Coda Decay Research Articles

Lateral Variations of Lg Coda Q in Southern Mexico

—Broad band digital three-component data recorded at UNM, a GEOSCOPE station, were used to estimate Lg coda Q for 34 medium size (3.9 ≤m b ≤ 6.3) earthquakes with travel paths laying in different geological provinces of southern Mexico in an effort to establish the possible existence of geological structures acting as wave guides and/or travel paths of low attenuation between the Pacific coast and the Valley of Mexico. The stacked spectral ratio method proposed by XIE and NUTTLI (1988) was chosen for computing the coda Q. The variation range of Q 0 (Q at 1 Hz) and the frequency dependence parameter η estimates averaged on the frequency interval of 0.5 to 2 Hz for the regions and the three components considered are: i) Guerrero region 173 ≤Q¯ 0≤ 182 and 0.6 ≤Q¯ 0 ≤ 0.7, ii) Oaxaca region 183 ≤Q¯ 0 ≤ 198 and 0.6 ≤Q¯ 0 ≤ 0.8, iii) Michoacan-Jalisco region 187 ≤Q¯ 0 ≤ 204 and 0.7 ≤Q¯ 0 ≤ 0.8 and iv) eastern portion of the Transmexican Volcanic Belt (TMVB) 313 ≤Q 0≤ 335 and η = 0.9. ¶The results show a very high coda Q for the TMVB as compared to other regions of southern Mexico. This unexpected result is difficult to reconcile with the geophysical characteristics of the TMVB, e.g., low seismicity, high volcanic activity and high heat flow typical of a highly attenuating (low Q) region. Visual inspection of seismograms indicates that for earthquakes with seismic waves traveling along the TMVB, the amplitude decay of Lg coda is anomalously slow as compared to other earthquakes in southern Mexico. Thus, it seems that the high Q value found does not entirely reflect the attenuation characteristics of the TMVB but it is probably contaminated by a wave-guide effect. This phenomenon produces an enhancement in the time duration of the Lg wave trains travelling along this geological structure. This result is important to establish the role played by the transmission medium in the extremely long duration of ground motion observed during the September 19, 1985 Michoacan earthquake. ¶The overall spatial distribution of coda Q values indicates that events with focus in the Michoacan-Jalisco and Oaxaca regions yield slightly higher values than those from Guerrero. This feature is more pronounced for the horizontal component of coda Q. A slight dependence of average coda Q −1 on earthquake focal depth is observed in the frequency range of 0.2 to 1.0 Hz approximately on the horizontal component. Deeper (h > 50 km) events yield lower values of Q −1 than shallower events. For frequencies higher than 1.0 Hz no clear dependence of Q −1 on focal depth is observed. However, due to the estimates uncertainties this result is not clearly established.

Temporal variations of the coda decay rate on Kamchatka: Are they real and precursory?

Temporal variations of the decay rate of the coda of local earthquakes are studied for four Kamchatka stations. To suppress any bias caused by the coda Q versus lapse time dependence, I use the deviation of an individual coda decay function from the empirical reference decay function, and the analysis is done over a fixed lapse time window. For each individual coda record, a decay rate parameter “α” is determined by the following procedure. First, the reference log coda decay function is subtracted from an individual one giving a residual function; second, the slope of this residual versus lapse time is determined over the fixed lapse time window giving an α estimate. The data used are records of 150–250 Kamchatka earthquakes of 1967–1990 (ML=3.5–5) obtained by four stations employing three‐component 1‐s seismographs. The processed data show apparent temporal variation of α with high statistical significance. Several possibilities are then investigated of mimicking the genuine temporal variation of α by systematic variation of other parameters, first of all epicenter wandering and nodal plane rotation. This analysis does not reveal any strong bias and thus suggests that the observed variation is genuine. Then I show the significance of five apparently precursory anomalies identified retroactively. Also, I describe briefly the real‐time prediction experiment conducted on Kamchatka for 1982–1990 using coda decay, aimed at the intermediate‐term forecasting of large Benioff zone earthquakes. This experiment resulted in the successful forecast of the August 17, 1983, Mw=7.0 event with an accuracy of 2 months in time and 100–200 km in location; magnitude was overestimated by 0.5. Later, a false alarm was also issued. Thus the experiment confirms the reality of the coda decay rate precursor but also shows that it needs further improvement to become reliable. Physically, the variations of the coda decay rate are associated with time‐dependent local variations of scatterer density in the lithosphere.

