System and method to create three-dimensional images of non-linear acoustic properties in a region remote from a borehole

An apparatus for creating three-dimensional images of non-linear properties of the rock formations remote from a borehole using a conveyed logging tool, the apparatus comprising:

• a first source arranged in the borehole and configured to generate elastic energy at a first frequency;
• a second source arranged in the borehole and configured to generate elastic energy at a second frequency, wherein the energy at the first frequency and at the second frequency intersects at a location away from the borehole;
• a sensor array configured to receive a third elastic wave when non-linear properties of a region of interest result in creation, by a three wave mixing process a third elastic wave, having a frequency equal to a difference between the first and the second frequencies and a direction of propagation toward the borehole;
• and
• a processor arranged to identify a location of the region of interest based on the arrangement of the first and the second sources, the direction of the third wave and selection rules governing non-collinear mixing in acoustically non-linear media, and to create the three-dimensional images based, in part, on properties of the received third wave and the arrangement of the first and second sources.

A computer-implemented method arranged to perform processing of a third wave generated through a three wave mixing process of two non-collinear primary beams or waves in a remote non-linear region of a formation surrounding a borehole, and recorded in the borehole, in order to obtain three dimensional images of non-linear properties of a formation surrounding the borehole, the computer-implemented method comprising:

• analyzing a frequency content of a recorded third wave by spectral analysis and selecting a signal corresponding to a difference frequency to isolate the third wave signal generated by the non-linear mixing process;
• analyzing an amplitude of the recorded third wave as a function of frequency ratios of the primary mixing beams or waves and determining a mixing location where the third wave signals originated, from selection rules of non-collinear mixing in non-linear media, wavenumbers of the first and second beams or waves and the third wave and locations of two primary sources and a sensor array;
• confirming a direction of the third wave impinging on the borehole and recorded the sensor array based on analyzing the third elastic wave detected at the sensory array;
• and
• imaging, applied to the entire data set, in order to obtain three dimensional images both in time and in distance of the non-linear properties of the formation surrounding a borehole.