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.     

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 .     

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.     

Attenuation of High Frequency P and S Waves in the Gujarat Region,India

The local earthquake waveforms recorded on broadband seismograph network of Institute of Seismological Research in Gujarat, India have been analyzed to understand the attenuation of high frequency (2–25 Hz) P and S waves in the region. The frequency dependent relationships for quality factors for P (Q _P) and S (Q _S) waves have been obtained using the spectral ratio method for three regions namely, Kachchh, Saurashtra and Mainland Gujarat. The earthquakes recorded at nine stations of Kachchh, five stations of Saurashtra and one station in mainland Gujarat have been used for this analysis. The estimated relations for average Q _P and Q _S are: Q _P = (105 ± 2) f ^{0.82 ± 0.01}, Q _S = (74 ± 2) f ^{1.06 ± 0.01} for Kachchh region; Q _P = (148 ± 2) f ^{0.92 ± 0.01}, Q _S = (149 ± 14) f ^{1.43 ± 0.05} for Saurashtra region and Q _P = (163 ± 7) f ^{0.77 ± 0.03}, Q _S = (118 ± 34) f ^{0.65 ± 0.14} for mainland Gujarat region. The low Q (<200) and high exponent of f (>0.5) as obtained from present analysis indicate the predominant seismic activities in the region. The lowest Q values obtained for the Kachchh region implies that the area is relatively more attenuative and heterogeneous than other two regions. A comparison between Q _S estimated in this study and coda Q (Qc) previously reported by others for Kachchh region shows that Q _C > Q _S for the frequency range of interest showing the enrichment of coda waves and the importance of scattering attenuation to the attenuation of S waves in the Kachchh region infested with faults and fractures. The Q _S/Q _P ratio is found to be less than 1 for Kachchh and Mainland Gujarat regions and close to unity for Saurashtra region. This reflects the difference in the geological composition of rocks in the regions. The frequency dependent relations developed in this study could be used for the estimation of earthquake source parameters as well as for simulating the strong earthquake ground motions in the region.     

A scattering model for seismic attenuation and its global applications

The attenuation characteristics of Indian lithosphere and its comparison with different tectonic settings in the world are determined from the observations of the Q for L_g(Q_Lg)-, and S(Q_S)-waves in the 1-30 Hz frequency range. The scattering is approximated with a Gaussian distribution of spherical scatterers. To approximate single scattering, we use Dainty's [Geophy. Res. Lett. 8 (11) (1981) 1126] model that attenuation is given by 1/Q(ω) = 1/Q_i + g(ω)v/ω, where Q_i is intrinsic Q due to anelastic attenuation, v is shear wave velocity, ω is angular frequency, g = ∫n(a)σ da is the total scattering coefficient for S-to-S scattering, n(a) da is the number of scattering spheres of radius a per unit volume, and σ is the scattering cross-section for the sphere. We find that if n(a) is described by a simple two parameter (a₀ and c) Gaussian of amplitude c and standard deviation and mean a₀, the attenuation data for different regions of the world are well approximated over the frequency band of seismic observations. Our major findings are: (1) the maximum effect of scattering on attenuation occurs at 0.84 Hz or a wavelength of 4.16 km; (2) the values of g are frequency dependent. Values of g are of the order of 10⁻³ km⁻¹ at 1-30 Hz, varying from 0.0031 to 0.01 and 0.001 to 0.0083 km⁻¹ for tectonically active and stable regions, respectively; (3) regions of active tectonics and seismicity generally have lower Q_i values (1000) than that in stable regions (2000); and (4) regions of high Q_i value exhibit low intensity of scattering.     

Body-wave Attenuation in the Region of Garda, Italy

We analyzed the spectral amplitude decay with hypocentral distance of P and S waves generated by 76 small magnitude earthquakes (M_L 0.9–3.8) located in the Garda region, Central-Eastern Alps, Italy. These events were recorded by 18 stations with velocity sensors, in a distance range between 8 and 120 km. We calculated nonparametric attenuation functions (NAF) and estimated the quality factor Q of both body waves at 17 different frequencies between 2 and 25 Hz. Assuming a homogeneous model we found that the Q frequency dependence of P and S can be approximated with the functions Q _P = 65 f ^0.9 and Q _S = 160 f ^0.6 , respectively. At 2 Hz the Q _S /Q _P ratio reaches the highest value of 2.8. At higher frequencies Q _S /Q _P varies between 0.7 and 1.7, suggesting that for this frequency band scattering may be an important attenuation mechanism in the region of Garda. To explore the variation of Q in depth, we estimated Q at short (r ≤ 30 km) and intermediate (35–90 km) distance paths. We found that in the shallow crust P waves attenuate more than S (1.3 < Q _S /Q _P < 2.5). Moreover, P waves traveling along paths in the lower crust (depths approximately greater than 30 km) attenuate more than S waves. To quantify the observed variability of Q in depth we considered a three-layer model and inverted the NAF to estimate Q in each layer. We found that in the crust Q increases with depth. However, in the upper mantle (~40–50 km depth) Q decreases and in particular the high frequency Q _S (f > 9 Hz) has values similar to those estimated for the shallow layer of the crust.     

