Electromagnetic imaging of a fuel oil spill at Sandia/CA

The multifrequency, multisource integral wave migration method commonly used in the analysis of seismic data is extended to electromagnetic (EM) data within the audio frequency range. The method is applied to the secondary magnetic fields produced by a borehole, vertical electric source (VES). The integral wave-migration method is a numerical reconstruction procedure utilizing Green`s theorem where the fields are migrated (extrapolated) from the measuring aperture into the interior of the earth. To form the image, the approach used here is to Fourier transform the constructed image from frequency domain to time domain and set time equal to zero. The image is formed when the in-phase part (real part) is a maximum or the out-of-phase (imaginary part) is a minimum; ie., the EM wave is phase coherent at its origination. In the application here, the secondary magnetic fields are treated as scattered fields. To determine the conductivity, the measured data migrated to a pixel location are equated to calculated data migrated to the same pixel. The conductivity is determined from solving a Fredholm integral equation of the first kind by solving a system of linear algebraic equations. The multifrequency, multisource integral wave-migration method is applied to calculated model data and to actual field data acquired to map a diesel fuel oil spill. For the application discussed here, a two dimensional resistivity slice is calculated from the solution to the Fredholm integral equation. The resistivity image of the fuel oil agrees with the known location.