论文标题

3D虚拟地震学

3D virtual seismology

论文作者

Brackenhoff, Joeri, Thorbecke, Jan, Wapenaar, Kees

论文摘要

我们使用先前派生的单面均匀绿色的函数表示,在3D地下中创建虚拟源和接收器。我们采用了Green的功能和聚焦功能,这些功能是使用地球表面的反射数据,宏速度模型和Marchenko方法获得的。均匀的绿色功能是绿色的功能,其时间为逆转。与经典的均匀绿色功能表示不同,我们的方法不需要在封闭边界上的接收器,但是,它确实需要源信号是对称的。我们证明,在3D中,单面表示是通过将表示形式应用于数值数据来改进经典表示形式。我们使用各向同性和双式辐射模式检索对虚拟点源的响应,并将结果与​​直接建模的参考结果进行比较。我们还演示了单面表示的应用,以检索由双相点源叠加组成的虚拟破裂的响应。这是通过分别获得每个源的均匀绿色功能,然后将其转换为因果绿色的功能,时间缩短和超级实现。单面表示也用于监视由数值建模破裂引起的完整波场。但是,实际破裂的源信号在时间上不是对称的,因此单面代表只能用于获得因果绿色的功能。这种方法在最终结果中留下了工件,但是,这些文物在时空上受到限制。

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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