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.     

Attenuation of coda waves in northern Greece

The single scattering model has been applied for the estimation of codaQ values for local earthquakes that occurred in northern Greece during the period 1983–1989 and recorded by the telemetered network of the Geophysical Laboratory of the University of Thessaloniki. CodaQ estimations were made for four frequency bands centered at 1.5 Hz, 3.0 Hz, 6.0 Hz and 12.0 Hz and for the lapse time windows 10–20 sec, 15–30 sec, 20–45 sec, 30–60 sec and 50–100 sec. The codaQ values obtained show a clear frequency dependence of the formQ _c =Q ₀ f ⁿ , whileQ ₀ andn depend on the lapse time window.Q ₀ was found equal to 33 andn equal to 1.01 for the time window of 10 to 20 sec, while for the other windowsQ ₀ increased from 60 to 129, withn being stable, close to 0.75. This lapse time dependence is interpreted as due to a depth dependent attenuation. The high attenuation and the strong frequency dependence found are characteristic of an area with high seismicity, in agreement with studies in other seismic regions.     

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.     

Seismic Wave Attenuation in the Greater Cairo Region, Egypt

In the present study, a digital waveform dataset of 216 local earthquakes recorded by the Egyptian National Seismic Network (ENSN) was used to estimate the attenuation of seismic wave energy in the greater Cairo region. The quality factor and the frequency dependence for Coda waves and S-waves were estimated and clarified. The Coda waves (Q _c) and S-waves (Q _d) quality factor were estimated by applying the single scattering model and Coda Normalization method, respectively, to bandpass-filtered seismograms of frequency bands centering at 1.5, 3, 6, 12, 18 and 24?Hz. Lapse time dependence was also studied for the area, with the Coda waves analyzed through four lapse time windows (10, 20, 30 and 40?s). The average quality factor as function of frequency is found to be Q _c?=?35?±?9f ^0.9±0.02 and Q _d?=?10?±?2f ^0.9±0.02 for Coda and S-waves, respectively. This behavior is usually correlated with the degree of tectonic complexity and the presence of heterogeneities at several scales. The variation of Q _c with frequency and lapse time shows that the lithosphere becomes more homogeneous with depth. In fact, by using the Coda Normalization method we obtained low Q _d values as expected for a heterogeneous and active zone. The intrinsic quality factor (Q _i ^?1 ) was separated from the scattering quality factor (Q _s ^?1 ) by applying the Multiple Lapse Time Domain Window Analysis (MLTWA) method under the assumption of multiple isotropic scattering with uniform distribution of scatters. The obtained results suggest that the contribution of the intrinsic attenuation (Q _i ^?1 ) prevails on the scattering attenuation (Q _s ^?1 ) at frequencies higher than 3?Hz.     

High frequency fall-off of source spectra using Q -free spectra estimation

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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.     

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.     

Q c of three component seismograms of volcanic microearthquakes at Campi Flegrei volcanic area — Southern Italy

Digital recordings of three component microearthquake codas from shallow seismic events in the volcanic region of Campi Flegrei — Southern Italy — were used with an automatic technique to calculate the attenuation factorQ _c (codaQ) in the hypothesis of singleS toS backscattering.Results show the same value ofQ for each of the three components. This result is interpreted as due to isotropicS wave radiation pattern.A check of the coda method was performed using a single station method based on simple assumptions on the direct SH wave spectrum. Single stationQ was averaged over the stations and over the earthquakes. Results show that the two methods lead to comparable results.A frequency dependence quite different from that evaluated in active tectonic regions was found for coda attenuation, comparable to other volcanic areas throughout the world. This is interpreted as due to the presence of magma that affects anelasticity and scattering.     

