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

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

*臼井 嘉哉¹、上嶋 誠¹、坂中 伸也²、橋本 匡¹、市來 雅啓³、海田 俊輝³、山谷 祐介⁴、小川 康雄^3,5、増田 正孝¹、秋山 峻寛¹ (1.東京大学地震研究所、2.秋田大学工学資源学部、3.東北大学大学院理学研究科、4.産業技術総合研究所、5.東京科学大学総合研究院)

キーワード：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.