Precision of imaging cross-hole electromagnetic responses in real formation by using axial symmetric 2-D model

Key words:  cross-hole electromagnetic response  integral equation  axial symmetric 2-dimension model  3-dimension model  cross-hole electromagnetic imaging

Abstract:

The abnormal body 's responses in axial symmetric 2-D and 3-D cross-hole formation model were simulated by 2-D integral equation and volume integral equation respectively. The influence of the 3-D abnormal body 's thickness and eccentricity along the direction perpendicular to the transmitter-receiver section on its responses was analyzed, and the influence of the body 's horizontal position on its responses was also analyzed. The Born iteration method (BIM) was used to image the 2-D conductivity on the transmitter-receiver section by inverting the simulated data for different formation models. Both forward modeling and imaging results show that the imaging quality is directly related to the 3-D abnormal body 's thickness and eccentricity along the direction perpendicular to the transmitter-receiver section when the axial symmetric 2-D model is adopted to get the conductivity distribution on the transmitter-receiver section by inverting the data measured in 3-D cross-hole formation. As long as the 3-D abnormal body is thick enough along the direction perpendicular to the transmitter-receiver section and its center is close enough to the transmitter-receiver section, it is feasible to get high quality imaging by adopting axial symmetric 2-D cross-hole formation model. The imaging quality will become worse if the abnormal body 's thickness becomes much smaller and its eccentricity becomes much bigger.