Skip to Main Content
Book Chapter

Diffraction of seismic waves by cracks with application to hydraulic fracturing

By
Enru Liu
Enru Liu
British Geological Survey, Murchison House, West Mains Road, Edinburgh EH9 3LA, United Kingdom.
Search for other works by this author on:
Stuart Crampin
Stuart Crampin
Department of Geology and Geophysics, University of Edinburgh, West Mains Road, Edinburgh EH9 3JW, United Kingdom.
Search for other works by this author on:
John A. Hudson
John A. Hudson
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, United Kingdom.
Search for other works by this author on:
Published:
January 01, 2016

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.

You do not currently have access to this article.

Figures & Tables

Contents

Society of Exploration Geophysicists Geophysics Reprint Series

Seismic Diffraction

Kamil Klem-Musatov
Kamil Klem-Musatov
Search for other works by this author on:
Henning Hoeber
Henning Hoeber
Search for other works by this author on:
Michael Pelissier
Michael Pelissier
Search for other works by this author on:
Tijmen Jan Moser
Tijmen Jan Moser
Search for other works by this author on:
Society of Exploration Geophysicists
Volume
30
ISBN electronic:
9781560803188
Publication date:
January 01, 2016

GeoRef

References

Related

Citing Books via

Close Modal
This Feature Is Available To Subscribers Only

Sign In or Create an Account

Close Modal
Close Modal