An acoustic velocity inversion method based on convolutional autoencoder-Fourier neural operator

[Background] Seismic wave inversion serves as an effective method for obtaining the characteristics of structures, lithology, and physical properties of subsurface media using the arrival times, amplitude, and waveforms of seismic waves. Seismic inversion methods based on wave equations iteratively update model parameters using forward modeling. This generally involves extensive numerical simulations and optimization calculations, requiring large quantities of computational resources and time. In recent years, neural operators for deep learning, represented by the Fourier neural operator (FNO), have gained widespread attention. However, the original FNO structure fails to effectively learn the wavefield information with sharp changes in geological structures in the seismic wave inversion of complex media, leading to low accuracy of inversion results. [Objective and Methods] To enhance the accuracy and generalization performance of FNO in learning seismic wavefield information under complex geological models, this study developed a novel acoustic velocity inversion method—Fourier neural operator based on convolutional autoencoder (CAE-FNO), which utilized an encoder for feature extraction and performed efficient training based on FNO to effectively capture the fine features of the seismic wavefield and improved prediction accuracy. During the network training, the CAE-FNO method progressively reduced the size of the Fourier mode, thus effectively reducing the number of network parameters while enhancing the generalization capability of the network. [Results and Conclusions] The numerical experiments on homogeneous, heterogeneous, layered, and Marmousi2 models demonstrate that the CAE-FNO method exhibited significantly higher inversion accuracy than FNO and its variants UFNO and UNO. The experiments on the homogeneous model revealed that the velocity inversion results of the CAE-FNO method had a relative error of 1.3% and those of UFNO, UNO, and FNO exhibited relative errors of 1.7%, 2.3%, and up to 10.1%, respectively. In the experiments on the heterogeneous model, CAE-FNO yielded accurate inversion results of geological structures and velocity change positions, whereas UFNO and UNO exhibited higher errors for zones with sharp velocity fluctuations. During the experiments on the layered model, CAE-FNO clearly distinguished minor velocity changes between layers, while FNO failed. For both smooth zones and zones with abrupt changes in the Marmousi2 model, CAE-FNO exhibited higher accuracy in capturing irregular interfaces with velocity changes than UFNO and UNO, while FNO failed to effectively handle the abrupt changes in velocity and detail changes in these zones. Therefore, the CAE-FNO method, demonstrating small loss functions and high accuracy, enjoys advantages in the inversion of complex media, providing a novel research philosophy for seismic inversion.