Laboratory-scale study of field of view and the seismic interpretation of fracture specific stiffness

The effects of the scale of measurement, i.e., the field of view, on the interpretation of fracture properties from seismic wave propagation was investigated using an acoustic lens system to produce a pseudo-collimated wavefront. The incident wavefront had a controllable beam diameter that set the field of view at 15 mm, 30 mm and 60 mm. On a smaller scale, traditional acoustic scans were used to probe the fracture in 2 mm increments. This laboratory approach was applied to two limestone samples, each containing a single induced fracture and compared to an acrylic control sample. From the analysis of the average coherent sum of the signals measured on each scale, we observed that the scale of the field of view affected the interpretation of the fracture specific stiffness. Many small-scale measurements of the seismic response of a fracture, when summed, did not predict the large-scale response of the fracture. The change from a frequency-independent to frequency-dependent fracture stiffness occurs when the scale of the field of view exceeds the spatial correlation length associated with fracture geometry. A frequency-independent fracture specific stiffness is not sufficient to classify a fracture as homogeneous. A nonuniform spatial distribution of fracture specific stiffness and overlapping geometric scales in a fracture cause a scale-dependent seismic response, which requires measurements at different field of views to fully characterize the fracture.