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The detection of deep targets has always been a challenging topic for controlled source electromagnetic methods; however, the time–frequency electromagnetic method (TFEM) can overcome some of these challenges. In this paper, we introduce the method and showcase the technique for imaging deep targets using optimal offsets and transmission periods. In addition, we implement a simulated annealing constrained inversion, based on well-seismic data, to illustrate improvement in the effective detection depth and the ability to identify deep targets. We apply TFEM for two targets in North Xinjiang to show that internal multiple sets of layered series in a deep Carboniferous system and the volcanic rock mass developed in this area can be imaged. We conclude that the low-resistivity layer inside the Carboniferous system is the response of hydrocarbon source beds of muddy clastic rocks and predict that the high-resistivity layer is a favorable reservoir of volcanic rocks. Subsequent drilling confirmed the structural characteristics of the Carboniferous system revealed by TFEM data.

A special penalty method is presented to improve the accuracy of the standard penalty method for solving Stokes equation with nonconforming finite element. It is shown that this method with a larger penalty parameter can achieve the same accuracy as the standard method with a smaller penalty parameter. The convergence rate of the standard method is just half order of this penalty method when using the same penalty parameter, while the extrapolation method proposed by Faik et al can not yield so high accuracy of convergence. At last, we also get the super-convergence estimates for total flux.