Three-dimensional forward calculation of the electromagnetic fields induced by tsunamis

The motion of seawater induces electromotive force of significant intensity (Sanford, 1971) due to Faraday's law, and resulting electromagnetic (EM) field can be recorded by instruments installed on land or at ocean bottom (Tyler, 2005; Toh et al. 2011). However, only a few studies were successfully simulating Tsunami induced EM fields by an exact and accurate application of Maxwell equations that is essential for a quantitative interpretation to get geophysical information from observations of tsunami-related EM signals. There are a number of observations of such EM fields that were caused by the devastating Tohoku tsunami of 2011 not only on land observatories but also at some seafloor sites (e.g. Utada et al., 2011; Ichihara et al., 2012). Here we present a 3-D modeling scheme to simulate these observed fields. We apply a 3-D EM induction code in Cartesian coordinate system with the heterogeneous source term, which is based on the modified iterative dissipative method (MIDM) (Zhang et al. 2012), and several underground electrical conductivity structures were assumed in the calculations. The source current distribution is predicted by the flow data calculated by a tsunami simulation (Maeda and Furumura, 2011) which solves Navier-Stokes equations in 3-D Cartesian coordinates. In our previous study (Utada et al., 2011), we estimated tsunami-induced fields by applying Biot-Savart law to the same set of flow data and obtained qualitative agreement between observations on land and model results. However quantitatively, we noticed that the present result generally gives smaller amplitude than the result of Biot-Savart calculation. This can be ascribed to the EM induction effect in the sea. We also tried some underground structures, but the effect of the underground structure is negligible compared with that of the induction in the sea. Meanwhile, we found that the effect of the source current by the vertical motion, which was ignored in the previous study, can be comparable to that by the horizontal motion, especially in shallower water. The water motion generates source current in the sea both of poloidal and toroidal modes. Lateral heterogeneities would convert the toroidal to poloidal mode but the amplitude of converted mode is generally much smaller than that of original poloidal mode. Therefore the source of the toroidal mode can be ignored in case of modeling observations on land. Our numerical simulation shows that the toroidal mode can be effective for modeling seafloor observations, but only when the seafloor is very conducting. In such a case, the effect of toroidal mode would bias the estimation of the wave propagation direction by seafloor electromagnetic data. We also examined how the tsunami-induced EM field observations constrain the conductivity of the shallower part of the seabed, which is difficult to be resolved by using ordinary seafloor magnetotelluric signals. We found that the poloidal mode signals are sensitive to the conductivity of approximately down to 30 km depth. Although the toroidal mode is sensitive to the integrated resistance of the sediment layer, separation of its weak effect from the dominant effect of the poloidal mode is difficult.