A method for estimating a property of an earth formation penetrated by a borehole, the method comprising generating a first transient electromagnetic fields with a transmitter on a carrier located outside of the borehole and receiving associated signals, calculating a bucking coefficient using the measured signals, conveying the carrier through a borehole, generating a second transient electromagnetic field and receiving associated signals, calculating, a bucked signal using the bucking coefficient and the downhole signals, calculating synthetic formation signals, calculating synthetic formations signals by applying a Duhamel's integral to the measured signals and the synthetic formation signals, calculating a synthetic bucked signal, and performing an inversion of a formation model to estimate a property of the formation such that an inverted synthetic bucked signal and an inverted bucked signal coincide within a predetermined range.