Time–Frequency Characteristics of Tsunami Magnetic Signals from Four Pacific Ocean Events

Abstract

The recent deployment of highly sensitive seafloor magnetometers coinciding with the deep solar minimum has provided excellent opportunities for observing tsunami electromagnetic signals. These fluctuating signals (periods ranging from 10–20 min) are generally found to be within $\pm$ $\sim$1 nT and coincide with the arrival of the tsunami waves. Previous studies focused on tsunami electromagnetic characteristics, as well as modeling the signal for individual events. This study instead aims to provide the time–frequency characteristics for a range of tsunami signals and a method to separate the data’s noise using additional data from a remote observatory. We focus on four Pacific Ocean events of varying tsunami signal amplitude: (1) the 2011 Tohoku, Japan event (M9.0), (2) the 2010 Chile event (M8.8), (3) the 2009 Samoa event (M8.0) and, (4) the 2007 Kuril Islands event (M8.1). We find possible tsunami signals in high-pass filtered data and successfully isolate the signals from noise using a cross-wavelet analysis. The cross-wavelet analysis reveals that the longer period signals precede the stronger, shorter period signals. Our results are very encouraging for using tsunami magnetic signals in warning systems.

Appendix: COMCOT

COMCOT has been used to investigate many other tsunami events, including the 1992 Flores Islands, Indonesia tsunami (Liu et al. 1995), the 2003 Algeria tsunami (Wang and Liu 2005), and the 2004 Indian Ocean tsunami (Wang and Liu 2006). The model builds upon the analytical solutions of Okada (1985) to calculate the seafloor deformation from the fault mechanisms. The fault plane is divided into a certain number of rectangular subfaults and the parameters of each subfault are inputted (i.e. length, width, depth, strike angle, dip angle, rake angle and the amount of slip). The seafloor movement due to each subfault can be calculated assuming an elastic semi-infinite half space earth model. Earthquakes typically occur within seconds, thereby preventing the water column above the deforming seafloor from escaping. Consequently, the model does not account for the time dependence of the earthquake’s rupture and instead assumes that it happens instantaneously so that the sea surface mimics the deformation of the seafloor.

The fault plane is the interface between the subducting plate and the overriding plate. The strike direction is used to define strike and the angles of rake and dip. Strike direction is the direction one must face to stand on the top edge of the fault plane with the plane on one’s righthand side. From this, $\theta$ is the angle measured clockwise from north to the strike direction ($0^{\circ } \le \theta \le 360^{\circ }$). The dip angle $\delta$ is the angle between the horizontal top surface and the fault plane ($0^{\circ } \le \delta \le 90^{\circ }$). Lastly, the rake angle $\lambda$ is the angle measured anti-clockwise on the fault plane from the strike direction to the direction of the overriding plate’s motion relative to the subducting plate (−180$^{\circ } \le \lambda \le 180^{\circ }$).

The model is then used to solve the linear shallow water wave equations:

$$\begin{aligned} \frac{\partial \zeta }{\partial t}+\frac{\partial P}{\partial x}+\frac{\partial Q}{\partial y}= \,& {} 0 \end{aligned}$$

(10)

$$\begin{aligned} \frac{\partial P}{\partial t}+gH\frac{\partial \zeta }{\partial x}= \,& {} 0 \end{aligned}$$

(11)

$$\begin{aligned} \frac{\partial Q}{\partial t}+gH\frac{\partial \zeta }{\partial y}=\, & {} 0 \end{aligned}$$

(12)

where $\zeta$ denotes the free surface elevation, and P and Q are the volume flux in the x and y directions, respectively (ie. $P=hu$, $Q=hv$). These equations are solved via an explicit leap-frog finite differencing model that uses a staggered-grid scheme and the algorithm is parallelized based on FORTRAN and OpenMPI.