Comparative Study of Shallow Learning Models for Generating Compressional and Shear Traveltime Logs

Compressional and shear traveltime logs (DTC and DTS, respectively) acquired using sonic logging tools are used to estimate connected porosity, bulk modulus, shear modulus. Young's modulus, Poisson's ratio, brittleness coefficient, and Biot's constant for purposes of geomechanical characterization. We propose a data driven technique to synthesize DTC and DTS logs in the absence of a sonic logging tool. Six shallow learning methods, namely ordinary least squares (OLS), partial least squares (PLS), least absolute shrinkage and selection operator (LASSO), elastic-net regularization, multivariate adaptive regression splines (MARS) and artificial neural network (ANN), suitable for function approximation problems, are trained and tested to synthesize DTC and DTS logs. To that end, the six shallow learning models process 13 conventional and easy-to-acquire logs, namely Ethology, gamma ray, caliper, density porosity, neutron porosity, photoelectric factor, bulk density, and resistivity at six depths of investigations. A total of 8,481 observations along a 4,240-ft depth interval in a shale reservoir were available for the proposed data driven application. The ANN algorithm performs the best among the six algorithms. ANN-predicted DTC and DTS logs have coefficients of determination (R-2) of 0.87 and 0.85, respectively, for Well I. The next best prediction performance is provided by the MARS-predicted DTC and DTS logs, with accuracies of 0.85 and 0.83, respectively. PLS- and OLS-predicted DTC and DTS have accuracies measured by R-2 of 0.83 and 0.80, respectively, whereas the LASSO- and elastic-net-predicted DTC and DTS have accuracies of 0.79 and 0.75, respectively. The prediction performances of the six algorithms for DTC are always better than those for DTS. The ANN model trained in Well 1 is deployed in Well 2, which was drilled in the same reservoir. The ANN-predicted DTC and DTS logs in the 1,460-ft depth interval of Well 2 have R-2 of 0.85 and 0.84, respectively.