- Letter
- Open Access

# Tsunami-induced magnetic fields detected at Chichijima Island before the arrival of the 2011 Tohoku earthquake tsunami

- Hidee Tatehata
^{1}Email author, - Hiroshi Ichihara
^{2, 3}and - Yozo Hamano
^{4}

**Received:**19 April 2015**Accepted:**23 October 2015**Published:**19 November 2015

## Abstract

Magnetic field disturbances associated with the tsunami caused by the 2011 Tohoku earthquake were observed at Chichijima Island, 1200 km south of the epicenter. The vertical component of the magnetic field showed a periodic signal at approximately 20 min before the tsunami arrived. This study investigated the mechanism of the magnetic field signal using simulation studies. First, we derived a tsunami source model that explained the tide gauge records and sea-level changes at Chichijima Island. Using this model, we then computed the electric current induced by the tsunami and the resulting secondary magnetic field. The computed changes in sea level and magnetic field are consistent with their respective observed waveforms, including the timing of the magnetic field signals. In our interpretation, the tsunami flow induced an electric current along the tsunami wave front, which in turn generated a secondary induced magnetic field ahead of the tsunami wave. Hence, magnetic variations preceding the tsunami were observed at Chichijima Island. This suggests that imminent arrivals of tsunamis can be detected by observations of the magnetic field.

## Keywords

- Tsunami Wave
- Tide Gauge
- Japan Meteorological Agency
- Magnetic Signal
- Tohoku Earthquake

## Findings

### Introduction

The oceanic dynamo effect was anticipated theoretically by Michael Faraday (Faraday 1832) and has been studied in further detail during recent decades (e.g., Sanford 1971; Tyler 2005; Tyler et al. 2003). With the advancement of observational devices, tsunami-induced dynamo effects have recently been observed on the seafloor (Toh et al. 2011; Ichihara et al. 2013; Sugioka et al. 2014; Zhang et al. 2014a). A few instances of these effects have been documented on land. One was a magnetic signal associated with the 27 February 2010 earthquake (M8.8) off the coast of Chile, which was observed at Easter Island, 3500 km from the epicenter (Manoj 2011). A magnetic signal associated with the tsunami caused by the 11 March 2011 Tohoku earthquake (M9.0) was observed in Chichijima Island, from which a clear signal of the oceanic dynamo effect was reported by Zhang et al. (2014b). They reproduced the observed magnetic field but did not perform a comparison between the tsunami and the magnetic field.

In this paper, we report on tsunami-induced magnetic field variations that were observed at Chichijima Island at approximately 20 min before the tide gauge there recorded the arrival of the tsunami.

The aims of this study were to confirm that the oceanic dynamo effect caused the magnetic field variations and to understand the mechanism that allowed the detection of the magnetic field variations before the sea-level change. In this paper, we first present and compare the sea-level changes and magnetic field variations after the 2011 Tohoku earthquake. Next, we report on our numerical simulations of tsunamis and induced magnetic fields at Chichijima Island to explain the corresponding observations. Finally, we discuss the mechanism by which the tsunami-induced magnetic field can signal a tsunami before the occurrence of changes in sea level.

### Observations at Chichijima Island

#### Tide gauge

#### Magnetic observations

Figure 2 shows the horizontal component *H* and vertical component *Z* of the filtered geomagnetic records from CBI and KNY. Most of the simultaneous variations in these records are explained by a weak magnetic storm on 11 March 2011 (Japan Meteorological Agency 2013). However, the record of *Z* at CBI showed anomalous behavior starting around 7:00 (UTC) that could not be explained by the external source (see Appendix 1).

#### Comparison of tide gauge and magnetic records

*Z*component were strikingly similar, displaying seven sharp peaks between 7:00 and 9:30 (UTC) (Fig. 3).

Tidal records show that the tsunami arrived at 07:11 (UTC), with a maximum height (half amplitude) of 182 cm (Japan Meteorological Agency 2013). The dominant period of the tsunami between the first and seventh waves was around 20 min. The maximum amplitude of *Z*, observed in the second peak, was 1.6 nT. The predominant period of both waveforms was consistently about 20 min. The arrival times of the magnetic signal were recorded at 06:50 showing that the initial magnetic signal preceded the initial tide gauge signal by about 20 min. The first peak of the magnetic signal preceded that of the tsunami wave by about 14 min, and the third through seventh magnetic peaks preceded those of the tsunami waves by about 5 min. For our purposes, the locations of the tidal and magnetic stations can be considered the same. Thus, the magnetic variations were detected 5–20 min ahead of the tsunami.

### Simulations of tsunami flows and induced magnetic fields

We performed a numerical tsunami simulation that explains the tsunami observations at Chichijima Island and nearby offshore tide gauges. Then we computed the magnetic variation induced by the oceanic dynamo effect and compared the results to the magnetic observations. Our analysis involved three steps: first, computation of the flow of seawater in the simulation; second, computation of the electric current induced by seawater flow; and third, computation of the resulting magnetic field variations on the basis of the Biot-Savart law.

#### Tsunami flow model

Zhang et al. (2014b) studied the induced magnetic field at CBI through a numerical simulation. The amplitude of their computed magnetic waveform was slightly higher than that of the observation. They mentioned that the reason might be the low accuracy of the numerical tsunami simulation, which used a planar coordinate system.

