A method for creating three-dimensional images of non-linear properties in a region remote from a borehole using a conveyed logging tool, the method comprising: arranging a first source in the borehole and generating elastic energy at a first frequency; arranging a second source in the borehole and generating elastic energy at a second frequency, wherein the elastic energy at the first and the second frequency intersect at a mixing zone located away from the borehole; characterized in that the method further comprises: receiving, by an array of sensors, at the borehole a third elastic wave, with a frequency equal to a difference between the first and second frequencies and a direction of propagation towards the borehole created by a three wave non-collinear mixing process in a non-linear mixing zone; identifying a location of the three wave mixing zone based on the arrangement of the first and the second sources (105, 115), the direction of the third wave and selection rules governing non-collinear mixing in acoustically non-linear media; and creating three-dimensional images of the non-linear properties using data recorded by repeating the generating, receiving and identifying at a plurality of azimuths, inclinations and longitudinal locations of the first source or the second source, or both within the borehole. arranging a first source in the borehole and generating elastic energy at a first frequency; arranging a second source in the borehole and generating elastic energy at a second frequency, wherein the elastic energy at the first and the second frequency intersect at a mixing zone located away from the borehole; characterized in that the method further comprises: receiving, by an array of sensors, at the borehole a third elastic wave, with a frequency equal to a difference between the first and second frequencies and a direction of propagation towards the borehole created by a three wave non-collinear mixing process in a non-linear mixing zone; identifying a location of the three wave mixing zone based on the arrangement of the first and the second sources (105, 115), the direction of the third wave and selection rules governing non-collinear mixing in acoustically non-linear media; and creating three-dimensional images of the non-linear properties using data recorded by repeating the generating, receiving and identifying at a plurality of azimuths, inclinations and longitudinal locations of the first source or the second source, or both within the borehole. receiving, by an array of sensors, at the borehole a third elastic wave, with a frequency equal to a difference between the first and second frequencies and a direction of propagation towards the borehole created by a three wave non-collinear mixing process in a non-linear mixing zone; identifying a location of the three wave mixing zone based on the arrangement of the first and the second sources (105, 115), the direction of the third wave and selection rules governing non-collinear mixing in acoustically non-linear media; and creating three-dimensional images of the non-linear properties using data recorded by repeating the generating, receiving and identifying at a plurality of azimuths, inclinations and longitudinal locations of the first source or the second source, or both within the borehole.