ESTIMATION OF FAULT STRENGTH FROM INPLACE STRESS MEASUREMENTS

In principle, measurements of the magnitude and orientation of crystal stress in the vicinity of the San Andreas fault should provide the most direct evidence of the forces acting to cause interplate motion there. However, some essential problems exist with this approach. Because we have little understanding of the mechanics of the system, it is difficult to interpret the data. We are not dealing with a laboratory experiment in which a sample is loaded in a testing machine whose characteristics are well known; in such a situation, it is straightforward to use gages to estimate the magnitude of the load. In contrast to the well-controlled laboratory situation, we have little idea of the nature of the forces applied to the Earth's crust to cause a deviatoric state of stress and, in the case of tectonically active areas, slip across major through-going faults. We know neither where the forces are applied nor what is applying them; moreover, there is even debate about what the state of stress would be if only gravity were acting (McGarr, 1988).

In addition to the absence of a conceptual framework, there are numerous experimental difficulties in determining the state of stress, that is, the magnitudes and orientations of the three principal stresses as functions of position within the crust. Data must be obtained from depths below the zone of weathering, in rock that is sufficiently strong to support deviatoric stresses. In granitic rocks, this requirement, in effect, necessitates stress measurements at depths of about 50 m or more, thus limiting the measurement technique to hydraulic fracturing, the only common procedure that can be used at such depths (Haimson and Fairhurst, 1970).

The hydraulic-fracturing, or "hydrofrac," method involves isolating a section of a borehole and then pressurizIng this cylinder by pumping in fluid until a tensile crack forms and propagates into the previously unfractured rock. By monitoring the pressure-time history of the fluid in the isolated section, both the maximum and minimum horizontal stresses can be estimated (Hubbert and Willis, 1957; Zoback and Haimson, 1983). This approach assumes that one of the principal stresses sigmav is oriented vertically and can be calculated from the weight of overburden (eq. 20). The other two principal stresses are the maximum, sigmaH, and minimum, sigmah, horizontal stresses. In contrast to engineering usage, the convention adopted here is for compressional stresses to be positive because, in the Earth's crust, tensional stresses are rarely encountered, even at the surface.

Although the uppermost crust near the San Andreas fault system has not been sampled as much for stress as for heat flow, enough inplace stresses have been measured to provide an indication of the state of stress there and how it compares with crustal stresses in other tectonic settings. To date, 41 successful hydrofrac measurements have been made in the 12 wells shown in figure 10.11 at depths of as much as 850m. A total of 29 of these data, in wells along the Mojave reach of the fault (fig. 10. 11C), were analyzed by McGarr and others (1982). Since that study, four stress measurements have been made at Black Butte (BB, fig. 10.11C) in the Mojave Desert (Stock and Healy, 1988), the data from the Hi Vista well have been reanalyzed by Hickman and others (1988), and additional measurements have been made in central California (Zoback and others, 1980). Currently, stress measurements are being made at the Cajon Pass well near the southeast end of the Mojave reach of the San Andreas fault, with some observations at depths below 3 km. Because no clear picture has yet emerged (see Healy and Zoback, 1988), we have not incorporated the Cajon Pass results into this review.

The state of horizontal deviatoric stress can be characterized in terms of two parameters: the maximum horizontal shear stress taum given by

(22)

and the angle theta between the trace of the fault and the direction of maximum horizontal compressive stress sigmaH. Under favorable conditions, both parameters can be determined by the hydrofrac technique. We have shown that if theta ~ 45°, then taum is entirely resolved onto the plane of the fault to produce its slip; as theta approaches 0° or 90°, the resolved stress on the fault becomes arbitrarily small irrespective of the magnitude of taum (eq. 16).

Evidence regarding the actual orientation of sigmaH relative to the strike of the San Andreas fault is contradictory. Observations favoring theta distributed about 45°, so as to cause dextral fault slip, were presented by McNalley and others (1978), Zoback and others (1980), Zoback and Zoback (1980), and Hickman and others (1988); however, these data, from the Mojave Desert, show considerable scatter. In contrast, Mount and Suppe (1987) and Zoback and others (1987) reviewed a broad set of data, including many borehole breakout orientations, that suggest theta ~~ 90°; Oppenheimer and others (1988) came to a similar conclusion. An intermediate result was obtained by Jones (1988), who stated that sigmaH is oriented at 65° to the local strike of the San Andreas fault in southern California. Thus, currently, we know neither the preferred value of theta nor whether such a value even exists. For the foregoing values of theta (45°, 65°, or 90°), the shear stress resolved on the fault (eq. 16) would be taum, 0.77 taum, or 0, respectively. In view of this uncertainty, we leave theta unspecified and describe what is known of taum the upper limit to the shear stress that can be resolved on the fault.

