Much of our understanding of earthquakes comes from the simple conceptual model of two blocks of the Earth's crust sliding past one another in a process governed by laws of static and dynamic friction. Therefore, knowledge of the frictional properties of faults and the frictional behavior of fault materials should be fundamental to studies of active tectonics. This investigation helps resolve the uncertainty of the frictional strength of faults by presenting new field observations of frictionally generated heat.
Laboratory studies of rock friction pioneered by Byerlee (1978) found that the coefficient of friction of almost every type of crustal rock falls within the surprisingly narrow range of 0.6 - 1.0, a range that is commonly referred to as Byerlee's Law.
One of the implications of the frictional nature of fault slip is that significant amounts of heat should be generated during earthquakes and aseismic creep. The amount of heat can be calculated assuming Byerlee's Law, and models for conductive heat flow can predict the effects of this heat on measurable quantities such as surface heat flow. However, when researchers began looking along the San Andreas Fault for this predicted heat, it was nowhere to be found (Lachenbruch and Sass, 1980). In order to satisfy the heat flow data, the coefficient of friction of real faults must be almost an order of magnitude lower than Byerlee observed, about 0.1. Debate has raged over the apparent contradiction between laboratory studies and heat flow measurements, but there has never been confirmation of the surface heat flow findings by an independent technique even though there are strong criticisms of those observations (e.g., Hanks and Scholz, 1980). We propose an independent method for measuring frictional heating with fission track thermochronology.
We use fission track's ability to record the thermal history of a rock as a new way to measure the amount of frictional heating on faults. We have constructed a numerical model that includes calculations of frictional heat generation, heat flow, and fission track annealing. Our model shows that temperature spikes from a single large earthquake along a fault obeying Byerlee's law should cause measurable changes of fission track ages and track lengths. These effects should be extremely localized and restricted to within a few centimeters of a fault surface.
We used these calculations to guide preliminary sample collection along the San Gabriel fault zone in Southern California (Figure 16.1). The San Gabriel fault is an ancient and abandoned trace of the San Andreas fault that accommodated about 40 km of plate boundary motion from 13 to 4 Ma (Powell, 1993). Since the fault became inactive, uplift and erosion have brought exposures of the fault to the surface that were originally between 2 and 5 km deep while the fault was slipping (Blythe et al., 2000). At our sample locality, slip is extremely localized along a layer of ultracataclasite 1 - 8 cm thick and we approximate it as an infinitely thin source of heat. Unlike other locations in the area, this site shows little evidence of fluid-rock interaction (Chester et al., 1996) and a simplifying assumption of purely conductive heat flow is acceptable.
We collected samples along two transects perpendicular to the fault for fission track analysis. Fission track ages are shown as a function of distance from the fault in Figures 16.2 and 16.3. There is no localized resetting of the fission track ages.
Figure 16.3 reveals that ages increase within a zone adjacent to the principle slip surface in transect 8B. These elevated ages all occur within a block of granodiorite that has undergone significant brittle deformation and can best be described as a foliated cataclasite. The age of a sample adjacent to the fault in transect 8E (where the foliated layer is absent) is equivalent to the mean age far from the fault (within error). We interpret this observation as evidence that vertical displacement within the block resulted in the present-day juxtaposition of rocks from different paleo-depths. While this hypothesis adds complexity to the quantitative interpretation, qualitatively there is still no localized reduction in fission track age in either transect.
Interpretation of the lack of a fission track "age anomaly" is complicated. Because heat generation is linearly related to both slip distance and fault strength, any method that constrains thermal histories will never be able to uniquely determine the relative contribution of these two variables. For example, we use forward modeling of faults with Byerlee friction and hydrostatic pore pressure to determine the minimum size earthquake that would produce sufficient heat to change the fission track age by an observable amount. Such an event would require only 4 m of slip at the sample locality. Similarly, if we assume an 8 m slip event, the effective coefficient of friction is constrained to less than about 0.25. These calculations all assume a single earthquake but each additional earthquake should cause progressive reduction of the fission track age and further lower the estimated coefficient of friction required to be consistent with our data.
We introduce and test a new methodology for constraining frictionally generated heat along faults using fission track thermochronology. Assuming coefficients of friction consistent with Byerlee's Law (0.6 - 0.8) and hydrostatic pore pressure, we determine that the San Gabriel fault never experienced a single earthquake with more than 4 m of slip at the sample locality. However, assuming that at least one earthquake of that size occurred, the San Gabriel fault is weaker than predicted by Byerlee's law.
This project could not have been completed without the detailed fission track analysis performed by Ann E. Blythe from the University of Southern California.
Blythe, A. E., Burbank, D. W., Farley, K. A., and Fielding, E. J., Structural and topographic evolution of the central Transverse Ranges, California, from apatite fission-track, (U-Th)/He and digital elevation model analysis, Basin Research, 12 , 97-114, 2000.
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Chester, F.M., J.P. Evans, and R.L. Biegel, Internal structure and weakening mechanisms of the San Andreas Fault, J. Geophys. Res., 98, 771-786, 1993.
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