Interpretation of time-domain induced polarization and resistivity data for Earth modeling

Numerical algorithms are suggested for the interpretation of the time-domain induced polarization (IP), and the d-c resistivity methods used for the modeling of the Earth´s subsurface. The Earth´s layers are assumed to be horizontally stratified. Each of the N layers of the Earth´s model is characterized by the d-c resistivity ρ_n, the chargability M_n, and the thickness d_n. Assuming that a Schlumberger array is used for current and voltage electrodes on the Earth´s surface. The measured apparent resistivity data is interpreted using the resistivity transform method to solve the inverse resistivity problem to find the d-c resistivities and thicknesses of each layer in the resistivity model. The obtained parameters of the resistivity model are used to calculate the dilution factors of each layer. The apparent chargability measured at the Earth´s surface in the IP method is expressed as a linear summation of the products of the chargability and the dilution factor of each of the N layers. The chargability and the thickness of each layer in the IP model are obtained by solving the inverse problem using the calculated theoretical apparent chargability data obtained from the assumed theoretical IP model, and the measured chargability data on the Earth´s surface. Numerical simulation examples have been used to generate simulated experimental data for both the IP and resistivity models. This data is used to solve the inverse problem to find the parameters of both models. Numerical examples are used to verify the effectiveness of the suggested algorithms. These methods are extremely useful in modeling Earth´s subsurface layers for groundwater prospection purposes, search for oil and other minerals, and to obtain subsurface pollution models