S-Waves on Crack? Not So Much

This month we continue our series on S waves and factures by taking a look at another laboratory measurement that illustrates an important behavior of S waves that propagate in fractured media.

Experimental work done by Xu and King (1989) are presented as figure 1.

In this lab experiment, P, S1 (fast-S) and S2 (slow-S) modes propagate through a test sample before and after the sample was cracked to create a series of internal fracture planes. Wave transit times through the sample were measured to determine the effect of cracks on the velocity of each wave mode.

For both the cracked and uncracked samples, transit time measurements were made for a series of confining pressure conditions varying from 1.4 MPa to almost 21 MPa. P-wave travel time behavior is described on the top panel of the figure; S1 and S2travel times are summarized on panels b and c, respectively.

On each data panel, the transit time for uncracked rock is marked as A. Point B indicates the travel time through the cracked sample.

The travel times for P and S1modes exhibit little pressure dependence over the applied pressure range for either cracked or uncracked media.

There is a noticeable decrease in transit time for the S2mode as confining pressure is increased. This behavior is indicated by the dashed line drawn across the S2waveforms on panel C.

The wave physics confirmed by this test is that P and S1velocities decrease by only a small amount – often a negligible amount – when a seismic propagation medium changes from non-fractured rock to a medium with aligned-fractures. The observed delay in transit time through the small test sample is less than 2 μs for each of these wave modes when fractures are present.

In contrast, the delay in travel time for the S2modes exceeds 5 μs – more than twice the transit-time delays of the P and S1modes. Data point B for the S2mode propagating in the cracked rock is arbitrarily selected from the waveform observed at the mid-pressure range used in the test.

Physical measurements of S-wave transit time through fractured media – such as those documented on figure 1 – establish the relationship between slow-S velocity and fracture density illustrated on figure 2. This model simulates a seismic profile traversing an Earth system consisting of blocks of anisotropic rock bounded by blocks of isotropic rock.

Anisotropic conditions in blocks B, C and D are caused by aligned fractures that have different fracture density (FD) and fracture azimuth (?) from block to block.

When this Earth system is illuminated with an elastic wavefield, slow-S velocity has the generalized behavior diagramed below the Earth model. As fracture density FD increases, slow-S velocity S2velocity decreases.

The magnitude by which S2decreases is a qualitative, not quantitative, indicator of fracture density. S2velocity behavior can be used to predict fracture density in a quantitative manner only if fracture density can be independently determined at several calibration points across seismic image space – and establishing such calibration is difficult.

Restricting the use of S2 velocity behavior to that of only a qualitative predictor of fracture density is still important and valuable for understanding fracture distribution across areas imaged with multicomponent seismic data. Variations in fracture azimuth Φ affect only the polarization direction of the slow-S mode, not the magnitude of S2 velocity.

Fast-S velocity in a fractured medium is approximately the same as it is in an unfractured sample of that same medium (figure 1b). S1 velocity may decrease by a small amount if fracture density is sufficient to alter bulk density; otherwise, it is reasonably correct to assume S1 has the same magnitude in fractured rock as it has in non-fractured sections of the same rock.

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