Analysis Of Coda Research Articles

Coda communication by sperm whales (Physeter macrocephalus) off the Galápagos Islands

To gain insight into the function of sperm whale vocalizations known as codas (short, patterned series of clicks), sperm whales (Physeter macrocephalus) were tracked continuously for periods of days totalling months off the Galápagos Islands, Ecuador, and vocalizations were tape recorded systematically. In total, 1333 codas were classified according to their temporal pattern and the number of clicks they contained. Codas were found to be temporally very clustered, and could be categorized into 23 fairly discrete types. Sequential analysis of codas revealed that they overlapped one another according to type in a nonrandom way, and that type 5 tended to initiate coda exchanges. "Regular" coda types (with evenly spaced clicks) tended to occur with other regular coda types and "irregular" coda types (with one or two delayed final clicks) were heard with other irregular coda types. Codas may function principally as a means of communication, to maintain social cohesion within stable groups of females following periods of dispersion during foraging.

Spectral analysis and inversion of experimental codas

A method developed for the determination of the characteristic lengths of an heterogeneous medium from the spectral analysis of codas is based on an extension of Aki’s theory to anisotropic elastic media. An equivalent Gaussian model is obtained and seems to be in good agreement with the two experimental data sets that illustrate the method. The first set was obtained in a laboratory experiment with an isotropic marble sample. This sample is characterized by a submillimetric length scale that can be directly observed on a thin section. The spectral analysis of codas and their inversion yields an equivalent correlation length that is in good agreement with the observed one. The second data set is obtained in a crosshole experiment at the usual scale of a seismic survey. The codas are recorded, analysed, and inverted. The analysis yields a vertical characteristic length for the studied subsurface that compares well with the characteristic length measured by seismic and stratigraphic logs.

Estimates of Coda-Q Using a Non-Linear Regression.

A non-linear regression technique (Gauss-Newton method) is used to fit the single-scattering model of coda wave generation to experimental data. Comparisons between these results and those obtained applying the technique used in seismological practice (logarithmic linearization of the model equation and least-squares fit) are made. Data used are: a) a synthetic coda generated by white Gaussian noise modulated with an attenuation factor, exp(-kt), and a geometrical spreading factor; b) seismograms provided by two seismic series that occurred in the Abruzzo (Italy) and Antequera (Southern Spain) regions.The study from synthetic data shows that when the signal-to-noise ratio of the final part of the coda is greater or equal to 5, there are no significant differences in the values of Qc inferred by both techniques. When the signal-to-noise ratio is less than 5, we observed that the log-log technique produces a systematic overestimation of the values of Qc. Results obtained with real seismograms show that the log-log technique overestimates the Qc values when compared with the Gauss-Newton method, when the whole coda is used. When a long coda is used, the Qc dependence on frequency estimated using log-log is different in some cases from the one obtained with the Gauss-Newton technique. The Qc dependence on the lapse-time is less pronounced when the Gauss-Newton technique is used. This effect is more evident when different coda durations are obtained fixing the start-time of coda analysis, and increasing the end-time of the same coda. This pattern is also observed for the Abruzzo (Italy) and Antequera (Spain) series; when the log-log technique is used, a lapse-time dependence is observed, but, when the Gauss-Newton technique is used, this dependence is less significant.

Teleseismic coda analysis with simultaneous modeling of single and multiple scattering

Spectra from teleseismic coda waves are used to estimate Earth and source properties through generalized linear inversion (GLI) techniques. High‐frequency teleseismic (66°–98°) P wave codas recorded by the Regional Seismic Test Network (RSTN) are analyzed. The spectra of the teleseismic coda were found to be described by the following two models:(A/t2 + B) exp (−Ct) and (A/t + B) exp ( − Ct). A two‐term model consisting of a time dependent and time independent part were required to fit the single and multiple scattering effects observed in the data. Two near‐surface explosions (eastern Kazakh) of magnitude 6.1 and one earthquake (northern Argentina‐Chile, 559 km depth) of magnitude 5.8 are analyzed to evaluate near‐source scattering. The five three‐component North America RSTN receiving stations are used to evaluate the effect of near‐receiver scattering. Coda Q estimates from the inversions increased with frequency in the approximate range from 800 at 1 Hz to 1600 at 4 Hz. The same range of coda Q values were obtained for both of the models tested; however, the (A/t + B) exp (−Ct) model results had higher variances, suggesting poorer fit of this model to the data. Coda Q estimates are higher at stations RSCP and RSNY compared to the other stations. The coda Q results from the GLI analyses are in agreement with Q values determined from the analysis of local coda. These results suggest that teleseismic coda Q are dominated by near‐receiver scattering effects. The coda analysis method outlined in this paper represents an alternative to normal single scattering analysis methods performed over small time windows early in the coda. This method, which accounts for multiple scattering effects, models the entire coda (500–600 s) where signal is above background noise. Good results were obtained for both earthquake and explosion data. While coda analysis on multiple scattered waves at teleseismic distances was the emphasis in this paper these methods should also work at local and regional distances.

