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.     

The Q value variations in the preparing process of rock rupture

In this paper, the "spectral amplitude ratio method" (SAR), "energy method" (EN) and "coda wave method" (CW) are used to calculate theQ value variations of gneiss in the preparing rupture process. The obtained results show that the variation state ofQ values by SAR features the shape of relative stability—gradual increment to the maximum—then decrement and final rupture. The variation state ofQ values by EN is just contrary to that by SAR, i. e. with the shape of stability—decrement—increment—and final rupture. The varation state ofQ values by CW is similar to that by EN, its main frequency features the shape of relatively high value—decrement to the minimum—increment—and final rupture. But to the high frequency (higher than the main frequency), the variation state ofQ values features the shape of the stable value-increment to the maximum-decrement-and final rupture. At the same time, the results by coda wave amplitude spectrum show that, when stress reaches 70% of rupture stress, the high frequency component of S wave rapidly reduces (Q _c increasing); at the time of impending the main rupture, the main frequency component reduces with a large scale (Q _c increasing again), this may be the reason which causes the different variation states of two codaQ values. The result of amplitude spectra of P, S (initial wave) waves also show that with the appearance of microcracks the frequency band of S wave turn to be narrow, the high frequency component is reduced quickly, i. e. the S wave spectra have different variation states with different frequency components. That is why theQ _s obtained by different methods have different variation characteristics.     

Spatial variation of crustal codaQ in California

Coda wave data from California microearthquakes were studied in order to delineate regional fluctuations of apparent crustal attenuation in the band 1.5 to 24 Hz. Apparent attenuation was estimated using a single back scattering model of coda waves. The coda wave data were restricted to 30 s following the origin time; this insures that crustal effects dominate the results as the backscattered shear waves thought to form the coda would not have had time to penetrate much deeper. Results indicate a strong variation in apparent crustal attenuation at high frequencies between the Franciscan and Salinian regions of central California and the Long Valley area of the Sierra Nevada. Although the codaQ measurements coincide at 1.5 Hz (Q _c =100), at 24 Hz there is a factor of four difference between the measurements made in Franciscan (Q _c =525) and Long Valley (Q _c =2100) with the Salinian midway between (Q _c =900). These are extremely large variations compared to measures of seismic velocities of comparable resolution, demonstrating the exceptional sensitivity of the high frequency codaQ measurement to regional geology. In addition, the frequency trend of the results is opposite to that seen in a compilation of codaQ measurements made worldwide by other authors which tend to converge at high and diverge at low frequencies, however, the worldwide results generally were obtained without limiting the coda lengths and probably reflect upper mantle rather than crustal properties. Our results match those expected due to scattering in random media represented by Von Karman autocorrelation functions of orders 1/2 to 1/3. The Von Karman medium of order 1/3 corresponding to the Franciscan codaQ measurement contains greater amounts of high wavenumber fluctuations. This indicates relatively large medium fluctuations with wavelengths on the order of 100 m in the highly deformed crust associated with the Franciscan, however, the influence of scattering on the codaQ measurement is currently a matter of controversy.     

Comparison of techniques that use the single scattering model to compute the quality factorQ from coda waves

Using simulated coda waves, the resolution of the single-scattering model to extract codaQ (Q _c ) and its power law frequency dependence was tested. The back-scattering model ofAki andChouet (1975) and the single isotropic-scattering model ofSato (1977) were examined. The results indicate that: (1) The inputQ _c models are reasonably well approximated by the two methods; (2) almost equalQ _c values are recovered when the techniques sample the same coda windows; (3) lowQ _c models are well estimated in the frequency domain from the early and late part of the coda; and (4) models with highQ _c values are more accurately extracted from late code measurements.     

<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.     

