VSP Upgoing and Downgoing Wavefield Separation: A Hybrid Model-Data-Driven Approach

The separation of upgoing and downgoing waves in vertical seismic profiling (VSP) data is crucial for subsequent imaging, interpretation, and inversion. The interweaving of upgoing and downgoing waves and the presence of noise complicate the entire wave field, making it difficult to separate upgoing and downgoing waves. Various model-driven separation methods including low-rank approximation (LRA) and data-driven methods have achieved promising results. However, the performance of pure model-driven methods, such as F-K filtering and Radon transform, rely on domain transformation sparse representation for both upgoing and downgoing wavefield. Additionally, pure data-driven methods require a large number of precisely separated signals as training samples, which is a nontrivial task. To overcome these difficulties, this article proposes a model-data-driven VSP wavefield separation framework that iteratively completes the task of wavefield separation in an unsupervised manner. The key to this model is to use the powerful feature representation capability of the deep convolutional autoencoder (DCAE) to model the downgoing waves and use LRA to model the upgoing waves. By accurately modeling the upgoing and downgoing waves, we integrate the model-driven and data-driven methods together, while protecting both the upgoing and downgoing waves, and inheriting the advantages of the DCAE and LRA methods. Subsequently, we also proposed an alternating minimization optimization strategy to optimize the parameters of the model and iteratively obtain high-quality solutions. Comparative experiments on synthetic data and real data show that our method can achieve effective separation results while suppressing Gaussian noise.