Deriving analytical solution of the pseudo wavefield from transient electromagnetic data
LI Hai1,2(), ZHAO Pan3, LI Ke-Ying1,2,4, LIU Zheng5
1. Key Laboratory of Mineral Resources, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing 100029, China 2. Institutions of Earth Science, Chinese Academy of Sciences, Beijing 100029, China 3. RDFZ Chaoyang School, Beijing 100028, China 4. College of Earth and Planetary Sciences, University of Chinese Academy of Sciences, Beijing 100049, China 5. Hebei Geophysical Exploration Institute, Hebei Shallow Geothermal Energy Research Center, Langfang 065000, China
The transform from transient electromagnetic (TEM) field to pseudo wavefield is the basis for using the imaging technique. The TEM field follows the diffusion equation, while the pseudo wavefield follows the wave equation. These two can be transformed into each other via the Q-transform. As the integral transformation from TEM field to pseudo wavefield is ill-posed, numerical method is used to get the desired pseudo wavefield. As a result, it is often the case that the methods and parameters are need to be optimized to get a optimal pseudo wavefield. Therefore, here in this paper, we derived the analytical solution of the pseudo wavefield from the TEM field. We start from the analytical formula of TEM field, and utilize the Laplace transform to establish the analytical solution pairs. The pairs can be used to test the accuracy and stability of the numerical method, as well as examining the features of the pseudo wavefield to get an effective imaging method.
李海, 赵攀, 李柯颖, 刘峥. 电性源瞬变电磁法虚拟波场解析推导[J]. 物探与化探, 2024, 48(5): 1193-1198.
LI Hai, ZHAO Pan, LI Ke-Ying, LIU Zheng. Deriving analytical solution of the pseudo wavefield from transient electromagnetic data. Geophysical and Geochemical Exploration, 2024, 48(5): 1193-1198.
Li H, Xue G Q, Zhong H S, et al. Joint inversion of CMP gathers of multi-channel transient electromagnetic data[J]. Chinese Journal of Geophysics, 2016, 59(12):4439-4447.
Xue G Q, Chen W Y, Zhou N N, et al. Short-offset TEM technique with a grounded wire source for deep sounding[J]. Chinese Journal of Geophysics, 2013, 56(1):255-261.
[3]
Di Q Y, Xue G Q, Yin C C, et al. New methods of controlled-source electromagnetic detection in China[J]. Science China Earth Sciences, 2020, 63(9):1268-1277.
[4]
Lee K H, Liu G, Morrison H F. A new approach to modeling the electromagnetic response of conductive media[J]. Geophysics, 1989, 54(9):1180-1192.
Qi Z P, Li X, Wu Q, et al. A new algorithm for full-time-domain wave-field transformation based on transient electromagnetic method[J]. Chinese Journal of Geophysics, 2013, 56(10):3581-3595.
Xue J J, Zhong H S, Li H, et al. An improvement to the transformation algorithm for the transient electromagnetic field[J]. Chinese Journal of Geophysics, 2018, 61(12):5077-5083.
Lu K L, Li X, Qi Z P, et al. A precise integration transform algorithm for transformation from the transient electromagnetic diffusion field into the pseudo wave field[J]. Chinese Journal of Geophysics, 2021, 64(9):3379-3390.
[8]
Xue G Q, Bai C Y, Li X. Extracting the virtual reflected wavelet from TEM data based on regularizing method[J]. Pure and Applied Geophysics, 2012, 169(7):1269-1282.
Zhong H S, Xue G Q, Li X, et al. Pseudo wavefield extraction in the multi-channel transient electromagnetic (MTEM) method[J]. Chinese Journal of Geophysics, 2016, 59(12):4424-4431.
Xue G Q, Li X, Guo W B, et al. Equivalent transformation from TEM field sounding data to plane-wave electromagnetic sounding data[J]. Chinese Journal of Geophysics, 2006, 49(5):1539-1545.
Xue G Q, Li X. The technology of TEM tunnel prediction imaging[J]. Chinese Journal of Geophysics, 2008, 51(3):894-900.
[14]
Xue G Q, Gelius L J, Li X, et al. 3D pseudo-seismic imaging of transient electromagnetic data:A feasibility study[J]. Geophysical Prospecting, 2013, 61(s1):561-571.
[15]
Li H, Xue G Q, Zhao P. A new imaging approach for dipole-dipole time-domain electromagnetic data based on the q-transform[J]. Pure and Applied Geophysics, 2017, 174(10):3939-3953.
[16]
Weir G J. Transient electromagnetic fields about an infinitesimally long grounded horizontal electric dipole on the surface of a uniform half-space[J]. Geophysical Journal International, 1980, 61(1):41-56.
[17]
李海. 多道瞬变电磁法数据处理关键技术研究与应用[D]. 北京: 中国科学院大学, 2016.
[17]
Li H. Research and application of key technologies in data processing of multi-channel transient electromagnetic method[D]. Beijing: University of Chinese Academy of Sciences, 2016.
[18]
Ziolkowski A, Hobbs B A, Wright D. Multitransient electromagnetic demonstration survey in France[J]. Geophysics, 2007, 72(4):F197.
