基于深度神经网络EikoNet走时计算方法及应用

姚时; 侯爵; 黄跃鹏; 徐涛; 白志明; 高正辉

doi:10.19975/j.dqyxx.2021-049

基于深度神经网络EikoNet走时计算方法及应用

doi: 10.19975/j.dqyxx.2021-049

姚时^{1, 2,},
侯爵^{3, 1, 2},
黄跃鹏^{1, 2},
徐涛^{1, 4},
白志明^{1, 4},
高正辉⁵

1.
中国科学院地质与地球物理研究所岩石圈演化国家重点实验室，北京 100029
2.
中国科学院大学，北京 100049
3.
中国地震局地球物理研究所，北京 100081
4.
中国科学院地球科学研究院，北京100029
5.
吉林大学地球探测科学与技术学院，长春 130026

基金项目: 国家自然科学基金资助项目（42130807）

详细信息

作者简介:
姚时（1998- ），男，硕士生，主要从事地震学研究. E-mail：yaoshi@mail.iggcas.ac.cn

中图分类号: P315
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- 文章访问数: 2385
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- 被引次数: 0
出版历程
- 收稿日期: 2021-09-04
- 录用日期: 2021-11-04
- 网络出版日期: 2021-11-19
- 刊出日期: 2023-01-01

EikoNet traveltime calculation method and application based on deep neural network

Yao Shi^{1, 2
,},
Hou Jue^{3, 1, 2},
Huang Yuepeng^{1, 2},
Xu Tao^{1, 4},
Bai Zhiming^{1, 4},
Gao Zhenghui⁵

1.
State Key Laboratory of Lithospheric Evolution, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing 100029, China
2.
University of the Chinese Academy of Sciences, Beijing 100049, China
3.
Institute of Geophysics, China Earthquake Administration, Beijing 100081, China
4.
Innovation Academy for Earth Science, Chinese Academy of Sciences, Beijing 100029, China
5.
College of Geo-exploration Science and Technology, Jilin University, Changchun 130026, China

Funds: Supported by the National Natural Science Foundation of China（Grant No. 42130807）

摘要

摘要: 地震波走时计算在层析成像、偏移成像和微震定位等地震学领域中都有重要作用. 使用有限差分方法求解程函方程是地震波走时计算的重要方法之一. 常规程函方程求解方法需要计算每一个震源激发的走时场，随着网格数量的增加会消耗大量的时间和存储空间. 本文介绍了基于深度神经网络的EikoNet走时计算方法，该方法构建了一个包含速度和走时场偏差之间关系的深度神经网络，通过在三维空间中采样生成训练样本，以给定的速度模型为标签实现训练过程中对网络的优化，在计算走时过程中，能传递关于地震波场和速度结构的信息，而且高度适用于GPU，可以无网格地快速确定三维域中任意两点之间的走时，大大提高了计算效率并降低了内存消耗. EikoNet方法和常规快速推进法（FMM）在几个速度模型上的数值实验表明EikoNet方法在保持高精度的同时还具有更高的效率.
- 走时计算 /
- 程函方程 /
- EikoNet /
- 快速推进法
Abstract: Seismic wave traveltime calculation plays an important role in many areas of seismology, such as seismic tomography, migration and microseismic location. Solving the eikonal equation with the finite difference method is an essential method for calculating traveltime. The conventional method of solving the eikonal equation needs to calculate the traveltime field of each source. As the number of grids increases, it will consume a lot of time and memory. We introduce the EikoNet based on a deep neural network. Its samples are generated by sampling in the three-dimensional space, using the given velocity model as labels to optimize the network. Furthermore, it can transmit information about seismic wavefield and velocity structure during calculation and is highly suited for GPU. The EikoNet can quickly determine the traveltime between any two points in a three-dimensional domain without meshes, significantly improving calculation efficiency and reducing memory consumption. Numerical experiments of the EikoNet and the fast marching method (FMM) on several velocity models show that the EikoNet has higher efficiency while maintaining high accuracy.
- traveltime calculation /
- EikoNet /
- deep neural network /
- fast marching method

HTML全文

图 1 处理工作流概述.（a）由全连接层和残差块组成的神经网络体系结构，每个残差块由3个全连接层组成，有512个神经元，ELU激活应用于所有隐藏层.（b）$ {T}_{\mathrm{s}\to \mathrm{r}} $ 和 $ {V}_{\mathrm{r}} $的程函方程总结.（c）在整个三维空间采样源-接收对构建训练数据集.（d）通过最小化与预测和已知速度值相关的损失函数进行网络训练.（e）通过传递用户定义的源-接收对检查神经网络输出（修改自Smith et al., 2020）

