应用二维非均匀曲波变换压制地震随机噪声

由于野外地表条件及采集环境的影响，实际地震数据经常呈现不规则的空间采样，而常规的曲波变换去噪方法无法对非均匀空间采样的地震数据进行处理。为此，将非均匀快速傅里叶变换引入多尺度、多方向二维曲波变换，建立均匀曲波系数与空间非均匀采样地震数据之间的规则化反演算子，使用线性Bregman算法反演，在每次迭代过程中采用软阈值对曲波系数去噪，得到无噪声的均匀曲波系数，再进行常规二维曲波反变换，得到去噪后的地震数据。理论模型与实际资料的处理结果表明，该方法在将非均匀采样地震数据内插为均匀采样数据的同时，有效地压制了噪声干扰。

A random noise suppression with 2D non-uniform curvelet transform

Real seismic data are often non-uniformly sampled due to limits of field acquisition environment and terrain conditions.But conventional curvelet-based denoising cannot process non-uniform sampled and noisy data.We first introduce the non-uniform fast Fourier transform (NFFT) in the multi-scale and multi-directional curvelet transform,and construct the regularized inversion of operator that takes the uniformly sampled curvelet coefficients to non-uniformly data.Then we use linearized Bregman method for the inversion calculation,and adopt soft thresholds to remove noise of the curvelet coefficients in each iteration,and get the noise free uniform curvelet coefficients.Finally we perform the conventional inverse fast discrete curvelet transform (FDCT) and get denoised seismic data.Tests on synthetic and real data reveal that the proposed method can better suppress random noise when it interpolates non-uniformly sampled data to uniformly sampled data.