Generation of Synthetic Density Log Response using Multivariate Adaptive Regression Splines

Abstract

There are instances in well logging operations where log response can be missing or inaccurate for a specific depth of interest due to wellbore conditions such as wellbore size, wellbore rugosity and mud cake effects. The conventional approach is to rerun the logs at definite depths, however, this remedial technique is costly, time-consuming and prone to errors due to the presence of a casing. Machine learning methods are currently implemented as an innovative way of predicting missing log responses. The present study seeks to investigate the potential of multivariate adaptive regression splines (MARS) as a density log predictive model. The performance of the developed MARS model was judged with the widely used artificial neural networks (ANN). The results reveal that MARS generalise better when predicting the density log response of the testing data. The MARS density log model achieved the highest correlation of 0.869, an error rate of 0.01196 and 0.1094 for MSE and RMSE respectively on the withheld dataset. While back propagation neural network (BPNN) and radial basis function neural network (RBFNN) had 0.855 and 0.802 as R, 0.0128 and 0.0147 as MSE, 0.1131 and 0.1212 as RMSE respectively. Therefore, a cost-effective MARS model can accurately generate synthetic density well log response.