Crustal attenuation for Jamaica, West Indies

The S and coda wave spectra of small earthquakes on the island of Jamaica were used to determine the near surface and coda Q attenuation, and Q _c,respectively. Q _c determined by the single-station method was found in the range of 1 to 10 Hertz to be given by the relationship, Q _c= 60 ± 5f ^0.87±0.05. This suggests that the Jamaican crust is highly attenuating which is further supported by the observation of rapid intensity fall-off with distance for earthquakes that have affected the island in the past. , determined from S-wave spectra with short travel times was found to be 0.058 ± 0.012 on the central crustal block, which makes up nearly two-thirds of the island, and 0.080 ± 0.014 in surrounding belt sub-regions. The pattern of values seems to fit with the surface geology in that the central block has areas of exposed outcrops of older and harder rock than the belts, which are characterized by thicker sedimentary sequences as well as intense fracturing and faulting.Atkinson and Boore (1998) and Atkinson(2001) presented an alternative method to stochastic modelling for ground motion in Eastern North America, whereby California attenuation relationships were modified to account for crustal differences invelocity-depth profile, Q and between both regions. Following their example, the California spectral attenuation relation of Boore, Joyner and Fumal (1997) was modified to account for differences between the California and Jamaica crust, resulting in an attenuation relation that is deemed to be more appropriate for Jamaica. Spectral accelerations for Jamaica when compared to California, are especially reduced beyond 20 km from the source and at high frequencies, f 1 hertz.The study concludes that the Jamaican crust, although having an oceanic composition is highly attenuating, which may be a result of intensive tectonic processes, whereas is consistent with near-rock conditions on the central block and soft rock conditions elsewhere on the island.     

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.     

Intrinsic absorption and scattering attenuation in the southern part of the Netherlands

We present the first systematic study of attenuation derived from the S-wave coda in the frequency range 1-32 Hz for the southern part of the Netherlands and its surroundings. For this we used two methods, the codaQ (Q _c) method and the Multiple Lapse Time Window (MLTW) method. In the interpretation of the results both single and multiple scattering in a half space are considered. Our aim is to validate these interpretations in our region and to try to identify theeffects of attenuation due to intrinsic absoprtion (Q _i)and scattering attenuation (Q _s). For this we analyzedmore than 100 3-component high-quality digital seismograms from 43 crustalevents and 23 different stations in the Netherlands, Germany and Belgium.Coda Q results show smaller Q _c (=Q ₀fⁿ) values for epicentral distances shorter than 25 km (Q ₀=90) compared to larger epicentral distances (Q ₀=190), but similar frequency dependence (f^-0.9). Interpretation of MLTW results provided a seismic albedo smaller then 0.5, suggesting that the intrinsic absorption dominates over scattering in this region. Both Q _i and Q _s show similar frequency dependences as Q _c. These results are comparable to those obtained in other areas, but we also show that more sophisticated models are required to remove ambiguities in the interpretation. For short lapse times and shortevent-station distances we find for the simple half space model a correspondinginterpretation of both methodologies, where Q _c correspondsto Q _t, suggesting that a model with single scattering in ahalf space is appropriate. For long lapse times and long event station distances, however, we find that the S-wave coda is, most probably, too much influenced by crust-mantel heterogenities and more sophisticated Qinversion models using larger data sets are required for more reliable attenuation estimates.     

Unified approach to amplitude attenuation and coda excitation in the randomly inhomogeneous lithosphere

A unified model is proposed for explaining the frequency dependent amplitude attenuation and the coda wave excitation on the basis of the single scattering process in the randomly inhomogeneous lithosphere. Adopting Birch's law and a direct proportion between density and wave velocity, we statistically describe the inhomogeneous medium by one random function characterized by the von Karman autocorrelation function. We calculate the amplitude attenuation from the solid angle integral of scattered wave energy on the basis of the Born approxiimation after subtracting the travel-time fluctuation effect caused by slowly varying velocity inhomogeneities. This subtraction is equivalent to neglect energy loss by scattering within a cone around the forward direction. The random inhomogeneity of the von Karman autocorrelation function of order 0.35 with the mean square fractional fluctuation of 7.2×10^–3 1.3×10^–2 and the correlation distance of 2.15.1 km well explains observed backward scattering coefficientg and the ratioQ _P ^–1 /Q _S ^–1 , and observed and partially conjecturedQ _S ^–1 for frequencies between 0.5 Hz and 30 Hz.     

