LOCATING SOURCES IN 3-D

To search for sources (such as the drill bit) in 3-D, I first construct a cube of possible source locations. Then, given an estimate of the velocity structure, I compute the moveout trajectory for energy arriving at the array from each possible source. I compute semblance over this moveout trajectory and examine the resulting 3-D semblance cube.

Figure  shows constant-depth slices from such a cube, taken at the known depth of the drill bit. A constant velocity of 10000 ft/sec has been used to compute moveout trajectories. The four frames correspond to four different data records; the two top records are from the ``quiet'' period where pumps within the array were turned off. In the case of the bottom two records the pumps were operating. The asterisk denotes the surface position of the drilling rig. When the pumps are turned off, the largest semblance values (shown in white) occur at the drill bit location. These semblance values are likely due to direct arrivals from the drill bit.

 

plotxy
Figure 2 plotxy

Stacking semblance as a function of x and y coordinates at the drill-bit depth for four different data records. The largest semblance values are shaded in white. For the top two records, taken while pumps within the array were turned off, the largest semblance values are at the drill bit location, suggesting that we are able to see direct arrivals from the drill bit. For the bottom two records, where the pumps were operating, the results are much poorer. Note that the top and bottom plots are scaled differently for comparison; the largest semblances in the top plots are nearly three times those on the bottom.

Figures and show constant y-coordinate and constant x-coordinate slices through the same cube, for the same four data records. The agreement with the drill bit location in all three dimensions strengthens the claim that these large semblance values are due to direct arrivals from the drill bit. The resolution in space is not very good because only frequencies up to 40 Hertz have been used. Higher frequencies degrade the pictures - probably not because the drill bit signal does not contain higher frequencies but rather because the moveout of the signal departs from a constant-velocity hyperbola, and the higher frequencies are more sensitive to mis-stacking.

 

plotxz
Figure 3 plotxz

Stacking semblance as a function of x and z coordinates for a plane passing through the drill bit location. The asterisk denotes the location of the drill bit; note the change in depth between the top and bottom pictures. The largest semblance values, shaded in white, coincide with the drill bit location for the two records from the recording period where pumps within the array were turned off.

 

plotyz
Figure 4 plotyz

Stacking semblance as a function of y and z coordinates for a plane passing through the drill bit location. The asterisk denotes the location of the drill bit. As in the previous two plots, the largest semblance values correspond to the drill bit location, further suggesting that the semblance values are due to direct arrivals from the drill bit.