绕射波是由地下局部非均质性引起的地震响应，携带了高分辨率的地质异质信息，利用绕射波识别和追踪异质体(区)的关键是将其准确成像。发展了一种基于路径积分的叠后绕射波偏移成像方法。通过求解各向同性零偏移距速度延拓偏微分方程，获得其f-k域解析解，再结合路径积分理论构建偏移滤波器；然后利用积分区间(速度)改变其滤波特性，通过振幅和相位控制来突出绕射弧顶点并弱化大倾角成分，从而实现绕射波的成像。为进一步提高绕射波成像质量，在滤波器中引入了高斯加权因子，并深入讨论了成像控制参数的选取原则。研究结果表明：该成像过程等效于将给定速度区间内所有等速延拓剖面进行连续求和，依靠累积稳定贡献提高绕射弧顶点能量的同时，通过连续相移抵消了偏移同相轴侧翼；然而，这种积分成像方式无法抵消区间端点值引起的偏移成分，将会导致结果中残存部分欠、过偏同相轴；为了压制尾线干扰，并使绕射同相轴收敛更聚焦，可在滤波器中引入高斯因子，利用高斯权值增强准确速度附近的叠加贡献，同时有效削弱错误速度引起的偏移成分。此外，对于高斯加权路径积分法，速度区间两侧端点值分别对应成像剖面中的欠、过偏成分，区间大小与偏移同相轴顶点的能量成正比，速度偏量和标准差则决定了绕射点的聚焦程度。绕射模型验证了方法的有效性，实际地震资料处理结果表明：该方法无需预先构建成像速度模型，而且在绕射波提取较为完整的前提下，能有效改善绕射波的成像质量。

Diffracted waves are seismic responses caused by local heterogeneities of underground strata, which carry high resolution heterogeneous information. The key to identify and track the heterogeneous body (or region) by diffractions is to accurately image them. A post stacked diffraction migration imaging method based on path integral has been developed. Firstly, a migration filter in f k domain is constructed by combining the path integral theory with the analytical solution of the isotropic zero migration velocity continuation partial differential equation. Then, the filtering characteristics are varied according to the integral interval (velocity). Finally, the post stacked diffraction imaging is achieved after using an amplitude and phase control in the f k domain to highlight the top of the diffraction arc and weaken the steep wings of the diffraction event. In addition, a Gaussian weighting factor is introduced into the filter to suppress the tail line interferences and improve the imaging quality, and a selection principle of imaging control parameters is also discussed. The results show that this imaging process is equivalent to a continuous summation of all constant velocity continuation sections in a given velocity range. It accumulates stable contribution to boost the energy of the diffraction arc apex, and simultaneously offsets the wings of the event by continuous phase shifting. However, the migration components caused by interval endpoints cannot be offset in this way, which may lead to residual events under and over migrated in the imaging results. To suppress the tail lines and converge the diffraction event, a Gaussian factor can be introduced into the filter. The Gaussian weight can enhance the contribution near the accurate velocity and diminish the migration components caused by wrong velocities. Moreover, for the Gaussian method, the endpoint values on both sides of the velocity interval correspond respectively to the under and over migration components in the imaging section. The size of the velocity range is directly proportional to the energy of the migrated event apex. The focusing degree of diffraction points is determined by the velocity bias and standard deviation. Two theoretical diffraction models verified the effectiveness of this method. The processed results of real seismic data sets show that this method does not need to build an imaging velocity model in advance, and it can effectively improve the imaging quality under the premise of complete extraction of diffracted waves.

1 方法原理

   1.1 路径积分速度延拓

   1.2 成像流程

2 模型数据处理与分析

   2.1 单点绕射模型

   2.2 多点绕射模型

3 实际资料处理与分析

4 结论