Coda Decay Research Articles

Q in southern Norway

Q was determined for the southern Norway region using short-period data from local events. The spectral ratio and the coda decay method were used to determine Q as a function of frequency for P , S , and coda waves, respectively. Q(f) was generally found to fit the relationship Q = Qofm where f is the frequency and Qo and m constants. The following results were obtained: View this table: where Qc , Qp , and Qs are coda Q , Q of P waves, and Q of S waves, respectively. There is a good agreement between coda Q and spectral ratio Qs values, which supports the hypothesis that coda waves are backscattered S waves. The increase in coda Q as a function of window length is thought to reflect an increase of Q with depth, because coda waves for a longer time window will sample deeper parts of the crust. At higher frequencies (12 to 15 Hz), our results are quite similar to what has been found for the Canadian Shield area, but with a much stronger frequency dependence. This could be interpreted in terms of a stronger presence of scatterers in southern Norway as compared to the Canadian Shield.

Scattering of long-period Rayleigh waves in Western North America and the interpretation of codaQmeasurements

AbstractThe codas of long-period Rayleigh waves recorded at WWSSN and Canadian network stations in Western North America from eight underground explosions at NTS are examined in an effort to separate scattering and anelastic attenuation effects. Coda behavior of 0.1 and 0.2 hz Rayleigh waves follows coda characteristics seen in studies of short-period S waves. Coda decay rate is seen to be a stable observation over most stations in Western North America and is consistent with the hypothesis that backscattered surface waves from heterogeneities contained within the western half of the continent form the Rayleigh wave coda. The basic data observables of coda level and decay are interpreted using several plausible models. The single scattering model yields a coda Q consistent with previously determined Rayleigh anelastic attenuation coefficients. Separation of anelastic and scattering Q is possible using an energy flux model and shows that scattering Q is one to two orders of magnitude higher than anelastic Q. However, an energy flux model that incorporates a layer of scatterers over a homogeneous half-space shows that all Rayleigh-wave attenuation can be explained purely by scattering effects which include Rayleigh- to body-wave conversion. Coda can be fit equally well by these mutually incompatible models. It is not likely that the mechanisms of scattering or anelastic attenuation can be addressed by coda observations of a single homogeneous data set.

Scattering of teleseismic body waves under Pasadena, California

Teleseismic receiver functions for structure under Pasadena, California (PAS) are derived from azimuthally distributed teleseismic P waves recorded on Benioff 1–90 instrumentation. The broadband three‐component Benioff 1–90 system is peaked at a 1‐s period and allows resolution of major crustal interfaces from large Ps conversions seen in the receiver function data. The observed body wave data are quite complex, showing exceptionally large Ps conversions and scattered waves on horizontal components. Radial and tangential motions are of equal magnitude and show major off‐azimuth converted Ps waves, suggesting large‐scale crustal heterogeneity beneath the station. Stochastic simulations of one‐dimensional plane layered structure show that geologically unreasonable one‐dimensional models are required to fit the data. The observed coda decay yields a scattering Q estimate of 239 at a 2‐s period using an energy flux model for a propagating plane wave interacting with a scattering layer over a homogeneous half‐space. Observed and synthetic coda decay follows the theoretical exponential decay predicted by the model and is due entirely to diffusion of coda energy out of the layer into the half‐space. PAS coda is compared to coda from deep teleseisms recorded at State College, Pennsylvania, and it is seen that scattering is more severe at PAS, as reflected in higher coda levels and slower decay rate. Consideration of energy partitioning and coda amplitude suggests that much of the coda consists of scattered surface waves. Analysis of a major Ps conversion arriving 3 s after direct P indicates that a major crustal discontinuity at about 20 km depth dips at moderate angles to the north under the San Gabriel Mountains. This interface probably represents the crustal tectonic boundary between the Transverse Ranges and the Los Angeles Basin.

