Physics-based Simulations of 3D Wave Propagation - Case study deriving from the Le Teil earthquake

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

本数据集包含4000组基于2019年法国勒泰伊（Le Teil）地震场景的三维弹性波动方程模拟结果。弹性波动方程描述了三维传播介质中波的传播规律。

本数据集包含两类数据：介质数据集与速度场数据集。

### 介质数据集
每份介质对应一次数值模拟所用的传播域，由附加于参考一维速度剖面的非平稳随机场构建，表征剪切波速。其速度取值范围为1500m/s至4500m/s。所有介质均包含一层厚度1800m的底部恒定层，层内速度固定为4500m/s。所有介质均为形状32×32×32的三维数组，对应物理尺寸为9.6×9.6×9.6 km³。

### 使用说明
介质以`.npy`数组格式存储，可通过Python读取：`a = np.load("materials0-1999.npy")`。每个文件包含2000份介质，因此数组`a`的形状为(2000, 32, 32, 32)，各维度依次对应介质索引、x坐标（西→东）、y坐标（南→北）与z坐标（下→上）。

### 速度场数据集
速度场数据集包含各传播域地表处的模拟速度波场，通过基于谱元法（Spectral Element Method）的高性能计算代码SEM3D（https://github.com/sem3d/SEM）求解三维弹性波动方程生成。每份介质对应一个速度场，由波在该介质中传播得到。
速度场由布置于传播域地表的16×16虚拟传感器网格记录，传感器间距为600m，分布范围为150m至450m。每个传感器以100Hz的采样率记录三分量速度数据，采样时长为0s至20s。

### 计算细节
计算网格采用尺寸为300m的单元与7个高斯-洛巴托-勒让德积分点，可准确模拟最高5Hz的波传播。波源为置于域底部恒定层内的点源，坐标为(4800, 4800, -8400)m。
该地震源源自勒泰伊地震[Delouis et al., 2021, doi:10.5802/crgeos.78]，采用固定方位的矩张量描述（走向=48°，倾角=45°，倾滑角=88°），振幅为矩震级M0=2.47×10^16 N·m。

### 速度场使用说明
结果以`.feather`数据框格式存储，可通过Python的pandas库读取：`v = pd.read_feather("velocity0-99.feather")`。每个数据框包含100组模拟结果，数据框每行格式如下：

| 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 |
| ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... |

其中`run`表示本次模拟所用介质的索引，`field`表示速度场分量（`Veloc E`为东西向、`Veloc N`为南北向、`Veloc Z`为垂向）；`x`、`y`、`z`为传感器坐标（单位：米）；后续2000列依次对应时刻0、0.01、……、19.99的速度场数据。

### 相关研究
本数据集曾用于微调分解傅里叶神经算子（Factorized Fourier Neural Operator, F-FNO，Lehmann et al. 2024, doi:10.1016/j.cma.2023.116718），以实现从三维地质结构预测地震动波场。F-FNO的训练代码可从https://github.com/lehmannfa/HEMEW3D获取。

搜集汇总

背景与挑战

背景概述

该数据集包含4000个基于法国2019年Le Teil地震案例的三维弹性波传播物理模拟结果，分为材料数据集（描述传播介质的速度场）和速度数据集（记录表面波场）。数据集规模较大（约49.1 GB），专为训练因子化傅里叶神经算子（F-FNO）以预测地面运动波场而设计，适用于地震工程、地球物理和人工智能领域的研究。