Geophysical Prospecting, 2009, 57, 209–224 doi: 10.1111/j.1365-2478.2008.00771.x Laboratory-scale study of field of view and the seismic interpretation of fracture specific stiffness Angel Acosta-Colon 1 , Laura J. Pyrak-Nolte 1,2∗ and David D. Nolte 2 1 Department of Earth and Atmospheric Sciences, Purdue University, 525 Northwestern Avenue, West Lafayette, IN 47907-2036, USA, and 2 Department of Physics, Purdue University, 525 Northwestern Avenue, West Lafayette, IN 47907-2036, USA Received January 2008, revision accepted May 2008 ABSTRACT 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 acous- tic 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 sam- ple. 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 associ- ated 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. INTRODUCTION The scaling behaviour of the hydraulic and seismic properties of a fracture determines how properties observed on the lab- oratory size (typically less than tens of centimetres) relate to the same properties measured at larger sizes. To understand the scaling behaviour of fracture properties, the length scales of the fracture geometry (apertures, contact areas and spa- tial correlations) and the fluid phase distribution (wetting and non-wetting phase areas and interfacial areas) must be charac- terized and compared to the length scales associated with the seismic probe (wavelength, beam size, divergence angle and field of view). ∗ E-mail: ljpn@purdue.edu For fractures in rock, measurements on the laboratory scale encompass several different length scales that include the size of the sample and fracture. A single fracture can be viewed as two rough surfaces in contact that produce regions of con- tact and open voids in a quasi two-dimensional fashion. This fracture geometry has many length scales that are described as contact area and its spatial distribution, as well as by the size (aperture) and spatial distribution of the void space. From lab- oratory measurements, Pyrak-Nolte, Montemagno and Nolte (1997) found that the aperture distribution of natural fracture networks in whole-drill coal cores were spatially correlated over 10 mm to 30 mm, i.e., distances that were comparable to the size of the core samples. However, asperities on natural joint surfaces have been observed to be correlated over only about 0.5 mm from surface roughness measurements (Brown, Kranz and Bonner 1986). These two quoted values for C  2009 European Association of Geoscientists & Engineers 209