Seismic Random Noise Attenuation Based On Modal Decomposition Technique

Random noise attenuation of seismic data is a hot and difficult problem in the field of seismic data processing.Effective removal of random noise interference from obscuring observations improves signal-to-noise ratio and resolution is an important premise of forward modeling and inversion and geological interpretation.In this paper,the generalized sparse mode decomposition technique applied to the task of seismic random noise attenuation.Some efficient algorithms have been proposed,such as complete ensemble empirical mode decomposition with adaptive noise and its combined noise attenuation strategy are proposed to 2D seismic data denoising;The functional process of 1D variational modal decomposition is studied.An adaptive variational modal decomposition method in the frequency domain is introduced,and its two-dimensional complex expansion form is proposed to apply to 2D and 3D seismic data denoising.The main works can be summarized as follows:(1)An complete ensemble empirical mode decomposition with adaptive noise method(CEEMDAN)and its combined noise attenuation strategy are proposed.Complete ensemble empirical mode decomposition(CEEMD)can better solve the problem of noise pollution in ensemble empirical mode decomposition(EEMD)by adding positive and negative pairwise auxiliary noise,but improper parameter settings will lead to erroneous components.The number of intrinsic mode function(IMF)is inconsistent.A new modal decomposition method CEEMDAN is proposed by transforming the auxiliary noise form and the transformation decomposition process.The computational efficiency of this method is 10 times that of EEMD and 6 times that of CEEMD,with high decomposition accuracy and complete features.In the denoising task,directly discarding the high-frequency IMFs will result in the loss of the effective energy of high-wavenumbers.In this paper,CEEMDAN and the synchronous compression wavelet transform(SWT)jointly construct a multi-step attenuation strategy to avoid the loss of some high-frequency energy.In the noise attenuation experiments of theoretical models and field data,it is verified that the joint multi-step seismic random noise attenuation strategy has strong denoising effect and energy holding ability.However,the recursive iterative filtering and decomposition process is still used in CEEMDAN methods.The non-stationary seismic signal extreme point interpolation and envelope calculation process still takes a long time,and this is a major limitations when dealing with multi-dimensional and multi-scale seismic data.(2)To deal with the computational burden of the CEEMDAN method,a new nonlinear,non-recursive fully adaptive temporal sequence decomposition algorithm-Variational Mode Decomposition(VMD)is introduced.The decomposition process of the VMD method can be considered as solving the problem of the optimal solution of the functional,with the sum of the estimated bandwidths of each band-limited intrinsic mode function(BIMF)being the minimum.By introducing an augmented Lagrange function,and the alternate direction method of multipliers is used to seek the optimal solution of the variational functional to achieve signal decomposition.During the iterative solution process,the frequency center and bandwidth of each component are constantly updated.The Wiener filter feature is available during the update of BIMF.Therefore,the VMD can be regarded as the multiplexing of the Wiener filter and the generalization of the adaptive order.Then,the 1D VMD is extended to the 2D generalized form of the frequency domain.Finally,the theoretical and field data processing examples show that the VMD method has excellent noise attenuation and amplitude maintaining performance,as well as high computational efficiency,which can satisfy the processing requirements of high-dimensional and large-scale seismic data.