## 5 Conclusions  
This paper presented a performance acceleration framework for earthquake source parameter estimation based on the Okada dislocation model using CUDA GPU. To this end, we first carefully set the optimization technique candidates considering the characteristics of the target application and analyzed the effects of various combinations from the suggested optimization options in terms of efficiency and occupancy. Then, based on the analysis, we performed the CUDA kernel optimization of the Okada model and evaluated its performance improvement compared to multi-threaded CPU-based and baseline GPU implementations. We also explored the performance and correctness of different line search algorithms for the L-BFGS-B optimization, which is one of the most time-consuming parts of our target problem. Finally, using the assessment result, we selected the Armijo line search as the most efficient one.  
The performance evaluation results for CUDA kernel optimization showed that the _CUDA_optimized_ implementation achieved up to 2.99\(\times\) and 14.00\(\times\) speedups over the _CUDA_baseline_ and 16 threads CPU implementations, respectively. We also observed that Armijo shows a 42\(\sim\)84% reduction in confidence interval size over other candidates, and all parameters derived from Armijo feature a unimodal histogram with a small standard deviation. The best-fit parameters from Armijo had the best consistency between geodetic and modeled displacement, at most 0.50 cm RMSE for each direction. Consequently, the results demonstrated that our proposed approach successfully accelerates earthquake source parameter estimation procedure with correctness verification of the best-fit parameters.  
Conceptualization, S.L. and T.K.; methodology, S.L.; implementation, S.L.; evaluation, S.L.; writing, S.L. and T.K.; supervision, T.K.; funding acquisition, T.K. All authors have read and agreed to the published version of the manuscript.  
Figure 12: Final results of source modeling.  
**Funding:** This work was supported by the 2020 Research Fund of the University of Seoul.  
**Data Availability Statement:** The surface deformation maps were provided by [PERSON] and [PERSON]. They have generated the maps from the ALOS PALSAR-2 interferometric data that were provided through the JAXA's ALOS-2 research program (RA4, PI No. 1412).  
**Conflicts of Interest:** The authors declare no conflict of interest.  
**Abbreviations**  
The following abbreviations are used in this manuscript:  
\begin{tabular}{l l} InSAR & Interferometric synthetic aperture radar \\
3D & Three-dimensional \\
2D & Two-dimensional \\ GPU & Graphics processing unit \\ CUDA & Compute unified device architecture \\ RMSE & Root-mean-square-error \\ LOS & Line-of-sight \\ MAI & Multiple aperture interferometry \\ BFGS & Broyden-Fletcher-Goldfarb-Shanno \\ L-BFGS & Limited memory Broyden-Fletcher-Goldfarb-Shanno \\ L-BFGS-B & Limited memory Broyden-Fletcher-Goldfarb-Shanno with boundaries \\ Armijo & Armijo line search \\ BWW & Bisection method for weak-Wolfe conditions \\ MT & More-Thuente line search \\ PTX & Parallel thread execution \\ SM & Streaming multiprocessor \\ SIMD & single instruction, multiple data \\ DRAM & Dynamic random access memory \\ cuLBFGSB & Parallel implementation of the L-BFGS-B \\ CSE & Common subexpression elimination \\ GFLOPS & Giga floating point operations per second \\ \end{tabular}