The first-order feature seen in data from the San Andreas fault zone (fig. 10.12) is a marked tendency for taum to increase with depth. The solid line, a regression fit to all of the data, indicates a depth gradient of 8.3 MPa/km, not significantly greater than the gradient of 7.9 MPa/km reported by McGarr and others (1982) on the basis of 29 of the 41 data plotted in figure 10.12. We note that the observed depth gradient of taum also agrees well with the curves for strike-slip faults (solid curves, fig. 10.9) for a coefficient of friction of 0.6 or greater. In addition to the general increase in taum with depth, considerable variation from one well to another and within individual wells is suggested by figure 10.12.

Figure 10.13 shows that the departure of the measured values of taum from the regression line in figure 10.12 does not vary systematically with distance from the San Andreas fault. The principal conclusion to be drawn from figure 10.13 seems to be that the magnitude of deviatoric stress is not measurably affected by proximity to the San Andreas fault. Thus, whatever effect the fault may have on the magnitude of the shear stress, it is either too subtle, too localized, or too deep to be recognized in the current data set.

We note that there is no detectable difference between the Mojave Desert residuals, measured near a locked section of the San Andreas fault, and those in central California (fig. 10.11A), where the fault is creeping and presumably does not produce great earthquakes. If measurements were made to greater depths, some differences might appear, but at least in the topmost several hundred meters, the magnitude of shear stress seems to be largely independent of position along the strike of the San Andreas fault.

Having failed to discover any spatial relation between the San Andreas fault and deviatoric-stress magnitudes, we now consider the question of whether or not any detectable differences exist between the stress states measured near the San Andreas fault (fig. 10.12) and those measured elsewhere in different tectonic settings. A review of crustal shear stress by McGarr (1980) considered a large suite of stress data in "hard" rocks measured at depths extending to 3.6 km. The resulting regression line of

(23)

has a greater surface intercept but a similar depth gradient to the San Andreas regression

(24)

fitted to the crystalline-rock data in figure 10.12. The comparison between equations 23 and 24 is not entirely appropriate because the data used to develop equation 23 represent all three stress states; stresses measured in regions of strike-slip tectonics were not considered separately by McGarr (1980) (see fig. 10.9). More recently, however, data measured in a 2,000-m-deep well in Cornwall, U.K. (Pine and others, 1983), permit quite an interesting comparison. For both the San Andreas and the Cornwall data sets, most of the stress observations are compatible with strike-slip tectonics; that is, sigmav is the intermediate principal stress. For most of the San Andreas and all of the Cornwall measurements, the rock is granitic. In contrast to the San Andreas system, however, the tectonic setting in Cornwall is presently inactive. The deviatoric stresses at Cornwall are believed to be a consequence of the Alpine orogeny, which apparently has caused the maximum horizontal stress to be oriented northwestward throughout much of Europe (for example, McGarr and Gay, 1978).

The 12 data sets obtained by Pine and others (1983) indicate a stress state (fig. 10.14) surprisingly similar to that of the San Andreas fault (fig. 10.12). For the maximum shear stress, the depth gradient of 7.52 MPa/km is indistinguishable from its counterpart in the crystalline San Andreas crust of 7.46 MPa/km; however, the surface intercept at Cornwall is larger. If the state of deviatoric stress is much the same in Cornwall as along the San Andreas system, then we must conclude that the plate-tectonic motion in California along the San Andreas fault has no expression in the shallow (1-2 km deep) stress field. Accordingly, much of what has been discovered about continental-crustal stress in general may apply to the crust adjacent to the San Andreas fault.

This generalization implies that the applied forces which give rise to taum in the vicinity of the San Andreas fault are not specific to the Pacific-North American plate boundary. In terms of observed shear stress, a major active plate-boundary fault would be at least as likely in Cornwall, U.K., as in California from what we currently know of stress magnitudes, at depths down to a few kilometers.