S Waves Prove Their Worth With Fractures
When a shear (S) wave propagates through a rock unit that has vertical fractures oriented at a reasonably consistent azimuth, it splits into two S waves that propagate with distinct velocities.
- One of these S waves is a fast-velocity mode called S1, which is polarized in the same direction as the fracture orientation.
- The other is a slow-velocity mode called S2, which is polarized in a direction orthogonal to the fracture planes.
The S1 mode has approximately the same velocity as an S wave that propagates in the rock when fractures are absent. In contrast to this S-wave physics, a compressional (P) wave does not split into fast and slow modes when it encounters a fractured interval.
When fracturing causes significant differences in elastic moduli parallel and perpendicular to fractures, P-wave velocity can vary when measured parallel to and perpendicular to oriented fractures, as does S-wave velocity – but differences in P-wave velocity are not as dramatic as those in S-wave velocity.
Thus, S waves are preferred over P waves for seismic-based evaluations of fractured rocks.
S-wave splitting phenomenon is illustrated on figure 1, where an S wave illuminates a zone of well-aligned vertical fractures.
The incident S wave is polarized so that its particle-displacement vector is oriented at an angle ? relative to the azimuth of the vertical fractures. S1 and S2 modes exit the base of the fracture zone at different times because they propagate with different velocities inside the fracture space (S1 = fast; S2 = slow).
As expected, the S1 mode is polarized parallel to the fracture planes, and the S2 mode is polarized perpendicular to the fracture planes.
S1 and S2 modes also reflect from the fracture zone, but are not shown.
A laboratory test that documents the S-wave physics described by this model was published by Sondergeld and Rai (1992). Their test procedure is illustrated on figure 2.
In this test, a piezoceramic element was secured to one end of a cylindrical volume of laminated shale to serve as an S-wave source. A similar piezoceramic element was positioned at the opposite end of the cylinder as an S-wave sensor.
This layered propagation medium, and the fact that the source-receiver geometry causes S-waves to propagate parallel to the embedded interfaces of the rock sample, are a good simulation of S-wave propagation through a system of vertical fractures.
In one test, the source remained in a fixed orientation relative to the plane of the simulated fractures and the receiver element was rotated at azimuth increments of 10 degrees to determine the azimuth dependence of S-wave propagation through the sample.
The test results are illustrated on figure 3 as an end-on view of the test sample from the source end; the objective was to simulate the propagation of a fast-S (or S1) mode, where the source displacement vector is parallel to the fracture planes (figure 3a), and then to simulate the propagation of a slow-S (or S2) mode in which the displacement vector is perpendicular to the fracture planes (figure 3b).
Note how much longer it takes for the S2 wavelet to propagate through the test sample than the S1 wavelet – a confirmation that S2 velocity is slower than S1 velocity.
The positive-polarity end of the source is oriented in the direction indicated by the arrowhead on the source vector. For response A, the positive-polarity of the receiver is oriented the same as the source. For response C, the receiver has been rotated so that its positive-polarity end points in an opposing direction. Thus the polarity of wavelet B is opposite to the polarity of wavelet A.
In actual seismic fieldwork with S-wave sources and receivers, the positive polarities of all receivers are oriented in the same direction across a data-acquisition template so that wavelet polarities are identical in all quadrants around a source station. At receiver orientations B and D, the receiver is orthogonal to the source vector, which produces zero-amplitude responses.
The translation of these experimental results into exploration practice means that seismic prospecting across fracture prospects should involve the acquisition of S-wave data – and further, the data-acquisition geometry should allow S-wave velocity to be measured as a function of azimuth.
When an azimuth direction is found in which S velocity across the depth interval of a fracture system has its maximum velocity, then the orientation direction of the dominant vertical fracture in that interval is defined as that maximum-velocity azimuth.
Next month: The behavior of seismic S waves as they propagate through a fractured interval, with emphasis on laboratory data of real S waves propagating through fractured real-earth media.