CodaQin two-layer random media

Using the indirect boundary integral scheme for multiple scattering of seismic waves developed by Benites, Aki & Yomogida (1992), we compute SH-wave seismograms and measure frequency-dependent characters of coda Q in 2-D random media with a flat layer over a half-space. Many circular cavities are randomly distributed in both the upper layer and the half-space, down to a certain depth (called the lower layer), simulating the upper and lower crusts. The scattering strength and the intrinsic attenuation, Qi, are varied for each layer, and the S-wave velocity is prescribed to be constant throughout the medium so that the computation of Green's functions for the boundary integral is simple. Considering two basic parameters of our random media, scattering strength and intrinsic attenuation Qi, we represent the shallow-earth structure by an upper crust with large intrinsic attenuation and a lower crust with effective scatterers. Computations of coda Q for several values of those parameters show that when the scattering is relatively strong, coda Q-1 is roughly independent of frequency. This result differs from the case of a uniformly random model where coda Q-1 peaks around kd = 2, where k is the wavenumber and d is the cavity diameter. If the scattering strength in the lower layer is large enough for multiple scattering to dominate over single scattering, coda Q-1 strongly depends on the intrinsic attenuation in the lower layer, Q-1i2, and these two values (coda Q-1 and Q-1i2) become similar. We explain this feature as follows. Waves scattered in the upper layer attenuate quickly due to high intrinsic attenuation and contribute little to the coda envelope in a time window starting at twice the traveltime of the direct wave. Multiply scattered waves in the lower layer eventually arrive at the surface, dominating the coda envelope, which decays at a rate determined by the intrinsic attenuation in the lower layer, Q-1i2. The hypothesis that the temporal decay of coda is controlled not by the scattering but by the energy leakage into a ‘transparent’ underlying mantle is ruled out in general by our numerical simulations, except at low frequencies. Although our model may be too simple to simulate the details of observed coda Q, coda Q is likely to reflect the intrinsic attenuation in the Earth's lower crust

ランダム媒質中の波動伝播の数値シミュレーション

This paper reviews numerical studies on acoustic as well as elastic wave propagation in random media, to model the earth's crust. For a long time, stochastic properties of wave propagation in random media, such as scattering attenuation, coda decay, velocity dispersion, and fluctuations of waveforms and traveltimes, have been studied analytically and approximately. Recent development of computer capability enables us to investigate them by solving the wave equation directly and numerically. Numerical wave simulations have also become an important strategy in seismic exploration. We concentrate here on types of inhomogeneities described suitably by autocorrelation functions of the elastic fluctuations of media, and summarize how to model them. For simulating waves scattered by such “random fluctuations”, the finite difference scheme is popularly used and the pseudospectral method is also in use. Isotropic and continuous fluctuations are usually assumed in the modeling, though anisotropic and/or discrete ones, that are often recognized in geological observations, have also been considered just recently.

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 (Qc) 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 Qc 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 km<d<43 km and 43 km<d<94 km. As in many other investigations, the Qc values are frequency dependent in the range 1–9 Hz, and are approximated by a least-squares fit to the power law Qc(f) = Q0(f/f0)n. The estimated parameters of the power-law dependence of Qc 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 Qc 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 Qc 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 Qc 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.

Single-station spectral discrimination using coda waves

Abstract Spectral discrimination methods applied at regional distances are based on the observation that there is a difference in the frequency content of the seismic waves radiated from the source region of earthquakes and explosions. We have investigated a spectral discrimination method that exploits the scattered energy contained in the event codas of seismograms to measure the relative source excitation of earthquakes and explosions as a function of frequency. Key strengths of the coda method include the following: (1) it is not affected by source radiation pattern because the scattering process averages the radiation over the focal sphere, (2) path corrections are not required with the coda method because coda waves are scattered throughout a common crustal volume, (3) it can be successfully applied using data from only a single station, and (4) it can be successfully applied using data with clipped direct arrivals. To implement the coda method, we first estimate a “type curve,” which represents the average shape of all the individual coda decay curves for a particular frequency band. The shape of the type curve (as well as the shape of all individual coda decay curves) is controlled by the scattering and attenuation properties of the crustal volume sampled by the coda waves (a common path effect). The amplitude of the type curve is not defined, and we arbitrarily adjust it to have a zero mean. The amplitude difference between an individual event coda decay curve and the type curve provides a relative measure of the event's source size within the particular frequency band. We define this amplitude difference as the “relative source factor.” Our approach exploits all of an event's usable coda for each spectral measurement, thus providing a more stable measure of relative source size than could be obtained from using a predefined, fixed-length time window. Analysis of 27 Nevada Test Site explosions and 15 southern Great Basin earthquakes (3.1 ≦ M ≦ 4.7), shows that the source factor difference between the 0.5- to 1- and 2- to 4-Hz bands plotted against the 1- to 2-Hz source factor is a stable event discriminant. The method reliably distinguishes small explosions from small earthquakes (3.0 &amp;lt; M &amp;lt; 3.5), even if the explosions are overburied. Because the coda method requires only one seismic station, we believe that it would be especially useful in identifying small, clandestine underground nuclear tests that occur far from established networks.

