Seismic Data Denoising Based On Advanced Curvelet Transforms And Low Rank Minimization

A higher quality of seismic data processing is required because of increasing difficulty of oil and gas exploration and more complexity of the exploration targets.However,there is a variety of noise in seismic data,such as random noise,ground roll and so on,which reduces the signal-to-noise ratio of seismic data,brings great difficulties to velocity analysis and migration imaging,and seriously affects the authenticity and reliability of imaging.Therefore,denoising is an important step to provide high quality,high signal-tonoise ratio and high resolution of seismic data.The methods of seismic data denoising are mainly divided into two categories: sparse transform and low rank optimization.Based on these two kinds of research methods,we make full use of characteristics between noise and reflections in seismic data,preserve amplitude of reflections while removing noise.The specific research contents and work results are as follows:Firstly,with the development of multi-scale geometric analysis,curvelet transform has become an important tool of sparse representation of seismic data.An advanced curvelet transform,i.e.,synchrosqueezed curvelet transform is introduced,which adds synchrosqueezed transform to traditional curvelet transform.So the synchrosqueezed curvelet transform not only inherits the advantages of curvelet transform,but also solves the tailing phenomenon in curvelet domain,which accurately estimates instantaneous frequency and sharpens the time-frequency spectrum.According to the difference of frequency between ground roll and reflections,we apply instantaneous frequency which is extracted by synchrosqueezed curvelet transform and use clustering method further to decompose different components of ground roll and reflection in order to suppress ground roll.Compared with traditional curvelet thresholding method and f-k fan filtering method,denoising method based on synchrosqueezed curvelet transform performs better on denoised results of both synthetic and field seismic data.Secondly,because basis elements of traditional curvelet transform are fixed,they can not represent the data adaptively.Another advanced curvelet transform,empirical curvelet transform,is introduced for an adaptive curvelet transform.It can be used to segment f-k spectrum adaptively according to data.Depending on low frequency,low velocity characteristics of ground roll,ground roll and reflection locate on different supports of frequency spectrum.We utilize empirical curvelet transform to adaptively decompose different components of ground roll and reflections,and combine with singular value decomposition further.Numerical results show that denoising method based on empirical curvelet transform can completely suppress ground roll while retaining the energy of reflections.Finally,considering that high redundancy and similarity of adjacent seismic records in a line survey,random noise removal algorithm joint seismic line survey based on low rank minimization is proposed.Different from reformed low rank matrix by Hankel transform,we extract similar blocks from different shot gathers in a line survey to rearrange into a low rank matrix.The addition of random noise increases the rank of matrix.So the denoising problem is transformed into a mathematical low rank minimization.In order to avoid the operation cost of singular value decomposition,orthogonal rank-one matrix pursuit algorithm is used to solve the corresponding optimization problem,thus removing random noise.Synthetic data and field data show that the proposed method outperforms the state-of-the-art f-x deconvolution method and f-x singular spectrum analysis method.