Errors in average velocities

To demonstrate effect of using a velocity model differing from the actual medium velocity I constructed a synthetic dataset that is representative of the drill-bit problem: 240 channels, one source at a depth of 1000 feet, and a velocity 9000 feet/sec. Random noise was added to seismic traces; the power of the noise equals the power of the signal. The data were filtered with a 70-100 Hz bandpass filter. The semblance coefficient was computed for two velocity models: (1) a velocity 9000 feet/sec (corresponding to the ``true'' velocity), and (2) a velocity of 10000 feet/sec. Figure  and show the maximum value of semblance as a function of depth for these two cases. It can be seen that using wrong velocity, we still are able to locate the source, though the depth of maximum is shifted and the maximum value of the semblance has been decreased.

 

v9000
Figure 3 v9000

Semblance as function of depth using the true velocity model.
V_true=V_model=9000 feet/sec.

 

v10000
Figure 4 v10000

Semblance as function of depth using an incorrect velocity model.
V_true=9000 feet/sec
V_model=10000 feet/sec