DOI: 10.5281/zenodo.11505295
title: Physics-based Simulations of 3D Wave Propagation - Case study deriving from the Le Teil earthquake

description: This dataset contains 4,000 simulation results of the 3D elastic wave equation in a setting deriving from the Le Teil earthquake (France, 2019). The elastic wave equation governs the propagation of waves in a 3D propagation medium. Two types of data are given in this dataset: a materials dataset and a velocity dataset.

Materials dataset

Each material describes the propagation domain used for one numerical simulation. It is built from non-stationary random fields added to the reference 1D velocity profile and corresponds to the velocity of shear waves. The minimum value is 1500m/s and the maximum is 4500m/s. All materials contain a 1800m-thick bottom layer with a constant velocity of 4500m/s. 

All materials are 3D arrays of shape 32 x 32 x 32.They correspond to a physical size of 9.6 x 9.6 x 9.6km³. 

Practical use

Materials are provided as `.npy` arrays, readable with python: `a = np.load(‘materials0-1999.npy’)`Each file contains 2000 materials. Therefore, `a` is of shape (2000, 32, 32, 32). Indices correspond to the material index, the x coordinate (from West to East), the y coordinate (from South to North), and the z coordinate (from bottom to top). 

Velocity dataset

The velocity dataset contains the velocity wavefields simulated at the surface of each propagation domain. They have been generated by solving the 3D elastic wave equation with the high-performance computing code SEM3D based on the Spectral Element Method (https://github.com/sem3d/SEM). To each material described above corresponds one velocity field, obtained by the propagation of waves through this material.

Velocity fields were recorded by a grid of 16 x 16 virtual sensors located at the surface of the propagation domain between 150m and 450m (600m between consecutive sensors). Each sensor records the 3-component velocity with a 100Hz sampling between 0s and 20s. 

Computational details: The computational mesh was designed with elements of size 300m and 7 Gauss-Lobato-Legendre quadrature points. It can accurately represent the propagation of waves up to 5Hz frequency. Waves were generated by a point-wise source placed at the bottom of the domain, inside the constant layer (the position of the source is 4800, 4800, -8400m). The seismic source derives from the Le Teil earthquake [Delouis et al., 2021, doi:10.5802/crgeos.78]. The seismic source is described by a moment tensor with fixed orientation (strike = 48°, dip = 45°, and rake = 88°) and amplitude (moment magnitude M0=2.47 · 10^16 N.m).

Practical use

Results are given in .feather dataframes, readable with pandas library in Python: v = pd.read_feather(‘velocity0-99.feather’). Each dataframe contains 100 simulation results. Each row of the dataframe has the following format: 




run
field
x
y
z
0.0
0.01
0.02
...
19.98
19.99


12
Veloc E


150.0

770.0
-1.0
0
0
0
...
1.1e-5
1.0e-5


12
Veloc N


150.0

770.0
-1.0
0
0
0
...
3e-6
3e-6


12
Veloc Z


150.0

770.0
-1.0
0
0
0
...
-2.6e-5
-2.7e-5


...
...
...
...
...
...
...
...
...
...
...




where `run` indicates the index of the material used in this simulation, `field` indicates the component of the velocity field (`Veloc E` for East-West, `Veloc N` for North-South, `Veloc Z` for Vertical). `x`, `y`, `z` are the coordinates of the sensor (in meters). The next 2000 columns contain the velocity field for times 0, 0.01, …, 19.99.

Related work

This dataset was used to fine-tune a Factorized Fourier Neural Operator (F-FNO, Lehmann et al. 2024, doi:10.1016/j.cma.2023.116718) to predict ground motion wavefields from 3D geologies. The code to train the F-FNO is available at https://github.com/lehmannfa/HEMEW3D