Stabilizing seismic source inversion by accounting for P-wave picking uncertainty: A waveform-shift covariance approach

Yuji Yagi

In seismic source inversion using teleseismic P waves, P-wave arrival times are picked from observed waveforms and used to adjust their timing relative to the predicted arrivals. However, uncertainty in the picked arrival times remains after this correction. Picking errors shift the entire waveform and produce temporally correlated waveform errors. If these errors are not properly accounted for, small differences in arrival-time picks may substantially alter the inferred source models and contribute to discrepancies among analysts. In this study, I propose a waveform-shift covariance approach that approximately constructs the component of the data covariance matrix associated with P-wave picking uncertainty from observed waveforms and a probability distribution of time shifts. I incorporate this approach into potency density tensor inversion (PDTI) and compare it with a conventional approach that neglects picking uncertainty, using 125 synthetic waveform datasets that differ only in picking errors. Relative to the conventional approach, the proposed method reduces the normalized model root mean square error (RMSE) by approximately 0.09 and reduces the variability among inferred source models across datasets to less than 40% of that for the conventional approach. Although the normalized data RMSE is comparable between the two approaches, the normalized model RMSE for individual datasets is concentrated within 0.32–0.36 for the proposed method, whereas it spans 0.35–0.50 for the conventional approach. These results show that incorporating P-wave picking uncertainty into the data covariance matrix yields more accurate and stable source models, even though the proposed and conventional approaches fit the observed waveforms similarly well. Application to real earthquake data with uncertain P-wave picks suggests that neglecting the data error structure may lead to overfitting in the conventional approach. Accounting for picking uncertainty changes how waveform discrepancies are weighted in the inversion, reducing the tendency to interpret waveform-shift errors as source complexity. These findings underscore the importance of returning to a basic principle for reliable estimation of earthquake rupture processes: interpreting source signals in observed data requires an understanding of not only the signal structure but also the error structure.