This paper introduces a novel deep learning architecture for solving inverse problems using LWD azimuthal resistivity measurements, which are essential to adjusting the wellbore trajectory while drilling, or geosteering. Since geosteering inversion belongs to "logging-whiledrilling (LWD)" techniques, it requires real-time processing for industrial use to help the drilling states updated in time.

The main challenge of the geosteering inversion is the conflict between the limited computational resources and the requirement for fast processing. For geosteering using LWD azimuthal resistivity measurements, the parameters of earth model surrounding the wellbore need to be inferred from a set of logging measurements, and these inverse problems are oftentimes highly nonlinear. Due to the non-linearity, traditional methods that rely on iterative procedures and pre-defined regularization are usually sensitive to the selection of initial values and could be inefficient with convergence issues. In industrial applications, a lookup table is utilized to produce fast predictions. However, this approach could not reach a high accuracy due to the limitation of memory or storage.

In this paper, we propose a novel physics-driven deep learning framework for providing a fast and accurate surrogate to solve geosteering inverse problems. Particularly, leveraged by the rigorous forward model and 1D Convolutional Neural Network (1D-CNN), and with the introduction of a new physics-driven loss function accommodating both the model misfit and the data misfit, the proposed method provides more reliable inversion solutions with improved performance.

Our experiments are performed based on synthetic data. The whole workflow could be described as

  1. Generate a large synthetic dataset for training the network. The dataset is in the whole data space of earth model parameters.

  2. Generate the testing set. Each testing sample is used to describe a continuously distributed underground formation.

  3. Train the network with the training set. Both model misfit and data misfit are utilized.

  4. Test the proposed inverse model with the testing set. Analyze the testing results by varying the configuration of the network.

The experiments demonstrate the effectiveness of our method. We compare our proposed model with the lookup table method and a conventional data-driven network. The testing results show that our method could achieve both lower model misfit and lower data misfit statistically. To test the feasibility and sensitivity of our work, we have also performed the following tests:

  1. We compare both the time cost and memory cost of our model with that of the lookup table and a traditional iterative method. Results show that our method could achieve a high accuracy without causing high computational costs.

  2. We compare traditional artificial networks and our model. The results prove that the 1D-CNN is more suitable for solving this problem because of the low costs and high performance.

  3. We test the sensitivity of our model by adding different levels of white noise to the observed measurements. The results indicate that the stability of our model could be obviously improved by injecting noise to the training set.

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