Abdolrasool Anooshehpoor

Frictional heat generation and seismic radiation in a foam rubber model of earthquakes

Results from a study of stick-slip particle motion at the interface between two stressed foam rubber blocks indicate that normal vibrations and interface separation are an important part of the stick-slip process in foam rubber. The dimension of the dynamic slip pulse is small compared to the dimension of the model (approximately 10 cm vs. 200 cm) consistent with the abrupt-locking slip pulse model ofBrune (1970, 1976), andHeaton (1990). A comparison of frictional heat generation between stable-sliding and stick-slip foam rubber models indicates a linear relation between the temperature increase on the fault surface (for a given distance of slip) and the driving shear force for the stable-sliding model, while for the stick-slip model there is essentially no variation in frictional heat generation with an increase in shear stress. We performed experiments to investigate the ratio of normal motion to shear motion at different levels of normal stress in the stick-slip foam rubber model. Preliminary result indicate that the normal component of the particle motion increases more rapidly with increasing normal stress than the shear component. The phenomenon of interface separation and normal vibrations may thus explain some of the most frustrating problems in earthquake mechanics, e.g., the heat flow paradox, the long-term weakness of major active faults, and anomalousP-wave radiation.

Methodology for Obtaining Constraints on Ground Motion from Precariously Balanced Rocks

Precariously balanced rocks provide constraints on the level of ground motion that could have occurred during the time the rocks have been in their current positions. Field measurements of the quasi-static toppling accelerations of precariously balanced rocks provide information for computer modeling of the response of the rocks to given ground-motion histories. The quasi-static toppling acceleration is determined by the ratio of the quasi-static force through the center of mass whose moment about the rocking point counterbalances that of gravity and the mass of the rock. For an estimate of dynamic toppling peak ground accelerations, we use a finite-difference numerical code to model the dynamic response of rocks to arbitrarily complex acceleration time histories. We test our computational methodology and results using the University of Nevada shake table. The shake-table tests of both idealized rectangular shapes and actual rocks confirm the accuracy of our methodology for estimating dynamic toppling accelerations of precarious rocks for different waveforms representing earthquake ground-motion time histories. A study of statistical variation of the dynamic toppling acceleration for a suite of seismograms provides constraints on the peak ground acceleration on hard-rock sites in Mojave Desert, about 15 km from the San Andreas fault, of about 0.5 g for synthetic seismograms with relatively high frequency content, or about 0.4 g for seismograms with spectra similar to the recent Izmit, Turkey, earthquake. A major source of uncertainty is the uncertainty in the spectrum of ground motion for large earthquakes. Waveforms with relatively more low frequencies can topple the rocks with lower peak ground accelerations. We describe methods for reducing the uncertainties with further study and more data.

Wrinkle‐like Weertman pulse at the interface between two blocks of foam rubber with different velocities

We verify the existence of self-sustaining wrinkle-like Weertman velocity pulses along a pre-stressed interface between two dissimilar (ΔV = 60%) blocks of foam rubber. Properties of the observed velocity pulses are similar to the theoretical prediction of Weertman (1980), and the numerical calculations of Andrews and Ben-Zion (1997). Particle displacement, in the direction perpendicular to the fault, is much larger in the slower medium than in the faster medium, resulting in a separation of the interface during the passage of the slip pulse. The rupture velocity is near the shear wave velocity in the slower material, and the direction of propagation is nearly always in the direction of the shear particle motion in the slower block. The pulse is self-maintaining, that is, it does not die out from radiation damping, obtaining the necessary energy by releasing locally stored shear potential energy.

Quasi-Static Slip-Rate Shielding by Locked and Creeping Zones as an Explanation for Small Repeating Earthquakes at Parkfield

In a recent study of microearthquakes along the Parkfield segment of the San Andreas fault, Nadeau et al. (1995) have found that much of the seismicity in the region is characterized by quasi-periodic repeating sequences of small earthquakes that are essentially identical in waveform, size and, location. Nadeau and Johnson (1998) interpreted these as repeated slip on a given asperity driven by a steady slip rate of 2.3 cm/yr and concluded that the stress drops needed to be extremely high, of the order of 20 kilobars. We propose another explanation for these small repeating events, namely that an inner asperity is surrounded by a larger creeping zone, which in turn is surrounded by a still larger locked zone. This geometry produces a local slip velocity much less than the overall creep velocity observed on a still larger scale (slip velocity shielding). We have constructed a foam rubber model to illustrate the phenomenon. The time sequences of small events at the asperity, punctuated by large events which rupture the whole block, look very similar to the cumulative moment plots of Nadeau and Johnson. The actual dynamic stress drops are of the same order as for the large events. Thus the results of the model correspond to the observations of Nadeau and Johnson and suggest that the model may be appropriate to explain their observations, without requiring super strong asperities.

