Physics-Constrained Deep Learning of Geomechanical Logs

Geomechanical logs are of ultimate importance for subsurface description and evaluation, as well as for the exploration of underground resources, such as oil and gas, groundwater, minerals, and geothermal energy. Together with geological and hydrological properties, low-cost and high-accuracy models can be generated based on geomechanical parameters. However, it is challenging to directly measure geomechanical parameters, and they are usually estimated based on other measured quantities. For example, geomechanical logs may be obtained with certain empirical models from sonic logs together with prior information such as rock types, which are not readily available. Finding a way to directly estimate geomechanical logs based on easily available conventional well logs can result in significant cost savings and increased efficiency. In this article, we showed that deep learning via the long short-term memory network (LSTM) is effective in constructing an end-to-end model that takes the spatial dependence in well logs into consideration. We further proposed a physics-constrained LSTM, in which the physical mechanism behind the geomechanical parameters is utilized as a priori information. This state-of-the-art model is capable to directly estimate geomechanical logs based on easily available data, and it achieves higher prediction accuracy since the domain knowledge of the problem is considered.