The inverted velocity model obtained from the reflection tomography based on the angle domain common‐image gathers has a certain fuzziness. The inverted velocity model's stratigraphic interface is always not clear enough in areas with complex stratigraphic structure. In order to improve the accuracy and resolution of the inverted velocity model, a double‐difference constraint condition is added on the basis of minimizing the absolute travel‐time residual at the subsurface imaging points. This constraint makes the inverted velocity model local structure information more refined by minimizing the differential travel‐time residual at adjacent imaging points (i.e. closely spaced points within the same layer) and makes the variation of velocity model information within a certain range more accurate. The method in this paper is based on angle domain common‐image gathers, the tomography inversion equation is established by using the ray tracing method, and the conversion relationship between the traveltime residual and the residual curvature of the angle domain common‐image gathers. Then, by adding differential constraint and double‐differential constraint conditions and using the least squares QR decomposition method to solve the set of equations, the inverted velocity model can be obtained through multiple iterations, which provides a high‐precision velocity field for the migration and improves the accuracy of seismic imaging. Numerical experiments on both one typical model and a field data example demonstrate the effectiveness of the proposed double‐difference constrained elastic reflection tomography in generating high‐precision velocity models.

中文翻译：

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二维弹性介质中的双差约束反射层析成像

基于角域共像道集的反射层析成像反演速度模型具有一定的模糊性。在地层结构复杂的地区，反演速度模型的地层界面往往不够清晰。为了提高反演速度模型的精度和分辨率，在最小化地下成像点绝对走时残差的基础上，加入双差约束条件。该约束通过最小化相邻成像点（即同一层内间隔较近的点）的差分走时残差，使得反演的速度模型局部结构信息更加精细，使得一定范围内的速度模型信息的变化更加准确。该方法基于角域共像道集，利用射线追踪方法建立层析反演方程，建立角域共像道集走时残差与残差曲率的转换关系。然后，通过添加微分约束和双微分约束条件，采用最小二乘QR分解方法求解方程组，经过多次迭代即可得到反演的速度模型，为偏移和偏移提供了高精度的速度场。提高了地震成像的精度。对一个典型模型和现场数据示例的数值实验证明了所提出的双差约束弹性反射层析成像在生成高精度速度模型方面的有效性。