基于Seislet域分数阶阈值去噪算法的地震资料去噪

相较于由图像领域发展的去噪算法,Seislet阈值去噪算法更好适用于地震数据的去噪处理,但在Seislet阈值去噪算法中,常规硬阈值函数在阈值处存在断点,软阈值函数处理得到的系数与原有系数之间存在恒定偏差,且传统阈值确定准则难以适用于Seislet域。为此,将Riemann-Liouville分数阶积分理论应用到阈值函数中,推导出分数阶阈值函数;再根据地震数据在Seislet域低尺度中有效信号分量远多于高尺度中有效信号分量的特点,提出了一种适用于Seislet域的尺度加权阈值;最后将分数阶阈值函数、尺度加权阈值和Seislet稀疏变换相结合,得到Seislet域分数阶阈值去噪算法。人工合成含噪地震记录和实际地震资料测试结果表明:常规硬阈值和软阈值去噪算法虽然能够在一定程度上压制噪声,但压制效果并不明显,且容易损伤与噪声差异较小的有效信号;分数阶阈值去噪算法较好地克服了硬阈值和软阈值去噪算法的缺点,能够有效压制地震资料中的随机噪声,减少了有效信号的损失,提高了地震资料的信噪比。

The seislet threshold denoising algorithm is more suitable for seismic data as compared to the denoising algorithm developed by the image field.However,in the seislet algorithm,the conventional hard threshold function has breakpoints at the threshold value.There is constant deviation between the original coefficients and the coefficients processed by the soft threshold function;the traditional threshold determination criterion is difficult to apply to the seislet domain.Therefore,the Riemann-Liouville fractional integral theory was applied to the threshold function to derive the fractional threshold function.Because the effective signal components in the low-scale seislet domain were greater than those in high-scale seismic data,a scale-weighted threshold was proposed for the seislet domain.Finally,a fractional threshold algorithm in the seislet domain was obtained by combining the scale-weighted threshold in the seislet domain with the seislet sparse transform.The experimental results of synthetic seismic records and actual seismic data showed that the conventional hard and soft threshold denoising algorithms could suppress noise to a certain extent,but also damage effective signals that show little difference from noise.The proposed fractional threshold denoising algorithm could overcome the disadvantage of the hard and soft threshold denoising algorithms,which could effectively suppress random noise in seismic data thereby reducing loss of effective signal and improving the SNR of seismic data.

国家自然科学基金面上项目(41874149)、中国科学院战略性先导科技专项(A)(XDA14010303)、泰山学者青年专家计划(SF1503002001)、中石化项目(G5800-17-ZS-WX004)共同资助。