The knowledge of hidden resources present inside the earth layers is vital for the exploration of petroleum and hydrocarbons. However, the recorded seismic data is noisy and incomplete with missing traces that leads to misinterpretation of the earth layers. In this manuscript, we consider seismic data with Gaussian, non-Gaussian noise distribution, regular and irregular missing traces. We propose a method for simultaneous noise attenuation and reconstruction of the incomplete seismic data with attention based wavelet convolutional neural network (AWUN). The wavelet transform is used as pooling layer and inverse wavelet transform is used for upsampling layers to avoid information loss. The attention module is used to obtain weights for various feature channels with higher weights assigned to the more significant information. In addition, we propose to use hybrid loss function (logcosh + huberloss) to denoise and accurately reconstruct the seismic data. Moreover, the effect of various hyper-parameters in the training process of convolutional neural networks is studied. Further, we tested the performance of proposed method on synthetically generated data and field data examples. The quantitative results demonstrated that our proposed deep learning method has shown improved signal-to-noise ratio (SNR) and mean squared error (MSE) when compared to the existing state-of-the-art methods.

Seismic inversion is an approach to obtain the physical properties of the earth layers from the seismic data which aids in reservoir characterization. In seismic inversion, spatially variable physical parameters such as impedance ( $Z$ ), wave velocities $(V_{p}$ , $V_{s})$ and density can be determined from the seismic data. Among these, impedance is an important parameter used for lithology interpretation. However, the inversion problem is nonlinear and ill-posed due to unknown seismic wavelet, observed data band limitation, and noise. This requires complex wave equation analysis, prior assumptions, human expert effort, and time to analyze the seismic data. To address these issues, deep learning methods were deployed to solve the seismic inversion problem. In this paper, we develop a deep learning framework with an attention module for seismic impedance inversion. The relevant features from the seismic data are emphasized with the integration of the attention module into the network. First, we train the attention-based deep convolutional neural network (ADCNN) by supervised learning with pre-defined acoustic impedance (AI) labels. Next, we train the ADCNN in an unsupervised way with the physics of the forward problem. In the proposed method, the predicted AI is used to calculate the seismic data (calculated seismic) and error is minimized between the input seismic data and calculated seismic data. Unsupervised learning has an advantage when the labeled data is inadequate. The proposed network is trained with Marmousi 2 dataset, and the predicted experimental results show that the proposed method outperforms in comparison to the existing state-of-the-art method.

We consider a two-way relaying (TWR) system over Rayleigh fading channels. An accurate closed form expression for its outage performance is derived assuming a fixed-gain relay. Unlike previous works that consider interference only at the relay or at the terminals, we assume interference at all three terminals of the system. Computer simulations demonstrate that the derived expressions are accurate at low and medium SNRs.

In seismic data processing, denoising is one of the essential steps to identifying the earth’s subsurface layer information. The noise present in the seismic data is categorized into two types: random and erratic noise. The random noise is distributed uniformly over the seismic data. The erratic noise attenuation is always challenging due to the unknown distribution of high-amplitude peaks over seismic data. The existing double sparsity dictionary learning (DSDL) method performs with analytical and adaptive transforms; both the transforms include iterative algorithms with K-singular-value decomposition (SVD); it is computationally costly, and the dictionary is initialized with trained data. To address these limitations, we propose a novel method of dictionary learning with double regularization (DLDR) to denoise both random and erratic noise from seismic data. In double regularization, we used with $\ell _{1}$ -norm and nuclear norm. The denoised data is applied to the alternating direction method of multipliers (ADMMs) to improve denoising while preserving the signal features from seismic data while reducing the computational cost. We evaluated the performance of the proposed method using signal-to-noise ratio (SNR), mean squared error (MSE), and local similarity map. The numerical results demonstrated that the proposed method resulted in higher SNR, lower MSE, and less signal leakage from seismic data. The method gives precise interpretation from the denoised seismic data.