ABSTRACT: A majority of well logs contain basic petrophysical and lithological values which usually include density, porosity, resistivity, gamma-ray, and customarily, the caliper measurement of borehole diameter to provide an indication of borehole and log quality. Acoustic log acquisition may not be routine, especially in older wells and in cost-constrained environments. Attempts can be made to create synthetic acoustic logs relying on petrophysical and empirical models. However, their reliability and applicability do depend to a large extent on the complexity, variability, and uncertainty of subsurface rocks and fluids. Often, the challenge is compounded by rock heterogeneity such as the highly variable and laminated unconventional shales. In this paper, we tackle the problem of predicting acoustic log response given common well log values such as gamma-ray, resistivity, porosity, and density. Well logs from two very different/contrasting rock formations are used in this exercise. Accurate prediction of acoustic response is shown to be considerably more challenging when rock formation is highly heterogeneous. We consider the generation of synthetic acoustic well log values as a regression task between lithological/petrophysical parameters and acoustic well log values. We survey common machine learning methods in this problem and introduce the use of more advanced techniques. Our methodology includes the adoption of Monte Carlo dropout as a probabilistic inference alternative to regular inference, which allows the quantification of uncertainty in model prediction without having to significantly increase the model’s computational complexity. We survey the performance of all models using two well log datasets, one set of well logs is taken from a relatively homogenous rock formation and the other from a heterogenous rock formation. Out of all models, the proposed Convolutional Neural Network coupled with Monte Carlo dropout provides the most robust results with adequate quantification of prediction uncertainty.

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