INVERSION OF INDUCED POLARIZATION DATA

We develop three methods to invert induced polarization (IP) data. The foundation for our algorithms is an assumption that the ultimate effe ct of chargeability is to alter the effective conductivity when curren t is applied. This assumption, which was first put forth by Siegel and has been routinely adopted in the literature, permits the IP response s to be numerically modeled by carrying out two forward modelings usin g a DC resistivity algorithm. The intimate connection between DC and I P data means that inversion of IP data is a two-step process. First, t he DC potentials are inverted to recover a background conductivity. Th e distribution of chargeability can then be found by using any one of the three following techniques: (1) linearizing the IP data equation a nd solving a linear inverse problem, (2) manipulating the conductiviti es obtained after performing two DC resistivity inversions, and (3) so lving a nonlinear inverse problem. Our procedure for performing the in version is to divide the earth into rectangular prisms and to assume t hat the conductivity sigma and chargeability eta are constant in each cell. To emulate complicated earth structure we allow many cells, usua lly far more than there are data. The inverse problem, which has many solutions, is then solved as a problem in optimization theory. A model objective function is designed, and a ''model'' (either the distribut ion of sigma or eta) is sought that minimizes the objective function s ubject to adequately fitting the data. Generalized subspace methodolog ies are used to solve both inverse problems, and positivity constraint s are included. The IP inversion procedures we design are generic and can be applied to 1-D, 2-D, or 3-D earth models and with any configura tion of current and potential electrodes. We illustrate our methods by inverting synthetic DC/IP data taken over a 2-D earth structure and b y inverting dipole-dipole data taken in Quebec.