In vector-based elastic reverse time migration, the scalar images (PP and PS) can be effectively obtained by applying dot product-based scalar imaging conditions to the vector wavefields. However, the PP image suffers from polarity reversal problem while opening angles are greater than 90° and backscattering artifacts while opening angles are near 180°. To cope with these above-mentioned issues, we propose the pseudo-Laplace filter for the dot product-based scalar imaging condition. Based on the analysis of Laplace filter in scalar image of vector-based wavefields, the 2-nd parallel-oriented partial derivatives of Cartesian components cross-correlation results are selected to construct the pseudo-Laplace filter, omitting 2-nd normal-oriented partial derivatives of Cartesian components cross-correlation results. Theoretical analysis with assumption of plane wave has proved that the proposed pseudo-Laplace filter can solve the problems of backscattering artifacts and polarity reversal in PP image through scalar imaging condition. Numerical examples show excellent performance in PP image with pseudo-Laplace filter due to additional polarity correction and backscattering attenuation. Besides, the application of the pseudo-Laplace filter requires little additional computation or storage.

中文翻译：

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基于向量的弹性逆时偏移的伪拉普拉斯滤波器

在基于矢量的弹性逆时偏移中，通过将基于点积的标量成像条件应用于矢量波场，可以有效地获得标量图像（PP 和 PS）。然而，PP 图像在开度角大于 90° 时存在极性反转问题，在开度角接近 180° 时会出现反向散射伪影。为了解决上述这些问题，我们提出了基于点积的标量成像条件的伪拉普拉斯滤波器。基于矢量波场标量图像中拉普拉斯滤波器的分析，选取笛卡尔分量互相关结果的二次平行偏导数构造伪拉普拉斯滤波器，省略二次法向偏导数笛卡尔分量互相关结果的导数。假设平面波的理论分析证明，所提出的伪拉普拉斯滤波器可以通过标量成像条件解决PP图像中的背向散射伪影和极性反转问题。由于额外的极性校正和反向散射衰减，数值示例显示了在具有伪拉普拉斯滤波器的 PP 图像中的出色性能。此外，伪拉普拉斯滤波器的应用几乎不需要额外的计算或存储。