Nonlinear imaging condition and the effect of source illumination

Abstract

Fluid flow through a fractured reservoir is often controlled by the large fractures. Seismically imaging these large fractures has the potential to illuminate their hydraulic properties.We derived a nonlinear imaging condition considering a medium containing nonwelded interfaces such as fractures for high-resolution fracture imaging. This was achieved by using the general correlation-type representation theorem relating the wavefield between two different states representing different fracture compliances. We numerically tested the imaging condition to investigate the effect of the nonlinear term and that of the one-sided source illumination. Assuming a dry fracture, we calculated the wavefield from a nonwelded interface. We obtained a P-wave imaging result from P-wave sources. In the case of perfect source illumination, we found that introducing the nonlinear term in the imaging condition enhances the image because the nonwelded interface is imaged as a thin layer in an otherwise homogeneous medium. Investigating the effect of one-sided illumination by horizontally aligned sources revealed interesting limitations and possibilities. The imaging result for a horizontal fracture showed a volumetric distribution of nonzero amplitudes around the polarity change at the fracture that can be misinterpreted as a welded thick layer boundary. However, when the fracture was not horizontal, the imaging result was quite good and was closer to that with a perfect source illumination. These led to a new possibility of imaging subvertical fractures from surface seismic measurements, or subhorizontal fractures from vertical seismic profiling data, assuming that we successfully estimated the perturbed wavefield from the receiver responses.