Simultaneous Source Deblending Using Modified Dictionary Learning And Sparse Approximation Approach

The simultaneous source acquisition method also known as the blended acquisition was introduced as a solution to either low data quality or the high cost of acquiring conventional seismic data.The blended acquisition method incorporated two approaches to overcome the problems of the conventional acquisition mentioned above.They are:to either reduce source firing time interval resulting in reduced cost or increase the number of sources fired within the conventional source firing time interval thereby increasing the data quality.However,the solution proffered by this method also comes with its challenge of overlapping source or source interference that needs to be removed before the traditional seismic data processing can be applied.Several authors have proposed various means of removing the source interference noise from blended data with different degrees of success.Two major methods are applied to handle the problem of source interference noise also known as blended noise and they are:(ⅰ)direct imaging which involves direct migration of the blended data with some constraint to suppress the interference,and(ⅱ)source separation.However,the dictionary learning and sparse approximation method using the K-Singular Value Decomposition(KSVD)algorithm has played a tremendous role in the simultaneous-source separation process also known as deblending over the past decade.Just like most optimization methods,conventional dictionary learning utilizes some constraints in its sparse approximation stage which require the knowledge of the sparsity or cardinality of the data and the noise variance.However,the determination of sparsity or noise variance can be tricky and sometimes unknown,especially in seismic field data.Therefore,we propose an alternative constraint for the KSVD algorithm that does not rely on the conventional sparsity or noise variance constraint but utilizes the statistical coherence present in the noise removed from the noisy data relative to the dictionary learned from the noisy data for simultaneous-source separation.We refer to this approach as coherence dictionary learning which is a modification to the orthogonal matching pursuit algorithm by using coherence as a constraint.Simultaneous-source data acquired using a blending structure designed with random time-dithering of sequential shooting to guarantee the blending noise is adequately random is used to test the effectiveness of the proposed coherence dictionary learning method.The procedure for the coherence dictionary learning is the same as the conventional KSVD methods which are:(ⅰ)extract two-dimensional overlap patches of the blended common receiver gather to train the dictionary,(ⅱ)solve their maximum aposteriori(MAP)as a pursuit that aims to get their sparse representation in a learned dictionary,and(ⅲ)average the overlap patches to reconstruct the clean data.Hence,the difference in our approach occurs in stage two above where the traditional constraint of the KSVD algorithm is replaced with the coherence constraint.Thus,without the prior knowledge of the noise level or the sparsity of the data,the solution that minimizes the l0-norm of the sparse approximation problem can easily be achieved by our proposed method.This is particularly very important in simultaneous source field data where noise level and data sparsity cannot be accurately determined.We applied our method to both synthetic and field simultaneous source data and the results with those obtained with the classic KSVD dictionary learning methods.The results show the coherence-constrain dictionary learning achieves better data recovery and blending noise removal than the classic KSVD algorithm.Apart from improved deblelnded data by the coherence-constrain dictionary learning,the computational time is also significantly lesser than the traditional KSVD methods.Meanwhile,the KSVD and its numerous hybrid methods were a state-of-the-art method in data denoising until recently,with the advent of the likes of convolutional neural network(CNN),deep convolutional neural network(DNN),etc.have been proven to be a better alternative.Therefore,we aim to find the means to enhance the KSVD method to compete favorably with these trailblazing methods.Even with the knowledge of the appropriate constraints,obtaining the exact KSVD for each patch of the data has been one of the major drawbacks of the K-singular value decomposition approach.This is because the KSVD method only utilizes the first update.The subsequent update cannot be achieved because the noise level is unknown after the initial modification.However,several updates are believed to guarantee a better result.Hence,it is assumed that a far better result can be achieved only if the KSVD parameters can be calibrated in a supervised manner.Therefore,the KSVD denoising steps are redesigned into a differentiable and learnable computational scheme that is capable of training the parameters for each of the data patches while it retains the dictionary learning essence.The learnable version of the Iterative Soft Thresholding Algorithm(ISTA)was used.This supervised learning which we called learned-KSVD(LKSVD)was carried out in the form of deep learning using the Multi-Layer Perceptron(MLP).The network involves seven(7)hidden layers with the Rectified Linear Unit(ReLU)activation function except for the last layer which uses the Adaptive Moment Estimation(Adam)optimizer.This method was also tested on both synthetic and field simultaneous-source data,and the result,as expected,significantly outperforms the classic KSVD methods.At the same time,when compared with the DNN,our method shows a slightly improved outcome at both signal recovery and noise attenuation.However,the LKSVD method has a higher computational time than both the classic KSVD and the DNN methods.