[S-EM14] Electric, magnetic and electromagnetic survey technologies and scientific achievements

[SEM14-P04] Evaluation on uncertainty of three-dimensional magnetotelluric forward modeling for practical conductivity structure models

*Kiyoshi Baba¹ (1.Earthquake Research Institute, The University of Tokyo)

Keywords:magnetotellurics, three-dimensional modeling, uncertainty of forward calculation

Forward calculation of magnetotelluric (MT) responses is generally assumed to be enough accurate compared to typical observational errors in modeling and inversion studies. Although the uncertainty of the forward calculation can be evaluated by comparing with analytical solutions for some simple models such as layered structure, the evaluation is difficult for complex structures. The uncertainty of the forward calculation should have systematic and random components. In this study, I propose a method to evaluate the random components of three-dimensional (3-D) MT forward modeling. An electrical conductivity structure can be discretized into a 3-D numerical blocks in different coordinate systems that the horizontal axes are rotated with arbitrary angles. Two rotational invariants of the MT responses, Z_tr=(Z_xx+Z_yy)/2 and Z_ad=(Z_xy-Z_yx)/2, are calculated for each model. The diagonal and anti-diagonal elements of MT impedance tensors vary around Z_tr and Z_ad, respectively, with the rotational angle. The calculated Z_tr and Z_ad should be invariant for different coordinate system ideally but the actual responses are not identical. The standard deviation of these responses can be used as the index of uncertainty of the forward calculations, which should include uncertainties because of the difference in grid meshing and outer boundaries (model area) for different rotational angles and uncertainties because of numerical errors in each calculation. I applied this method to evaluate the uncertainty of the forward calculation for the MT responses in the northwestern Pacific. The MT responses were simulated for 17 sites of the seafloor array deployed through Normal Oceanic Mantle (NOMan) project (Baba et al., 2017). For simplicity, just topography and bathymetry were incorporated as the laterally heterogeneous structure and a one-dimensional structure is assumed beneath the seafloor. 10 rotation angles were randomly selected to create different numerical models. The results show that the standard deviations of Z_ad is less than 2% of the mean amplitude while those of Z_tr are relatively larger but they decrease with increasing the mean amplitudes. Empirical relations of the uncertainty may be found from these trends. I am applying the method to another seafloor MT array to test the generality of the relations and the results will also be presented. In inversion analysis, it is meaningless to fit data better than the forward uncertainty. The uncertainty of forward calculation obtained by the proposed method would be useful to provide a warrant for error floors in inversion analysis.