ABSTRACT The conventional reverse time migration of ground‐penetrating radar data is implemented with the two‐way wave equation. The cross‐correlation result contains low‐frequency noise and false images caused by improper wave paths. To eliminate low‐frequency noise and improve the quality of the migration image, we propose to separate the left‐up‐going, left‐down‐going, right‐up‐going and right‐down‐going wavefield components in the forward‐ and backward‐propagated wavefields based on the Hilbert transform. By applying the reverse time migration of ground‐penetrating radar data with full wavefield decomposition based on the Hilbert transform, we obtain the reverse time migration images of different wavefield components and combine correct imaging conditions to generate complete migration images. The proposed method is tested on the synthetic ground‐penetrating radar data of a tilt‐interface model and a complex model. The migration results show that the imaging condition of different wavefield components can highlight the desired structures. We further discuss the reasons for incomplete images by reverse time migration with partial wavefields. Compared with the conventional reverse time migration methods for ground‐penetrating radar data, low‐frequency noise can be eliminated in images generated by the reverse time migration method with full wavefield decomposition based on the Hilbert transform.

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基于希尔伯特变换的全波场分解探地雷达逆时偏移

摘要 探地雷达数据的常规逆时偏移是通过双向波动方程实现的。互相关结果包含由不正确的波路径引起的低频噪声和假图像。为了消除低频噪声并提高偏移图像的质量，我们建议将前向和左上向、左下向、右上向和右下向波场分量分开。基于希尔伯特变换的后向传播波场。应用基于希尔伯特变换的全波场分解的探地雷达数据逆时偏移，得到不同波场分量的逆时偏移图像，并结合正确的成像条件，生成完整的偏移图像。所提出的方法在倾斜界面模型和复杂模型的合成探地雷达数据上进行了测试。偏移结果表明，不同波场分量的成像条件可以突出所需的结构。我们进一步讨论了部分波场逆时偏移导致图像不完整的原因。与传统的探地雷达数据逆时偏移方法相比，基于希尔伯特变换的全波场分解逆时偏移方法生成的图像可以消除低频噪声。我们进一步讨论了部分波场逆时偏移导致图像不完整的原因。与传统的探地雷达数据逆时偏移方法相比，基于希尔伯特变换的全波场分解逆时偏移方法生成的图像可以消除低频噪声。我们进一步讨论了部分波场逆时偏移导致图像不完整的原因。与传统的探地雷达数据逆时偏移方法相比，基于希尔伯特变换的全波场分解逆时偏移方法生成的图像可以消除低频噪声。