An efficiency-improved GPU algorithm for the 2 + 2 + 1 method in nonlinear beamforming

Nonlinear beamforming (NLBF) has emerged as a highly effective technology for enhancing seismic data quality. The crux of NLBF's success lies in its ability to robustly estimate local traveltime operators directly from input data, a process that entails solving millions or even billions of nonlinear optimization problems per input gather. Among the solvers utilized for estimating these operators is the 2 + 2 + 1 method, for which we have previously introduced algorithmic implementations on both the CPU and GPU platforms. In this paper, we present an efficiency-improved GPU algorithm for the 2 + 2 + 1 method, particularly beneficial when dealing with small data apertures in NLBF. Our enhanced GPU algorithm brings significant improvements in computation efficiency through several strategic measures, which include leveraging Horner's method to minimize the mathematical overhead of traveltime calculation, implementing a GPU-friendly data reduction algorithm to exploit GPU computational power, and optimizing shared GPU memory usage as the primary workspace whenever feasible. To demonstrate the tangible efficiency enhancement achieved by our new GPU algorithm, via two illustrative examples, we compare its performance with that of our previous implementation.