Stochastic characterization and seismic response of upper and middle crustal rocks based on the Lewisian gneiss complex, Scotland

SUMMARY We have developed statistical models of upper and middle crustal seismic velocity heterogeneity based on geologic maps and petrophysical data from the Lewisian gneiss complex, Scotland. the level of heterogeneity we have measured is relevant to seismic exploration of the crystalline crust using conventional reflection and refraction techniques. We digitized two 1:10560 geologic maps of Laxfordian (Archean) age Lewisian rocks on a 26.8m grid. Both maps are believed to be representative of the upper and middle crust in north-western Scotland, and both are believed to provide cross-sectional views of parts of the crust. the digital maps were characterized by the statistics of their lithologic populations and by their 2-D spatial autocorrelation functions. Different lithologies were assigned seismic velocities appropriate for the mid-crust using petrophysical data. Three lithologies are dominant: silicic gneisses (Vp∼6.2 km s−1), mafic amphibolites (Vp— 6.75 kms−1), and intermediate composition schists (Vp—6.5kms−1). Both maps have self-affine spatial fabrics. The first map covers the core of a syncline. Its autocorrelation function defines a medium with a fractal dimension of 2.78, a horizontal characteristic length of about 244m and a vertical correlation of about 133m (aspect ratio is 2:1). It has an essentially trimodal velocity (lithology) population consisting of 37 per cent silicicgneiss, 43 per cent mafic amphibolites, and 20 per cent schists. This map is representative of 30-40 per cent of Laxfordian rocks. the second map is a plan view which can be rotated 90° about an axis perpendicular to strike to give a cross-section. This map is characterized by a fractal dimension of 2.55, with a horizontal correlation length of about 111m and a vertical correlation of about 38m (aspect ratio 3:1). It has a nearly bimodal population consisting of 77 per cent silicic gneisses and 22 per cent mafic amphibotites. It is representative of 60-70 per cent of Laxfordian rocks. Lastly we examine the seismic response of an upper to middle crust based on our statistical models using acoustic and elastic 2-D finite-difference synthetic seismograms. Short-offset shot records demonstrate that a Lewisian upper crust produces scattered waves which significantly disrupt signals reflecting from deeper levels. Measurements of transmission scattering Q, and coda decay rates confirm that seismic scattering in Lewisian-type crust is strong. the migrated CMP response of a Lewisian crustal model shows the characteristic ‘salt and pepper’ pattern often observed in the upper crust, and described, incorrectly, as ‘transparent'. We suggest that ‘translucent’ is a more appropriate descriptor.

Coda attenuation in the area of El Chichón volcano, Chiapas, Mexico

Coda-wave attenuation is investigated using the single scattering approximation on analog records from stations of a telemetered network situated close to El Chichón volcano in southern Mexico, as well as from temporary stations deployed during 1982. The single scattering model was applied to the envelope of coda waves to characterize the coda decay rate. We obtained values of Q c which, according to the filter settings of the seismographs, and the average period measured in the traces, correspond to frequencies of about 1.3 ± 0.3 Hz. Results indicate apparently larger attenuation than observed with similar techniques in other regions of Mexico, including the Mexican Volcanic Belt. Within the limitation imposed by the data, the spatial distribution of coda Q with respect to the volcanic edifice was investigated. For paths sampling the near vicinity of the volcano a value of approximately Q c = 30 was obtained. The highest attenuation results are obtained for volumes with a slight E-W tendency, with Q c values of 28 and 25, respectively. The location of a gravity high as well as microseismic activity correlates well with this result, which is interpreted as due to the probable presence of an intrusive magma body. Lower attenuation is obtained for volumes sampling deeper than the Moho, reaching a value of Q c ≈ 87, suggesting that rocks below this boundary play a major role in controlling the overall attenuation of paths traversed by coda waves. The results also suggest a decrease in attenuation towards the south and north possibly reflecting a decrease in magmatic processes in both of these directions.