Spectral analysis and inversion of codas

A systematic investigation of codas in media with Gaussian and exponential correlation function is presented. By means of various tools such as the wavelet decomposition, it is shown that the spectral analysis of codas has to be limited to a restricted time interval whose boundaries are given. When this condition is fulfilled and when the fluctuations of the sound velocity are smaller than 4%, the average codas power spectrum is indeed proportional to the backscattering coefficient as predicted by the linear theory developed by Aki and Chouet. This coefficient can be successfully inverted to retrieve the statistical properties of the velocity distribution. Various numerical and practical recommendations are suggested.

Array analysis of seismic scattering

Abstract The use of high frequency arrays permits investigation of the spatial as well as the temporal character of the seismic wavefield in the frequency band 1-10 Hz. The authors have carried out investigations into seismic scattering at NORESS, FINESA, and ARCESS. Two principal methods have been used, frequency-wavenumber analysis of coda and coherency analysis of seismic phases. For regional seismograms, frequency-wavenumber analysis of Lg coda shows that Lg-to-Lg scattering dominates and that scattering is initially concentrated in the forward direction, changing to isotropic backscatter later in the coda. The P coda is more complex, although all cases studied show that energy is concentrated in the on-azimuth direction. However, different phase velocities are found for the three different cases studied, indicating that P coda is made up of several different contributions whose balance varies in different situations. In previous work, we have found that the decay of coherency with spatial separation scales as the wavelength for the Lg phase of regional events in the frequency band 1-10 Hz, declining to about 0.5 within one wavelength. Analysis of synthetic seismograms for realistic models of the area suggests that this loss of coherency is not due to dispersion, reaffirming a scattering interpretation. However, the decline in coherency is isotropic, seemingly contradicting the finding of forward scattering found in the frequency-wavenumber analysis. This may reflect a sensitivity of the coherency analysis to scattering within or very close to the array, while the frequency-wavenumber analysis favors scatterers at greater distance.

P-wave coda analysis of short-period array data and the scattering and absorptive properties of the lithosphere

Short-period registrations of events at regional distances usually show a considerable amount of energy arriving after the initial P onset. This is caused by the scattering of the wavefield at heterogeneities along the propagation path. I have studied the P coda of Indonesian earthquakes recorded at the Warramunga array in central Australia. The data show a decrease of the coda energy relative to the energy of the direct wave with increasing source depth. Coherency measurements by means of semblance-enhanced stacks reveal that the coda of deep-focus events is mostly incoherent across the array, while the coda of shallower events contains a certain amount of partly-coherent energy. This points to the existence of heterogeneities with various scale lengths. Small-scale heterogeneities of only a few kilometres correlation length beneath the array are responsible for the generation of the incoherent part of the coda, while the partly-coherent arrivals are produced by larger-scale heterogeneities in the deeper lithosphere and by reflections from plane layering. In order to study further the small-scale fluctuations of the seismic parameters I have computed the power spectral density of the P coda in four frequency bands between 0.75 Hz and 6 Hz. An energy-flux model (Frankel & Wennerberg 1987) which assumes multiple scattering and allows for the independent determination of intrinsic Q and scattering Q has been fitted to the data. The results show an almost linear increase of intrinsic Q with frequency. Q is about 300 at 1 Hz. The frequency dependence of scattering Q is somewhat less pronounced with a value of about 340 at 1 Hz and an exponent of 0.85. A comparison of this frequency dependence with results from single-scattering theory imply a correlation length of about 5.5 km and a rms velocity fluctuation of 5 per cent for the scattering medium.

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.