An efficient inversion method of array induction logging using LSTM neural network

Abstract Array induction logging technology plays a crucial role in the identification and fluids quantitative evaluation in oil and gas wells. In conventional inversion methodologies, software focusing is initially applied to raw data to derive key parameters, which serve as priors for subsequent inversion processes. Precise resistivity inversion is critical for identification of oil- and water zones/layers. Compared to the direct utilization of raw measurements, software focusing generates additional computational overhead and increases processing time, and it also exhibits slow convergence and a propensity to become trapped in local optima, limiting the inversion efficiency and robustness. To address these challenges, this paper proposes an efficient inversion method of long short-term memory (LSTM) neural networks, which directly processes raw array data, simplifying the inversion workflow and overcoming the limitations of traditional inversion methods. First, a fast forward algorithm for 2D horizontally layered formations in vertical wells was developed by numerical mode matching, and a sample database of array induction logging curves is generated. Second, a deep learning model of LSTM network was constructed, which was then trained and optimized to automatically capture the complex mapping relationship between logging responses and formation parameters based on the sample data. Finally, the optimized deep learning network is employed to inverse logging data. The results indicate that the proposed LSTM-based inversion method significantly enhances computational efficiency, reducing the single-point inversion time to less than 1 ms, which corresponds to a four to five orders of magnitude improvement over conventional approaches. Furthermore, the resistivity estimation exhibits a relative error predominantly within 5%, while the absolute error in the invaded zone radius remains largely within 0.1 m, demonstrating the method's high accuracy. Additionally, the robustness tests indicate that the method retains high accuracy even when dealing with samples exhibiting different relative noise levels. Further application of the network to complex synthetic formation models reveals that the inversion results are accurate, underscoring the strong generalization ability of the network.