一种融合模型和数据的全波形反演方法
A Full Waveform Inversion Method Combining Model and Data

全波形反演算法(Full Waveform Inversion, FWI)是一种强大的地球物理成像技术，它通过迭代最小化模拟和观测地震图之间的失配来生成高分辨率地下模型。近年来，随着机器学习方法和深度学习方法的发展，研究者提出了一些基于机器学习和深度学习的全波形反演技术。其中有一种融合模型和数据全波形反演方法(physics-informed training-free frameworks for two-dimensional FWI, FWIGAN)引人瞩目，其使用生成对抗网络的思想与物理学相结合，使用无监督学习的方式来自动地估计出符合物理学规律的模型，但其网络生成图像的质量及稳定性还有待提升。本研究在此方法上引入零中心梯度惩罚(Zero-centered gradient penalty, 0-GP)，它是一种用于生成对抗网络的正则化技术，通过将判别器推向理论最优判别器来提高网络的稳定性和样本质量。结合正则化的新方法称之为(Full Waveform Inversion with Zero-Centered Gradient Penalty, FWILP) FWILP。经过实验，证明了FWILP可以提高模型质量和收敛速度，使得网络更加具有稳定性。
Full Waveform Inversion (FWI) is a powerful geophysical imaging technique that generates high-resolution underground models by iteratively minimizing the mismatch between simulated and observed seismic waveforms. In recent years, researchers have proposed some machine learning and deep learning-based FWI techniques with the development of these methods. One such method is the physics-informed training-free frameworks for two-dimensional FWI (FWIGAN), which combines the idea of generative adversarial networks with physics to automatically estimate physically consistent models using unsupervised learning. However, the quality and stability of the generated images still need to be improved. In this study, we introduced the zero-centered gradient penalty (0-GP) to FWIGAN as a regularization technique for generative adversarial networks. This technique improves the stability and sample quality of the network by pushing the discriminator towards the theoretically optimal discriminator. The new method, combining regularization, is called Full Waveform Inversion with Zero-Centered Gradient Penalty (FWILP). Experimental results show that FWILP can improve model quality and convergence speed, making the network more stable.