Internal multiples seriously affecting seismic inversion and imaging need to be suppressed. To suppress internal multiples, we propose a self-supervised deep learning method based on a local orthogonalization constraint (SDL-LOC). The self-supervised deep learning (SDL) consists of one multi-attention-based U-net (MA-net), two input data, and one output data. The predicted internal multiples (PIMs), obtained by the adaptive virtual event (AVE) method, and the original data are used as input data. SDL utilizes the excellent nonlinear optimization capability of MA-net to transform PIMs into the estimated true internal multiples that are the output data of SDL. Finally, the de-multiple result can be obtained by subtracting the output data from the original data. The proposed SDL-LOC uses the local orthogonalization constraint (LOC) function as part of the total loss function. The LOC function can help SDL to correctly maps PIMs into the true internal multiples with the right amplitudes and phases and prevent the output data from containing residual primaries and leaked internal multiples. Our proposed SDL-LOC method does not require true primaries or true internal multiples as the training dataset. Therefore, our proposed method has a wide range of applications and can well solve the problem of missing training datasets. We use the synthetic and land field data examples to demonstrate that our proposed method has a good internal multiple suppression effect.

In seismic data processing, the suppression of internal multiple is a challenging direction. To suppress internal multiples, we propose an unsupervised deep neural network (DNN) method based on adaptive virtual events (AVEs) and joint constraints of multi-DNNs (JCMDNNs). First, we use an AVE method to obtain predicted internal multiples by convolution and cross correlation. The predicted internal multiples can well calibrate true internal multiples and provide good prior information. Second, we use the unsupervised DNN (UDNN) to map the predicted internal multiples to the estimated true internal multiples. Finally, the demultiple results can be obtained by subtracting the estimated true internal multiples from the data containing internal multiples. Three DNNs, one input data, six output data, and six pseudo-labels (PLs), are combined into the base learners and auxiliary learners of UDNN. UDNN uses the nonlinear optimization ability of DNNs to map predicted internal multiples to true internal multiples through the JCMDNNs. Three auxiliary learners correct the outputs of the base learners to reduce the nonlinear mapping deviation of UDNN. Using JCMDNNs by combining all base learners and auxiliary learners is called ensemble learning. Our proposed JCMDNN method does not need true internal multiples and true primaries as the input and output data, which solves the problem of missing training datasets and has wide use ranges. The effectiveness and superiority of our proposed method to suppress internal multiples are demonstrated through two synthetic and one field data examples.

Random noise suppression can greatly improve the signal-to-noise ratio (SNR) of seismic signals. To suppress random seismic noise, we propose an unsupervised deep neural network (UDNN) method based on the local cross-correlation (LCC) loss function and ensemble learning. UDNN with two base learners mainly consists of one input data, two deep neural networks (DNNs), and two output data. The proposed UDNN based on the LCC loss function and ensemble learning (UDNN-LCCEL) method takes full advantage of the nonlinear mapping capabilities of DNNs and maps noisy data into effective noise-free signals by minimizing the total loss function. The total loss function includes the LCC and mean-absolute-error (MAE) loss functions. LCC calculates the local correlation or orthogonalization between output data and the removed noise. By reducing the value of the LCC loss function, we automatically reduce the residual noise and leakage of effective signals in the output data, thus avoiding the overfitting of UDNN. UDNN-LCCEL combines the advantages of two DNNs to obtain ensemble denoised results by ensemble learning. The biggest advantage of our proposed UDNN-LCCEL method is that it does not need to use noise-free data as label data, which can well solve the problem of missing training datasets. The synthetic and field data examples are used to demonstrate that UDNN-LCCEL can achieve good random noise suppression effectiveness.

