Resistivity and induced polarization inversion and resolution at low contrasts.

摘要

By computing only the diagonal terms of the volume integral equation forward solution of the three-dimensional (3-D) dc resistivity/induced polarization problem, I have achieved a fast forward solution that is accurate at low to moderate resistivity contrasts. The speed and accuracy of the solution make it practical for use in two-dimensional (2-D) or three-dimensional inverse algorithms. By using a 3-D forward solution, but constraining the resistivities and polarizabilities along any row of cells in the strike direction to be held constant, I effect a fast 2-D resistivity inversion that contains end corrections. Because the low-contrast solution is inaccurate for cells near the electrodes, I employ a full solution to compute the response of the near surface. This response is stored and used in the resistivity inversion. Once an adequate estimated resistivity model has been found, derivatives from this model are used with Seigel's formula to compute the inverse solution to the linear polarizability problem.; I used the solution to examine variations in inversion for the different arrays. I found that for a particular structure, the estimated resistivity and polarizability models obtained from inversion of the dipole-dipole data were very similar to the pole-dipole estimated models. If pole-pole data contain even a fraction of a percent of noise, the transformation of such data through superposition to equivalent data of other array types is virtually impossible.; I examine the resolution of three common array types: the dipole-dipole, pole-dipole, and pole-pole. The resolution of the dipole-dipole array attenuates more rapidly than that of the pole-pole or pole-dipole arrays. Although the shallow resolution of the pole-pole array is lower than that of the dipole-dipole array, the falloff in resolution with depth is much more gradual.