Publications
Experiment design study in 3d dc resistivity: Adjoint sensitivities in a horizontal steel-cased borehole
We investigate a novel application of Fŕechet derivatives for time-lapse mapping of deep, electrically-enhanced fracture systems with a borehole to surface DC resistivity array. The simulations are evaluated for a cased horizontal wellbore embedded in a homogeneous halfspace, where measurements are evaluated near, mid-range, and far from the well head. We show that, in all cases, measurements are sensitive to perturbations centered on the borehole axis and that the sensitivity volume decreases as a function of increased measurement offset from the well head. The sensitivity analysis also illustrates that careful consideration must be taken when developing an electrical survey design for these scenarios. Specifically, we show that positive perturbations in earth conductivity near the wellbore can manifest as both positive and negative measurement perturbations, depending on where the measurement is taken. Furthermore, we show that the transition between the regions along the wellbore of positive and negative contribution results in a "pinch point", representing a region along the wellbore where a given surface measurement is blind to any changes or enhancement of electrical conductivity.