Tsunami source inference

Overview

In this benchmark we model the propagation of the 2011 Tohoku tsunami by solving the shallow water equations. For the numerical solution of the PDE, we apply an ADER-DG method implemented in the ExaHyPE framework. The aim is to obtain the parameters describing the initial displacements from the data of two available buoys located near the Japanese coast.

Authors

Run

docker run -it -p 4243:4243 linusseelinger/benchmark-exahype-tsunami

Properties

Model

Description

posterior

Posterior density

forward

Forward model

posterior

Mapping

Dimensions

Description

input

[2]

x and y coordinates of a proposed tsunami origin

output

[1]

Log posterior density

Feature

Supported

Evaluate

True

Gradient

False

ApplyJacobian

False

ApplyHessian

False

Config

Type

Default

Description

level

int

0

chooses the model level to run (see below for further details)

verbose

bool

false

switches text output on/off

vtk_output

bool

false

switches vtk output to the /output directory on/off

forward

Mapping

Dimensions

Description

inputSizes

[2]

x and y coordinates of a proposed tsunami origin

outputSizes

[4]

Arrival time and maximum water height at two buoy points

Feature

Supported

Evaluate

True

Gradient

False

ApplyJacobian

False

ApplyHessian

False

Config

Type

Default

Description

level

int

0

between 0 and 2, the model level to run (see below for further details)

verbose

bool

false

switches text output on/off

vtk_output

bool

false

switches vtk output to the /output directory on/off

Mount directories

Mount directory

Purpose

/output

VTK output for visualization

Source code

Model sources here.

Description

The likelihood of a given set of parameters given the simulation results is computed using weighted average of the maximal wave height and the time at which it is reached. The likelihood is given by a normal distribution \(\mathcal{N}\left(\mu, \Sigma \right)\) with mean \(\mu\) given by maximum waveheight \(\max\{h\}\) and the time \(t\) at which it is reached for the the two DART buoys 21418 and 21419 (This data can be obtained from NDBC). The covariance matrix \(\Sigma\) depends on the level, but not the probe point.

\(\mu\)

\(\Sigma\) l=0

\(\Sigma\) l=1

\(\Sigma\) l=2

1.85232

0.15

0.1

0.1

0.6368

0.15

0.1

0.1

30.23

2.5

1.5

0.75

87.98

2.5

1.5

0.75

The prior cuts off all parameters which would lead to an initial displacement which is too close to the domain boundary. Some parameters may lead to unstable models, e.g. a parameter which initialise the tsunami on dry land, in this case we have treated the parameter as unphysical and assigned an almost zero likelihood.

The parallel MLMCMC was implemented in the MUQ library.