To estimate the depth errors in a subsurface model obtained from the inversion of seismic data, the stationary‐phase approximation in a two‐dimensional constant‐velocity model with a dipped reflector is applied to migration with a time‐shift extension. This produces two asymptotic solutions: one is a straight line, and the other is a curve. If the velocity differs from the true one, a closed‐form expression of the depth error follows from the depth and apparent dip of the reflector as well as the position of the amplitude peak at a non‐zero time shift, where the two solutions meet and the extended migration image focuses. The results are compared to finite‐frequency results from a finite‐difference code. A two‐dimensional synthetic example with a salt diapir illustrates how depth errors can be estimated in an inhomogeneous model after inverting the seismic data for the velocity model.

中文翻译：

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等速模型中时移扩展成像的稳态分析

为了估计从地震数据反演获得的地下模型中的深度误差，将带有倾斜反射器的二维恒速模型中的稳态近似应用于具有时移扩展的偏移。这会产生两个渐近解：一个是直线，另一个是曲线。如果速度与真实速度不同，则根据反射器的深度和表观倾角以及非零时移处的振幅峰值位置得出深度误差的封闭式表达式，其中两个解满足和扩展迁移图像焦点。将结果与有限差分代码的有限频率结果进行比较。具有盐底辟的二维合成示例说明了在反演速度模型的地震数据后如何在非均匀模型中估计深度误差。