Seismic migration commonly yields an incomplete reconstruction of the Earth model due to restricted survey aperture, band-limited frequency content and propagation effects. This affects both illumination and resolution of the structures of interest. Through the application of spatial convolution operators commonly referred to as point-spread functions, simulated prestack depth-migrated images incorporating these effects may be obtained. Such simulated images are tailored for analysing distortion effects and enhance our understanding of seismic imaging and subsequent interpretation. Target-oriented point-spread functions may be obtained through a variety of waveform and ray-based approaches. Waveform approaches are generally more robust, but the computational cost involved may be prohibitive. Ray-based approaches, on the other hand, allow for efficient and flexible sensitivity studies at a low computational cost, but inherent limitations may lead to less accuracy. To yield more insight into the similarities and differences between point-spread functions obtained via these two approaches, we first derive analytical expressions of both wave- and ray-based point-spread functions in homogeneous media. By considering single-point scatterers embedded in a uniform velocity field, we demonstrate the conditions under which the derived equations diverge. The accuracy of wave-based and ray-based point-spread functions is further assessed and validated at selected targets in a subsection of the complex BP Statics Benchmark model. We also compare our simulated prestack depth migrated images with the output obtained from an actual prestack depth migration (reverse time migration). Our results reveal that both the wave- and ray-based approaches accurately model illumination, resolution and amplitude effects observed in the reverse time-migrated image. Furthermore, although some minor deviations between the wave-based and ray-based approaches are observed, the overall results indicate that both approaches can be used also for complex models.

中文翻译：

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点扩展函数卷积模拟叠前深度偏移图像：验证研究

由于测量孔径受限、频带受限的频率内容和传播效应，地震迁移通常会产生不完整的地球模型重建。这会影响感兴趣结构的照明和分辨率。通过应用通常称为点扩展函数的空间卷积算子，可以获得包含这些效应的模拟叠前深度偏移图像。此类模拟图像专门用于分析畸变效应并增强我们对地震成像和后续解释的理解。可以通过各种基于波形和射线的方法获得面向目标的点扩展函数。波形方法通常更稳健，但所涉及的计算成本可能令人望而却步。另一方面，基于光线的方法，允许以较低的计算成本进行有效和灵活的灵敏度研究，但固有的局限性可能会导致准确性较低。为了更深入地了解通过这两种方法获得的点扩展函数之间的异同，我们首先推导出均质介质中基于波和射线的点扩展函数的解析表达式。通过考虑嵌入在均匀速度场中的单点散射体，我们证明了导出方程发散的条件。在复杂 BP 静态基准模型的一个子部分中，在选定的目标上进一步评估和验证了基于波和基于射线的点扩展函数的准确性。我们还将我们模拟的叠前深度偏移图像与从实际叠前深度偏移（逆时偏移）获得的输出进行比较。我们的结果表明，基于波和基于射线的方法都准确地模拟了在逆时偏移图像中观察到的照明、分辨率和幅度效应。此外，虽然观察到基于波和基于射线的方法之间存在一些细微的偏差，但总体结果表明这两种方法也可用于复杂模型。