Parallel Inversion of 3D Airborne Transient Electromagnetic Data Using an Approximate Jacobi Matrix

Abstract

In geophysical inversion issues, the Jacobian matrix computation takes the greatest time, and it is the most significant factor limiting the inversion’s calculation speed. We think that the correctness of the inverse problem is determined by the difference between the inversion data and the real data, not the precision of the gradient solution in each iteration. Based on this, we present an approximate computation approach for the Jacobian matrix that may rapidly solve the inverse issue by estimating the gradient information. In this research, the approximate gradient information is solved in each iteration process, and the approximate gradient is utilized for computation; nevertheless, the poor fitting of the evaluation data is correctly evaluated, and the inversion model that fits the criteria is achieved. We employed this approach of estimating the Jacobian matrix to invert the 3D airborne transient electromagnetic method (ATEM) on synthetic data, and it was able to significantly minimize the time necessary for the inversion while maintaining inversion accuracy. When the model mesh is more precise, this technique outperforms the previous way of finding the exact Jacobian matrix in terms of acceleration.