Origins of Amplitude Variations In Seismic Doublets: Source Or Attenuation Process?

SUMMARY Accurate estimates of spectral ratios of two doublets (i.e. similar seismic events) occurring along the San Andreas Fault, in the Hollister region have been computed using a cross-spectral method. Both events of each doublet occurred within a 24 hr interval. Although both waveforms of a doublet are remarkably similar, computed spectral ratios exhibit strong, but steady variations with frequency in the first arrivals. the attenuation process can explain neither the sign nor the order of magnitude of these variations. On the contrary, they are closely related to the source mechanism: we show that the slope computed from the linear and coherent part of the spectral ratio is an estimation of the variation in the apparent rupture duration between the two events. One doublet exhibits an azimuthal distribution of the spectral-ratio variations that is interpreted as the result of a change in the position of the hypocentres, relative to the rupture area. For this doublet, location of hypocentres varies only from 10 to 30 per cent of the source length: this points out that small changes in rupture kinematics can lead to significant variations in the spectral ratio of earthquake doublets, i.e. in the amplitude of each event. For the other doublet, the variations are related to a change in source length. We also have computed spectral ratios all along the seismograms, using a moving window technique. When an azimuthal distribution of the spectral ratio is observed in the first arrivals, we notice a decrease of the spectral ratio all along the seismograms. the doublet with strong, but non-azimuthal variations of the spectral ratio in the first arrivals, does not indicate such a decrease of the spectral ratio along the seismogram. This implies that the variations of the coda decay are related not only to temporal or spatial changes of attenuation but also to source parameters. These variations have the same order of magnitude as those provoked by a temporal change in coda Q of 10 per cent. They can occult time changes of spectral ratio, for instance in case the attenuation in the crust would vary before a strong earthquake.

Determination of Site-Dependent ScatteringQFromP-Wave Coda Analysis With an Energy-Flux Model

The seismic coda of deep events is mainly generated by near-receiver scattering in the lithosphere and therefore contains information about its small-scale structure. A theoretical model which describes coda excitation and decay rate in terms of scattering and anelastic attenuation of the medium is the energy-flux model. Here, a version of the model appropriate for a wavefront propagating through a scattering layer above a homogeneous half space is used to interpret short period data from several stations of the Global Digital Seismic Network which are available on CD-ROMs, Data from events with depths greater than 300 km and epicentral distances less than 60° allow P-coda observations for about 70 s after the first onset undisturbed by later arrivals. At nine stations in the circumpacific area estimates of scattering Q (Qs) are obtained for the frequency range 0.5 Hz to 4 Hz. Qs differs significantly between sites: strong scattering (Qs= 100–200) was found under stations MAJO, TATO, GUMO and API. Relatively weak scattering (Qs 500) occurs at NWAO and CTAO, which are located on stable continental areas. the variation of Qs with frequency qualitatively agrees with Qs obtained from single-scattering theory for von Karman type autocorrelation functions of the heterogeneities. At several sites correlation distances a and rms velocity fluctuations e could be determined. At other sites only the ratio ε/av was obtained, where v is the order of the von Karman autocorrelation function. Anelastic Q (Qi) could only be estimated at TATO, GUMO and SNZO. However, resolution is poor, because the coda decay is dominated by the leaking of scattered energy into the mantle and not by anelastic effects. There is an indication that scattering (except at TATO) is limited mainly to the uppermost 30 to 50 km.

Single Scattering Theory Versus Numerical Modelling In 2-D Random Media

SUMMARY The scattering of acoustic waves in random media is investigated numerically by a finite difference method and is compared with the predictions of single scattering theory. The random media are characterized by autocorrelation functions which allow the construction of spatially anisotropic random structures with different correlation lengths a and b perpendicular and parallel to the propagation direction. If a equals b, the attenuation of the transmitted wave can be successfully explained by single scattering theory. The attenuation maximum occurs at kb = 1-2, where k is the wavenumber. For media with a > b we observe a stronger attenuation than expected from single scattering theory for kb greater than 6. The attenuation peak is shifted to smaller kb values when the spatial anisotropy of the random fluctuations is increased. The investigation of the seismic coda shows that the single scattering theory cannot explain the time dependence of the coda. Coda Q, as determined from the coda decay rate under the single scattering assumption, does not describe the scattering attenuation. In 1-D random media the decay rate of the coda observed in transmission decreases with increasing standard deviation of the impedance fluctuations. In the 2-D case the decay rate increases slightly with the standard deviation.

