Seismic Data Reconstruction Based On Adaptive Sparse Inversion

Sparse transforms are tools for sparse representation and play an important role in seismic signal processing steps such as prestack noise attenuation and data reconstruction.We can save lots of storage and computational expense under sparse domain,especially for high dimensional and large scale data.Analytic sparse transforms such as Fourier,wavelet and curvelet transforms,are often used to represent seismic data.There are situations,however,where complex data requires adaptive sparse transform methods whose basis functions are determined via adaptive methods rather analytic sparse transform.We study the adaptive methods in the data domain and the frequency domain and applications in seismic data reconstruction.To deal with the computational burden of adaptive methods for high dimensional seismic data,we propose an application of the data-driven tight frame(DDTF)method to noise suppression and reconstruction of seismic data.DDTF is a fast dictionary learning method with tight frame property and it derives the model from the data itself in an optimum sparse representation manner.We apply DDTF to high dimensional seismic data denoising and reconstruction and it achieves higher efficiency than traditional dictionary learning methods meanwhile obtains similar result.However for large scale and high dimensional seismic data,the DDTF method still results in high computational expense,since the huge training set leads to low efficiency in dictionary training.To accelerate the filter bank training process in DDTF,we study the patch selection method under certain sample size and propose a new Monte Carlo patch selection method.Every sample contributes the same to the dictionary training,however,we care more about the detailed structures.If the samples with detailed structures dominate the training set,the trained dictionary will sparsely represent the detailed structures.So we suppose that patches with higher variance contain more information related to complex structures,and should be selected into the training set with higher probability.Numerical results using this Monte Carlo DDTF method improve the efficiency a lot and surpass random or regular patch selection DDTF when the sizes of the training sets are the same.Finally,under the band-limited assumption of seismic spectrum,we introduce a new adaptive decomposition method in frequency domain for seismic data,termed variational mode decomposition(VMD).The resulting VMD based noise attenuation method is equivalent to applying a Wiener filter on each decomposed mode,which is achieved during the decomposition progress.Numerical results show that the VMD method achieves better result than the empirical mode decomposition method.To further utilize the information across the frequency slices,this paper proposes a new decomposition algorithm for seismic data based on a linear band-limited priori information on the Fourier spectrum,called geometry mode decomposition(GMD).By considering the relationship between different frequency slices,GMD adaptively obtains the geometry parameters in the data and is equivalent to an adaptive transform in the frequency domain.GMD is solved by alternatively pursuing the geometry parameters and the corresponding modes in the Fourier or Radon domain.We applied GMD to seismic events splitting,noise attenuation,interpolation,and demultiple.The results show that our method is a promising adaptive tool for seismic signal processing.