Random Forest Regressor for Layered Earth Data Inversion

Interpretation of geophysical data sets involves solving an inverse problem for recovering information on subsurface physical properties from observed data. Geophysical inversion problems are ill-posed non-linear problems. We have attempted to achieve global convergence for this problem using a Machine learning approach- Random Forest Regressor (RFR). It fits a number of decision trees on various equal sub-samples of dataset and averages the result from each decision tree to give an output. RFR approach has been preferred due to its ability to solve highly complex inversion problems, if trained using sufficient number of training examples without the need of computing forward code in each iteration to determine the output. In this study, inversion of synthetic magnetotelluric (MT) and DC resistivity data sets for a three-layered earth has been performed. For comparison sake, MT results have been compared to those obtained from Particle Swarm Optimization (PSO), Genetic algorithm (GA) and ridge regression (RR) algorithm. The resistivity results have been compared with PSO and Grey Wolf optimization (GWO) techniques. The results obtained for MT apparent resistivity problem from RFR are in close agreement with true model parameters and are much better than those obtained from RR, GA and PSO. The considered model for resistivity is a typical equivalence problem. The obtained results are closer to the true model and are far better than those obtained from GWO and PSO. The obtained result demonstrates the efficacy of the regressor and probably helps in tackling equivalence problem.