A review of numerical experiments on seismic wave scattering

This paper reviews applications of the finite-difference and finite-element methods to the study of seismic wave scattering in both simple and complex velocity models. These numerical simulations have improved our understanding of seismic scattering in portions of the earth where there is significant lateral heterogeneity, such as the crust. The methods propagate complete seismic wavefields through highly complex media and include multiply scattered waves and converted phases (e.g.,P toSV, SV toP, body wave to surface wave). The numerical methods have been especially useful in cases of moderate and strong scattering in complex media where multiple scattering becomes important. Progress has been made with numerical methods in understanding how near-surface, low-velocity basin structures scatter surface waves and vertically-incident body waves. The numerical methods have proven useful in evaluating scattering of surface waves and body waves from topography of both the free surface and interfaces buried at depth. Numerical studies have demonstrated the importance of conversions from body waves to surface waves (andvice versa) when lateral heterogeneities and topographic relief are present in the uppermost crust. Recently, several investigations have applied numerical methods to study seismic wave propagation in velocity models which vary randomly in space. This stochastic approach seeks to understand the effects of small-scale complexity in the earth which cannot be resolved deterministically. These experiments have quantified the relationships between the statistical properties of the random heterogeneity and the measurable properties of high-frequency (≥1 Hz) seismograms. These simulations have been applied to the study of many features observed in actual high-frequency seismic waves, including: the amplitude and time decay of seismic coda, the apparent attenuation from scattering, the dispersion of waveforms, and the travel time and waveform variations across arrays of receivers.

Measurements of coda buildup and decay rates of western Pacific P, Po, and So phases and their relevance to lithospheric scattering

We use empirical functions to characterize the shape of band‐passed P, Po, and So coda envelopes of 93 earthquakes. The data sets consist of earthquake data from the western and northwestern Pacific recorded by arrays of several stations and include both hydrophone and geophone recordings on analog and digital instruments. Each earthquake was band‐passed into six octave‐wide frequency bands between 0.8 and 50 Hz. The empirical function (a Poisson function, Pn(γ,t) = A γn+1 tn e−γt /n!) has parameters A (a measure of energy), γ (falloff rate), and nç//γ (time of the maximum). The study showed that these parameters varied in systematic ways. Po/So area (A) ratios were found to be considerably higher for hydrophone data in the 20°–35° range than for geophone and hydrophone data in the 8°–20° range. The difference was significantly larger than between vertical and hydrophone data in the same range. In some instances a strong frequency dependence or “reverse dispersion” of the time of maximum amplitude (n/γ) was observed, with the lower (1–2 Hz) frequencies arriving up to 25s later than the higher (10–20 Hz) frequencies. P, Po, and So average falloff rates ã vary systematically with frequency, where the lowest frequencies most commonly have the minimum falloff rates and the middle frequencies have the maximum falloff rates. The variation in falloff between earthquakes is large, with the trends only becoming apparent upon averaging many measurements. A strong increase in falloff rates at about 3 Hz may be associated with a decrease in the amount of scatterers with scale lengths of about one half the wavelength of a 3‐Hz compressional wave, which is about 1.3 km. Falloff rates were seen to decrease with epicentral range, reflecting an increased scattering with length of propagation path. The scattering that produces the coda is thus not concentrated in the source region but distributed along the propagation path. Falloff rates were seen to decrease with increasing age of crust. The difference may be due to the different average age of the lithosphere in these two geographical areas. Earthquakes at a depth of 100–300 km have systematically lower Po falloff values than shallower events. This effect is clearly seen in trench earthquakes and indicates that significant scattering occurs within (or near) the deeper buried part of the subducting plate. The So/Po falloff ratio is a factor of 2 lower for the hydrophone data than for the geophone measurements. This difference is most likely due to conversion of shear waves at or below the seafloor. If we assume that the coda decay is controlled by intrinsic attenuation, then measurements of coda decay can be converted into estimates of the quality factor Q. At 10 Hz our falloff rates give QPo = 1250, which is a reasonable number for a compressional wave quality factor in the uppermost mantle, and QSo ≈ QPo/2 The low snear wave Q is in disagreement with inferences made by other observers. However, the fact that the falloff rates are fairly constant in the frequency range 5–30 Hz but vary with propagation distance suggests that attenuation cannot be the only phenomenon determining the decay of the coda. Other factors, such as reverberations in the water column, may play an important part in the coda formation as well and may bias these estimates Q.

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 −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 −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.

