In some aspects of the disclosure, a method for creating three-dimensional images of non-linear properties and the compressional to shear velocity ratio in a region (130) remote from a borehole using a conveyed logging tool (140) is disclosed. In some aspects, the method includes arranging a first source (105) in the borehole (110) and generating a steered beam of elastic energy at a first frequency; arranging a second source (115) in the borehole (110) and generating a steerable beam of elastic energy at a second frequency, such that the steerable beam at the first frequency and the steerable beam at the second frequency intercept at a location (130) away from the borehole (110); receiving at the borehole (110) by a sensor (135) a third elastic wave, created by a three wave mixing process, with a frequency equal to a difference between the first and second frequencies and a direction of propagation towards the borehole (110).