Mapping the Functional Roles of Cap Cells in the Response of Arabidopsis Primary Roots to Gravity1

The cap is widely accepted to be the site of gravity sensing in roots because removal of the cap abolishes root curvature. Circumstantial evidence favors the columella cells as the gravisensory cells because amyloplasts (and often other cellular components) are polarized with respect to the gravity vector. However, there has been no functional confirmation of their role. To address this problem, we used laser ablation to remove defined cells in the cap of Arabidopsis primary roots and quantified the response of the roots to gravity using three parameters: time course of curvature, presentation time, and deviation from vertical growth. Ablation of the peripheral cap cells and tip cells did not alter root curvature. Ablation of the innermost columella cells caused the strongest inhibitory effect on root curvature without affecting growth rates. Many of these roots deviated significantly from vertical growth and had a presentation time 6-fold longer than the controls. Among the two inner columella stories, the central cells of story 2 contributed the most to root gravitropism. These cells also exhibited the largest amyloplast sedimentation velocities. Therefore, these results are consistent with the starch-statolith sedimentation hypothesis for gravity sensing.

Intermediate- and long-term earthquake prediction.

Progress in long- and intermediate-term earthquake prediction is reviewed emphasizing results from California. Earthquake prediction as a scientific discipline is still in its infancy. Probabilistic estimates that segments of several faults in California will be the sites of large shocks in the next 30 years are now generally accepted and widely used. Several examples are presented of changes in rates of moderate-size earthquakes and seismic moment release on time scales of a few to 30 years that occurred prior to large shocks. A distinction is made between large earthquakes that rupture the entire downdip width of the outer brittle part of the earth's crust and small shocks that do not. Large events occur quasi-periodically in time along a fault segment and happen much more often than predicted from the rates of small shocks along that segment. I am moderately optimistic about improving predictions of large events for time scales of a few to 30 years although little work of that type is currently underway in the United States. Precursory effects, like the changes in stress they reflect, should be examined from a tensorial rather than a scalar perspective. A broad pattern of increased numbers of moderate-size shocks in southern California since 1986 resembles the pattern in the 25 years before the great 1906 earthquake. Since it may be a long-term precursor to a great event on the southern San Andreas fault, that area deserves detailed intensified study.

Intermediate-term earthquake prediction.

An earthquake of magnitude M and linear source dimension L(M) is preceded within a few years by certain patterns of seismicity in the magnitude range down to about (M - 3) in an area of linear dimension about 5L-10L. Prediction algorithms based on such patterns may allow one to predict approximately 80% of strong earthquakes with alarms occupying altogether 20-30% of the time-space considered. An area of alarm can be narrowed down to 2L-3L when observations include lower magnitudes, down to about (M - 4). In spite of their limited accuracy, such predictions open a possibility to prevent considerable damage. The following findings may provide for further development of prediction methods: (i) long-range correlations in fault system dynamics and accordingly large size of the areas over which different observed fields could be averaged and analyzed jointly, (ii) specific symptoms of an approaching strong earthquake, (iii) the partial similarity of these symptoms worldwide, (iv) the fact that some of them are not Earth specific: we probably encountered in seismicity the symptoms of instability common for a wide class of nonlinear systems.

Hypothesis testing and earthquake prediction.

Requirements for testing include advance specification of the conditional rate density (probability per unit time, area, and magnitude) or, alternatively, probabilities for specified intervals of time, space, and magnitude. Here I consider testing fully specified hypotheses, with no parameter adjustments or arbitrary decisions allowed during the test period. Because it may take decades to validate prediction methods, it is worthwhile to formulate testable hypotheses carefully in advance. Earthquake prediction generally implies that the probability will be temporarily higher than normal. Such a statement requires knowledge of "normal behavior"--that is, it requires a null hypothesis. Hypotheses can be tested in three ways: (i) by comparing the number of actual earth-quakes to the number predicted, (ii) by comparing the likelihood score of actual earthquakes to the predicted distribution, and (iii) by comparing the likelihood ratio to that of a null hypothesis. The first two tests are purely self-consistency tests, while the third is a direct comparison of two hypotheses. Predictions made without a statement of probability are very difficult to test, and any test must be based on the ratio of earthquakes in and out of the forecast regions.

Implications of fault constitutive properties for earthquake prediction.

