Three-Dimensional Transient Electromagnetic Modeling Using Rational Chebyshev Approximation

doi:10.1109/tgrs.2026.3721644

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Three-Dimensional Transient Electromagnetic Modeling Using Rational Chebyshev Approximation

2026-08-07

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DOI：10.1109/tgrs.2026.3721644

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Abstract

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The transient electromagnetics method (TEM) is important in geophysical exploration. We propose an efficient 3-D TEM forward modeling algorithm based on rational Chebyshev approximation (RCA). The proposed algorithm is based on a family of uniform-in-time rational approximants with a shared concentrated real pole. The location of the concentrated pole is designed to enhance late-time accuracy. Once the simulation time interval and error tolerance are defined, the optimal approximation order $n$ and the optimal real pole are automatically determined. Subsequently, through a three-term recurrence relation, the products of a series of rational Chebyshev interpolants and the initial vector are efficiently computed, requiring only a single coefficient matrix factorization followed by a minimal number of back-substitutions. Finally, the electric field responses at arbitrary decay times are obtained through a linear combination of these products and time-dependent weighting coefficients. Numerical experiments demonstrate the efficacy of the proposed method. We first establish the theoretical error bounds of the RCA algorithm using surrogate matrices and then compute the TEM responses for both 1-D layered and complex 3-D geoelectrical models. Comparisons with conventional algorithms indicate that the proposed RCA algorithm can significantly accelerate forward simulations while maintaining high accuracy.

Keywords:

3-D forward modeling

rational Chebyshev approximation (RCA)

transient electromagnetic method (TEM)