Hybrid Geophysical Inversion Using Genetic Algorithm and Gradient Descendant Methods

Abstract:

Inversion and joint inversion are very popular methods for geophysical parameter estimation. Different algorithms can be used to calibrate one or several models during an inversion process, including statistical and stochastic, evolutionary and gradient descendant algorithms. Stochastic and evolutionary methods can be classified as global search algorithms, as they search for the best solution in a wide parameter space, often the full system domain. The main advantages of global search methods are the ability to avoid local minima regions and estimate parameters with non-linear relationship with physical observations, while their disadvantages include high computational effort and low performance to find the overall best solution. Gradient descendant algorithms nevertheless simplify the problem linearizing the system and minimizing the differences between field and synthetic observations (objective function), being able to find the actual best solution. However, this method works mainly for one minima region, being highly susceptible to local minima solutions, and the system derivatives must exist in all searchable parameter space.

Applying both methods in a sequential procedure can combine their advantages while avoiding their weaknesses. This work proposes a hybrid inversion procedure based on Genetic Algorithm and Gauss-Marquardt-Levenberg numerical modeling for geophysical inversion problems.