The present invention provides a method and apparatus for using an acoustic logging tool conveyed in a borehole in an earth formation for determining a characteristic of the formation. The method comprises using a first acoustic source for generating an acoustic signal in the earth formation at a first frequency. A second acoustic source spaced apart from the first source is used for generating an acoustic signal in the earth formation at a second frequency different from the first frequency. An acoustic receiver is used for receiving a third acoustic signal indicative of said characteristic. The third acoustic signal has a frequency substantially equal to a difference between the first frequency and the second frequency. The third acoustic signal is produced by a nonlinear interaction between the first signal and the second signal in a portion of said earth formation. It is emphasized that this abstract is provided to comply with the rules requiring an abstract which will allow a searcher or other reader to quickly ascertain the subject matter of the technical disclosure. It is submitted with the understanding that it will not be used to interpret or limit the scope or meaning of the claims.