Figure 1. Overview of the processing workflow. (a) Neural network architecture composed of fully connected layers and residual blocks. Each residual block is composed of three fully connected layers with 512 neurons. ELU activations are applied on all hidden layers. (b) Summary of Eikonal equation for $ {T}_{\mathrm{s}\to \mathrm{r}} $ and $ {V}_{\mathrm{r}} $. (c) Sampling of source-receiver pairs across the 3-D volume to build the training data set. (d) Network training through the minimization of loss function relating predicted and observed velocity values. (e) Inspection of neural network outputs by passing user-defined source-receiver pairs (modified from Smith et al., 2020)

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图 2 （a）窄带技术原理示意图. （b）从源点开始的窄带拓展示例（修改自Rawlinson and Sambridge, 2004）

Figure 2. (a) The principle of the narrow-band method. (b) Example of how the narrow band evolves from a source point (modified from Rawlinson and Sambridge, 2004)

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图 3 EikoNet方法的走时计算结果. （a）、（b）和（c）依次代表走时的X-Y、X-Z和Y-Z切片

Figure 3. The traveltime result of the EikoNet. (a), (b) and (c) represent the X-Y, X-Z and Y-Z slices of the travel time

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图 4 均匀速度模型走时计算相对误差. （a）、（b）、（c）和（d）、（e）、（f）依次EikoNet走时计算相对误差和FMM走时计算相对误差的X-Y、X-Z和Y-Z切片

Figure 4. The relative error of the traveltime calculation of the homogeneous model. (a), (b), (c) and (d), (e), (f) represent the X-Y, X-Z and Y-Z slices of the relative error of the EikoNet and the relative error of the FMM

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图 5 EikoNet方法的走时计算结果. （a）、（b）、（c）和（d）、（e）、（f）依次代表速度模型和走时的X-Y、X-Z和Y-Z切片

Figure 5. The traveltime result of the EikoNet. (a), (b), (c) and (d), (e), (f) represent the X-Y, X-Z and Y-Z slices of the velocity model and the the travel time

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图 6 块状速度模型走时计算相对误差. （a）、（b）、（c）和（d）、（e）、（f）依次代表EikoNet走时计算相对误差和FMM走时计算相对误差的X-Y、X-Z和Y-Z切片

Figure 6. The relative error of the traveltime calculation of the block model. (a), (b), (c) and (d), (e), (f) represent the X-Y, X-Z and Y-Z slices of the relative error of the EikoNet and the relative error of the FMM

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图 7 EikoNet方法的走时计算结果. （a）、（b）、（c）和（d）、（e）、（f）依次代表速度模型和走时的X-Y、X-Z和Y-Z切片

Figure 7. The traveltime result of the EikoNet. (a), (b), (c) and (d), (e), (f) represent the X-Y, X-Z and Y-Z slices of the velocity model and the travel time

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图 8 层状速度模型走时计算相对误差. （a）、（b）、（c）和（d）、（e）、（f）依次代表EikoNet走时计算相对误差和FMM走时计算相对误差的X-Y、X-Z和Y-Z切片

Figure 8. The relative error of the traveltime calculation of the layered model. (a), (b), (c) and (d), (e), (f) represent the X-Y, X-Z and Y-Z slices ofthe relative error of the EikoNet and the relative error of the FMM

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图 9 EikoNet方法的走时计算结果.（a）、（b）、（c）和（d）、（e）、（f）依次代表速度模型和走时的X-Y、X-Z和Y-Z切片

Figure 9. The traveltime result of the EikoNet. (a), (b), (c) and (d), (e), (f) represent the X-Y, X-Z and Y-Z slices of the velocity model and the travel time

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图 10 棋盘格速度模型走时计算相对误差. （a）、（b）、（c）和（d）、（e）、（f）依次EikoNet走时计算相对误差和FMM走时计算相对误差的X-Y、X-Z和Y-Z切片

Figure 10. The relative error of the traveltime calculation of the checkerboard model. (a), (b), (c) and (d), (e), (f) represent the X-Y, X-Z and Y-Z slices ofthe relative error of the EikoNet and the relative error of the FMM from top to bottom

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