基于压缩感知的复杂地表菲涅尔束偏移

Fresnel beam migration method based on compressed sensing under complex topographic conditions

高斯束偏移是一种束类地震数据成像方法,该方法可以处理多波至走时,具有良好的成像精度。但在复杂地表条件下应用存在两个问题:一是原有的局部平面波分解方法计算精度不足,影响低信噪比数据成像质量;二是偏移精度取决于射线束传播算子,高斯束传播算子随着传播距离增大发散过快,难以同时保证浅层和中深层构造成像精度,并且高斯束射线传播算子在模型浅部覆盖范围不足,对复杂地表模型成像精度较低。为了解决上述问题,本文将基于压缩感知理论的平面波分解技术应用到复杂地表菲涅尔束偏移中,不仅有效提高了局部平面波分解精度,同时菲涅尔束传播算子有效解决了高斯束算子随传播距离增加束宽发散过大的问题,典型的模型算例验证了本文方法的有效性和稳定性。

Gaussian beam migration(GBM)is a ray?based seismic imaging method,which can handle multi?arrivals and has good ima?ging accuracy.However,two problems should be taken into consideration when this method is used in complex topographic conditions:First,the original local plane wave decomposition method has insufficient calculation accuracy,which affects the imaging quality of low signal?noise ratio data.Second,the ray beam propagator is the most important factor for migration accuracy.With the enhancement of the propagation distance,the Gaussian beam width increases rapidly and cannot ensure the imaging accuracy of the near surface and depth structures at the same time.In addition,the insufficient coverage of the Gaussian beam in the shallow part of the model might affect the imaging quality of this region.In order to solve the above problem,the authors apply wave decomposition technique based on compressed sensing theory to the complex surface in Fresnel beam migration.It not only effectively improves the precision of local plane wave decom?position,but also solves the problem that the width of Gaussian beam operator is increased quickly with the increase of propagation dis?tance according to the Fresnel beam operator.Typical numerical examples prove the validity and stability of this method.