3D 虚拟地震学
3D virtual seismology
AI总结：
本文利用单侧均匀格林函数表示，在三维地下介质中创建虚拟震源和接收器，无需包围边界接收器，通过数值实验验证了其优于经典表示，并能用于监测虚拟破裂波场。
摘要：
我们利用先前推导的单侧均匀格林函数表示，在三维地下介质中创建虚拟震源和接收器。我们采用通过地表反射数据、宏观速度模型和 Marchenko 方法获得的格林函数和聚焦函数。均匀格林函数是格林函数与其时间反转的叠加。与经典的均匀格林函数表示不同，我们的方法不需要在包围边界上设置接收器，但确实要求震源信号在时间上对称。我们通过将表示应用于数值数据，证明了在三维情况下，单侧表示优于经典表示。我们检索了具有各向同性和双力偶辐射模式的虚拟点源的响应，并将结果与直接建模的参考结果进行了比较。我们还演示了单侧表示在检索由双力偶点源叠加组成的虚拟破裂响应中的应用。这是通过分别获取每个源的均匀格林函数，然后将它们转换为因果格林函数、进行时间平移和叠加来实现的。单侧表示还用于监测由数值模拟破裂引起的完整波场。然而，实际破裂的震源信号在时间上并不对称，因此单侧表示只能用于获取因果格林函数。这种方法会在最终结果中留下伪影，但这些伪影在空间和时间上都是有限的。
英文摘要：
We create virtual sources and receivers in a 3D subsurface using the previously derived single-sided homogeneous Green's function representation. We employ Green's functions and focusing functions that are obtained using reflection data at the Earth's surface, a macro velocity model and the Marchenko method. The homogeneous Green's function is a Green's function superposed with its time-reversal. Unlike the classical homogeneous Green's function representation, our approach requires no receivers on an enclosing boundary, however, it does require the source signal to be symmetric in time. We demonstrate that in 3D, the single-sided representation is an improvement over the classical representation by applying the representations to numerical data. We retrieve responses to virtual point sources with an isotropic and with a double-couple radiation pattern and compare the results to a directly modeled reference result. We also demonstrate the application of the single-sided representation for retrieving the response to a virtual rupture that consists of a superposition of double-couple point sources. This is achieved by obtaining the homogeneous Green's function for each source separately, before they are transformed to the causal Green's function, time-shifted and superposed. The single-sided representation is also used to monitor the complete wavefield that is caused by a numerically modeled rupture. However, the source signal of an actual rupture is not symmetric in time and the single-sided represenation can therefore only be used to obtain the causal Green's function. This approach leaves artifacts in the final result, however, these artifacts are limited in space and time.
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