单程波方程偏移算法的相位问题研究

Study of phases in one way wave equation migration methods

（1.美国Hess公司，美国得克萨斯州休斯敦TX77002；2.斯坦福大学地球物理系，美国加利福尼亚州CA94075）

Hess Corporation, Houston, TX 77002, USA

利用稳相原理对叠后单程波方程偏移、二维和三维叠前偏移算法中的相位进行了分析和研究，从理论上论证了叠后偏移算法可以保持输入子波的相位特征，而叠前偏移算法会改变输入子波的相位特征，叠前单炮深度偏移结果相位与输入数据子波相位之间相差了一个因子。上述理论通过基本单位脉冲响应和一个水平反射界面模型的数值模拟得到了验证。从而从理论上解决了波动方程偏移与Kirchhoff积分偏移结果相位不一致问题，这对于正确标定反射层的振幅和深度具有实用意义。

Stationary phase rule was used to analyze and study the phases of one way wave equation post-stack migration,2D and 3D pre-stack depth migration algorithms. It theoretically proves that post-stack migration algorithm can preserve the phase characteristic of the input wavelet. However, pre-stack migration algorithm will change phase characteristic of the input wavelet. The result of single shot pre-stack depth migration has a constant phase difference from that of the input wavelet. The above mentioned theory was demonstrated by using numerical simulations of fundamental unit impulse response and one horizontal reflection boundary model. Therefore, the phase difference between the wave equation migration and the Kirchhoff integral migration were theoretically solved, which is useful for correctly calibrating the amplitude and depth of reflectors.