An efficient noise-tolerant, two-dimensional conductivity-imaging technique has been developed to invert the data measured by an electromagnetic (EM) cross-hole tool. The method is successfully applied to image the field data measured by the Lawrence Livermore and Lawrence Berkeley National Laboratories at the Richmond Field Station at the University of California, Berkeley. The Richmond project aimed at monitoring the migration of salt water injected into a fresh water table. The cross-hole distance is 20 to 26 m and a depth of 55 m is reached. A continuous wave EM system with an operating frequency of 18.5 kHz was used. A center injection well and four monitoring wells were drilled. After the first EM cross-hole measurement between the center well and the four monitoring wells was made, 50,000 gallons (189,450 L) of salt water were injected from the center well at a depth of 26 to 30 m where a fresh water table is located. Another set of EM cross-hole data was obtained after the saltwater injection. The migration of salt water can be clearly seen from the EM tomographs. The misfit between the measured data and computed data at the final iteration is less than 7% for all the conductivity tomographs reconstructed. The inversion method is a two-dimensional full-wave inversion process with an assumption of axial symmetry about the transmitter well. An iterative image reconstruction algorithm is used to reduce the computational complexity.

Inversion is regularized by applying a maximum entropy constraint. A distorted Born approximation is employed in which a layered background is allowed. The inversion starts with an estimated homogeneous formation and inverts the homogeneous average conductivity first. Then, a layered conductivity image is constructed using the homogeneous data as the initial value. Finally, a two-dimensional conductivity image is reconstructed iteratively using the one-dimensional image as the initial input. Conductivity tomographs obtained from Richmond site show that there is a high-conductivity layer at the depth of 17 m with a conductivity approximately equal to 0.25 S/m, which is not shown in the resistivity logs. The formation around the transmitter well is a layered formation with relatively low conductivity. The average conductivity of the test field is approximately 0.05 S/m. The conductivity of the formation near the lower portion of the test field keeps a low value of less than 0.03 S/m. The success of the EM cross-hole measurement and the inversion revealed the potential of using such a device to detect contaminated soil and monitor the migration of contaminants in the ground. ¿ American Geophysical Union 1995