Application of scaling-rule theory in crustal rock fracture to studying characteristics of seismological precursors associated with M=6.1 Shandan-Minle earthquake

In the paper, we introduce Allegre＇s scaling-rule theory of rock fracture and the probability to develop a method for predicting earthquake occurrence time on its basis. As an example, we study the characteristics of seismological precursors （seismic spatial correlation length and coda Qc） associated with the earthquake （M=6.1） occurred in Shandan-Minle, Gansu Province. The results show an increasing trend of seismic spatial correlation length and coda Qc before the earthquake. And a power exponent relation is used to fit the increasing variation form of these two parameters. The study has provided a basis for creating a method and finding indexes to predict the earthquake occurrence time by using the monitored seismic spatial correlation length and coda Qc.     

Estimation of coda and shear wave attenuation in the volcanic area in SE Sabalan Mountain,NW Iran

The quality factors of coda and shear waves have been estimated for the SE Sabalan Mountain, geothermal region in northwestern Iran. We have analyzed 65 local earthquakes with magnitude of 2.8 to 6.1 and 2.8 to 5 for shear and coda wave quality factor estimation, respectively. These events were recorded on five stations installed by Building and Housing Research Center Network. Coda normalization and Spectral decay methods have been used to estimate the frequency dependence attenuation relation for shear wave, and single back-scattering method for coda waves. We have observed that the coda normalization method has supplied significantly higher Q _S values as compared to the spectral method. The results show that, in general, Q values are significantly smaller for the entire frequency range as compared to tectonically active areas and are close to the values for volcanic areas.     

Estimates of coda Q attenuation in the João Câmara area (Northeastern Brazil)

S coda wave of seventy-four local earthquakes recorded in a network of ten seismic stations were used to calculate coda Q attenuation (Q_c) in the João Câmara area (northeastern Brazil). The estimates show Q_c as a strong function of frequency in the range from 6.0 to 20.0 Hz. We found out that Q_c in João Câmara has a functional form given by Q_c= Q₀ f, where Q₀= 151 ± 99 and = 0.98 ± 0.05. If the standard deviations are taken into account,we conclude that there are no relevant changes in both Q₀ and values from one station to another. The estimated Q₀ values at the different stations suggest that the Samambaia fault is a boundary between two different seismic attenuation zones. In one side of the fault (left), where stations were installed in Pre-Cambrian terrain and thick sedimentary layer, the seismic attenuation is stronger than in the other side (stations installed in thin sedimentary layer and limestone outcrop).The anomalous Q₀ values in the left side of the Samambaia fault can be explained due to the presence of a shallow conductive layer in the upper crust( 10 km), such as proposed by Padilha et al. (1992). According to our results, if there is a conductive layer in the area, it probably spreads over João Câmara city and surrounding regions.However, more detailed investigation either with seismic methods (seismic attenuation,3D tomography with P and/or S wave velocities) or with other geophysical methods is needed to interpret the observed differences in Q₀ values between the two sides of the Samambaia fault.     

