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3. Experimental Results
3.1 Marmousi model
The first example is an adjoint map on a scaled-down version of the so-called "Marmousi" model. We used 24 shots, on a 1650_450 grid, with 1450 time steps. This experiment was performed at the IBM Center in Dallas, on a cluster of 8 RS600 370 workstations, of which one acted as the manager (no worker ran on the manager node). The time and Mops rate on a single node were 624 s and 40 Mops. The time with 6 workers is 45 mins 24 s, giving a speedup of 4.4 (or an efficiency of 72 %).
3.2 The Gas Cloud Model
The geophysical implications of this example consists of a low velocity perturbation in an otherwise layered medium. The experiment consists of simulating 30 shot positions, on a 512 by 128 grid. There are 500 time steps, and 34 receiver positions. This is representative of the model sizes we are currently able to use for inversion, as shown in the next subsection. We first ran on a single node to evaluate floating performance of the chip. The execution time was 527 s, the elapsed time was 560 s, or 94% use of the machine. On a Cray Y-MP (at Cray Research Corporate Computing Network), execution time was 83 s. The Mops rate were 254 on the Y-MP, and 40 Mops on the RS6000.
Then, the cluster was used, using 6 workers in addition to the manager. Execution time was 130 s. Both alog and upshot were used to produce and examine a log files for this run. The log files show that the workers are busy computing most of the time. Also, the master has only bursts of activity, when it is doing I/O. This is the expected behavior, and justifies the design decisions, at least for doing simulations.
4. Inversion Example
For this example, the physical model is the same as in 3.2, but now inversion will be attempted. This includes a significant amount of linear algebra which is not parallelized. Note that a run in this section is the equivalent of 58 runs of the previous section. This task was ran on a dedicated cluster of 4 IBM RS600 workstations, connected by a 10 Mb/s Ethernet. Performance results are shown in the table below (maximum speedup is computed from Amdahl's law and actual speedup is what was actually measured).
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An important point to remember is that Amdahl's law has not been violated, instead this scheme has benefited from super-linear speedup due to computation and I/O overlap, which is not taken into account by Amdahl's law. In this case, again, the workers were kept busy all the time, their loads were balanced, and communication costs were insignificant
5. Discussions
The above case study presents a task level parallel implementation of DSO. The study described the implementation, given the rationale on which it is built, and also presented some preliminary evidence that the design works, at least for modeling. The method however has limitations for doing inversion.
6. References
1. W.W. Symes and J.J. Carazzone, Velocity inversion by differential semblance optimization, Geophysics, volume 56, 1991.
