Full-waveform inversion of cross-hole radio frequency electromagnetic data

We consider application of full-waveform inversion (FWI) to radio-frequency electromagnetic (EM) data. Radio-frequency imaging (RIM) is a cross-borehole technique to image EM subsurface properties from measurements of transmitted radio-frequency waves. It is used in coal seam imaging, ore exploration and various engineering and civil engineering applications. RIM operates at frequencies from 50 kHz to several tens of MHz. It differs from other geophysical EM methods, because the frequency band includes the transition between the wave propagation and diffusion regimes. RIM data are acquired in 2-D cross-hole sections in a reciprocal manner. Traditionally, radio-frequency data are inverted by straight-ray tomography because it is inexpensive and easy to implement. It is argued that due to attenuation, the sensitivity of the transmitted electric field is the strongest within the first Fresnel zone of the ray connecting the transmitter and receiver. While straight-ray tomography is a simple method to implement and fast, the nonlinearity in the relationship between model parameters and data is often strong enough to warrant nonlinear inversion techniques. FWI is an iterative high-resolution technique, in which the physical properties are updated to minimize the misfit between the measured and modelled wavefields. Full-waveform techniques have been used and extensively studied for the inversion of seismic data, and more recently, they have been applied to the inversion of ground penetrating radar data. Nonlinear inversion methods for RIM data are less advanced. Their use has been hindered by the high cost of full-wave modelling and the high conductivity contrasts of many RIM targets, and, to some extent, by the limitations of the measuring instruments. We present the first application of this methodology to perform simultaneous conductivity and permittivity inversion of RIM data. We implement the inversion in the frequency domain in two dimensions using Limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) optimization. We analyse the sensitivity of the data to the model parameters and the parameter trade-off and validate the proposed methodology on a synthetic example with moderate conductivity variations and localized highly conductive targets. We then apply the FWI methodology to a field data set from Sudbury, Canada. For the field data set, we determine the most appropriate pre-processing steps that take into account specific peculiarities of RIM: the insufficient prior information about the subsurface and the limitations of the measuring equipment. We show that FWI is applicable under the conditions of RIM and is robust to imperfect prior knowledge: we obtain satisfactory model recoveries starting from homogeneous initial models in all of our examples. Just as other methods, FWI underestimates large conductivity contrasts due to the loss of sensitivity of the transmitted electric field to the conductivity variations as the conductivity increases above a certain level. The permittivity inside high conductors cannot be recovered, however, recovering permittivity variations in the resistive zones helps obtain better focused conductivity images with fewer artefacts. Overall, FWI produces cleaner, less noisy and higher resolution reconstructions than the methods currently used in practice.