DIFFRACTION OF SEISMIC-WAVES BY CRACKS WITH APPLICATION TO HYDRAULIC FRACTURING

We describe a method of modeling seismic waves interacting with single liquid-filled large cracks based on the Kirchhoff approximation and t hen apply it to field data in an attempt to estimate the size of a hyd raulic fracture. We first present the theory of diffraction of seismic waves by fractures using a Green's function representation and then c ompute 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 fro m single cracks are sensitive to both crack size and crack shape. Fina lly, we compare synthetic waveforms to observed waveforms recorded dur ing a hydraulic fracturing experiment and are able to predict successf ully the size of a hydraulically induced fracture (length and height). In contrast to previously published work based on the Born approximat ion, 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 exam ple demonstrates that it is possible to estimate fracture dimensions b y analyzing diffracted waves.