Because the DMO elliptic operator is dip-limited, it does not extend all the way up to the Earth's surface (t=0). The time spread of the impulse response is given by:
(1) |
magic
Figure 4 Time spread of the impulse responses of DMO as a function of the impulse location, t_{n}. The maximum time spread occurs for the input time where G is the golden number. Click on the following button to see the curve for different times t_{m}. |
An interesting feature of these curves is that the time spread of the impulse responses never exceeds where is
(2) |
During the process, the time slices are shifted upward until they reach the maximum time spread. Of course, only the time slice corresponding to the maximum time spread will have to be processed all the way. Other time slices, like for example t_{n}=5 seconds (Figure ), will be processed for the first .1 second and then pass through idle processors. Obviously, the later time slices require less processing than the earlier ones, and thus represent a waste of processing capacity. The following formula gives the load balance as a function of trace length:
(3) |
integ
Figure 5 Load balance as a function of the trace length. The optimal load balance of eighty percent corresponds to a trace length which is a function of t_{m} (=2h/v). The bigger t_{m} is, the later the load balance is optimal. Click on the following button to see a movie of the load balance for different values of t_{m}. |
This algorithm allows a more efficient distribution of work between processors than the spiral trace processing described earlier. I implemented this algorithm for a two-dimensional model (Figure is an output of the program) but the run time is similar to a serial implementation of DMO (in 2-D, trace processing is more straightforward than time slice spreading). However, the real advantage of the method will appear in processing 3-D land data.