[S-EM15] Electric, magnetic and electromagnetic survey technologies and scientific achievements

[SEM15-14] Modification of the robust remote reference multivariate regression S-estimator

*Yoshiya Usui¹, Makoto Uyeshima¹, Shin'ya Sakanaka², Tasuku Hashimoto¹, Masahiro Ichiki³, Toshiki Kaida³, Yusuke Yamaya⁴, Yasuo Ogawa^3,5, Masataka Masuda¹, Takahiro Akiyama¹ (1.Earthquake Research Institute, the University of Tokyo, 2.Graduate School of International Resource Sciences, Akita University, 3.Graduate School of Science, Tohoku University, 4.National Institute of Advanced Industrial Science and Technology, 5.Institute of Integrated Research, Institute of Science Tokyo)

Keywords:Magnetotellurics, Statistical method, Time series analysis, Robust statistic, Multivariate analysis

Cultural noises can significantly distort observed electromagnetic field data of magnetotelluric measurements, impeding the accurate estimation of the magnetotelluric response function. To handle the outlying data in the response function estimation, robust data processing methods have been used. Recently, we developed a new robust remote reference method called the robust remote reference multivariate regression S-estimator (Usui et al., 2024). We derived it by robustfying the two-input–multiple-output system between the local electromagnetic and reference magnetic fields, which leads to the classical robust reference estimator, and confirmed the superiority of the new estimator compared to previously proposed robust remote reference estimators. However, in deriving the estimator, we made an unrealistic assumption about the covariance matrix of regression residuals that its off-diagonal components are zeros. This means that the noises of respective channels are independent of each other, although, in the real world, some dependences of noises among different channels generally exist. In this study, we re-derived the robust remote reference multivariate regression S-estimator by allowing non-zero off-diagonals in the covariance matrix. We succeeded in deriving the modified method under the constraints that real and imaginary components of residuals are independent and covariances as well as variances of them are equal. By applying to some magnetotelluric data, we confirmed that the modified method could give smoother sounding curves than the original method.