Synthesizing Missing Travel Time of P-Wave and S-Wave: A Two-Stage Evolutionary Modeling Approach

Abstract

Acquiring sonic waves is an essential part of oil and gas exploration as they give critical information about the well’s data and lithography at each well depth progression. However, these measurements are not always accessible, making analysis challenging. As computational power has improved, machine learning methods may now be used to predict these values from other data. Nonetheless, one shortcoming of existing models is that the most of them are not transparent (i.e., black box models). As a result, although promising great performance, they do not offer much insights to petrophysicists and geologists. This research aims to generate mathematical models for predicting compression wave (P-wave) and shear wave (S-wave) readings using a multistage evolutionary modelling approach. In particular, a multistage equation modelling approach using tree-based Genetic Programming (GP) and Adaptive Differential Evolution (ADE) is proposed. The obtained best mathematical models yield R <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> of 0.745 and 0.9066 for P-wave and S-wave regression on normalized data, respectively. The average performance of models are R <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> = 0.90 (P-Wave) and R <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> = 0.75 (S-Wave). The performance of these mathematical models are comparable with other ”black box” models but with more compact mathematical approach in regression thereby opening opportunities for interpretability and analysis. Finally, the ”white box” models presented in this paper can be fine-tuned further as needed.