Frequency-Dependent Attenuation of Coda Waves in the Crust in Southwest Anatolia (Turkey)

The attenuation of coda waves in the earth’s crust in southwest (SW) Anatolia is estimated by using the coda wave method, which is based on the decrease of coda wave amplitude in time and distance. A total of 159 earthquakes were recorded between 1997 and 2010 by 11 stations belonging to the KOERI array. The coda quality factor Q _c is determined from the properties of scattered coda waves in a heterogeneous medium. Firstly, the quality factor Q ₀ (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 for frequencies of 1.5, 3.0, 6.0, 8.0, 12 and 20 Hz. Secondly, the attenuation coefficients (δ) are estimated. The shape of the curve is controlled by the scattering and attenuation in the crustal volume sampled by the coda waves. The average Q _c values vary from 110 ± 15 to 1,436 ± 202 for the frequencies above. The Q ₀ and η values vary from 63 ± 7 to 95 ± 10 and from 0.87 ± 0.03 to 1.04 ± 0.09, respectively, for SW Anatolia. In this region, the average coda Q–f relation is described by Q _c = (78 ± 9)f ^0.98±0.07 and δ = 0.012 km^?1. The low Q ₀ and high η are consistent with a region characterized by high tectonic activity. The Q _c values were correlated with the tectonic pattern in SW Anatolia.     

Attenuation of Coda Waves at the Changbaishan Tianchi Volcanic Area in Northeast China

21 earthquakes recorded by a temporary seismic network in the Changbaishan Tianchi volcanic area in Northeast China operated during the summer of 2002 and 2003 were analyzed to estimate the S coda attenuation. The attenuation quality factor Q_c was estimated using the single scattering attenuation model of Sato (1977) in the frequency band from 4 to 24 Hz. All the events studied in this paper occurred at depths from 2 to 6 km with ML of 1.4–2.8. The epicentral distances are less than 25 km. For all events which occurred near the Tianchi Lake (caldera), the Q_c patterns obtained at the stations near the lake are similar, and the Q_c values are relatively small. At the stations located about 15 km east of the Tianchi Lake, however, the average Q_c is significantly higher. For an event which occurred 25km from the lake to the west, Q_c patterns derived at the stations near the lake are quite similar to the above mentioned Q_c for stations located in the east. Further study shows that Q_c value in the north and central areas of the volcano is relatively lower than that in the surrounding area. Compared to other volcanic areas in the world, the average Q_c of the Changbaishan Tianchi volcanic area is obviously lower. The deep seismic sounding and teleseismic receiver function studies indicated more than one lower velocity layer in the crust. The MT studies suggested the presence of high conductive bodies beneath the area. We interpret the strong attenuation of coda waves near the Changbaishan Tianchi volcano as being possibly related to high temperature medium caused by shallow magma chambers.     

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.     

Estimation of Coda Wave Attenuation for the National Capital Region, Delhi, India Using Local Earthquakes

Attenuation of seismic waves is very essential for the study of earthquake source parameters and also for ground-motion simulations, and this is important for the seismic hazard estimation of a region. The digital data acquired by 16 short-period seismic stations of the Delhi Telemetric Network for 55 earthquakes of magnitude 1.5 to 4.2, which occurred within an epicentral distance of 100 km in an area around Delhi, have been used to estimate the coda attenuation Q_c. Using the Single Backscattering Model, the seismograms have been analyzed at 10 central frequencies. The frequency dependence average attenuation relationship Q_c = 142f ^1.04 has been attained. Four Lapse-Time windows from 20 to 50 seconds duration with a difference of 10 seconds have been analyzed to study the lapse time dependence of Q_c. The Q_c values show that frequency dependence (exponent n) remains similar at all the lapse time window lengths. While the change in Q₀ values is significant, change in Q₀ with larger lapsetime reflects the rate of homogeneity at the depth. The variation of Q_c indicates a definitive trend from west to east in accordance with the geology of the region.     

