An Approximate Hybrid Method for Electromagnetic Scattering From an Underground Target

A hybrid method for modeling marine controlled-source electromagnetics, simplified integral equation (IE) (SIE) modeling, has shown very promising results in 2-D. The computational gain of SIE is very large for large problems in 3-D. We assess the accuracy and range of validity of SIE modeling in 3-D through order-of-magnitude analysis and through an extensive numerical comparison with rigorous IE modeling. A previously proposed order-of-magnitude analysis results in a dimensionless parameter which is easy to use as an a priori indicator for when SIE is valid. Unfortunately, this parameter is found to be sometimes inconsistent with our numerical results. Order-of-magnitude analysis for Maxwell´s equations is then reassessed in an attempt to rectify the shortcomings of the parameter adapted from the work “Electrical Impedance Tomography” by Cheney The dimensionless parameter resulting from the novel order-of-magnitude analysis is found to have generally good predictive capability. Unfortunately, this parameter is not suitable for deciding a priori if the use of SIE is justified for a particular case, since it depends on numerical results from IE modeling. For future use of SIE, it is therefore recommended to compare the problem characteristics of the case at hand with those covered by the extensive numerical comparison in this paper. From the numerical investigation, it is found that the accuracy of SIE is very good for resistive targets and for frequencies lower than about 10 Hz. For conductive targets, the accuracy is mostly very good for frequencies lower than about 5 Hz but somewhat more dependent also on other problem characteristics.