In 3D seismic data acquisition, sufficiently dense spatial sampling is most often not possible, because of physical, financial, and temporal constraints. The resulting aliased data is a major obstacle for accurate subsurface images. Therefore, methods are needed to reconstruct these sparse data to an adequate sampling. We develop a novel kinematic wavefront-based seismic data reconstruction method that uses the existing nonlinear beamforming (NLBF) framework, which allows for building a more detailed sampling from a sparse input. We present the theory and methodology of our NLBF reconstruction algorithm and test it on a synthetic Society of Exploration Geophysicists Advanced Modeling (SEAM) Arid dataset and a field dataset. We attempt to answer the following question: can the NLBF framework be used for seismic data reconstruction, and how do these results compare to some conventional reconstruction methods? Control parameter tests are performed to find the optimal NLBF reconstruction, and results are compared to those from several control methods including the convergent alternating projection onto convex sets (POCS) and bootstrap POCS methods, which were also developed for this study. Our NLBF reconstruction method successfully reconstructs high-quality data on both datasets. We find that the optimal NLBF control parameters are ultimately dataset-dependent as the concrete data acquisition geometry plays a central role. Specifically for our datasets, optimal parameters include a time window of 12∆ts, an operator aperture of 600 m x 600 m, and a parameter trace interval of ∆x = ∆y = 60 m. The synthetic SEAM Arid NLBF reconstruction results show high trace fidelity to the ground truth. The field data NLBF results show better-reconstructed gaps, and wavefield variations closer to those of physical propagating waves in comparison to our control methods. These results show the potential of the NLBF reconstruction method to become a common data reconstruction tool used in the seismic industry.

Since its inception in 1975, Genetics Algorithms (GAs) have been successfully used as a tool for global optimization on non-convex problems in a wide range of real world applications. Its creation was inspired by natural adaptation and selection mechanisms that evolve from one population of chromosomes to a fitter population by means of an artificial natural selection dictated by the operators of elitism, crossover and mutation. An advanced Genetic Algorithm (aGA) was proposed by Sun et al. [2017], and this algorithm seeks the global maximum of n-th dimensional non-convex functions. However, convergence speed is a key factor for the success of a global optimization algorithm when it comes to scalability; in production even a slight efficiency improvement matters as it can easily takes weeks or even months to process a huge data set. Therefore, the goal of this project is to improve the convergence speed of the currently available aGA by simultaneously enhancing both its global and its local search capabilities. To this end, two solutions were proposed. The first is a modified version of the well known Island model GAs and the second was named Self Adaptive Differential Evolution (SADE) fine tuning scheme.
After a successful demonstration of its improved performance on several multi-modal test functions, the enhanced Genetic Algorithm (eGA) is used to tackle two common non-linear geophysical problems: static correction and Common Reflection Surface (CRS) stacking. In the former, the near-surface related time-shifts are estimated without resorting to an explicit velocity-depth model; instead, the events of interest are aligned in a data-driven fashion by maximizing the stacking power. The latter is a novel alternative to the traditional Common Midpoint (CMP) stacking that has proven to yield higher quality images, specially when applied to low Signal to Noise Ratio (SNR) data or data with challenging structures like the anomalies encountered in the subsurface. This improvement in the quality of the stacked image is attributed to a non-local mean mentality, which enables using traces from different CMP gathers to the CMP gather being resolved. Owing to the high non-linearity of both problems, they are ideal test beds for global optimization algorithms. The effectiveness of the eGA is demonstrated on synthetic data sets with promising results in these problems.