4:30 PM - 4:45 PM

# [SCG59-11] Drifting float measurement of pressure change by tsunami

Keywords:tsunami, float, hydrophone, differential pressure gauge

It was reported that tsunamis were recorded by hydrophones (e.g. Okal et al., 2007), notably in frequency bands extending outside the range of the Shallow Water Approximation. If MERMAID floats can cover the oceans as dense as the Argo project of which almost 4000 floats are now drifting to measure temperature and salinity in the oceans, we acquire valuable tsunami data. Here we estimate what signals are observed by a MERMAID, by comparing to the pressure change of the 2010 Chile Tsunami measured by a differential pressure gauge (DPG) at about 4800 m deep seafloor.

We assume linearized water wave with period

*T*, amplitude

*H*, and phase velocity

*c*as shown in Figure 1. Phase velocity

*c*is given by

*c*=

*(*

*g*tanh (

*kD*)

*/ k*)

^{1/2}, where

*k*is horizontal wavenumber

*k*=

*ω/c*,

*ω*=

*2π/T*is angular frequency and

*g*is gravity. The wavenumber

*k*(

*ω, D*) of the water waves in a constant depth ocean as a function of a wave period is obtained by the recursion equation. The water wave height

*W*(

*x, t*) as the function of time

*t*and horizontal position

*x*is expressed as

*W*(

*x,t*)

*= H*

*e*

^{i }^{(}

^{kx-ωt}^{)}

The MERMAID is Lagrangian float drifting at a depth of

*z*(

*0 > z > -D*)

*and measures Lagrangian pressure of water, where*

*D*is water depth.

Lagrangian pressure

*δp*(

*x, z, t*) is given by

*δp*(

*x, z, t*) =-{

*H*

*ρ*

_{o }

*g*sinh (

*kz*) /(sinh(

*kD*)

*cosh(*

*kD*))}

*e*

^{i }^{(kx-ωt)}

Eulerian pressure is given by

*p'*(

*x, z, t*) = {

*Hρ*

_{o }

*g*cosh (

*k*(

*D*+

*z*)) / cosh (

*kD*)}

*e*

^{i }^{(kx-ωt)}

Therefore, pressure measured by a DPG at seafloor is expressed as

*p*

*'*(

*x,-D, t*) = {

*H*

*ρ*

_{o }

*g /*cosh(

*kD*)}

*e*

^{i (kx-ωt)}

and the pressure

*δp*(

*z*) measured by a MERMAID at

*z*depth can be related

with the DPG pressure

*p*

*'*(

*D*) by

*δp*(

*z*) =

*R*

*p*

*'*(-

*D*)

*,R*=

*-*sinh (

*kz*)

*/*sinh (

*kD*)

If

*T*is large enough that

*k*is close to 0,

*R*becomes close to

*z/D*. Figure 2 shows the

*R*as the function of

*T*for floats at 1000 (blue) and 2000 (red) m depth, suggesting the

*R*acts as a low-pass filter. Figure 3 shows the predicted pressure changes observed floats drifting at 1000 (blue) and 2000 (red) m depth. In the presentation, we will discuss availability of tsunami measurement by a float.