# 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.

## 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#

## 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.