基于波动方程偏移的地震数据地层成像

地层成像是对地下地层物性空间变化的近似反演，对于岩性油气藏和非常规油气藏的勘探开发具有重要价值。文中根据波动方程偏移的思想提出了一种有关反射体波阻抗相对扰动的地层成像方法。基于地震波运动学特征准确的地下介质光滑模型，应用地震波传播理论推导了基于反射体波阻抗相对扰动的地震数据线性正演表达式；然后结合线性反演理论，利用地震数据近似反演波阻抗相对扰动，构建了基于波动方程偏移的以波阻抗变化为主要目标的地震数据地层成像方法。在地层成像中，如果对波场做角度分解，则可得到地层成像的角度域共成像点道集，如果对波场不做角度分解，则可快捷地得到角度域平均的地层成像结果。对于声波方程描述的地震数据，利用该地层成像方法可获得地层的声波阻抗相对扰动成像；对于标量波方程描述的地震数据，利用该成像方法可获得地层的速度相对扰动成像。该地层成像方法与地震数据逆时偏移方法的计算过程相同、计算量相当，合成地震数据试验取得了理想的地层成像效果。

Stratigraphic imaging with seismic data based on wave equation migration

Stratigraphic imaging, an approximate inversion of the spatial variation of the physical properties of subsurface strata, is of great value for the exploration and development of lithological and unconventional reservoirs. In this paper, a stratigraphic imaging method involving the relative perturbation of wave impedance of the reflector is proposed according to the idea of wave equation migration. On the basis of a smooth subsurface me-dium model featuring accurate kinematic characte-ristics of seismic waves, a linear forward expression of seismic data based on the relative perturbation of wave impedance of the reflector is derived by applying the seismic wave propagation theory. Then, the relative perturbation of wave impedance is obtained through approximate inversion from seismic data according to the linear inversion theory. A method of stratigraphic imaging with seismic data that is based on wave equation migration and takes wave impedance variation as the main target is constructed. During stratigraphic imaging, angle decomposition of the wavefield generates angle-domain common imaging-point gathers for stratigraphic imaging. In contrast, stratigraphic imaging results under an angle-domain average can be obtained quickly when angle decomposition of the wavefield is not performed. When the seismic data are described by the acoustic wave equation, the proposed stratigraphic imaging method can be employed to obtain stratum imaging based on the relative perturbation of acoustic wave impedance. When the seismic data are described by the scalar wave equation, the proposed method can be applied to attain stratum imaging based on relative velocity perturbation. Compared with the reverse time migration method based on seismic data, the proposed stratigraphic imaging method has the same calculation process and a comparable amount of calculation. This method also achieves a satisfactory stratigraphic imaging effect when it is applied to a test with synthetic seismic data.