应用L_(p)拟范数稀疏约束的纵横波速比直接反演

Direct inversion of P⁃wave to S⁃wave velocity ratio by L_(p)quasi⁃norm sparse constraints

纵横波速比(vP/vS)是识别气藏、描述储层特征和判别岩性的重要解释工具。目前主要是通过反射系数近似方程反演得到纵、横波速度,再进一步计算纵横波速比,但是这种间接计算方法会产生累积误差。为了直接从叠前地震数据反演纵横波速比,文中提出了一种新的广义弹性阻抗方程,再进一步推导出一个与纵横波速比、纵波速度、密度相关的纵波反射系数近似方程。为了得到精度较高的反演结果,基于推导出的反射系数近似方程,提出一种基于Lp拟范数稀疏约束的叠前地震反演方法,并通过交替方向乘子算法求解。将提出的直接反演方法应用于理论模型和实际数据,并与间接反演方法相对比,结果表明该直接反演方法的反演结果精度较高,对含气储层的边界刻画更清晰。

The P‑wave to S‑wave velocity ratio(vP/vS)is a vital tool for gas reservoir identification,reservoir characterization,and lithology recognition.At present,the P‑wave velocity and S‑wave velocity are mainly obtained through the inversion of the reflection coefficient approximate equation,and then the vP/vS is calculated.However,this indirect calculation method creates a cumulative error.To obtain the vP/vS directly from pre‑stack seismic data,this paper proposes a new generalized elastic impedance equation and further derives an approximate equation of the P‑wave reflection coefficient,which is linked to the vP/vS,P‑wave velocity,and density.To achieve high‑precision inversion results,this paper proposes a prestack seismic inversion method based on the sparse constraint of the Lp quasi‑norm utilizing the derived approximation equation of reflection coefficient,which is solved by the alternating direction multiplier algorithm.The proposed direct inversion method is applied to theoretical models and practical data and compared with the indirect inversion method.The results demonstrate that the direct inversion method exhibits higher inversion accuracy and clearer boundary characterization of gas‑bearing reservoirs.