Applying three-dimensional inversion to the frequency-domain response converted from transient electromagnetic data for a rectangular fixed loop

The computationally expensive cost and complexity are practical challenges in solving the three-dimensional (3D) inverse problem in the time domain, and many real-world surveys are still inverted in one dimension (1-D). We present a new way to invert transient electromagnetic (TEM) data from a rectangular fixed loop to image subsurface electrical conductivity, which overcomes this limitation and permits efficient implementation of the inversion process on a personal computer. A TEM signal was transformed to the real and imaginary components of a frequency-domain (FD) electromagnetic (EM) response. The transformation was performed by a regularization inversion method. The recovered FD EM response was used as the data for the 3-D inversion. The forward problem and sensitivity were solved by using a staggered-grid finite-difference technique in the FD, and the background Green's function was carried out using the virtual interface method. The non-linear conjugate gradient method (NLCG) was employed to solve the 3-D inverse problem. A synthetic example revealed the basic functionality of the approach, and the FD inversion of a TEM field dataset acquired in the northeastern Qinshui Basin, Shanxi Province, China demonstrated a real-world application. Our inversion approach is general and suitable for different-type sources, such as a vertical magnetic dipole or horizontal electric dipole.