Estimation of Q p and Q s of Kinnaur Himalaya

The attenuation characteristics of the Kinnaur area of the North West Himalayas were studied using local earthquakes that occurred during 2008–2009. Most of the analyzed events are from the vicinity of the Panjal Thrust (PT) and South Tibetan Detachment Thrust, which are well-defined tectonic discontinuities in the Himalayas. The frequency-dependent attenuation of P and S waves was estimated using the extended coda normalization method. Data from 64 local earthquakes recorded at 10 broadband stations were used. The coda normalization of the spectral amplitudes of P and S waves was done at central frequencies of 1.5, 3, 6, 9, and 12 Hz. Q _p increases from about 58 at 1.5 Hz to 706 at 12 Hz, and Q _s increases from 105 at 1.5 Hz to 1,207 at 12 Hz. The results show that the quality factors for both P and S waves (Q _p and Q _s) increase as a function of frequency according to the relation Q?=?Q _o f ⁿ , where Q _o is the corresponding Q value at 1 Hz frequency and “n” is the frequency relation parameter. We obtained Q _p?=?(47?±?2)f ^(1.04±0.04) and Q _s?=?(86?±?4)f ^(0.96±0.03) by fitting power law dependency model for the estimated values of the entire study region. The Q ₀ and n values show that the region is seismically very active and the crust is highly heterogeneous. There was no systematic variation of values of Q _p and Q _s at different frequencies from one tectonic unit to another. As a consequence, average values of these parameters were obtained for each frequency for the entire region, and these were used for interpretation and for comparison with worldwide data. Q _p values lie within the range of values observed for some tectonically active regions of the world, whereas Q _s values were the lowest among the values compared for different parts of the world. Q _s/Q _p values were >1 for the entire range of frequencies studied. All these factors indicate that the crust is highly heterogeneous in the study region. The high Q _s/Q _p values also indicate that the region is partially saturated with fluids.     

Rock-mass characterization using intrinsic and scattering attenuation estimates at frequencies from 400 to 1600 Hz

Intrinsic and scatteringS-wave quality factors (Q ) were estimated using the Multiple Lapse Time Window Analysis (MLTWA) for microseismic events (M<–1) with source-sensor distances of 45 to 120 m, associated with an excavation at 630 m depth in Strathcona Mine, Sudbury, Canada. Additional information on the rock mass was provided by underground structural mapping data. IntrinsicQ values, at 800 Hz, were on the order of 140, similar to quality factor values obtained in previous studies using Spectral Decay and Coda-Q methods (120 to 170). The scattering quality factor at this frequency was about 520. An observed frequency dependence of the scattering attenuation suggested that a decrease in the density of scatterers, with scale lengths on the order of 2 m, exists at the site. Characteristic fracture scale lengths were considered to range from 4 to 6 m as identified in the mapping data. These observations were supported by the increase in scattering found for seismic waves with frequencies less than 1000 Hz. By assuming that the identified scatters are characteristic faults, these scatterers can then be considered to increase nonsimilar behavior in source scaling. Overall, our results suggest that MLTWA provides a practical method for remotely characterizing the quality of a rock mass when visual observations are not attainable.     

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.     

The Effect of Porous Medium Storage on Unstable Density‐Driven Solute Transport

Unstable density‐driven groundwater flow and solute transport (i.e., free convection) leads to spatiotemporal variations in pressure. Specific storage (S_o) indicates the capability of a confined aquifer to release or store groundwater associated with a pressure change. Although S_o is known to dampen pressure propagation, S_o has been implicitly assumed to have a negligible impact on the unstable free convective process in prior studies. This work explores the effect of S_o on both the classic onset criterion and the fingering process using numerical models. Results show that the classic onset criterion is applicable when S_o is smaller than 10^–1 m^–1. Results also demonstrate that S_o does not play a significant role in the free convective fingering process unless it is greater than 10^–3 m^–1. For most practical purposes in hydrogeology (large Rayleigh number and small S_o), the implicit assumption of small or zero S_o is appropriate.     

Scattering attenuation and intrinsic absorption using uniform and depth dependent model – Application to full seismogram envelope recorded in Northern Chile

Two seismic wave attenuation factors, scatteringattenuation Q _s ^-1 and intrinsicabsorption Q _i ^-1 are measured using theMultiple Lapse Time Window (MLTW) analysis method forthree different frequency bands, 1–2, 2–4, and 4–8 Hz.Data from 54 temporally deployed seismic stationslocated in northern Chile are used. This methodcompares time integrated seismic wave energies withsynthetic coda wave envelopes for a multiple isotropicscattering model. In the present analysis, the waveenergy is assumed to decay with distance in proportionto1/GSF·exp(- (Q _s ^-1+Q _i ^-1)· r/v), where r, and v are the propagationdistance, angular frequency and S wave velocity,respectively, and GSF is the geometricalspreading factor. When spatial uniformity of Q _s ^-1, Q _i ^-1 and v isassumed, i.e. GSF = 4r ², theestimates of the reciprocal of the extinction length,L _e ^-1 (= (Q _s ^-1+Q _i ^-1)·/v), are 0.017,0.012 and 0.010 km^-1, and those of the seismicalbedo, B ₀ (= Q _s ^-1/ (Q _s ^-1+Q _i ^-1)), are 0.48, 0.40and 0.34 for 1–2, 2–4 and 4–8 Hz, respectively, whichindicates that scattering attenuation is comparable toor smaller than intrinsic absorption. When we assumea depth dependent velocity structure, we also findthat scattering attenuation is comparable to orsmaller than intrinsic absorption. However, since thequantitative estimates of scattering attenuationdepend on the assumed velocity structure (strength ofvelocity discontinuity and/or Moho depth), it isimportant to consider differences in velocitystructure models when comparing attenuation estimates.