Fracture Intersection Waves: Theory and Experiment
Abstract
Fractures and fracture intersections are found nearly everywhere on earth and have also been observed on planetary surfaces within our solar system. The presence of fracture intersections adds complexity to the three-dimensional flow paths through rock and alters the scattered seismic wave field in a manner that does not occur for single fractures or parallel sets of fractures. A main challenge in working with intersecting fractures is how to determine the properties of intersections, whether intersections act as barriers to flow or as highly conductive paths. In this study, we determine theoretically and experimentally that the existence and velocity of intersection waves depends on the specific stiffness of the intersection which is stress dependent. It is well known that a single block supports a wedge wave along the corner or edge of a block. Conceptually, an intersection between two orthogonal fractures can be represented as four blocks coupled along their edges or as the coupling of four wedge waves. In this study, displacement discontinuity boundary conditions (discontinuity in displacement with continuity in stress) were used to represent the coupling among the blocks that form the fractures and the fracture intersection. Based on this approach, intersection waves were derived that are dispersive and range in velocity from a single wedge-mode to the bulk shear wave velocity. For low intersection stiffness, an intersection wave travels at the single wedge wave velocity because the intersection behaves as a free surface. As the intersection stiffness increases, the intersection wave velocity increases continuously to the Rayleigh velocity when two of the blocks forming the intersection are coupled. Finally, the intersection wave velocity increases continuously to the bulk shear wave velocity as coupling between all four blocks approaches the condition of a welded interface as the stiffness of the intersection and fractures increases. The velocity of the intersection waves depends on the relative stiffness between the two orthogonal fractures. Laboratory experiments were performed on an intersection between four aluminum blocks (0.29 m x 0.76 m x 0.76 m) as a function of stress. Piezoelectric contact transducers (1MHz) were used to propagate and measure intersection waves propagated along the intersection between the aluminum samples. Compressional and shear wave data were collected for samples subjected to bi-axial loading conditions used to close both the horizontal and vertical fracture planes individually. The measured waveforms verified that the velocity of the intersection wave did indeed range from the wedge velocity, at low applied loads, to the bulk velocity, when both fractures were under high load; indicating an agreement with the theoretical formulation for intersection waves. Intersection waves are a potential tool for characterizing the mechanical and hydraulic properties of fracture intersections because the velocity of these waves depends on the specific stiffness of the intersection. Acknowledgments: The authors wish to acknowledge support of this work by the Geosciences Research Program, Office of Basic Energy Sciences US Department of Energy (DE-FG02-09ER16022) and by the Geo-mathematical Imaging Group at Purdue University.
- Publication:
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AGU Fall Meeting Abstracts
- Pub Date:
- December 2013
- Bibcode:
- 2013AGUFM.H53A1407A
- Keywords:
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- 1822 HYDROLOGY Geomechanics;
- 3285 MATHEMATICAL GEOPHYSICS Wave propagation;
- 1859 HYDROLOGY Rocks: physical properties;
- 7255 SEISMOLOGY Surface waves and free oscillations