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.     

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.     

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.     

Effect of anelastic and scattering structures of the lithosphere on the shape of local earthquake coda

A simple model of single acoustic scattering is used to study the dependence of the shape of local earthquake coda on the anelastic and scattering structures of the lithosphere. The model is applied to the coda of earthquakes located near Stone Canyon, central California, and provides an explanation for the features observed in the data, which include an interesting temporal variation in the coda shape. A surficial layer with aQ of 50 and thickness of 10 or 25 km underlain by a zone with aQ of 1000 extending to the bottom of the lithosphere, together with a scattering scale length,a, that varies with depthz according to the relationa=0.3 exp[-(z/45)²] are found to constitute the simplest structure of the medium compatible with the coda data and with body and surface wave attenuation data. The profile of heterogeneity sizes implies that the scattering strength increases strongly with depth, a constraint required by the necessity to boost the energy of the later coda without forcing the intrinsicQ to be excessively high in the uppermost mantle. This constraint is viewed as an artifact of the single scattering model which overstimates the scattering coefficient due to the neglect of multiple scattering. The observed temporal variation of the signal is difficult to explain by a simple change of the intrinsicQ at some depth. Rather, it is suggested that the scattering properties at depth changed with time through a variation of the fractional rms velocity fluctuation on the order of one percent.     

Propagation and attenuation characteristics of the crustal phaseLg

TheLg wave consists of the superposition ofS waves supercritically reflected, and thus trapped, in the crust. This mode of propagation explains the strong amplitude of this phase and the large distance range in which it is observed. The numerical simulation leads to successful comparison between observed seismograms in stable continental areas and synthetics computed for simple standard crustal models. In regions with strong lateral variations, the influence of large-scale heterogeneities on theLg amplitude is not yet clearly established in terms of the geometrical characteristics of the crustal structure.The analysis of the decay of amplitude ofLg with epicentral distance allows the evaluation of the quality factor ofS waves in the crust. The results obtained show the same trends as codaQ: a clear correlation with the tectonic activity of the region considered, both for the value ofQ at 1 Hz and for its frequency dependence, suggesting that scattering plays a prominent part among the processes that cause the attenuation.The coda ofLg is made up of scatteredS waves. The study of the spatial attenuation of the coda indicated that a large part of the arrivals that compose the coda propagate asLg. The relative amplitude of the coda is larger at sites located on sediments because, in these conditions, a part ofLg energy can be converted locally into lower order surface modes.     

The physical implication of coda amplitude ratio and its possible application

The physical implication of coda amplitude ratio is discussed in term of energy ratio. The digitized data recorded at the station of Beijing Telemetered Seismograph Network between 1989 and 1990 are used to calculate amplitude ratios of coda to direct S wave, and energy ratios. The spectral energy ratios are used to estimate the coda Q and mean free path l in the Beijing area, as well as the two quality factors Q _i and Q _S separately due to intrinsic absorption and scattering attenuation. The decay of seismic waves in their propagation seems mainly resulted from the intrinsic absorption in Beijing region. The temporal variations of amplitude ratio and energy ratio at Changli station during the above two years are inspected; some of them largely depart from their mean value. It may reflect the seismogenic process, but using the data lasting longer time with more case histories needs further study. This study is sponsored by the Key Project of State Science and Technology of China, No. 96-918.     

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.     

Coda waves: A review

The analysis and interpretation of coda waves have received increasing attention since the early seventies. In the past few years interest in this subject has spread worldwide, and the study of high-frequency seismic coda waves has become a very important seismological topic. As a conclusion of the studies accomplished in this time, coda waves are considered the result of scattering processes caused by heterogeneities acting on seismic waves.P andS waves play a particularly important role in this interaction. The process introduces an attenuation which, added to the intrinsic absorption, gives the observed apparent attenuation. Therefore, coda waves constitute a thumbprint left by the heterogeneities on the seismograms. Coda waves offer decisive information about the mechanism of how scattering and attenuation take place. This review describes coda waves in detail, and summarizes the work done in this subject to 1986. The relation between coda waves and attenuation in the context of research on seismic scattering problems is stressed. Particular attention has been given to the application of coda waves to estimate source and medium parameters. The state-of-the-art of the temporal variations of coda wave shape, and the possible use of these variations as an earthquake precursor also are presented. Care has been taken to introduce the statistical models used to deal with the heterogeneities responsible for scattering.     

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.     

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.     

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.     

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.     

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.     

双相介质中地震波衰减的物理机制

High-frequency seismic attenuation is conventionally attributed to anelastic absorption. In this paper, I present three studies on high-frequency seismic attenuation and propose that the physical mechanism results from the interference of elastic microscopic multiple scattering waves. First, I propose a new theory on wave propagation in a two-phase medium which is based on the concept that the basic unit for wave propagation is a nano- mass point. As a result of the elasticity variations of pore fluid and rock framework, micro multiple scattering waves would emerge at the wavelength of the seismic waves passing through the two-phase medium and their interference and overlap would generate high- frequency seismic attenuation. Second, I present a study of the frequency response of seismic transmitted waves by modeling thin-layers with thicknesses no larger than pore diameters. Results indicate that high-frequency seismic waves attenuate slightly in a near-surface water zone but decay significantly in a near-surface gas zone. Third, I analyze the seismic attenuation characteristics in near-surface water and gas zones using dual-well shots in the Songliao Basin, and demonstrate that the high-frequency seismic waves attenuate slightly in water zones but in gas zones the 160-1600 Hz propagating waves decay significantly. The seismic attenuation characteristics from field observations coincide with the modeling results. Conclusions drawn from these studies theoretically support seismic attenuation recovery.     

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.     

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.     

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.     

Pure path attenuation measurements of long-period Rayleigh waves across the Tibet Plateau

A method is presented to derive pure path attenuation coefficients of Rayleigh waves, in the period range 30–90 s, across the Tibet Plateau, using events located within Tibet and observed at teleseismic distances. This method uses data from 2 events and 2 stations simultaneously, these being aligned along a great circle path, and, for relatively small events, is practically free of errors due to inaccurate knowledge of the source radiation patterns.In spite of large standard errors due to the impossibility of separating effects of anclasticity from spurious effects on amplitudes such as scattering or multipathing, results seem to indicate an anelastic model of the crust and upper mantle compatible with shear velocity models derived independently, with a thick crust and in particular, a thick high Q lid and thin low Q zone consistent with a shield like upper mantle beneath Tibet.     

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.