We used a nonlinear numerical tsunami model that takes seabed friction and Coriolis force into consideration, where one grid size is 1 min of arc (along longitude and latitude), the time difference is 3.06 s, and the system of coordinates is spherical.

The computed waveform was sufficiently accurate considering the tsunami flow around Chichijima Island.

#### Induced electric current and magnetic field

*J*are then derived using the following expression:

where *μ* is the magnetic permeability, *J*
_{⊥} is the total electric current density in the direction perpendicular to the propagation of the tsunami, *i* is the imaginary unit, *C*
_{
d
} is the magnetic diffusivity (the phase velocity of the electric current wave in seawater), *C* is the tsunami velocity, *η* is the tsunami height, *F*
_{
z
} is the *Z* component of the geomagnetic field *F*, and *h* is the water depth. The imaginary unit represents the phase difference between the tsunami wave and the electric current in complex phase space. Details are presented in Appendix 3.

- 1.
Time domain data of tsunami height for every numerical grid point are decomposed to frequency domain data by fast Fourier transform (FFT). The formula (1) converts the frequency domain data to electric currents in complex space. Inverse FFT is then used to convert the frequency domain data of the current to time domain data (in real space), expressed as the length of a current vector.

- 2.
The flow direction of the tsunami is computed from the numerical tsunami model. According to Ampere’s law, the electric current direction is obtained by rotated flow direction by 90°. The electric current density and its direction are then obtained for each grid cell.

- 3.
The induced magnetic field at the observation point is computed from the induced current source in each grid cell according to the Biot-Savart law (Fig. 5b). The induced magnetic field at CBI is obtained by integrating a sufficient area centered on Chichijima Island.

In sum, our computed sea-level changes and magnetic field variations agreed well with the observations, although we used only a simple electrical conductivity structure. This result indicates that the tsunami-induced magnetic field variations at Chichijima Island could be suitably computed by assuming an insulating seafloor.

### Discussion

- 1
First motion

The flow of the first tsunami wave was more than 100 km northeast of Chichijima Island. Simultaneously, a weak induced magnetic field extended to Chichijima Island.

- 2
Positive slope

The first tsunami wave was northeast of Chichijima Island. Positive and negative variations of the magnetic field were south (front) and farther north (back) of the tsunami wave, respectively.

- 3
First peak

The first tsunami wave was near the east coast of Chichijima Island. Induced electric currents near the island flowed from the north to the east. A positive variation of the magnetic field lay over the island, and the following negative variation moved south into the area shown in Fig. 7.

- 4
First trough

The first trough of the tsunami reached the northern side of Chichijima Island, and rip flows of the tsunami moved away from the island. A negative variation of the magnetic field lay over the island, and a new positive variation entered the area shown in Fig. 7, moving south.

Equation 14 indicates that an induced electric current is delayed when a tsunami wave is in a phase with the positive slope, but the phase-delay effect of the *C*
_{d}/*C* term becomes weak as ocean depth decreases. As such, the induced electric current near the coastline is substantially in phase with the tsunami. Minami et al. (2015) discussed these phenomena in detail.

The first tsunami wave approaching Chichijima Island from the northeast induced an electric current in the leftward direction relative to the tsunami propagation. Around 7:05–7:10, northeast of Chichijima Island, there were large and parallel electric currents (purple arrows in Fig. 7). According to Ampere’s right-hand rule, these currents induced large magnetic fields (red arcs in Fig. 7).

From this exercise, we conclude the following: if a tsunami wave is approximately planar, the lines representing the induced electric current and the peak of the tsunami wave are parallel and coincident, and thus, the induced magnetic field must curl over both the electric current and the tsunami wave. Because this induced magnetic field can reach beyond the tsunami wave, its signal precedes the wave and can be detected at least several minutes before the tsunami’s arrival.

The amplitudes of the induced magnetic field and the tsunami’s height are related with an approximate ratio of 1 nT/m. Four other examples of induced magnetic phenomena recorded at CBI had similar ratios (Tatehata 2015). This sensitivity is sufficient for detecting tsunamis with height of above 1 m, considering the typical signal-to-noise ratio of geomagnetic observations. Our findings suggest the possibility that magnetic field observations can serve as a method for rapid detection of imminent tsunamis.

### Conclusion

We showed that the vertical component of the geomagnetic field and the tide gauge records at Chichijima Island exhibited very similar patterns as the tsunami caused by the 2011 Tohoku earthquake. The first magnetic signal preceded the arrival of the first tsunami wave at the Chichijima Island tide gauge by about 20 min.

We quantitatively modeled the tsunami and the corresponding magnetic field variations at Chichijima Island. Not only was the computed magnetic field signal in close agreement with the observed signal, but also the mechanism before the arrival of the tsunami wave was quantitatively explained. Our numerical simulation showed that the straight-line electric current induced a secondary magnetic field that curled at the front of the first tsunami wave.

## Declarations

### Acknowledgements

We thank Kenji Satake for the fruitful discussions regarding the high-resolution fault model and the reviewers for helping us substantially improve this paper. We thank the JMA Global Environment and Marine Department for the tidal data, the Kakioka Magnetic Observatory for the magnetic field data at Chichijima Island, and the U.S. National Oceanic and Atmospheric Administration for the DART buoy data, which are available at https://www.ngdc.noaa.gov/hazard/dart/2011honshu_dart.html. We dedicate this paper to the 23,000 victims of the Tohoku earthquake tsunami.

**Open Access**This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

## Authors’ Affiliations

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