This month we expand our insights into the behavior of seismic S waves as they propagate through a fractured interval, with the emphasis placed on laboratory data of real S waves propagating through fractured real-Earth media.
The experimental data illustrated on figure 1, again taken from work published by Sondergeld and Rai, simulate the general case of S-wave illumination of a fracture system in which the illuminating source vector is polarized at an arbitrary angle ? relative to aligned fractures.
The test sample used to acquire the data was illustrated and discussed in the April EXPLORER.
The wavefields that propagate through the medium are now a combination of S1 (fast-S) and S2 (slow-S) wavelets, and not S1-only or S2-only wavelets as were generated in the experimental data discussed last month.
Wavelets A, B, C and D are again the responses observed when the receiver is either parallel to or orthogonal to the illuminating source vector.
The observed data contain both S1 and S2 arrivals. The length of the propagation path through the sample is such that the difference in S1 and S2 travel times causes the S1 and S2 wavelets to not overlap.
In real seismic data, when a fracture interval is thin compared to a seismic wavelength and the difference in S1 and S2 travel times is not too large, the response will be a complicated waveform representing the sum of partially overlapping S1 and S2 wavelets.
The wavelets at positions A’, B’, C’ and D’ illustrate important S-wave physics:
- Only a S1 mode propagates parallel to the fracture planes (responses A’ and C’).
- Only a S2 mode propagates perpendicular to the fracture planes (responses B’ and D’).
The experiment documented as figure 2 (above) illustrates the results that should be observed when S-wave data are acquired across a fracture system as a 3-D seismic survey in which there is a full azimuth range between selected pairs of sources and receivers.
In this test, the source and receiver are rotated in unison so that the positive-polarity ends of both source and receiver are always pointing in the same azimuth. This source-receiver geometry is what is accomplished during S-wave data processing when field data are converted from inline and crossline data-acquisition space to radial and transverse coordinate space that allows better recognition of S-wave modes.
This type of source and receiver rotation is common practice among seismic data processors that have reasonable familiarity with S waves.
The test data show convincing proof that only a fast-S mode propagates parallel to fractures, and only a slow-S mode propagates perpendicular to fractures. At all intermediate azimuths between these two directions, S-wave propagation involves a mixture of fast-S and slow-S wavefields.
The objective of real-Earth fracture evaluation is to acquire seismic data in a way that allows source and receiver rotations to be done to create data similar to that shown on figure 2. These rotated data are then searched to find the azimuth direction in which S-wave velocity is a maximum.
That maximum-velocity azimuth defines the orientation of the set of vertical fractures that dominate the fracture population.
Next month: A look at another laboratory measurement that illustrated the important behavior of S waves that propagate in fractured media.