Abstract
Herein, a three-dimensional (3D) inversion method in the frequency domain based on a time–frequency transformation was developed to improve the efficiency of the 3D inversion of transient electromagnetic (TEM) data. The Fourier transform related to the electromagnetic response in the frequency and time domains becomes a sine or cosine transform under the excitation of downward-step current. We established a transformation matrix based on the digital filtering calculation for the sine transform, and then the frequency domain projection of the TEM data was determined from the linear transformation system using the smoothing constrained least squares inversion method, in which only the imaginary part was used to maintain the TEM data transformation equivalence in the bidirectional projection. Thus, the time-domain TEM inversion problem was indirectly and effectively solved in the frequency domain. In the 3D inversion of the transformed frequency-domain data, the limited-memory Broyden–Fletcher–Goldfarb–Shannoquasi–Newton (L-BFGS) method was used and modified with a restart strategy to adjust the regularization parameter when the algorithm tended to a local minimum. Synthetic data tests showed that our domain transformation method can stably project the TEM data into the frequency domain with very high accuracy; furthermore, the 3D inversion of the transformed frequency-domain data is stable, can be used to recover the real resistivity model with an acceptable efficiency.
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Acknowledgments
We would like to thank the four reviewers and the editors for their helpful suggestions and comments. We are also grateful to Dr. Ruan Shuai for his suggestions.
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This research was supported by the National Key Research and Development Program of China (No. 2016YFC060110403).
Yang Yun-Jian, a senior engineer, was born in 1975. He graduated from China University of Geosciences (Wuhan) with a Bachelor’s degree in Applied Geophysics in 1997 and a Master’s degree in Geophysics from Chengdu University of Technology in 2006. He is now working in BGP Inc., engaged in electrical exploration research and application.
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Yang, YJ., Wang, XB., Liu, XJ. et al. A three-dimensional transient electromagnetic data inversion method based on a time—frequency transformation. Appl. Geophys. 17, 361–376 (2020). https://doi.org/10.1007/s11770-020-0826-6
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DOI: https://doi.org/10.1007/s11770-020-0826-6