ソ連邦タジク共和国ガルム近傍の地震 (<i>K</i>=13.3, 1983年) に関連したコーダ減衰<i>Q</i><sup>-1</sup><sub>C</sub>の時間的変化

Coda decay of band-pass filtered seismograms were studied in relation to the occurrence of an earthquake of K=13.3 (ML=5.2) in Soviet Central Asia. The gradient of coda decay is characterized by coda attenuation Q-1C for each frequency band. Examining the temporal variation of log10(Q-1Cf) for small earthquakes which occurred in a restricted volume around the main shock focus during the period between 1979 and 1984, we found that the variances of log10(Q-1Cf) for forerhocks were significantly larger than those for aftershocks for the frequency bands of 0.62-5Hz and 18Hz. Especially at the 5 Hz band, log10(Q-1Cf) took a significantly lower value in the three-year period preceding the main shock compared with the preceding and following time periods. In the earthquake preparation stage, we may expect the formation of crack-clusters, which are composed of new cracks and reopened and connected existing cracks, in a fairly large region compared with the focal region due to the stress accumulation. The gradual appearance of inhomogeneously distributed crackclusters in the heterogeneous crust seems to be the most plausible mechanism by which the coda decay gradients are caused to scatter largely.

Attenuation and backscattering from local coda

AbstractCoda decay and excitation for local events were examined at Mammoth Lakes and Morgan Hill, California, Monticello, South Carolina, and New Brunswick, Canada, in the frequency range of 3 to 50 Hz. The single-scattering theory of attenuation and coda generation was used to interpret the data. Coda decay was parameterized by the total apparent turbidity, which is inversely proportional to the conventional coda Q, and the backscattering turbidity, which is proportional to the ratio of the coda power at the time of the direct S and the energy of the direct S pulse. This is a scattering parameterization, since turbidities are cross-sections per unit volume; the term “apparent” is used for the total apparent turbidity because in actuality this parameter contains the effect of anelastic attenuation as well as scattering. For short times (less than 10 sec), the total (apparent) turbidity determined from coda decay was about 0.1 km−1 for all regions, or a Q of about 60 (3 Hz) to 1000 (50 Hz). The backscattering turbidity determined from coda excitation at short times is often larger than the total apparent turbidity and thus indicates strong, multiple scattering in the upper crust, especially for frequencies in the 3- to 10-Hz range. This means that coda Q is not equivalent to direct S Q in this frequency range, since it does not include the full effect of scattering. At times longer than 10 to 15 sec for the codas from Monticello and New Brunswick, the coda energy appeared to be channeled into a horizontally propagating mode such as Lg. This change was seen as a change in decay rate and excitation; the total turbidity for this portion of the coda was lower than for short codas, about 0.01 km−1, indicating less scattering. At Monticello, the conditions for the validity of the single-scattering theory appeared to be satisfied, meaning that coda Q includes the effect of scattering and is a proper measure of the Q of the wave type that makes up the coda—most likely Lg. The backscattering turbidity, which is controlled solely by scattering, and the total apparent turbidity at Monticello both show a minimum around 10 Hz. This correlation between coda excitation and decay indicates that a substantial portion (at least 50 per cent) of coda Q in this case is due to scattering. The evidence for strong scattering observed in other codas indicates that scattering will play an important role in attenuation at those sites also. Codas from California, however, did not show the phenomenon of a change at 10 to 15 sec, indicating either that this mode is not present or that it is more strongly scattered. All of the scattering observed in this study probably occurs in the crust. Reverberation under the station cannot be excluded for most codas, but the existence of two types of coda at Monticello and New Brunswick demonstrates that this cannot be the dominant mechanism at these sites.

Studies of the seismic coda using an earthquake cluster as a deeply buried seismograph array

Loosely speaking, the principle of Green's function reciprocity means that the source and receiver positions in a seismic experiment can be exchanged without affecting the observed seismograms. Consequently, the seismograms observed at a single observation location o and caused by a cluster of microearthquakes at locations {ei} are identical to the time series that would be measured by an array of stress meters emplaced at positions {ei}, recording waves generated by a source acting at o. By applying array analysis techniques like slant stacking and frequency‐wave number analysis to these seismograms, we can determine the directions and velocities of the component waves as they travel in the earthquake focal region rather than at the surface. We have developed a computationally rapid plane‐wave decomposition which we have applied to single‐station recordings of aftershocks of the 1984 Morgan Hill, California, earthquake. The analysis is applied to data from three seismic stations having considerably different site geologies. One is a relatively hard rock station situated on Franciscan metamorphics, one is within the Calaveras fault zone, and one is on semiconsolidated sand and gravels. We define the early coda to be the part of the coda initiating immediately after the direct S wave and ending at twice the S wave lapse time. The character of the S wave and early coda varies from being impulsive at the first station to highly reverberative at the last. We examine waves in sequential time windows starting at the S wave and continuing through the early part of the coda. At all seismic stations the early coda is dominated by a persistent signal that must be caused by multiple scattering, probably within 2 km of each seismic station. Despite clear station‐to‐station differences in the character of the early coda, coda Q values measured in the late coda (greater than twice the S lapse time) agree well among stations, implying that the mechanisms causing the varying behavior of the early coda do not control the coda decay rate at the stations we have considered. Coda Q values measured on horizontal components of motion agree within a factor of 2 with those measured on vertical components. We have not been able to determine the composition of the late coda because of a low signal‐to‐noise ratio. Our analysis technique, however, is quite appropriate for such a task.

