A method for estimating a formation resistivity of a subterranean formation penetrated by a borehole, comprising: using an apparent impedance function (Z app) depending on a frequency variable (ω) and on a plurality of unknown parameters, at least one of the unknown parameters depending on a formation impedance (Z form) of the subterranean formation, so that the apparent impedance function (Z app) is non-linear relative to the formation impedance (Z form), wherein the apparent impedance function (Z app) when multiplied by the frequency variable (ω) corresponds to a ratio of polynomials depending on the frequency variable (ω) and having the plurality of unknown parameters as coefficients: Z app. ω = ∑ i = 0 p a i. ω i 1 + ∑ i = 1 q b i. ω i wherein Z app is the apparent frequency function, ω is the frequency variable, a i and b i are the unknown parameters and p and q are positive integers, wherein the apparent impedance function has p+q+1 unknown parameters, applying a voltage, at each of a plurality of frequency values (ω1, ω2, ω3), between electrodes (420, 430) of a resistivity tool that is disposed in a wellbore proximate the subterranean formation penetrated by the wellbore, wherein the plurality of frequency values comprises at least p+q+1 frequency values; measuring, across the electrodes (420, 430), a plurality of apparent impedance values (Z app1, Z app2, Z app3), each corresponding to a different one of the plurality of frequency values (ω1, ω2, ω3); determining the plurality of unknown parameters based on the plurality of frequency values (ω1, ω2, ω3) and the plurality of apparent impedance values (Z app1, Z app2, Z app3); and estimating the formation resistivity based on an expression that includes at least one of the plurality of unknown parameters, wherein the expression is obtained by applying: lim ω → 0 ∂ Z app. ω ∂ ω. using an apparent impedance function (Z app) depending on a frequency variable (ω) and on a plurality of unknown parameters, at least one of the unknown parameters depending on a formation impedance (Z form) of the subterranean formation, so that the apparent impedance function (Z app) is non-linear relative to the formation impedance (Z form), wherein the apparent impedance function (Z app) when multiplied by the frequency variable (ω) corresponds to a ratio of polynomials depending on the frequency variable (ω) and having the plurality of unknown parameters as coefficients: Z app. ω = ∑ i = 0 p a i. ω i 1 + ∑ i = 1 q b i. ω i wherein Z app is the apparent frequency function, ω is the frequency variable, a i and b i are the unknown parameters and p and q are positive integers, wherein the apparent impedance function has p+q+1 unknown parameters, wherein Z app is the apparent frequency function, ω is the frequency variable, a i and b i are the unknown parameters and p and q are positive integers, wherein the apparent impedance function has p+q+1 unknown parameters, applying a voltage, at each of a plurality of frequency values (ω1, ω2, ω3), between electrodes (420, 430) of a resistivity tool that is disposed in a wellbore proximate the subterranean formation penetrated by the wellbore, wherein the plurality of frequency values comprises at least p+q+1 frequency values; measuring, across the electrodes (420, 430), a plurality of apparent impedance values (Z app1, Z app2, Z app3), each corresponding to a different one of the plurality of frequency values (ω1, ω2, ω3); determining the plurality of unknown parameters based on the plurality of frequency values (ω1, ω2, ω3) and the plurality of apparent impedance values (Z app1, Z app2, Z app3); and estimating the formation resistivity based on an expression that includes at least one of the plurality of unknown parameters, wherein the expression is obtained by applying: lim ω → 0 ∂ Z app. ω ∂ ω.