VSP直达波和反射波波动方程走时联合反演

Joint wave-equation traveltime inversion of direct and reflected waves for VSP data

地面资料全波形反演采用低波数回折波敏感核和高波数偏移等时线恢复地下模型的长波长和短波长分量.当回折波的穿透深度有限时,很容易陷入局部极值.波动方程反射波走时反演采用反射波的透射敏感核更新速度模型.当浅层速度存在较大误差时,仍无法得到满意的反演结果.VSP资料中直达波是一种透射波,穿透深度大,可用于井旁背景速度场建模.本文发展了针对VSP观测方式的波动方程走时联合反演(直达波和反射波)方法.采用全局优化参数反演法实现VSP上下行波和纵横波分离,构建了基于下行直达波和上行反射波走时残差的混合目标函数,推导了相应的伴随状态方程和梯度公式,给出了背景速度和反射系数分步反演流程.理论和实际VSP资料应用表明:直达波和反射波走时联合反演可以得到运动学特征精确的速度模型,为后续全波形反演提供可靠的初始模型;联合反演比单独直达波/反射波走时反演的精度高,比直达波和反射波走时级联反演的耗时少.

Full-Waveform Inversion(FWI)of surface data builds the long-and short-wavelength components of the subsurface model using the low-wavenumber kernel of the diving wave and the high-wavenumber migration isochrones,respectively.FWI is prone to falling into local extremes when the penetration depth of the diving wave is insufficient.Wave-Equation Reflection Traveltime Inversion(RWETI)adopts the tomographic kernel of reflections to update the velocity model.RWETI cannot obtain satisfactory inversion results,especially when large errors are present in the velocity of the shallow part.For VSP survey,the direct wave is a transmitted wave with a large penetration depth,which can be used for building the background velocity model around the borehole.We develop a joint Wave-Equation Traveltime Inversion(WETI)method of direct and reflected waves for VSP data.We employ a global optimization parameter inversion method to implement the separation of down-and up-going waves and the separation of and P-and S-waves,construct a joint objective function based on the traveltime residuals of down-going direct and up-going reflected waves,derive the corresponding adjoint-state equation and gradient formulas,and introduce a hierarchical inversion workflow of background velocity and reflectivity model.The applications on synthetic and field VSP data reveal that joint WETI of direct and reflected waves can reconstruct kinematically accurate velocity model,which is a reasonable starting model for subsequent FWI.Additionally,joint WETI is more accurate than direct/reflected-wave-based WETI and less time-consuming than cascaded WETI of direct and reflected waves.