Band of precariously balanced rocks between the Elsinore and San Jacinto, California, fault zones: Constraints on ground motion for large earthquakes

A spectacular band of precariously and semiprecariously bal- anced rocks extends from Riverside to near Borrego Valley, Cali- fornia, about halfway between the Elsinore and San Jacinto fault zones. The rocks are distributed in a band a few kilometers wide midway between the San Jacinto and Elsinore fault zones, an in- dication that the distribution is caused by attenuation of strong ground motion from numerous large events along these two fault zones. These rocks have apparently been in place for thousands of years, and thus place important constraints on ground motions from earthquakes. On the basis of field tests and photographic analysis, the estimated quasi-static toppling accelerations for the precariously balanced rocks are ;0.32 6 0.10 g (g 5 gravitational acceleration). The dynamic toppling accelerations are within this range for earthquakes with waveforms similar to those recorded during the Izmit and Denali earthquakes. These constraints are roughly consistent with the median predicted value of ground mo- tion for M7 earthquakes, but somewhat lower than 11s ground motion curves, and much lower than the values from the 2% in 50 yr hazard maps. The evidence from these rocks has importance for some of the assumptions that go into calculating probabilistic seismic hazard assessment, including median and standard devia- tion of ground motion attenuation curves (especially for hard rock, for which few instrumental data are available), the possible exis- tence of random background earthquakes, and the smoothing dis- tance for historical seismicity.

A PHYSICAL MODEL OF THE EFFECT OF A SHALLOW WEAK LAYER ON STRONG GROUND MOTION FOR STRIKE-SLIP RUPTURES

We report results of foam-rubber modeling of the effect of a shallow weak layer on ground motion from strike-slip ruptures. Computer modeling of strong ground motion from strike-slip earthquakes has involved somewhat arbitrary assumptions about the nature of slip along the shallow part of the fault (e.g., fixing the slip to be zero along the upper 2 kilometers of the fault plane) in order to match certain strong motion accelerograms. Most modeling studies of earthquake strong ground motion have used what is termed kinematic dislocation modeling. In kinematic modeling the time function for slip on the fault is prescribed, and the response of the layered medium is calculated. Unfortunately, there is no guarantee that the model and the prescribed slip are physically reasonable unless the true nature of the medium and its motions are known ahead of time. There is good reason to believe that in many cases faults are weak along the upper few kilometers of the fault zone and may not be able to maintain high levels of shear strain required for high dynamic energy release during earthquakes. Physical models of faulting, as distinct from numerical or mathematical models, are guaranteed to obey static and dynamic mechanical laws. Foam-rubber modeling studies have been reported in a number of publications. The object of this paper is to present results of physical modeling using a shallow weak layer, in order to verify the physical basis for assuming a long rise time and a reduced high frequency pulse for the slip on the shallow part of faults. It appears a 2-kilometer deep, weak zone along strike-slip faults could indeed reduce the high frequency energy radiated from shallow slip, and that this effect can best be represented by superimposing a small amplitude, short rise-time pulse at the onset of a much longer rise-time slip. A weak zone was modeled by inserting weak plastic layers of a few inches in thickness into the foam rubber model. For the 15 cm weak zone the average pulse is reduced by a factor of 0.46. The factor for the 20 cm case reduction is 0.11. For the 30 cm case it is 0.045. From these results we can see that, the thicker the weak layer, the more difficult it is for a short rise-time acceleration pulse to push its way through the weak layer to the surface. This is thus an approximate justification for reducing the high frequency radiation from shallower parts of strike-slip faults if it is known that the shallow part of the fault is weak or has not stored up shear stress.

Verification of precarious rock methodology using shake table tests of rock models

Precariously balanced rocks in seismically active regions are effectively upper-limit strong motion seismoscopes that have been in place for thousands of years. Thus, estimates of the dynamic toppling acceleration of these rocks (through rigid body rocking) can provide constraints on the peak ground accelerations experienced during past earthquakes. We have developed a methodology that uses a two-dimensional numerical code to calculate the dynamic rocking response of precarious rocks to realistic ground acceleration time histories. Statistical analyses of the dynamic response of these rocks to a range of synthetic seismograms, as well as strong motion records, can provide important information about the ground motion attenuation curves and seismic hazard maps. We use shake table tests to investigate the dynamic rocking response of 13 wooden rectangular blocks of various sizes and aspect ratios subjected to realistic seismograms and compare the results with those of numerical tests. Our results indicate good agreement between the shake table and numerical results.

