基于物理信息驱动神经网络的三维初至波旅行时计算方法

在地震勘探中，初至波旅行时的精确求取是偏移成像和旅行时反演等处理技术的重要基础。基于程函方程的有限差分算法在地震波旅行时求取中展现出良好的效果，但需要付出巨大的计算成本，尤其是对多震源、高密度网格的旅行时计算。为此，提出了一种基于物理信息驱动神经网络(PINN)的三维程函方程旅行时求取算法，由三维程函方程及其物理条件信息构成损失函数，再通过最小化该损失函数训练神经网络，最终输出满足程函方程的旅行时结果。不同速度模型的数值模拟实验结果表明，所提方法相对于传统算法具有更高的计算效率和更高的精确度。

3D traveltime calculation of first arrival waveusing physics-informed neural network

In seismic exploration, accurate calculation of the traveltime of the first arrival wave is an important basis for processing techniques such as migration imaging and traveltime inversion. The finite-difference algorithms based on an eikonal equation have shown excellent effect in solving seismic wave traveltime. However, It requires huge computational consumption, especially for calculating the traveltime of multiple-source and high-density grids. This paper develops an algorithm with a 3D eikonal equation for calculating traveltime based on a physics-informed neural network (PINN). Specifically, the algorithm trains the neural network by minimizing a loss function composed of 3D eikonal equation and other physical conditions information and finally outputs a traveltime satisfying the eikonal equation. Numerical simulation experiments based on different velocity models show that the proposed method has higher computational accuracy and efficiency than traditional finite-difference algorithms.