By increasing the source density, the blended data can significantly improve the seismic data quality. However, the blended data cannot be directly used in the subsequent seismic processing process, and it is necessary to separate the useful signals from the crosstalk noise. For a high-density acquisition with the denser shot coverage survey (DSCS), we propose an unsupervised deep learning (UDL) method to directly deblend the blended data in the common shot gather (CSG). Both the useful signal and the crosstalk noise in the pseudo-deblended data (PDD) are continuously coherent in CSG. By minimizing the final total loss function, the similar coherent signals from the PDD of the main and second sources are extracted using the proposed UDL method. The UDL consists of two U-nets, which extract similar features from the PDD of the main and second sources in the training stage, and directly obtain the deblended results in the test stage. The original unblended data, which may be needed for supervised learning, are not available from the actual collected blended data. However, the proposed UDL method does not require the original unblended data as training data, which solves the lack of training data. The proposed UDL method can be applied to the CSG without providing the delay time and the blending operator, so it has more flexibility. Synthetic data and field data examples show that the proposed UDL method can effectively and directly deblend the blended data in CSG under DSCS.

The simultaneous source acquisition method, which excites multiple sources in a narrow time interval, can greatly improve the efficiency of seismic data acquisition and provide good illumination. However, the simultaneous source data, also known as the blended data, contain the crosstalk noise from other sources, which brings trouble to the subsequent processing flow. Therefore, an effective deblending method for the simultaneous source data is needed. In order to suppress crosstalk noise, an iterative deblending method using a deep neural network (DNN) trained in the common shot gather (CSG) is developed in this article with the double-blended simultaneous source (DBSS) data being the input data and the blended CSG data being the label data. The proposed training method can not only solve the problem of difficult acquisition of the label data but also make the DNN applicable to any complex formation conditions without considering whether the DNN has the generalization ability of deblending in different work areas. In the test phase, the trained DNN is embedded into the iterative separation framework to deblend the data in the common receiver gather (CRG), which can achieve convergence in a few iterations and achieve a better separation effect. The synthetic and field data examples are tested to verify that the proposed method can effectively suppress the crosstalk noise when deblending the simultaneous source data.

Seismic internal multiples are the key factors affecting the accuracy and reliability of velocity analysis and migration. The removal of internal multiples is a challenging direction. To effectively remove the internal multiples from the seismic data, we propose the unsupervised deep neural network (DNN) combined with the adaptive virtual events (AVEs) method. First, we use the AVE method to get the predicted internal multiples, which can calibrate the true internal multiples in the original data, also called the full wavefield data. Second, the unsupervised learning with the DNN is used as a nonlinear operator to minimize the difference between the estimated internal multiples and original data. The trained DNN can obtain the estimated internal multiples through the predicted internal multiples, thereby completing the suppression of the internal multiples. Since our proposed unsupervised learning is essentially an optimization process, it does not require true primaries as the label data to participate in the training process for the DNN. Therefore, our proposed method can deal with the problem of lack of training set and would have some good practical application value with low computational cost. The effectiveness and efficiency of our proposed method are verified through two sets of synthetic data and one land field data examples.

Surface-related multiples are generally removed as noise. To suppress surface-related multiples, we propose an unsupervised deep neural network approach based on ensemble learning (UDNNEL). The unsupervised deep neural network (UDNN) has excellent nonlinear mapping ability, which maps the predicted surface-related multiples to true surface-related multiples, thereby completing the separation and estimation of multiples and primaries. UDNN consists of three deep neural networks (DNNs), one input data, six outputs, and six pseudo-labels (PLs). In practical use, input data are the predicted surface-related multiples, PLs consist of full-wavefield data and 0 matrices, and outputs are the desired results of estimated true surface-related multiples and differences between these desired results. Input data, one DNN, and corresponding output data are combined into a single base learner. Each base learner corrects amplitudes and phases of the predicted surface-related multiples and maps predicted multiples to true surface-related multiples under the minimization of the total loss function. The principle ensures that our UDNNEL method does not need true primaries or true multiples as training data and solves the problem of missing training datasets. Ensemble learning combines the advantages of three base learners and integrates the nonlinear optimization capabilities of three DNNs to achieve better multiple suppression effectiveness than a single base learner. Therefore, UDNNEL is better than UDNN based on a single base learner (UDNNSBL). Two synthetic data examples verify that our proposed method has good surface-related multiple suppression effectiveness. Another field data example demonstrates that our proposed method can efficiently suppress multiples under complex conditions.