基于曲波变换的地震数据去噪方法

Noise elimination method based on curvelet transform

（1.中国石油川庆钻探公司地球物理勘探公司,四川成都610213;2.西南石油大学资源与环境学院,四川成都610500）

Geophysical Prospecting Company, Sichuan-Changqing United Drilling & Exploration Engineering Company, CNPC, Chengdu 610213, China

地震记录中的随机噪声频带较宽，采用常规的去噪方法效果不理想；小波变换去噪方法虽然可以压制随机噪声，但会损伤有效信号，且去除二维信号中的随机噪声时存在一定的局限性。针对此局限性，Candè提出了脊波变换，但对于整幅图而言，脊波变换的效果并不理想。由此，发展了曲波变换，即基于小波变换和脊波变换的多尺度几何分析方法。该方法能够表示具有方向性的线性奇异边缘，克服了小波变换在表达图像边缘的方向特性等方面的内在缺陷。曲波变换结合了脊波变换的各向异性特点和小波变换的多尺度特点，可以在压制随机噪声的同时保护有效信号，达到更好的去噪效果。仿真数据和实际资料去噪结果验证了曲波变换压制随机噪声的可行性及其效果。

The random noise has a broad band in seismic record, the conventional denoise method can not get ideal result. Wavelet transform de-noise method will damage effective signals while pressing random noise and has some limitations in pressing random noise in 2-D signals. Aiming at the limitations, Candè proposed ridge-let transform. But for the whole profile, the ridgelet transform can not obtain ideal result either. Therefore, the curvelet transform is developed, which is a multi-scale geometric analysis method based on wavelet transform and ridgelet transform. The method can display the directional linear singularity edge, and overcome the inherence defects of wavelet transform in showing the directional characteristics of graph edge. The curvelet transform in combination with anisotropy characteristic of ridgelet transform and multi-scale characteristic of wavelet transform can protect effective signals while press random noise and achieve better de-noise result. The de-noise result of simulation data and actual data shows that the curvelet transform is feasible.