In order to test the efficiency of the method, we considered three different structures of covariance matrix: (i) diagonal matrix (contains a variance of individual measurements at seismic stations), (ii) block-diagonal matrix (considering cross-covariance among three components at each station), and (iii) full covariance matrix. Both uncorrelated and correlated random noise traces were added to the synthetic waveform data in amounts between 5 and 20 per cent of the maximum amplitude. To illustrate the proposed method’s performance, we conducted tests with synthetic data using configuration of the 2018 M w 6.8 Zakynthos (Ionian Sea, Greece) earthquake.
The used mathematical prescription allows us to use the covariance matrix for the three-component noise records at every station and all possible cross-correlations among the recorded noise wavefield. Hence, according to the considerable effects of random data errors in assessing the uncertainty of the moment tensor components, this paper aims to describe an MVUE of the data covariance matrix and its application on uncertainty quantification of the moment tensor. Furthermore, estimating the level and distribution of random errors in the observed waveforms is challenging due to assessing the minimum-variance unbiased estimator (MVUE). It needs a proper stochastic model of the observables for accurate and precise estimates of the unknown parameters. The linear Gauss–Markov model for waveform-based moment tensor inversion often relies on the overdetermined least-squares method.
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