The airborne transient electromagnetic (ATEM) method is a geophysical exploration technique that offers several advantages, including rapid exploration, minimal interference from complex terrains, dense data sampling, and environmental friendliness. However, the full-frequency time-domain secondary field signal acquisition of the ATEM data is susceptible to various electromagnetic interferences, resulting in noise in the collected data. This noise complicates subsequent processing and interpretation. To address this issue, we have developed a 1D minimum-curvature difference equation with unequal spacing based on minimum-curvature differential equations. Through research, we develop an ATEM noise-suppression method based on multiple single-step and multiple superposition-step implicit iterative formats. In addition, we have investigated the convergence of explicit and implicit iterative schemes via Fourier spectrum analysis and proven that the implicit iterative schemes converge. This method effectively suppresses noise in synthetic and real ATEM data during processing. Our results show that the minimum-curvature method is particularly effective in suppressing sferic and Gaussian noises in ATEM data. As a result, our method provides high-quality and reliable ATEM data for further data processing and interpretation. Moreover, the minimum-curvature method is also capable of suppressing noise in ground and ground-space transient electromagnetic data, as well as magnetotelluric data noise. Therefore, this method exhibits a wide range of potential applications.
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