Energy-flux model of seismic coda: Separation of scattering and intrinsic attenuation

AbstractA new model of seismic coda is presented, based on the balance between the energy scattered from the direct wave and the energy in the seismic coda. This energy-flux model results in a simple formula for the amplitude and time decay of the seismic coda that explicitly differentiates between the scattering and intrinsic (anelastic) attenuation of the medium. This formula is valid for both weak and strong scattering and implicitly includes multiple scattering. The model is tested using synthetic seismograms produced in finite difference simulations of wave propagation through media with random spatial variations in seismic velocity. Some of the simulations also included intrinsic dissipation. The energy-flux model explains the coda decay and amplitude observed in the synthetics, for random media with a wide range of scattering Q. In contrast, the single-scattering model commonly used in the analysis of microearthquake coda does not account for the gradual coda decay observed in the simulations for media with moderate or strong scattering attenuation (scattering Q ≦ 150). The simulations demonstrate that large differences in scattering attenuation cause only small changes in the coda decay rate, as predicted by the energy-flux model. The coda decay rate is sensitive, however, to the intrinsic Q of the medium. The ratio of the coda amplitude to the energy in the direct arrival is a measure of the scattering attenuation. Thus, analysis of the decay rate and amplitude of the coda can, in principle, produce separate estimates for the scattering and intrinsic Q values of the crust. We analyze the coda from two earthquakes near Anza, California. Intrinsic Q values determined from these seismograms using the energy-flux model are comparable to coda Q values found from the single-scattering theory. These results indicate that coda Q values are, at best, measures of the intrinsic Q of the lithosphere and are unrelated to the scattering Q.

Temporal change in coda associated with the Round Valley, California, Earthquake of November 23, 1984

Seven thousand seismograms of small earthquakes in the Mammoth Lakes‐Bishop area were used to measure values of Q from the decay of the earthquake coda. These measurements were compared between events that occurred before and after the Round Valley earthquake (M=5.7). We found that in regions near the main shock epicenter, measurements of coda Q−1 for earthquakes that occurred after the main shock were higher than for those earthquakes that occurred prior to the main shock. The opposite behavior was found for regions farther away from the main shock, namely, lower coda Q−1 after the main shock than before. Measurements of coda Q−1 in the Long Valley caldera, outside of the immediate source region of the earthquake, were higher than in surrounding areas before the main shock, but the difference disappeared after the occurrence of the main shock. This indicates that the temporal variation in coda Q−1 is comparable to its spatial variation. The doughnut model (seismicity quiescence surrounded by a zone of activity) which was invoked for explaining the precursory seismicity pattern appears to be similar with the observed coda Q−1 variation associated with the Round Valley earthquake. The observed spatial variations in coda Q−1 also help to reconcile conflicting results published in previous studies of the coda Q−1 precursor.

Finite difference simulations of seismic scattering: Implications for the propagation of short‐period seismic waves in the crust and models of crustal heterogeneity

