结合改进CNN和双约束损失函数的叠前地震数据低频补偿方法

陆地深层、超深层地震资料低频信息缺失、地震资料分辨率低，影响后续地震资料的准确解释。基于模型驱动的低频补偿方法依赖严格假设且参数调整不灵活；卷积神经网络(CNN)对细微变化的特征提取能力有限且梯度变化不明显、网络易陷入局部最优，导致低频欠补偿或补偿精度低。为此，提出一种结合改进CNN和双约束损失函数的叠前地震数据低频补偿方法。为解决梯度消失问题，在不增加CNN计算复杂度的前提下，加入可直接学习输入与输出之间残差特征的网络单元(残差块)，并采用批归一化处理，使网络对细微变化更敏感，从而提高网络训练效率。为解决梯度变化不明显导致网络过早收敛的问题，以网络输出与原始地震记录差异和相关度为优化目标，通过均方误差和皮尔逊距离的加权求和建立双约束条件的损失函数计算补偿误差，使梯度变化更明显以保证梯度下降过程可跳出局部最优，从而提高低频补偿精度。合成数据和中国西部X地区实际叠前地震数据低频补偿处理结果验证了该方法的可行性和有效性。与基于CNN低频补偿方法及反褶积结合宽带俞式低通滤波器的低频补偿方法相比，在补偿低频成分的同时不会破坏原始信号的中高频信息。

Low frequency compensation of pre-stack seismic data based on improved CNN and double constrained loss function

Due to the lacking low frequency information and the low resolution of seismic data for deep or ultra-deep land layers, the accurate interpretation of subsequent seismic data is affected. Model-dri-ven low frequency compensation methods have dependence on strict assumptions and inflexible parameter adjustment. The convolutional neural network (CNN) has limited feature extraction ability for subtle changes and no obvious gradient changes, and the network is easy to fall into local optimum, resulting in low frequency undercompensation or low compensation accuracy. Therefore, a low frequency compensation method for pre-stack seismic data combining improved CNN and double constrained loss function is proposed. On the premise of not increasing the computational complexity of CNN, residual blocks network units that can directly learn residual features between input and output are added to solve gradient disappearance. Additionally, batch normalization is adopted to make the network more sensitive to subtle changes, to improve network training efficiency. Since the gradient changes are not obvious, the network convergence is premature. To address the problem, this paper takes the difference and the correlation between the network output and original seismic record as optimization objectives and establishes the loss function by the weighted sum of the mean square error and Pearson distance to calculate the compensation error under double constraints. Finally, the gradient changes become more evident and ensure that the local optimal can be jumped out during gradient descent, so as to improve the low frequency compensation accuracy. The synthetic data and the low frequency compensation results of the real pre-stack seismic data in X area of western China verify the feasibility and effectiveness of the proposed method. Compared with the low frequency compensation method based on CNN and that based on deconvolution combined with broadband Yu low-pass filter, the proposed method can compensate the low frequency components without destroying the original medium and high frequency information.