Embedding the physics-based forward modeling function in training the deep network could improve the accuracy of the learning-based regression. Solving the geosteering inverse problem is a critical technique of logging while drilling (LWD). When the logging tool has an ultra-long sensitive distance, combining the geosteering inversion with the deep learning techniques may cause sensitivity issues and lead the training to fail. This paper proposes a cross-gradient based method for solving the highly sensitive geosteering inversion with a physics-driven deep network. By inspecting the relationship between earth-model-based gradients and measurement-based gradients, we develop a multi-objective optimization algorithm for training the network. Numerical experiments show that the proposed algorithm could handle the high sensitivity cases, and converge on a better solution with the performance of the predictions improved.

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