基于地震数据线性正演表达的波形成像(二):地震数据的波形成像

将第一部分论述中提出的地震数据线性正演表达公式作为地震数据线性反演的正演方程,利用线性反演理论提出包括散射数据波形成像和反射数据波形成像的地震数据波形成像方法理论,给出了标量波散射数据、声波反射数据和弹性波反射数据波形成像的具体计算公式。散射数据波形成像是对散射体物性参数相对扰动的线性反演,反射数据波形成像是对反射体波阻抗相对扰动或反射体边界局部反射系数的线性反演。在波形成像中,如果将波场传播算子的伴随算子作为波场传播算子的逆,则波形成像可转化为波形偏移;如果将波场传播算子的最小二乘逆作为波场传播算子的逆,则波形成像可以转化为最小二乘波形偏移。散射数据波形偏移可以实现对散射体空间位置的成像,反射数据波形偏移不仅可以实现对反射体构造的准确成像,还可以实现对反射体波阻抗相对扰动的成像。受角度域反偏移计算复杂度的限制,反射数据最小二乘波形偏移仅可实现反射体近法向波阻抗相对扰动的最小二乘反演和反射体边界局部近法向反射系数的最小二乘反演。相较于逆时偏移,波形偏移结果不仅在理论上具有更加准确的相位和更高的分辨率,而且还不增加偏移计算量。地震数据波形成像不仅弥补了当前构造成像的不足,还可以用于地下的岩性成像。合成地震数据的数值试验结果验证了方法的有效性。

This paper presents the second part of the theoretical work on seismic data waveform imaging.The method relies on the linear forward representation formulas proposed in the first part of the work and makes use of forward equations for the linear inversion of seismic data.Both scattering and reflection data waveform imaging are discussed.Specific calculation formulas are presented for waveform imaging of scalar wave scattering data,acoustic wave reflection data,and elastic wave reflection data.Waveform imaging of scattering data is achieved via a linear inversion of the relative perturbation of the scatterers physical parameters,whereas imaging of the reflected data stems from a linear inversion of the relative perturbation of the wave impedance of the reflector (or the local reflection coefficient of the reflector boundary).During the process of waveform imaging,if the adjoint operator of the wavefield propagator is used as the inverse of the wavefield propagator,the waveform imaging is transformed into waveform migration.In contrast,if the least-squares inverse of the wavefield propagator is used as the inverse of the wavefield propagator,the waveform imaging is transformed into the least-squares waveform migration.Imaging of the scatterers spatial position can be obtained via waveform migration of scattering data.Finally,accurate imaging of the structure of the reflector and imaging of the relative perturbation of the reflector wave impedance can both be realized by means of waveform migration of reflection data.Computational complexity of the angle-domain de-migration limits the least-squares waveform migration of reflection data; thus,least-squares inversion can only be performed with respect to the relative perturbation of the near-normal wave impedance of the reflector and the local near-normal reflection coefficient of the reflector boundary.Compared with the current reverse time migration method,waveform migration has a higher resolution and returns a theoretically correct phase without increasing the computational burden.The waveform imaging method proposed in this paper can not only address the shortcomings of current structural imaging but can also be used for subsurface lithology imaging,as demonstrated by the results of synthetic seismic data processing.

国家自然科学基金项目(41874133,U19B2008)资助。