Passive seismic imaging of subwavelength natural fractures: Theory and 2-D synthetic and ultrasonic data tests

I present a source-independent fracture imaging method to use passive seismic data for mapping subwavelength natural fractures. Unlike conventional source-dependent imaging that often adopts reflection-type seismic imaging with known source that is not available in passive seismic surveys, the proposed fracture imaging approach relies on the transmission and diffraction data without the need for source information. I assume that passive seismic data can be decomposed into two types of data: primary transmission wave data and diffraction (coda) wave data. The imaging formula states that primary waves should coincide with coda waves at scatterer points at the time of scattering. Instead of generating source wavefields in the conventional imaging method, the proposed method only need to propagate transmission wave data and diffraction wave data from the receiver arrays and apply an imaging condition to produce an image of fractures. This imaging procedure can be used for processing P wave or S wave. In synthetic examples, I evaluate the proposed method in several aspects: inaccurate source location, inaccurate velocity model, sparse receivers and irregular receiver spacing, elastic data and joint surface and borehole acquisitions. I found that the proposed approach performed well (or even better) comparable to source-dependent fracture imaging when assuming exact source information is known. With perturbed source locations with random shifts (e.g. estimated source location with errors), however, fractures were missing in the source-dependent fracture imaging results but the proposed approach was not influenced. In the presence of velocity errors and sparse and irregular receiver spacing, the proposed method produces better fracture images than the source-dependent imaging results.