The analytic solutions do not exist in the modeling situation where a tunnel dipping toward the east and ends somewhere within the model (See Fig. 1a). The total CPU time on my 18 core cluster is about 15 hours.
Fig. 1b provides a closer view of the tunnel and the spatial distribution of the 24 micro-earthquake sources. The “delay” on the figure is the original time delayed with respect to the first source. Source types are: ISO-explosion, DC-double couple, X-linear vector along X direction, and Z-linear vector along vertical direction. The frequencies ranges from 50 Hz to 300 Hz.
Fig. 1c and 1d shows the two components seismic traces acquired by the surface receivers and the borehole receivers, respectively. It is easy to observe that the second phase immediately following the first P-wave phase is not necessarily the shear-wave phase of the same earthquake. Instead, it can be a P-wave phase of a late earthquake.
Fig 1e and 1f shows the waveform from the middle channel from the surface receiver array (channel 76) and from the borehole receiver array ( channel 51). Can you identify all the phases in this noise-free environment? I actually lied when I say I used 24 sources. Can you find out how many sources I really used?
Here is a movie showing you what is really going on inside the earth, which in reality you never observe.