Abstract We describe a method of modeling seismic waves interacting with single liquid-filled large cracks based on the Kirchhoff approximation and then apply it to field data in an attempt to estimate the size of a hydraulic fracture. We first present the theory of diffraction of seismic waves by fractures using a Green’s function representation and then compute the scattered radiation patterns and synthetic seismograms for fractures with elliptical and rectangular shapes of various dimensions. It is shown that the characteristics of the diffracted wavefield from single cracks are sensitive to both crack size and crack shape. Finally, we compare synthetic waveforms to observed waveforms recorded during a hydraulic fracturing experiment and are able to predict successfully the size of a hydraulically induced fracture (length and height). In contrast to previously published work based on the Born approximation, we model both phases and amplitudes of observed diffracted waves. Our modeling has resulted in an estimation of a crack length 1.1 to 1.5 times larger than previously predicted, whereas the height remains essentially the same as that derived using other techniques. This example demonstrates that it is possible to estimate fracture dimensions by analyzing diffracted waves.

Abstract There have been significant advances over the last ten years in the use of the seismic anisotropy concept to characterize subsurface fracture systems. Measurements of seismic anisotropy are now used to deduce quantitative information about the fracture orientation and the spatial distribution of fracture intensity. Analysis of the data is based upon various equivalent medium theories that describe the elastic response of a rock containing cracks or fractures in the long wavelength limit. Conventional models assume scale/frequency independence and hence cannot distinguish between micro-cracks and macrofractures. The latter, however, control the fluid flow in many oil/gas reservoirs, as the fracture size and spacing (hence fracture storability) are essential parameters for reservoir engineers. Recently, a new equivalent medium theory for modelling of wave propagation in media with multi-scale fractures has been presented. The model predicts velocity dispersion and attenuation due to a squirt-flow mechanism at two different scales: the grain scale (micro-cracks and equant matrix porosity) and formation-scale fractures. Application of this model to field data shows that fracture density and fracture size can be inverted successfully from the frequency dependence of the time delay between split shear waves. The derived fracture length matches independent observations from borehole data. This paper presents the results of the latest development in the seismic characterization of natural fractures, with an emphasis on the quantitative determination of fracture sizes.