Coda Amplitude Research Articles

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.

Frequency dependent characteristics of coda wave quality factor in central and southcentral Alaska

Coda wave quality factor (Q c ) was investigated by using digital data (100 sample sec-1) recorded by a vertical component short-period station installed for this study. The station was located in the greater Fairbanks area in central Alaska. From several hundred earthquakes recorded by this station in about a year, 27 earthquakes were selected for the above study; 7 of these selected earthquakes were located along the Alaska Wadati-Benioffzone (Pacific plate). The other 20 earthquakes were located in the area of intraplate seismicity (North American plate). The data was filtered using 9 pass-bands with center frequency varying from 1.5 Hz to 16 Hz with octave bandwidth. The values of Q c obtained from the coda amplitude decay rates measured on the filtered data after corrections due to the recording instrument and source-receiver separation show appreciable frequency dependence. The value of Q c varies in the range of 253 and 1190 corresponding to the frequency interval from 1.5 Hz to 16 Hz for the study area. This variation is close to that reported by others for the Kanto region of Japan. Moreover, the characteristics of Q c obtained in the present case seem to be independent of epicentral distance and hypocentral depth.

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.

Magnitude‐frequency relation for small earthquakes: A clue to the origin of ƒmax of large earthquakes

In order to test the hyothesis that the ƒmax of large earthquakes is due to the source effect and is causally related to the corner frequency of small earthquakes when it becomes constant below magnitude about 3, we constructed the frequency‐magnitude relation for earthquakes with magnitude range from −1/3 to 4 recorded at a borehole seismograph station operated by the University of Southern California at Baldwin Hills in the middle of the Newport‐Inglewood fault. A procedure was developed for an accurate estimation of moment magnitude from the measurement of coda amplitude as a function of lapse time. The cumulative number of earthquakes per unit time period and area was estimated by finding the detection limit for ts‐p for each magnitude. We found a clear depature of the observed log frequency‐magnitude relation for M < 3 from the linear relation extrapolated from the data for M > 3. The observed frequency of earthquakes with M ≃ 0.5 is almost 10 times less than that expected from the extrapolation of empirical relation for earthquakes with magnitudes larger than 3. We conclude that the observed frequency‐magnitude relation departs from self‐similarity for earthquakes with magnitude smaller than about 3. This departure coincides with the widely observed departure of the moment‐corner frequency relation from self‐similarity. These observations are consistent with the interpretation of ƒmax of large earthquakes in terms of the slip‐weakening instability model in which the critical slip may be a few tenths of a meter to a few meters and the cohesive zone size may be a few hundred meters to a few kilometers.

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.

Use of P coda for determination of yield on nuclear explosions

Summary. Spectral analysis of P and P coda from NTS explosions recorded at NORSAR shows that magnitudes based on spectral integration of P coda provide a significantly more precise measure of yield than those based on the initial P. Coda amplitudes and spectra are considerably less sensitive to nearsource variations than the direct P. A plot of P-coda magnitude, after correcting for the effects of attenuation in the upper mantle and the source spectrum based on knowledge of approximate yield or mb, versus log yield appears to have a slope of unity. This implies that P coda from several stations (with different but known t* values) can be combined to improve the yield determinations further. Single station P coda from Soviet explosions can also be used to determine relative yields that appear to be at least as precise as those from Lg based on a network of stations.

Scattering and attenuation of shear waves in the lithosphere

Recent measurements of Qβ−1 of S waves in the lithosphere for frequency range from 0.02 to 25 Hz show a remarkable frequency dependence and systematic variation from place to place depending on the current tectonic activity. In order to test the hypothesis that the attenuation of S waves may be caused by the loss of energy by scattering due to heterogeneity, the amplitudes of S and coda waves were measured simultaneously for 900 local earthquakes in the central Japan for various frequency bands. The data were interpreted using the S to S single‐scattering theory for coda waves, which is now supported by the observed agreement between Q of coda and Qβ, and also by the observed identical local site effect on coda and S waves. The result shows that the loss of energy from S waves required to explain coda amplitudes agrees with the attenuation of S waves within the uncertainty of measurements. This conclusion is supported by several recent studies on Q of coda, Q of Lg, Qβ, and coda excitation by other workers.

A local earthquake coda magnitude and its relation to duration, moment Mo, and local Richter magnitude ML

abstract A relationship is found between the seismic moment, Mo, of shallow local earthquakes, coda amplitudes, and the total duration of the signal, t, in seconds, measured from the earthquake origin time. Following Aki, we assume that the end of the coda is composed of backscattering surface waves due to lateral heterogeneity in the shallow crust. Using the linear relationship between the logarithm of Mo and the local Richter magnitude ML, we obtain a relationship between ML and t, of the form: ML = a0 + a1 log t + a2t1/3 + f(t), where a0, a1, a2 are constants depending on an attenuation parameter (effective Q) and geometric spreading; and f(t) is a function of the instrument response and a (weak) function of the scattering process. This relationship is different from the empirical one generally used ML = a0 + a1 log τ + a2(log τ)2 + a3Δ, where τ is the duration measured from the first P arrival time and Δ is epicentral distance in kilometers. In the theoretical relationship, the dependence on epicentral distance is implicit in t. The theoretical relationship is used to calculate a coda magnitude MC that is compared to ML for southern California earthquakes which occurred during the period from 1972 to 1975. This comparison is made independently at six stations of the CIT network. At all stations, a good linear fit (ML = C0 + C1MC) is obtained. The standard errors range from 0.2 to 0.3 and the correlation coefficients from 0.80 to 0.90. Once station gain is accounted for, station correction terms are less than 0.17 magnitude unit when comparing ML and Mc. Mc calculation is not limited to a duration measurement but can utilize the entire earthquake coda in order to increase by many times the statistical confidence in an estimate of an earthquake's magnitude.