Seismic attenuation, parameterized as quality factor Q, holds great significance in enhancing seismic resolution and reservoir characterization. Most methods for estimating Q values are performed in the frequency domain, however, the frequency spectrum of the seismic data may usually be influenced by the closely adjacent reflections and the seismic noise, leading to an unreliable Q estimation. To address this challenge, we propose a kernel-based regression method for Q estimation on manifolds. This supervised learning model computes the kernel function on the tangent space of the manifold. We apply this method to Euclidean space, Spherical manifold, and Wasserstein spaces, and provide a detailed comparison of their performance. Our experimental results using synthetic data demonstrate a significant improvement in both robustness and accuracy compared to conventional methods. Furthermore, the validation of our methodology using real data confirms its effectiveness and superiority. Notably, our method on Wasserstein space consistently outperforms others in all experiments.
