PALEO-STRESS ESTIMATES ON ANCIENT SEISMOGENIC FAULTS, BASED ON FRICTIONAL HEATING OF COAL

The absence of a frictional heat flow anomaly on the San Andreas Fault has raised the question of whether it is a weak or a strong fault. A related, more general question, is whether the stress drops during earthquakes (~3–30 MPa) represent total stress drop on weak faults, or partial stress drops on strong faults.  

The above questions are addressed by examining the role of frictional heating of coal on ancient faults. An instantaneous frictional heat source is used to model the temperature-distance profile of frictional heat on a seismogenic fault using a co-efficient of friction of 0.7. A sharp temperature spike of 250-600 ^oC with a half-width of 1-10 cm is produced on a time scale of 0.25-1.0 hours, for a displacement of 1 m. The sensitivity of coal to heating makes vitrinite reflectance (R%) a good monitor of short-term temperature spikes. For example, the kinetics-based software “Easy R%” (Sweeney and Burnham 1990) indicates short-term temperature spikes of 375^oC and 500^oC will produce R% values of 1 and 3, respectively, consistent with laboratory data (Bustin 1983).

The area under the different temperature-distance curves is constant and is given by tD/rc (Lachenbruch 1986), where t is shear stress, D is fault displacement, r is density (1.3 g/cc for coal) and c is specific heat capacity. Re-arranging:

                                                    t=(Area) rc/D

This paleo-piezometer is independent of heating duration, normal stress, and the co-efficient of friction. Sheared coal on the Lewis thrust, Montana, has an R% value of 3 (corresponding to ~ 500^oC, assuming rapid heating) and drops to 0.7%, five centimeters away (Bustin 1983). The area under the temperature spike is then 25 degree-meters, corresponding to shear stresses of 8-34 MPa, for a displacement of 1-3 m. Sheared coal on three faults related to the Pine Mountain thrust, Kentucky, show elevated R% values of 0.85, 0.9 and 0.95 corresponding to a temperature spike of about 350^oC. Assuming a half width of 5 cm, the area under the temperature spike is 18 degree-meters, corresponding to shear stresses of 12-24 MPa, for reasonable displacements of 1-2 m. The Kentucky faults cross-cut well-cemented quartz-rich massive beds that appear to have been “strong”. These preliminary considerations, if confirmed, favor the partial stress drop, strong fault hypothesis.