2.5-Dimensional Electrical Resistivity Tomography for Cylindrical
Objects Incorporating the Modified Optimization Wavenumbers
Abstract
More and more applications of electrical resistivity tomography (ERT)
for cylindrical objects have been rising in recent decades. This paper
presents a 2.5-dimensional differential resistivity reconstruction
scheme of cylindrical objects. The forward modeling algorithm
incorporates the modified optimization wavenumbers to achieve an
accurate 2.5-dimensional forward modeling. The modified optimization
wavenumber selection is based on the approximate analytic solution of
the circumference potential distribution of an infinitely long
homogeneous cylindrical model, making it more accurate for cylindrical
objects compared to the traditional optimization wavenumber selection
which is only applicable for the half-space condition. In the
laboratory, we measured the resistivity and resistance distributions of
the sodium chloride solution-filled cylindrical tanks with/without a
high resistivity rubber bar in the central. The modified and traditional
optimization wavenumbers are included respectively to calculate the
resistance distribution of the measured objects. The comparison results
between the calculated and measured resistance distribution show that
the modified optimization wavenumbers proposed in this paper can obtain
higher calculation accuracy. The differential ERT incorporating the
modified optimization wavenumbers is then employed to reconstruct the
resistivity distribution of the cylindrical objects. The inversed
resistivity values are in good agreement with the measured values. We,
therefore, conclude that the modified optimization wavenumbers can
result in better accuracy than the traditional one and the proposed
2.5-dimensional differential resistivity reconstruction scheme is
time-saving and has great promise for the imaging of cylindrical
objects.