ANNUAL REPORT, 1997

DYNAMIC MODELING OF EARTHQUAKES ON INHOMOGENEOUS
FAULTS

Steven kl. Day
San Diego State University

Ruth Harris
U.S. Geological Survey

1.DYNAMIC STRESS CHANGES DURING EARTHQUAKE RUPTURE
(Day, Yu, and Wald)

During 1997, we completed a study assessing observational evidence for the selfhealing hypothesis of fault friction. A paper describing the results was submitted to Bulletin of the Seismological Society of America in April. The abstract follows:

Abstract

We assess two competing dynamic interpretations which have been proposed for the short slip durations characteristic of kinematic earthquake models derived by inversion of earthquake waveform and geodetic data. The f~rst interpretation would require a fault constitutive relationship in which rapid dynamic restrengthening of the fault surface occurs after passage of the rupture front, a hypothesized mechanical behavior which has been referred to as "self-healing". The second interpretation would require aufficient spatial heterogeneity of stress drop to permit rapid equilibration of elastic stresses with the residual dynamic friction level, a condition we refer to as "geometrical constraint". These interpretations imply contrasting predictions for the time dependence of the faultplane shear stresses. We compare dhese predictions with dynamic shear stress changes for the 1992 Landers (M 7.3), 1994 Northridge (M6.7), and 1995 Kobe (M6.9) earthquakes. Stress changes are computed from kinematic slip models of these earthquakes, using a finite difference medhod. For each event, static stress drop is highly variable,spatially, widh~high stress drop patches embedded in a background of low, and largely negative, stress drop. The time histories of stress change show predominancy monotonic stress change after passage of the rupture front, settling to a residual level, without significant evidence for dynamic restrengthening. The stress change at the rupture front is usually gradual rather dhan abrupt, probably reflecting the limited resolution inherent in the underlying kinematic inversions. On dhe basis of this analysis, as well as recent similar results obtained independently for the Kobe and Morgan Hill earthquakes, we conclude that, at the present time, the self-healing hypothesis is unnecessary to explain earthquake kinematics.

2. EFFECTS OF A LOW-VELOCITY ZONE ON DYNAMIC RUPIURE
(Harris, Day)

In 1997 we revised our paper on the effects of a damage zone on earthquake rupture. The paper was published in the October, 1997, issue of BSSA. This work shows dhe potential for important feedbacks between (i) the wavefield multiply scattered and partially trapped by the low-velocity damage zone and (ii) the propagation of rupture and fault slip. We are investigating this phenomenon further and believe that it may be a significant contributor to dynamic weakening of faults. Abstract of the paper follows:

Abstract

Dynamic-crack earthquake simulations generally assume that the crustal material surrounding faults is laterally homogeneous. Tomographic and near fault seismic studies indicate that the crust near faults is instead comprised of rocks of varying material-velocities. We have tested the effects of adding material-velocity variation to simulations of spontaneously propagating earthquakes. We used twodimensional plane strain conditions coupled with a slip-weakening fracture criterion and examined earthquakes on faults that bisect finite-width low-velocity zones embedded in country rock and earthquakes on faults that bound two differentvelocity materials. When a fault bisects a low-velocity zone, the normal stress remains unchanged, but both the rupture velocity and slip-velocity pulse shape are perturbed. The presence of the low velocity zone induces high frequency oscillations in the slip function near the rupture front. When the fault is on the edge of the low velocity zone, the oscillations are more pronounced, and repeated stacking and slipping can occur near the rupture front. For the slip-weakening (velocity-independent) friction model, however, the temporary sticking does not lead to permanent arrest of slip, and slip duration is still controlled by the overall rupture dimension. When an earthquake ruptures a fault juxtaposing a lowervelocity material against a higher velocity material, the normal stress across the fault near the crack dp is perturbed. The sign of the normal stress perturbadon depends on the direcdon of rupture, leading in some cases to a directional dependence of rupture velocity. When slip is accompanied by stress reducdon, a positive feedback develops between the normal and shear stress changes, as previously noted by Andrews and Ben-Zion [1997], resulting in an apparently unavoidable grid-size dependence in computation of stress change near the rupture front. Numerical experiments indicate, however, that the rupture velocity is insensidve to this zone size dependence, which is highly localized immediately behind the crack tip. The factors controlling the rupture velocity in the simuladons, including directional dependence, are further elucidated by a new analydcal soludon for rupture of an asperity on a frictionless interface.

3-D DYNAMIC MODELING OF AN EARTHQUAKE RUPTURING A SEGMENTED FAULT

(Harris and Day)

Previous simulations of spontaneous rupture of faults across stepovers have been limited to 2D. In 1997, we used the finite difference method (previously employed by Day, BSSA 72, pp. 1881-1902, to model single-segment ruptures in 3D) to investigate the rupture of segmented faults in. This extends the earlier work of Harris and Day (J. Geophys. Res., Vol. 98, pp. 4461-4472) to 3D. The work is currently being completed and prepared for publication. Summary of investigations to date: The magnitudes of strike-slip earthquakes may be controlled by along-strike changes in fault geometry. We have analyzed the effects of one type of fault geometry change, the fault stepover, on earthquake rupture-lengths by using a 3D dynamic finite-difference computer program to numerically simulate a spontaneously propagating strike-slip earthquake encountering a stepover. In 3D we were able to study the effects of the earth's traction-free surface and the effects of both lateral and vertical changes in strength and material properties. When stress drops and strengths were held fixed, 2D and 3D simulations resulted in similar event cascades. A persistent feature of the 3D solutions, however, was the propensity of rupture at the stepover to occur at or near the free surface (see Figure 1). The 3D models also predict sign)ficant static depression (uplift) at fault-bounded dilatational (compressional) stepovers, suggesting how basins may form by repeated strike-slip earthquakes on the bounding fault structures. We have also extended the modeling method to include estimated effects of previous historical events on the stress field.

4. OTHER ACTIVITIES FOR 1997

Harris co-convened (with R. Stein and L. Sykes) the SCEC Workshop "Stress Triggers,

Stress Shadows, and Implications for Seismic Hazard"

Harris acted as Associate Editor for JGR Special I-ssue of the same title as the above

workshop.

Day gave keynote presentation at SCEC-sponsored "(3eneral Earthquake Model"

Workshop in Santa Fe, NM.

Day presented research seminars at USC, UCLA, U.N. Reno, and SCEC Stress

Triggering Workshop

PUBLICATIONS

1) Harris, R.A. (1997). Stress triggers, stress shadows, and implications for seismic hazard, Introducdon to the special issue, submitted to JGR.

2) Harris, R.A., and S.M. Day (1997). Effects of a Low-Velocity Zone on a Dynamic Rupture, Bull. Seism. Soc. Am. 87, 1267-1280.

-3) Harris, R.A., and R.W. Simpson (1997). Suppression of large earthquakes by stress shadows-implications of rate-and-state fricdon laws: two examples, submitted to JGR.

4) Day, S.M., G. Yu, and D. Wald (1997). Dynamic stress changes during earthquake rupture, Bull. Seism. Soc. Am, accepted for publication.

5) Day, S.M. (1997). Efficient simulation of constant Q using coarse-grained memory variables, submitted to Bull. Seism. Soc. Am.