基于单程波算子的全波场最小二乘偏移方法

Least squares migration of full wavefield based on one⁃way wave operator

传统偏移成像方法是建立在波场一次反射的假设条件之上,事实上,完整的地震成像来自于地下全波场(一次波和多次波)。为了能够利用全波场信息以提高成像质量,提出了基于单程波算子的全波场最小二乘偏移(FW⁃LSM)方法。首先,引入地层上、下界面反射系数和背景速度,推导了基于单程波算子闭循环延拓的全波场正演算子,模拟了平滑速度模型情况下的全波场信息;其次,在二范数意义下求解FW⁃LSM的误差泛函和梯度项表达式,构建基于反演框架的全波场最小二乘偏移方法;最后,针对透镜体与加入水层的Marmousi模型进行测试分析,验证了方法的有效性。研究表明:多轮次反演迭代压制了复杂波场产生的相干假象,多次反射波信息的利用显著改善了成像品质;该方法拓宽了地震成像的手段,尤其在多次波发育的海域地震资料处理中有着重要的作用和潜在的推广价值。

Traditional migration methods are based on the assumption that the wave field reflects once.In fact,complete seismic imaging should be the contribution of all the subsurface wavefields(primaries and multiples).To improve the imaging quality with full wavefield information,this paper studies full wavefield least squares migration(FW⁃LSM)based on a one⁃way propagation operator.Firstly,the upper and lower reflection coefficients are introduced to derive the forward operator based on a one⁃way propagation operator with closed⁃loop continuation and simulate full wavefield information under the smooth velocity model.Secondly,2⁃norm⁃based least squares error functional and gradient term expressions of the full wavefield are solved to construct the least squares migration according to the inversion framework.Finally,the validity of the proposed method is tested by the lens model and Marmousi model with a water layer.Additionally,multiple inversion iterations suppress crosstalk generated by complex wavefields,and the imaging quality is significantly improved by adopting multiple reflection wave information.This study provides new seismic imaging methods and is of practical and popularization values,especially for seismic data processing in deep marine areas with strong multiples.