The Pseudotachylite Conundrum

We are now ready to face the central mystery of pseudotachylite formation. We have seen that, at strain rates and under stresses likely to occur in the vicinity of large impact craters, it is plausible that shear zones with widths of mm to cm may begin to develop melt by friction (narrower veins have been observed in meteorites, but these are likely produced in the very high strain rates occurring in shock waves). I have deduced a minimum fault length, Lmin, on which friction melts just form. But what about the larger faults that can easily attain the melt threshold and then keep sliding? Do these continue to produce larger and larger quantities of melt? To answer these questions we must address the difficult subjects of the rheology of partially molten granitic rocks (Petford, 2003) and the dynamics of rapidly sheared rock surfaces, both of which pose more questions than answers at the moment.

It seems obvious that, once the solidus temperature TS of the rock is reached and melt starts to appear, the resistance to sliding should decrease (Jeffreys 1942; Sibson 1975). But because the dynamics of fault slip ensures a nearly constant slip velocity S, a lowered resistance means less heat dissipation and hence a slower heating rate. Friction melting should be self-limiting.

The only relevant experiment on the friction coefficient during melting (Tsutsumi and Shimamoto 1997) showed complicated results: Just before melt appeared on the sliding surfaces, the friction coefficient declined. However, as melt appeared the friction coefficient increased dramatically. The experimenters noted that during the experiments melt actually sprayed out of the shear zone, suggesting that the expected self-limiting feature could not develop because the melt flowed away as quickly as it formed. Unfortunately, it is not clear just what was melting in these experiments. The rock contained a mixture of plagioclase, pyroxene, hornblende and biotite, all of which probably melt at different temperatures: Under the short time scales accompanying frictional melting there is little time for chemical equilibration.

What about deeply buried shearing surfaces? In the experiments of Tsutsumi and Shimamoto the sliding surface was only about 1 cm away from the edge of the sample and melt could thus escape readily. Is a similar escape possible for sliding surfaces many km below the surface?

It is easy to estimate the volume discharge Q (per unit width of the sheet) of fluid with Newtonian viscosity ^ from a narrow sheet of thickness r (Batchelor 1970):

12 r/ dx where P is the pressure and x is in the plane of the sheet.

Applying this idea to the crack illustrated in Figure 6 suggests that perhaps the friction melt appearing on a fault of length L (larger than the minimum length) might flow along the surface of the fault and accumulate in the wedge-shaped pockets at the fault tip. Since the crack-tip pockets open in a tensional (mode I) configuration, the pressure in them during sliding is almost zero, thus providing a strong pressure gradient out of the fault as well as a volume into which friction melt might flow. Indeed, the thicker pseudotachylite occurrences along fault planes often have the appearance of wedge-shaped pockets (Killick and Reimold 1990; Shand 1916). Sibson (1975) also noted a distinction between narrow sliding zones and adjacent "injection dikes" that suggested tensional failure. The question then becomes, can the melt flow out of the shear zone fast enough to keep the friction coefficient high? The answer is clearly a function of the fault length: If the fault is too long, the discharge will be too small to remove a substantial volume of melt during the time available for sliding. On the other hand, the duration of rapid sliding increases with fault length.

To estimate the importance of this effect, compare the volume of melt squeezed out of the shear zone, QL / VS, to the volume of melt remaining in the zone, r L, per unit length of the zone in the case of fault slip at the maximum rate. The pressure gradient is of order %/(L/2). The ratio, R, between these two volumes is:

volume of shear zone 6 rjVSL

Turning this relation around, the minimum viscosity ^ necessary for R to exceed 1 in this fast slip regime is given by.

6 VSL

Inserting rather generous estimates of r = 1 cm, x = 3 x 108 Pa and VS = 3000 m/s, reveals that the viscosity must be less than 1/L (m) Pa-s. Thus, even 1 m long faults require melts with viscosity of only about 1 Pa-s, about equivalent to motor oil. A 100 m long fault would require viscosities similar to that of water. This appears to pose a serious problem for this mechanism. Because of the high viscosities of silica-rich melts, it seems to rule out this mechanism for the granitic rock that underlies the Vredefort and Sudbury craters, although the high initial temperatures of the rocks deep beneath these craters (500-900 °C) may help make the lavas more fluid.

The only obvious way to redeem this process is to note that the time interval assigned to the outflow was that associated with the fast elastic

Fig. 7. When a shear zone fails, the initial displacement increases at a rate determined by the speed at which the adjacent rock can feed elastic energy into the developing shear zone. Later displacement may be governed either by stable sliding at a rate determined by the deformation of the enclosing rock mass, or by stick-slip jumps that produce the same average displacement rate.

Time, t

Fig. 7. When a shear zone fails, the initial displacement increases at a rate determined by the speed at which the adjacent rock can feed elastic energy into the developing shear zone. Later displacement may be governed either by stable sliding at a rate determined by the deformation of the enclosing rock mass, or by stick-slip jumps that produce the same average displacement rate.

slip of the fault. If, as I suggest in Fig. 7, slip continues for a much longer time (either in steady or stick-slip mode), then perhaps viscous squeeze-out of the melt might become important. Another possibility, suggested by observations of tectonic pseudotachylites (Sibson 1975) is that, instead of melt flowing to the end of the slipping fault, it escapes at numerous locations along the face of the fault. In this case the appropriate value for the distance of squeeze-out is much less than L, while the timescale for flow is still determined by L. This does improve the situation, but field observations support this proposal only for tectonic fault zones (Sibson 1975). If, instead of the elastic slip time, L/VS, I substitute the crater formation time Tf (which is the longest time scale available during crater formation and collapse), the ratio of the volume squeezed out to that in the shear zone becomes

6 rjL

From which the estimate of the minimum viscosity to reach R ~ 1 rises to 1 r 2 x

For a 100 km diameter transient crater Tf is about 100 seconds and, for the previous estimates of r and x, the minimum viscosity is 5 x 105/L2(m) Pas. For fault lengths of a few meters this suggests that squeeze-out is possible even in granitic rocks. The proviso is that it must occur on the long time scale of crater collapse, not on the scale of elastic fault slip. It also suggests that this process is important only for the very largest craters, for which both x and T are large enough to provide both the stress and time for relatively viscous granitic melts to squeeze out of frictionally slipping cracks. This long time scale also precludes slip zones r as narrow as 1 mm, as they would completely solidify on the time scale for melt expulsion.

Applying Equation (19) to the experiments of Tsutsumi and Shimamoto (1997), in which L was about 1 cm and r was about 1 mm, the minimum viscosity for the extraction of melt over the ca. 10 s duration of melting is 3 x 104 Pa-s, well within the range of possibility for a gabbroic melt. Thus, the simple estimate for the occurrence of melt expulsion from a sliding surface does seem to agree with the limited experimental data in hand. The only other controlled experiment on friction melt formation (Spray 1995) used a much more silica-rich rock (Westerly Granite) in a configuration with dimensions similar to those of Tsutsumi and Shimamoto. In that experiment Spray did not report any movement of the melt, consistent with its probably much greater viscosity. A poorly controlled "experiment" by Killick (1990) reported melt production by an unlubricated drill bit, but offered too little information to estimate melt mobility.

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