The Effectiveness and Application of the Gradient Sparse Regularization-Based Deconvolution Method

Abstract

Sparse constraint-based deconvolution can break through the limitation of the effective frequency band of seismic data and enable the acquisition of higher resolution data. Further, the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L_{0}$ </tex-math></inline-formula> -norm is the best measure of the sparsity of seismic data, and sparse deconvolution based on the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L_{0}$ </tex-math></inline-formula> -norm can lead to the acquisition of the sparsest solution. This method, which has the advantage of a simple solution form, has been widely used in iterative hard-threshold algorithms based on <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L_{0}$ </tex-math></inline-formula> -norm sparse deconvolution. However, with this method, it is difficult to select the appropriate threshold, and it has been demonstrated that selecting an inappropriate threshold significantly influences deconvolution. Therefore, to avoid the selection of an inappropriate threshold, we changed the conventional sparse regularization of the reflection coefficient to the adaptive sparse regularization of the reflection coefficient gradient. Further, via the iterative retention of the gradient of the reflection coefficient, the large gradient was gradually iterated to the small gradient of the weak signal, while avoiding the loss of weak signals and significantly improving the computational efficiency, accuracy, and adaptability of the method. Furthermore, both synthetic and field data indicated that this method is highly adaptable and possesses a good convergence speed. Additionally, the method showed high accuracy in extracting the amplitude and position of the reflection coefficient, and its antinoise performance was also good.