Elongated horizontal and vertical receivers in three-dimensional electromagnetic modelling and inversion

Electromagnetic geophysical methods often rely on measurements of naturally occurring or artificially impressed electric fields. It is technically impossible, however, to measure the electric field directly. Instead, the electric field is approximated by recording the voltage difference between two electrodes and dividing the obtained voltage by the distance between the electrodes. Typically, modelling and inversion algorithms assume that the electric fields are obtained over infinitely short point-dipoles and thus measured fields are assigned to a single point between the electrodes. Such procedures imply several assumptions: (1) The electric field between the two electrodes is regarded as constant or being a potential field and (2) the receiver dimensions are negligible compared to the dimensions of the underlying modelling grid. While these conditions are often fulfilled for horizontal electric fields, borehole sensors for recordings of the vertical electric field have dimensions in the order of approximate to 100 m and span several modelling grid cells. Observations from such elongated borehole sensors can therefore only be interpreted properly if true receiver dimensions and variations of electrical conductivity along the receiver are considered. Here, we introduce a numerical solution to include the true receiver geometry into electromagnetic modelling schemes, which does not rely on such simplifying assumptions. The algorithm is flexible, independent of the chosen numerical method to solve Maxwell's equations and can easily be implemented in other electromagnetic modelling and inversion codes. We present conceptual modelling results for land-based controlled source electromagnetic scenarios and discuss consideration of true receiver geometries for a series of examples of horizontal and vertical electric field measurements. Comparison with Ez data measured in an observation borehole in a producing oil field shows the importance of both considering the true length of the receiver and also its orientation. We show that misalignment from the vertical axis as small as 0.1 degrees may seriously distort the measured signal, as horizontal electric field components are mapped into the desired vertical component. Adequate inclusion of elongated receivers in modelling and inversion can also help reducing effects of static shift when interpreting (natural source) magnetotelluric data.