Synthetic seismograms produced by the finite difference method are used to study the scattering of elastic and acoustic waves in two‐dimensional media with random spatial variations in seismic velocity. The results of this study provide important insights about the propagation of short‐period (< 1 s) seismic waves in the earth's crust and place significant constraints on the fluctuation spectrum of crustal heterogeneity on length scales from tens of kilometers to tens of meters. The synthetic seismograms are analyzed to determine the variation in travel times and waveforms across arrays of receivers. The apparent attenuation caused by scattering and the time decay and amplitude of the seismic coda are also quantified with the numerical simulations. Random media with Gaussian and exponential correlation functions are considered, as well as a self‐similar medium with equal variations in seismic velocity over a broad range of length scales. These media differ in the spectral falloff of their velocity fluctuations at wavelengths smaller than 2π times the correlation distance a. The synthetic seismograms demonstrate that a random medium with self‐similar velocity fluctuations at length scales less than about 50 km (a ≥ 10 km) can explain both travel time anomalies reported for teleseismic arrivals across large‐scale seismic arrays (e.g., LASA and NORSAR) and the presence of seismic coda at frequencies of 30 Hz and greater commonly observed in microearthquake waveforms. Media with Gaussian and exponential correlation functions in velocity do not account for both sets of observations for reasonable standard deviations in velocity (≤10%). The scattering attenuation (Q−1) observed in the simulations for Gaussian media is peaked at ka between 1 and 2, where k is the seismic wave number. The observed attenuation in exponential media increases with frequency for ka < 1 and remains about constant for 1 ≤ ka ≤ 5.6. At high frequencies (ka > 5), the self‐similar medium is characterized by a scattering Q that is constant with frequency, whereas theory predicts that the apparent Q in an exponential medium is proportional to frequency. These alternative models of crustal heterogeneity can thus be tested by improved measurements of the frequency dependence of crustal Q at frequencies greater than about 1 Hz, assuming that scattering is responsible for most of the attenuation at these frequencies. Measurements of the time decay of the synthetic coda waves clearly show that the single scattering model of coda decay is not appropriate in the presence of moderate amounts of scattering attenuation (scattering Q ≤ 200). In these cases, Q values derived from the coda decay rate using the single scattering theory do not correspond to the transmission Q of the medium. The cross correlation of synthetic waveforms observed for an array of receivers along the free surface is observed to be dependent on the correlation distance of the medium. The self‐similar random medium proposed here for the crust produces waveform variations at high frequencies (15–30 Hz) similar to those reported for actual small‐scale seismic arrays with apertures of hundreds of meters.

Temporal change in coda Q before the Tangshan Earthquake of 1976 and the Haicheng Earthquake of 1975

A new earthquake precursor called “coda Q” is demonstrated for the Tangshan earthquake of 1976 and for the Haicheng earthquake of 1975. The precursor is based on the measurement of coda decay rate for small local earthquakes in the general area that is preparing for a major earthquake. During the 3‐year period preceding the Tangshan earthquake the coda Q was about 3 times lower than it was before or after this period. A comparable change also occured at the time of the Haicheng earthquake. The observed change cannot be due to the change in the source parameters, such as the focal depth or the source spectrum. The coda Q precursor appears to detect the same physical process detected by other precursors such as b value, quiescence, radon, water quality, Vp/Vs, and animal behavior but has advantages over them in its clearer physical mechanism, easier sampling, and better defined anomalous region.

Q determined from local earthquakes in the South Carolina Coastal Plain

Abstract Coda Q, or Qc, is determined from the rate of coda decay in the Coastal Plain near Charleston, South Carolina. The mean of Qc calculated from individual estmates is near 190 at 1 Hz and increases to over 1650 at 10 Hz. A possible temporal change in Qc is identified, high values being associated with increased seismic activity during late 1977. Temporal changes have been observed elsewhere and laboratory measurements of Q under different stress states correlate high Q with high stress. A spatial variation in Qc is identified, increasing from west (Qc at 10 Hz equal to 850) to east (Qc at 10 Hz greater than 2100) across the Coastal Plain. The demarcation of high to highest zones of Qc is coincident with the western boundary of the innermost isoseismal of the Charleston 1886 earthquake. It is hypothesized that the 1886 earthquake was mislocated originally because of this spatial variation in energy attenuation that was unrecognized at that time.

Evidence consistent with a multiple‐event mechanism for large earthquakes

We analyzed the short‐period codas of 418 small events (NOS mb ≤ 5.8) and 148 large‐events (NOS mb, NOS Ms, or mb from Pasadena or Berkeley ≥7.0). The normalized large‐event codas are found to be significantly larger at any given time after the first‐arrival onset than corresponding values for small‐event codas. This suggests that large events are multiple events, and that the occurrence of later events in a given sequence retards coda decay and elevates the relative amplitudes of the codas above those expected for a small (single) event. Large events are also found to be emergent, displaying a 0.2 to 0.3 mb increase in amplitude between 5 and 30 seconds after the P wave arrival over that observed in the first 5 seconds after the arrival. Coda decay characteristics for large events may be used to estimate the length of the fault zone. We suggest that multiple events are a more common phenomenon than has been generally suspected, and that most if not all events of high or intermediate Ms are probably multiple events.