A numerical investigation of scattering effects for teleseismic plane wave propagation in a heterogeneous layer over a homogeneous half-space

Numerical simulations of teleseismic wave propagation in a heterogeneous layer over a homogeneous half-space are conducted to further our understanding of teleseismic coda generation. Acoustic and elastic finite difference synthetics are generated for more than 150 different layer-over-a-half-space models. The models vary in scattering layer thickness (L), heterogeneity correlation distance (a, or ax and az), and heterogeneity standard deviation (σ). The synthetic data are analysed by examining coda intensity envelopes and frequency-wavenumber spectra. The level of scattered energy is found to be controlled by the ka and σ values. Coda levels increase with increasing ka from ka > 1 to ka∼ 1, and decrease with increasing ka for ka > 1. Scattered energy levels always increase with increasing σ. Models that vary in scattering layer thickness alone did not consistently produce changes in the coda level or rate of decay independently of the values of ka and/or σ. The rate of coda decay is controlled by the heterogeneity aspect ratio (ax/az). Models with spatially isotropic heterogeneities (ax/az = 1) produce the slowest rate of decay, while those with an infinite aspect ratio (homogeneous, plane-layered models) produce the most rapid rate of decay. Any decay rate between these two extremes can be obtained by varying the heterogenity aspect ratio. Acoustic and elastic models exhibit similar coda intensity envelope characteristics. Apparent scattering attenuation of the direct pulse is a function of ka and is strongest for models with spatially isotropic heterogeneities. Frequency-wavenumber analysis showed that coda for models with spatially isotropic heterogeneities is composed largely of low apparent velocity energy in the form of P-to-S and/or body-to-surface wave scattered energy. Coda for models with spatially anisotropic heterogeneities is composed largely of vertically propagating layer reverberations. Coda for extreme anisotropic models is composed solely of vertically propagating layer reverberations. The onset time of low apparent velocity energy is also controlled by the heterogeneity aspect ratio. For models with anisotropic heterogeneities, low apparent velocity energy appears immediately after the first arrival, for models with an infinite heterogeneity aspect ratio (1-D models), low apparent velocity energy never appears.

Lapse-time dependent Qc-spectra observed in the Dinarides region (Yugoslavia)

The paper presents results of the coda quality factor ( Q c) measurements in the central Outer Dinarides and the central Adriatic Sea regions. The main objective of this study was to analyse quantitatively the frequently observed Q c increase with lapse time, t, 108 earthquakes were chosen for analysis, with lapse times between 30 and 130 s. After computing the coda amplitude spectra A(ƒ) for 0.6 ⩽ ƒ ⩽ 5.0 Hz , the curve 1n( At) = a + bt c was fitted to observed data for each earthquake and for each frequency. Denoting its slope by p( t), Q c was then estimated as a function of t as Q c (t|ƒ) = −πƒ p(t) . In this way coda decay rate measurements were done in a consistent way, regardless of the lapse time window used. These individual values were then weighted and averaged in order to calculate the regional Q c (ƒ,t) . The results indicate that in the region studied Q c increases both with frequency and lapse time, while the degree of frequency dependence decreases with lapse time. If Q c is expressed as Q c (t) = Q 0(t) ƒ n(t) then for lapse times between 30 and 130 s Q 0 increases from 45 to 275 while n decreases from 1.0 to 0.6.

Laboratory tests of excitation and attenuation of coda waves using 2-D models of scattering media

Abstract Effects of the scattering and intrinsic Q measured for direct waves on the decay of seismic coda with time and the level of the coda excitation were investigated by laboratory experiments. Seismograms with long codas were produced using an ultrasonic technique and sufficiently large 2-D models of scattering media. The results are: (1) the level of coda excitation is high when scattering attenuation is large, whereas it is low when scattering attenuation is small; (2) the observed coda decay depends only on the intrinsic Q of media models as predicted by the energy transfer theory of Shang and Gao; and (3) the scattering Q−1 value has a peak around kd = 2–3 (k is the wave number and d is the scatterer size) and decreases steeply on both sides of the peak.

