# Enhancement of In-Plane Seismic Full Waveform Inversion with CPU and GPU Parallelization
## 6 Conclusions  
Parallel programming GPU using CUDA C is implemented for in-plane seismic full waveform inversion, and the computational efficiency is compared to the serial and openMP parallel codes. The forward seismic wave propagation is studied for an earthen water reservoir dam with a crack and water table in the first step. It is important to study the forward model, as the FWI is based on an iterative computation of several forward models with a gradual improvement model and minimisation of the misfit. The influence of the crack and water table is visible in the results. In the next step, the full waveform inversion model is programmed in CUDA C, and a study is conducted for a spherical inclusion in full space. A balance of impedance ratio of the medium parameters and the frequency content of the input signal is essential for successful FWI computations. The high-frequency content in the time signal gives more detailed inversion results; however, there are more chances of the existence of local minima, and the model may converge elsewhere than the global minima. On the other hand, the low-frequency content in the time signal usually guides the model toward the global minima. However, the inverted results are blurred or less detailed, so the necessary details can be missed.  
The computational efficiency of GPU parallelisation for the forward and full-waveform inversion models is studied compared to serial and CPU parallel codes. Comparing the computed results on different hardware and programming environments shows a significant reduction in computation time. The comparison is made for the change in the model size in time and space, which in the Finite Difference Method are grid sizes in Cartesian direction \((NX,NZ)\) and the number of time steps \((NT)\). For all the cases, the improvement in performance increases with an increase in the model dimension and remains constant after a certain threshold. The GPU parallel computation has shown up to the speed enhancement of about 60 to 100 times, whereas that CPU parallelisation in openMP (16 threads) is between 5 to 11 times that of the serial code. It can be concluded that GPU computation can significantly enhance the performance of in-plane seismic full waveform inversion. With the advancement of modern GPU, the FWI computation can be implemented into practical application by bringing the computation of the days into hours. It also provides further opportunities to implement robust optimisation and machine learning algorithms to enhance FWI computations.  
Conceptualization, M.B.B. and Z.H.R.; methodology, M.B.B.; software, M.B.B., M.A., A.H.A. and M.Z.; validation, M.B.B., M.A., A.H.A. and M.Z.; writing--original draft preparation, M.B.B., M.A. and Z.H.R.; writing--review and editing, Z.H.R., G.C. and F.W.; supervision, Z.H.R. and F.W.; project administration, M.B.B., Z.H.R. and F.W.; funding acquisition, F.W. All authors have read and agreed to the published version of the manuscript.  
M.B.B., Z.H.R. and F.W. would like to thank project Betonbauwerken funded by Zentrales Innovationsprogram Mittelstand, Germany.  
Not applicable.  
The data is available from corresponding author upon request.  
We acknowledge financial support by Land Schleswig-Holstein within the funding programme Open Access Publikationsfonds.