, forall methods, Q₀ (Q_c at 1 Hz) significantly increases with lapsetime. In particular, Q₀ is approximately 20 at short lapse time (10s) and increases to about 70 at longer lapse time (30 s). This is attributedto the fact that larger lapse times involve deeper parts of the crust andupper lithosphere which may be characterized by larger quality factors.Moreover, the value of the exponent n decreases with increasing codalengths from about 1.3 to 0.9, suggesting a decrease in heterogeneity ofthe medium with depth.Finally, Q_c-values here found are of the same order as thosereported from other tectonic regions like the Anatolian Highlands orSouthern Spain, while significantly higher than in the neighboring volcanicarea of Mt. Etna.