Mechanisms of seismic attenuation in the crust: Scattering and anelasticity in New York state, South Africa, and southern California

The envelopes of high‐frequency seismograms from earthquakes in New York State, South Africa, and southern California are analyzed to determine how much of the observed attenuation of shear waves in the crust is caused by anelasticity and how much is produced by scattering from small‐scale heterogeneities. For seismograms from New York and South Africa, there is a systematic enrichment of high‐frequency energy that develops in the coda relative to the direct S or Lg waves. This enrichment of high frequencies in the coda grows larger with increasing source‐receiver distance. This implies that high‐frequency energy is scattered from the direct wave into the coda as the shear wave propagates in the crust. I use the growth with source‐receiver distance of the high‐frequency energy in the coda relative to the direct wave to estimate the scattering attenuation of the crust. For seismograms from New York, it is consistently observed that the time decay of high‐frequency energy in the coda, when compared to the low‐frequency coda decay, is less than the relative decay of high‐frequency energy with travel time in the Lg wave. This observations supports the idea that the time decay of the coda is controlled mainly by the anelastic attenuation and is insensitive to the scattering attenuation, as suggested by coda models incorporating conservation of energy such as the energy flux model. I use the relative time decay of high‐frequency energy in the coda to determine the anelastic attenuation. This analysis indicates that the observed attenuation of 15‐Hz Lg waves in New York State (Δ = 100–400 km) is caused about equally by scattering and anelasticity. Using the estimate of Lg wave Q as a constraint, I find that the scattering Q in the crust of New York is either independent of frequency or increases with frequency ƒ slower than ƒ0.3. This implies that the one‐dimensional power spectrum of spatial velocity variations in the crust of New York decays with increasing wavenumber k more slowly than k−1.3, for length scales of about 0.2 to 1 km. A similar analysis for South Africa indicates that scattering is the major cause of the observed S wave attenuation of high‐frequency energy (30 Hz) at local distances (&lt;100 km). For southern California, the extent of the scattering attenuation is unclear from the data, although the relatively steep coda decay of southern California implies that anelastic attenuation is stronger there than in New York or South Africa. At 3 Hz, the coda decays for lapse times of 10–45 s are similar to the decays of S wave amplitudes with travel time for the three regions. However, the 30‐Hz coda decays are substantially less than the 30‐Hz S wave decays with travel time, producing coda Q values that are much higher than the S wave Q in each area. For southern California and New York State, the 3‐Hz coda Q taken from the late coda (50–110 s) is comparable to the Lg wave Q. However, the 3‐Hz coda Q for South Africa over these lapse times is about 5 times the estimated Lg wave Q. For all three areas, the frequency dependence of the coda Q does not match the frequency dependence of the S wave Q, and for New York and South Africa, it changes with lapse time.

Scattering of teleseismic body waves along the hayward-calaveras fault system

Abstract Broadband, digital, teleseismic P -wave data from the University of California, Berkeley, stations BKS, MHC, and SAO are used to study the character of teleseismic P coda. Velocity heterogeneity in structure near these stations gives rise to a variety of scattering effects, which include azimuthly dependent receiver functions, large tangential component particle motions, and high levels of P coda. P codas for shallow and deep teleseisms are analyzed for three frequency bands centered at 1.5, 0.75, and 0.375 Hz. Observed coda decay rate and level are fit with an energy flux theory to parameterize scattering effects near the source and at the receiver. Coda decay rate and level for deep earthquakes are seen to be stable observables between stations, implying that the scattered coda field is homogeneously distributed over the receiver network validating a major assumption in the energy flux model. Scattering Q ( Q s ) is not particularly well constrained by the data and is inferred to be affected by focusing and defocusing effects of the direct P waves. There is a pronounced difference in coda decay rate between shallow and deep earthquakes for 1.5 Hz coda, where coda decay rate for deep events is about a factor of 2 greater than for shallow events. There is no difference in coda decay rate between the two populations of events in the lower frequency bands. The observation at 1.5 Hz is consistent with a simple model of P -wave coda formation, where most coda forms in a scattering layer near the surface of the earth in regions near the source and near the receiver. The homogeneity of coda decay at 0.75 and 0.375 Hz for deep and shallow events suggests that a larger, near-receiver scattering mechanism, such as surface-wave formation, dominates the coda.

