2-D tomography of first-arrivals using the Genetic Algorithm with Elitism

Abstract

Traditionally, first-arrival travel-time tomographic problems are treated as nonlinear inverse problems solved by deterministic optimization methods. These methods minimize the objective function by taking its derivatives. In some problems these derivatives are slow to compute and the method becomes inefficient. Another limitation inherent to deterministic methods is the strong relation between the starting model and local minima entrapment. To deal with these drawbacks, we apply a genetic algorithm with elitism (EGA) to cross-hole tomography of Ground Penetrating Radar (GPR) data. Regardless the starting model, this heuristic method ideally finds the region of the solution space containing global minima without calculating derivatives. We obtain good results in applying our method in two noise-corrupted synthetic cross-hole data sets. The first simulates horizontal strata and the second consists of a homogeneous background medium with single low-slowness anomaly. The methodology is also applied to field data where a cross-strata pattern is achieved. This pattern is in accordance with the geological feature of the region. Heuristic methods applied to highdimensional geophysical problems yield good results but are computationally expensive. Coupling heuristic and deterministic methods is recommended to exploit the full power of each optimization technique.