Seismic data processing plays a pivotal role in extracting valuable subsurface information for various geophysical applications. However, seismic records often suffer from inherent random noise, which obscures meaningful geological features and reduces the reliability of interpretations. In recent years, deep learning methodologies have shown promising results in performing noise attenuation tasks on seismic data. In this research, we propose modifications to the standard U-Net structure by integrating dense and residual connections, which serve as the foundation of our approach named the dense and residual (DARE U-Net) network. Dense connections enhance the receptive field and ensure that information from different scales is considered during the denoising process. Our model implements local residual connections between layers within the encoder, which allows earlier layers to directly connect with deep layers. This promotes the flow of information, allowing the network to utilize filtered and unfiltered input. The combined network mechanisms preserve the spatial information loss during the contraction process so that the decoder can locate the features more accurately by retaining the high-resolution features, enabling precise location in seismic image denoising. We evaluate this adapted architecture by applying synthetic and real data sets and calculating the peak signal-to-noise ratio (PSNR) and structural similarity index measure (SSIM). The effectiveness of this method is well noted.

In the traditional framework of 3D controlled-source electromagnetic (CSEM) modeling, either the field formulation or the coupled potential formulation is implemented. We have developed an improved algorithm that can calculate the 3D CSEM responses based on a joint application of the secondary field and secondary coupled potential formulations. The vector finite-element method is implemented for the discretization of the curl-curl equation of the secondary field. The vector and nodal elements are implemented simultaneously for the discretization of the coupled potential formulation. We use the stiffness matrix resulting from the coupled potential formulation to construct an efficient preconditioner, which is used for the solution of the linear system of equations obtained based on the secondary field formulation. The linear system of the equations could be solved efficiently by the quasiminimum residual method within several hundred iterations with the constructed preconditioner. We compare different modeling schemes to calculate the CSEM responses for a horizontally layered earth model excited by an electric dipole and find that the iteration process of the improved algorithm converges faster on average than other modeling schemes for the frequency band considered. Thus, the least computation time can be obtained over the frequency band for the improved algorithm compared with other modeling schemes, with the same level of accuracy reached. We further verify the efficiency of the algorithm through a small-scale 3D earth model excited by a magnetic dipole. Finally, we illustrate the performance of the algorithm with two 3D subsurface models, including a land-based model and a marine disk model. By comparison with published work, it is illustrated that our algorithm can efficiently calculate accurate land-based and marine CSEM responses with the new constructed preconditioner implemented.