Dynamics of Earthquake Normal Faulting: Two-Dimensional Lattice Particle Model

A 2D lattice particle model is used to simulate the dynamic rupture process of a normal fault. The system equations for the particle motions are solved numerically by the finite-difference method, under a given block boundary condition. The flexibility of the implementation of a 2D lattice particle model to simulate an earthquake dynamic process was demonstrated in previous modeling of a shallow angle thrust fault (Shi et al. , 1998). Numerical results indicate that the particle motions (displacement, velocity, and acceleration) along the fault are discontinuous both in the fault-parallel and fault-normal directions, with a localized slip rupture and localized fault separation. In the vicinity of the fault outcrop (the position at which the fault intersects with the free surface), the particle velocity and acceleration increase rapidly, both on the hanging wall and the footwall. The particle motions on the hanging wall are larger than those on the footwall. These motions are amplified as the fault scarp develops (rupture breaks out at the surface), with strong asymmetry between the hanging wall and the footwall. Along the free surface, as the distance from the fault outcrop increases, the particle velocity and acceleration decrease rapidly on the footwall and less rapidly on the hanging wall. The asymmetrical particle motion results from the geometrical effect of the dip of the fault, the free surface, and the dynamic source rupture. The combination of all of these effects causes a strong asymmetry in stress when the rupture pulse approaches the free surface. The dynamically propagating rupture is characterized by a ramp slip time function accompanied with fault opening. The slip pulse becomes sharper when the rupture approaches the free surface; consequentially, the hanging wall in the vicinity of the fault exhibits a large vibration, which generates a strong surface wave propagating along the free surface away from the fault scarp on the hanging-wall side. This result is similar but significantly different from the numerical simulation of a normal fault with a moving double-couple dislocation source (Benz and Smith, 1988). In addition, the numerical result is qualitatively in agreement with recent foam-rubber experiments (Brune and Anooshehpoor, 1999) and similar to results from a finite-element simulation (Oglesby et al. , 1998; Oglesby, 1999). Comparing with a 2D strike-slip fault and thrust fault, the particle motions in the vicinity of the normal fault on the free surface are smaller for a same-size rupture pulse.

Frictional resistance of a fault zone with strong rotors

As a possible mechanism to explain the lack of a heat flow anomaly along the creeping section of the San Andreas Fault, we have determined the effect of placing hard rotors along a surface between two deformable media, in this case styrofoam balls between two blocks of foam rubber. The probable presence of Franciscan rocks at depth along the creeping section of the San Andreas Fault suggested this mechanism, since the Franciscan is characterized not only by basic serpentinous rocks which are weak, but also by embedded, more or less equidimensional, blocks of very strong rocks (knockers), e.g., high grade blueschists and eclogites, which might act as rotors. The results suggest that knocker rotation may be a viable mechanism for reduction of friction on the creeping section of the San Andreas fault, and thus be at least a partial explanation of the lack of any observed frictional heat flow anomaly there.

Precarious Rock and Overturned Transformer Evidence for Ground Shaking in the Ms 7.7 Kern County Earthquake: An Analog for Disastrous Shaking from a Major Thrust Fault in the Los Angeles Basin

Precariously balanced rocks and overturned transformers in the vicinity of the White Wolf fault provide constraints on ground motion during the 1952 M s 7.7 Kern County earthquake, a possible analog for an anticipated large earthquake in the Los Angeles basin (Shaw et al. , 2002; Dolan et al. , 2003). On the northeast part of the fault preliminary estimates of ground motion on the footwall give peak accelerations considerably lower than predicted by standard regression curves. On the other hand, on the hanging-wall, there is evidence of intense ground shattering and lack of precarious rocks, consistent with the intense hanging-wall accelerations suggested by foam-rubber modeling, numerical modeling, and observations from previous thrust fault earthquakes. There is clear evidence of the effects of rupture directivity in ground motions on the hanging-wall side of the fault (from both precarious rocks and numerical simulations). On the southwest part of the fault, which is covered by sediments, the thrust fault did not reach the surface (“blind” thrust). Overturned and damaged transformers indicate significant transfer of energy from the hanging wall to the footwall, an effect that may not be as effective when the rupture reaches the surface (is not “blind”). Transformers near the up-dip projection of the fault tip have been damaged or overturned on both the hanging-wall and footwall sides of the fault. The transfer of energy is confirmed in a numerical lattice model and could play an important role in a similar situation in Los Angeles. We suggest that the results of this study can provide important information for estimating the effects of a large thrust fault rupture in the Los Angeles basin, specially given the fact that there is so little instrumental data from large thrust fault earthquakes.