A comparative study of coda–Q values estimations from synthetic and digital seismograms


The main purposes of this research work are to estimate the coda–Q values using linear (log–log) and nonlinear (Gauss–Newton) regression techniques and to generate synthetic seismogram by white Gaussian noise modulated with an attenuation factor (ekt) and a geomechanical spreading factor using a single backscattered model. A comparative study is carried out, for the estimation of coda–Q values from synthetic seismogram and from digital seismogram provided by three events recorded in three different seismic stations, namely Tezpur (TZR), Dokmok (DMK) and Seijusa (SJA) that occurred in Tezpur region, Assam, India. Here, both the models are compared in terms of outputs and accuracy as a function of lapse time and frequencies. Generally, linear model is used in most of seismological practices. But in this study, I am trying to use both linear and nonlinear models. Here, the main challenge is the estimation of coda–Q values using the nonlinear model. During the analysis, it was observed that, at the final part of the coda where the signal-to-noise ratio is greater than and equal to 5, the estimated coda–Q values have no significant difference for both linear and nonlinear models. But on the decreasing signal-to-noise ratio less than 5, the coda–Q values are overestimated in the linear model as compared to the nonlinear model. These observations are made for both the synthetic and digital seismograms. Through this study, I am trying to conclude that the coda–Q values are dependent on lapse time in both the linear and nonlinear models but are less pronounced in nonlinear techniques for both synthetic and digital seismograms. This effect is more evident when different coda durations are obtained by fixing the start time of coda analysis and increasing the end time of the same coda. This pattern is observed for all three events in Tezpur region and synthetic seismogram. Finally, the conclusion was drawn that the coda–Q values are dependent on lapse time and central frequencies for both the models. But, the significance levels are less in the case of nonlinear model for both synthetic and digital seismograms.

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A :

Spectral amplitude of the coda wave.

a :

Accounts for geometric spreading (a = 1 or 0.5 for body wave or surface wave, respectively).

A 0 :

A term depending on site, source and medium.

A real :

Root-mean-square (RMS) amplitude of the coda recorded at seismic station.

A theoretical :

Root-mean-square (RMS) amplitude of the coda of synthetic seismogram.

f :



Fast Fourier transform.

k :

Attenuation coefficient.

Q :

Quality factor.

Q c :

Coda wave quality factor.

Q i :

Intrinsic quality factor.

Q s :

Scattering quality factor.

t :

Time measured from origin time.

t S :

Travel time of S wave measured from the origin.

σ :

Standard deviation

μ :


N :

Gaussian noise.

f c :

Central frequency.


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Correspondence to Jwngsar Brahma.

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Brahma, J. A comparative study of coda–Q values estimations from synthetic and digital seismograms. Arab J Geosci 14, 339 (2021). https://doi.org/10.1007/s12517-021-06529-1

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  • Coda
  • Digital seismogram
  • Synthetic seismogram
  • Attenuation
  • Nonlinear
  • Quality factor