Time domain solution for multiple scattering and the coda envelopes

This article summarizes work on multiple scattering based on models of media with randomly distributed scatterers. The scatterers are isotropic and statistically uniform. Measuring distance in terms of mean-free pathL _s and time in terms of the mean-free timesL _s/V, whereV is the velocity of scattered waves, we have more convenient dimensionless distance and time. It can be shown that after the dimensionless time equals 0.65 energy contributed from multiple scattering becomes predominant. Thus the later coda reflects the effect of multiple scattering rather than single scattering. Treating the seismic record, including starting and tail parts, as a whole, the diffusion theory predicts that at a dense distribution of scatterers and a small distance between source and receiver, codas reflect mainly intrinsicQ _i. Of course, this conclusion is coincident with the presumption of the diffusion theory,Q _s>Q _i. However, from a new integral equation of multiple scattering, which deals with the scattered waves and primary waves separately, the conclusion is similar but clearer. This article quotes the new expression for coda energy in two-dimensional space. It shows that if the receiver is close to the source, the coda decay reflects only intrinsicQ _i, then as the distance increases, effects of scatteringQ _s, are involved in the decay feature. The theoretical plots of coda decay show that it seems in most cases in the earthQ _i should not be smaller than one tenth ofQ _s.Project Sponsored by the Joint Earthquake Science Foundation of China.     

A model for attenuation and scattering in the Earth's crust

The mechanisms contributing to the attenuation of earthquake ground motion in the distance range of 10 to 200 km are studied with the aid of laboratory data, coda wavesRg attenuation, strong motion attenuation measurements in the northeast United States and Canada, and theoretical models. The frequency range 1–10 Hz has been studied. The relative contributions to attenuation of anelasticity of crustal rocks (constantQ), fluid flow and scattering are evaluated. Scattering is found to be strong with an albedoB ₀=0.8–0.9 and a scattering extinction length of 17–32 km. The albedo is defined as the ratio of the total extinction length to the scattering extinction length. TheRg results indicate thatQ increases with depth in the upper kilometer or two of the crust, at least in New England. CodaQ appears to be equivalent to intrinsic (anelastic)Q and indicates that thisQ increases with frequency asQ=Q _o f ⁿ , wheren is in the range of 0.2–0.9. The intrinsic attenuation in the crust can be explained by a high constantQ (500Q _o2000) and a frequency dependent mechanism most likely due to fluid effects in rocks and cracks. A fluid-flow attenuation model gives a frequency dependence (QQ _o f ^0.5) similar to those determined from the analysis of coda waves of regional seismograms.Q is low near the surface and high in the body of the crust.     

Regional characteristics of coda attenuation after the lancang-Gengma earthquake

In the light of the single scattering model of coda originating from local earthquakes, and based on the aftershock coda registered respectively at the 4 short period stations installed near the foci shortly after theM7.6 Lancang andM7.2 Gengma earthquakes, this paper has tentatively calculated the rate of amplitude attenuation and theQ _c-value of the coda in the Lancang and Gengma areas using a newly-founded synthetic determination method. Result of the study shows the rate of coda amplitude attenuation demonstrates remarkable regional differences respectively in the southern and northern areas. The southern area presents a faster attenuation (Q _c=114), whereas the northern area shows a slower attenuation (Q _c=231). The paper also discusses the reasons causing such differences. Result of the study also suggests a fairly good linear relation between the coda source factorA _o(f) and the seismic moment and the magnitude. Using the earthquake scaling law, the following formulas can be derived: lgM ₀=lgA ₀(f)+17.6,M _D=0.67lgA ₀(f)+1.21 and logM ₀=1.5M _D+15.79. In addition, the rates of amplitude attenuationβ _s andβ _m are respectively calculated using the single scattering and multiple scattering models, and the ratioβ _s/β_m=1.20−1.50 is found for the results respectively from the two models. Finally, the mean free pathL of the S-wave scattering in the southern and northern areas are determined to be 54 km and 122 km respectively by the relations which can distinguish between the inherentQ _i and scatteringQ _s, testify to this areas having lowQ-values correspond to stronger scatterings. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,14, 71–82, 1992. This study is partly supported by the Seismological Science Foundation of the State Seismological Bureau of China, and the present English version of the paper is translated from its Chinese original by Wenyi Xia, Seismological Bureau of Yunnan Province.     

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.