An LM Algorithm-Based Inversion and Applicability Analysis for Look-Ahead Electromagnetic Logging While Drilling

Look-ahead electromagnetic logging while drilling (EM LWD) technology has been widely used in geostopping due to its capability to characterize resistivity distributions ahead of the bit. However, a complex nonlinear relationship between tool responses and rock properties makes it difficult to image the geological structure. Therefore, inversion is essential to reconstruct resistivity distributions and determine formation boundary positions. Currently, gradient-based and artificial intelligence algorithms are commonly used for look-ahead inversion and have shown considerable potential. However, most related studies have focused on the analysis of tool detection capabilities, while research regarding inversion applicability and thin-layer formations remain insufficiently addressed. Additionally, due to the weak signal contribution from the area ahead of the drill bit, challenges still remain, such as the high tendency of inversion to fall into local optima and strong dependence on tool configuration.

In this paper, a look-ahead inversion framework based on the Levenberg-Marquardt (LM) algorithm is proposed, and its applicability to layered formation inversion is investigated. To prevent the inversion from being trapped in local optima, a continuous random multi-initial-value search strategy is proposed. Specifically, formation resistivity from look-around detection is used as a constraint, and random perturbations are applied to parameters to be inverted to select multiple initial values. Furthermore, the look-ahead signal decay is closely associated with tool configuration. By optimizing the selection of response curves through the adjustment of coil frequencies and transmitter-receiver spacings, the accuracy of the look-ahead inversion is further improved. Results demonstrate that the proposed inversion framework achieves an accuracy of up to 80% in the inversion of the distance to the nearest boundary for layered formations and yields favorable results in thin and multi-layer formations. It also provides algorithmic support for look-ahead EM LWD inversion and lays a theoretical foundation for further research on look-ahead inversion in formations with complex structures.

We are indebted to the financial support from the National Natural Science Foundation of China (42304140).