Discriminating quarry blasts from earthquakes using coda waves

AbstractA new quarry blast-earthquake discrimination method is presented based on the analysis of seismic coda waves. Quarry blasts and local earthquakes in the area encompassing the south-central Mojave Desert and Eastern Transverse Ranges were used to test this method. We found that the coda decay rate Qc−1 is significantly higher for quarry blasts than earthquakes for lower frequencies (1.5 and 3 Hz) for lapse time up to about 30 sec. This result is attributed to the greater contribution of surface waves to quarry blasts due to the shallowness of their source depth. The difference in Qc−1, however, disappears for lapse time greater than 30 sec for the same frequency range as well as for higher frequencies (6 and 12 Hz) for lapse time greater than 20 sec. This suggests that the coda waves, at the lapse time greater than these critical values, are dominated by the same type of body waves, probably S waves, for both quarry blasts and earthquakes. The power spectrum P0(ω) obtained after the correction for attenuation was compared between earthquakes and quarry blasts at the same stations, and a significant difference was found in the spectral shape between these two data sets. The curves of power spectrum P0(ω) versus frequency for quarry blasts decrease more sharply than for earthquakes at high frequencies, indicating a lack of energy in high frequencies for quarry blasts as compared to earthquakes. The different frequency dependence of power spectrum P0(ω) between quarry blasts and earthquakes is attributed to their different source properties and can be used for seismic discrimination of quarry blasts from earthquakes.

A modified energy flux model for lithospheric scattering of teleseismic body waves

grams and has been found to give reliable results for both weak and strong scattering environments. It was then used for the analysis of short-period data from deep events recorded at the Warramunga seismic array in central Australia. An average scattering Q of about 640 at 1 Hz was found for the lithosphere beneath the array with a strong increase of Q with frequency above 1 Hz. Intrinsic Q is much higher than scattering Q and most of the coda decay is caused by diffusion of coda energy into the half-space below the scattering layer.

A comparison of earthquake coda waves at surface versus subsurface seismometers

The coda waves of 21 Parkfield earthquakes were recorded simultaneously at the surface and at a depth of 198 m. We characterize these codas by computing (1) the time dependence of the integral of squared particle velocity, (2) their frequency content, (3) time‐frequency coda decay planes, (4) the frequency dependence of root mean square ellipticity, and (5) the difference in their normalized decay rates. These five measures reveal significant differences in the early portion of the uphole versus downhole codas. Our analysis solves for coda Q as an explicit function of both time and frequency. Average apparent coda Q for the 21 events observed both at the surface and downhole is Qa(f, τ) = 39(f/f0)0.43 (τ/τ0)0.37, with the reference frequency and time defined at 1 Hz and 1 s, respectively. Coda Q exhibits a trend in its value over the 1‐month period of the study. The trend correlates with a spatial variation in source locations and is not produced by temporal variations of the Q of the medium. The spectral ratio between the uphole signal and the downhole signal varies with time through the coda. The early portion of the uphole coda experiences a pulse of low‐frequency energy not seen in the downhole coda. To explain this observation, we propose a model of the coda that includes body wave to surface wave scattering near the site. In this model, the near‐surface acts as both a filter and a scattering waveguide. The coda at the surface is the sum of a coda produced by scattering deep in the lithosphere and a coda produced by scattering in the near‐surface. The scattering in the near‐surface is made up of near‐vertically traveling multiples and horizontally travelling surface waves. The guided waves are recorded in the surface coda but are absent from the coda recorded at depth. The time‐frequency structure of the surface waves in the uphole coda is determined by the velocity, scattering, and attenuation characteristics of the site. By fitting the model to our data, we have found that the fractional conversion factor of body waves to surface waves travelling toward the receiver is 0.03 at the Vineyard Canyon site. The relatively rapid damping of these trapped waves can be modelled by assuming a quality factor of QT = 50. The principles of this model are general enough to be of use at other locations.

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 pathLs and time in terms of the mean-free timesLs/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 intrinsicQi. Of course, this conclusion is coincident with the presumption of the diffusion theory,Qs>Qi. 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 intrinsicQi, then as the distance increases, effects of scatteringQs, are involved in the decay feature. The theoretical plots of coda decay show that it seems in most cases in the earthQi should not be smaller than one tenth ofQs.