Acoustic interrogation of subsurface features tends to be limited by the size and power of practical sources, and in practice, the output of down hole acoustic transducers is limited by the power transmission capabilities of the wireline cable. High frequency signals have a relatively short penetration distance, while low frequency signals generally require large sources, clamped to the borehole wall, to maximize energy transfer to the formation and minimize unwanted signals within the well bore. Currently, acoustic borehole tools are designed with acoustic sources in the borehole to detect returning acoustic waves that are propagating along the borehole walls or scattered by inhomogeneities of linear properties of rock formations surrounding the borehole. U.S. Pat. No. 7,301,852 by Leggett, III et al. discloses a Logging While Drilling tool, designed to detect rock formation boundaries, with two acoustic source arrays emitting from a borehole generating a third wave by assumed non-linear mixing in rocks at the location of intersection of the acoustic signals. The third wave is scattered by heterogeneities in subsurface properties, and the scattered signal is detected by sensors in the logging tool. The source arrays are merely disclosed to be directional without any further description.
Attempts have been made to characterize the non-linear properties of a formation in the area of oil and gas prospecting from boreholes, but each has its own limitations. For example, U.S. Pat. No. 5,521,882 by D'Angelo et al. discloses an acoustic tool designed to record with pressure receivers the non-linear waves that propagate along the borehole wall with limited penetration into the surrounding rock formation and refract back into the well bore fluid. U.S. Pat. No. 6,175,536 by Khan discloses a method to estimate the degree of non-linearity of earth formations from spectral analysis of seismic signals transmitted into the formation from one borehole and received in a second borehole. In light of these prior attempts, there is a need for an apparatus and method for generating three-dimensional images of non-linear properties in a remote region from a borehole.