Determination of the elastic parameters of a VTI medium from sonic logging data using deep learning

Abstract

Inversion of sonic logging data becomes a non-trivial problem for anisotropic media, especially for the case of vertical transverse isotropic (VTI) formation, when a well is parallel to its axis of symmetry. Most modern processing techniques use only the kinematic characteristics of the wavefield. Thus, they are incapable of determining all formation elastic parameters (density, compressional and shear wave velocities, and Thomsen parameters) that fully describe such a case unless some rigorous assumptions are made or the well has deviated sections. A sensitivity analysis based on modeled seismic response to the elastic parameters illustrates the fact that sufficient information is contained in the amplitudes of different sonic modes. To retrieve this information, we perform a method of the sonic data inversion using a machine learning algorithm such as the convolutional neural network. Powerful computing resources are needed only for synthetic seismograms generation by the spectral element method for the range of geologically admissible parameters (training dataset) and optimization of the neural network weights by minimizing a misfit function. The inversion process consists simply of applying the optimized neural network to the sonic data to retrieve the elastic parameters that fully describe the VTI medium. We generated a series of synthetic sonic data different from the training one (test dataset) and compared the outcome of the inversion to the actual parameters. The results show good agreement within a few per cent for all elastic parameters illustrating the feasibility of the proposed method.