A graphics processing unit implementation of time-domain full-waveform inversion

Speedup performance

The acceleration of GPU implementation on advanced computer hardware is a key concern of many researchers. There are many factors which may accelerate the FWI computation. Compared with saving the wavefield on disk, wavefield reconstruction will accelerate the GPU computing because no CPU-GPU data transfer is needed any more. The parallel reduction to find the maxium value of model vector $\textbf{m}_k$ and descent direction vector $\textbf{d}_k$ is another factor to speedup the FWI computation. However, among these factors, the forward modeling takes most of the computing time. Each iteration needs four times of forward modeling: two of them are for sources and receivers; one is performed for wavefield reconstruction and gradient calculation, and another one is to estimate the step length $\alpha_k$ . Therefore, we only focus on the speedup obtained in the forward modeling procedure.

To do the performance analysis, we run the sequential implementation CPU code and parallel multi-thread GPU code of forward modeling for 1000 time steps. We estimate the average time cost of 5 shots for different data sizes. Because the GPU block size is set to be 16x16. To make the comparison fair, we generate test models whose size is of multiple 16x16 blocks. The size of the test model is choosen to be $nx\cdot nz$ , $nx=nz=i\cdot160$ , where $i=1,\ldots,7$ is an integer. We only have a NVS5400 GPU card (compute capability 2.1, GDDR3) run on a laptop. Even so, compared with sequential implementation on host, we still achieve approximately 5.5-6 times speedup on the GPU device, as shown in Figure 5.

timecost
Figure 5. Comparison of the time cost for CPU- vs. GPU implementation under different model sizes with one shot, 1000 time steps of forward modeling.

A graphics processing unit implementation of time-domain full-waveform inversion