Interferometry in diffusive systems: Theory, limitation to its practical application and its use in Bayesian estimation of material properties

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Virginia Tech


Interferometry in geosciences uses mathematical techniques to image subsurface properties. This method turns a receiver in to a virtual source through utilizing either random noises or engineered sources. The method in seismology has been discussed extensively. Electromagnetic interferometry at high frequencies with coupled electromagnetic fields was developed in the past. However, the problem was not addressed for diffusive electromagnetic fields where the quasi-static limit holds. One of the objectives of this dissertation was to theoretically derive the impulse response of the Earth for low-frequency electromagnetic fields.

Applying the theory of interferometry in the regions where the wavefields are diffusive requires volumetrically distributed sources in an infinite domain. That precondition imposed by the theory is not practical in experiments. Hence, the aim of this study was to quantify the important areas and distribution of sources that makes it possible to apply the theory in practice through conducting numerical experiments. Results of the numerical analysis in double half-space models revealed that for surface-based exploration scenarios sources are required to reside in a region with higher diffusivity. In contrast, when the receivers straddle an interface, as in borehole experiments, there is no universal rule for which region is more important; it depends on the frequency, receiver separation and also diffusivity contrast between the layers and varies  for different scenarios. Time-series analysis of the sources confirmed previous findings that the accuracy of the Green's function retrieval is a function of both source density and its width. Extending previous works in homogenous media into inhomogeneous models, it was found that sources must be distributed asymmetrically in the system, and extend deeper into the high diffusivity region in comparison to the low diffusivity area.

The findings were applied in a three-layered example with a reservoir layer between two impermeable layers. Bayesian statistical inversion of the data obtained by interferometry was then used to estimate the fluid diffusivity (and permeability) along with associated uncertainties. The inversion results determined the estimated model parameters in the form of probability distributions. The output demonstrated that the algorithm converges closely to the true model.



Interferometry, Green's function, Bayesian, Electromagnetics, Diffusion