The rate- and state-dependent constitutive formulation for fault slip characterizes an exceptional variety of materials over a wide range of sliding conditions. This formulation provides a unified representation of diverse sliding phenomena including slip weakening over a characteristic sliding distance Dc, apparent fracture energy at a rupture front, time-dependent healing after rapid slip, and various other transient and slip rate effects. Laboratory observations and theoretical models both indicate that earthquake nucleation is accompanied by long intervals of accelerating slip. Strains from the nucleation process on buried faults generally could not be detected if laboratory values of Dc apply to faults in nature. However, scaling of Dc is presently an open question and the possibility exists that measurable premonitory creep may precede some earthquakes. Earthquake activity is modeled as a sequence of earthquake nucleation events. In this model, earthquake clustering arises from sensitivity of nucleation times to the stress changes induced by prior earthquakes. The model gives the characteristic Omori aftershock decay law and assigns physical interpretation to aftershock parameters. The seismicity formulation predicts large changes of earthquake probabilities result from stress changes. Two mechanisms for foreshocks are proposed that describe observed frequency of occurrence of foreshock-mainshock pairs by time and magnitude. With the first mechanism, foreshocks represent a manifestation of earthquake clustering in which the stress change at the time of the foreshock increases the probability of earthquakes at all magnitudes including the eventual mainshock. With the second model, accelerating fault slip on the mainshock nucleation zone triggers foreshocks.

Rock friction and its implications for earthquake prediction examined via models of Parkfield earthquakes.

The friction of rocks in the laboratory is a function of time, velocity of sliding, and displacement. Although the processes responsible for these dependencies are unknown, constitutive equations have been developed that do a reasonable job of describing the laboratory behavior. These constitutive laws have been used to create a model of earthquakes at Parkfield, CA, by using boundary conditions appropriate for the section of the fault that slips in magnitude 6 earthquakes every 20-30 years. The behavior of this model prior to the earthquakes is investigated to determine whether or not the model earthquakes could be predicted in the real world by using realistic instruments and instrument locations. Premonitory slip does occur in the model, but it is relatively restricted in time and space and detecting it from the surface may be difficult. The magnitude of the strain rate at the earth's surface due to this accelerating slip seems lower than the detectability limit of instruments in the presence of earth noise. Although not specifically modeled, microseismicity related to the accelerating creep and to creep events in the model should be detectable. In fact the logarithm of the moment rate on the hypocentral cell of the fault due to slip increases linearly with minus the logarithm of the time to the earthquake. This could conceivably be used to determine when the earthquake was going to occur. An unresolved question is whether this pattern of accelerating slip could be recognized from the microseismicity, given the discrete nature of seismic events. Nevertheless, the model results suggest that the most likely solution to earthquake prediction is to look for a pattern of acceleration in microseismicity and thereby identify the microearthquakes as foreshocks.

Slip complexity in earthquake fault models.

We summarize studies of earthquake fault models that give rise to slip complexities like those in natural earthquakes. For models of smooth faults between elastically deformable continua, it is critical that the friction laws involve a characteristic distance for slip weakening or evolution of surface state. That results in a finite nucleation size, or coherent slip patch size, h*. Models of smooth faults, using numerical cell size properly small compared to h*, show periodic response or complex and apparently chaotic histories of large events but have not been found to show small event complexity like the self-similar (power law) Gutenberg-Richter frequency-size statistics. This conclusion is supported in the present paper by fully inertial elastodynamic modeling of earthquake sequences. In contrast, some models of locally heterogeneous faults with quasi-independent fault segments, represented approximately by simulations with cell size larger than h* so that the model becomes "inherently discrete," do show small event complexity of the Gutenberg-Richter type. Models based on classical friction laws without a weakening length scale or for which the numerical procedure imposes an abrupt strength drop at the onset of slip have h* = 0 and hence always fall into the inherently discrete class. We suggest that the small-event complexity that some such models show will not survive regularization of the constitutive description, by inclusion of an appropriate length scale leading to a finite h*, and a corresponding reduction of numerical grid size.

Probes of the inner jets of blazars.

I review models for the "inner jet" in blazars, the section that connects the central engine with the radio jet. I discuss how the structure and physics of the inner jet can be explored using millimeter-wave VLBI (very-long-baseline radio interferometry) as well as multiwaveband observations of blazars. Flares at radio to gamma-ray frequencies should exhibit time delays at different wavebands that can test models for both the high-energy emission mechanisms and the nature of the inner jet in blazars.