Diffraction of seismic waves by cracks with application to hydraulic fracturing
Enru Liu, Stuart Crampin, John A. Hudson, 2016. "Diffraction of seismic waves by cracks with application to hydraulic fracturing", Seismic Diffraction, Kamil Klem-Musatov, Henning Hoeber, Michael Pelissier, Tijmen Jan Moser
Download citation file:
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.
Figures & Tables
The use of diffraction imaging to complement the seismic reflection method is rapidly gaining momentum in the oil and gas industry. As the industry moves toward exploiting smaller and more complex conventional reservoirs and extensive new unconventional resource plays, the application of the seismic diffraction method to image sub-wavelength features such as small-scale faults, fractures and stratigraphic pinchouts is expected to increase dramatically over the next few years. “Seismic Diffraction” covers seismic diffraction theory, modeling, observation, and imaging. Papers and discussion include an overview of seismic diffractions, including classic papers which introduced the potential of diffraction phenomena in seismic processing; papers on the forward modeling of seismic diffractions, with an emphasis on the theoretical principles; papers which describe techniques for diffraction mathematical modeling as well as laboratory experiments for the physical modeling of diffractions; key papers dealing with the observation of seismic diffractions, in near-surface-, reservoir-, as well as crustal studies; and key papers on diffraction imaging.