3D resistivity inversion using an improved Genetic Algorithm based on control method of mutation direction

Abstract

Abstract Traditional inversion method is the most commonly used procedure for three-dimensional (3D) resistivity inversion, which usually takes the linearization of the problem and accomplish it by iterations. However, its accuracy is often dependent on the initial model, which can make the inversion trapped in local optima, even cause a bad result. Non-linear method is a feasible way to eliminate the dependence on the initial model. However, for large problems such as 3D resistivity inversion with inversion parameters exceeding a thousand, main challenges of non-linear method are premature and quite low search efficiency. To deal with these problems, we present an improved Genetic Algorithm (GA) method. In the improved GA method, smooth constraint and inequality constraint are both applied on the object function, by which the degree of non-uniqueness and ill-conditioning is decreased. Some measures are adopted from others by reference to maintain the diversity and stability of GA, e.g. real-coded method, and the adaptive adjustment of crossover and mutation probabilities. Then a generation method of approximately uniform initial population is proposed in this paper, with which uniformly distributed initial generation can be produced and the dependence on initial model can be eliminated. Further, a mutation direction control method is presented based on the joint algorithm, in which the linearization method is embedded in GA. The update vector produced by linearization method is used as mutation increment to maintain a better search direction compared with the traditional GA with non-controlled mutation operation. By this method, the mutation direction is optimized and the search efficiency is improved greatly. The performance of improved GA is evaluated by comparing with traditional inversion results in synthetic example or with drilling columnar sections in practical example. The synthetic and practical examples illustrate that with the improved GA method we can eliminate the dependence on initial model, and obtain high-quality inversion results.