Charles G. Sammis

An observational test of the critical earthquake concept

We test the concept that seismicity prior to a large earthquake can be understood in terms of the statistical physics of a critical phase transition. In this model, the cumulative seismic strain release increases as a power law time to failure before the final event. Furthermore, the region of correlated seismicity predicted by this model is much greater than would be predicted from simple elastodynamic interactions. We present a systematic procedure to test for the accelerating seismicity predicted by the critical point model and to identify the region approaching criticality, based on a comparison between the observed cumulative energy (Benioff strain) release and the power law behavior predicted by theory. This method is used to find the critical region before all earthquakes along the San Andreas system since 1950 with M≥6.5. The statistical significance of our results is assessed by performing the same procedure on a large number of randomly generated synthetic catalogs. The null hypothesis, that the observed acceleration in all these earthquakes could result from spurious patterns generated by our procedure in purely random catalogs, is rejected with 99.5% confidence. An empirical relation between the logarithm of the critical region radius (R) and the magnitude of the final event (M) is found, such that log R∝0.5M, suggesting that the largest probable event in a given region scales with the size of the regional fault network.

The damage mechanics of brittle solids in compression

The development of microcrack damage in brittle solids in compression is analyzed, using a simple model. The model is developed from recent detailed analysis of the initiation, propagation and linkage of microfractures from pre-existing cracks, voids, or other inhomogeneities. It describes the evolution of damage with strain and from it a criteria for failure can be established. The results are used to construct failure surfaces in stress space which combine information about brittle failure with data describing the onset of plastic yielding. Such failure surfaces are constructed for a number of rocks and are compared with previously published experimental data.

The kinematics of gouge deformation

The methods and first results of a new approach to examining fault gouge are described. Samples of undisturbed fault gouge from the exhumed Lopez fault zone in the San Gabriel Mountains, California were impregnated with low viscosity epoxy resin and sectioned to produce microscope slides. The slides were photographed using optical and electron microscopy with magnifications ranging in factors of 2 from 12.5 to 1600. At all scales, the particles appeared angular with planar faces, suggesting tensile failure. No shear zones were discernable. The particle size distribution was studied. At each magnification the particles were sorted by diameter into four classes, differing in mean diameter by factors of 2. The numbers in each class were then scaled by the characteristic class dimension. The process revealed a remarkable degree of self-similarity. Over the range examined, the fractal dimension was within 5% of 2.60.On the basis of the observations, a new model for the mechanical processes that generate gouge is offered. It is argued that self-similarity results from repeated tensile splitting of grains. Unlike earlier models that consider splitting probability to be either independent of particle size or due to the preexisting distribution of defects, we propose that failure probability depends largely on the relative size of nearest neighbors. If nearest neighbors of the same size are preferentially broken, any initial distribution of particles will tend toward a self-similar distribution having a fractal dimension of 2.58.The model allows us to outline a procedure whereby the observed comminution in a fault zone can be related to the shear strain that the zone has accommodated and propose a theoretical frequency magnitude relation for the seismic energy emitted by the fracture process.

Characterization of Fault Zones

There are currently three major competing views on the essential geometrical, mechanical, and mathematical nature of faults. The standard view is that faults are (possibly segmented and heterogeneous) Euclidean zones in a continuum solid. The continuum-Euclidean view is supported by seismic, gravity, and electromagnetic imaging studies; by successful modeling of observed seismic radiation, geodetic data, and changes in seismicity patterns; by detailed field studies of earthquake rupture zones and exhumed faults; and by recent high resolution hypocenter distributions along several faults. The second view focuses on granular aspects of fault structures and deformation fields. The granular view is supported by observations of rock particles in fault zone gouge; by studies of block rotations and the mosaic structure of the lithosphere (which includes the overall geometry of plate tectonics); by concentration of deformation signals along block boundaries; by correlation of seismicity patterns on scales several times larger than those compatible with a continuum framework; and by strongly heterogeneous wave propagation effects on the earth’s surface. The third view is that faults are fractal objects with rough surfaces and branching geometry. The fractal view is supported by some statistical analysis of regional hypocenter locations; by long-range correlation of various measurements in geophysical boreholes; by the fact that observed power-law statistics of earthquakes are compatible with an underlying scale-invariant geometrical structure; by geometrical analysis of fault traces at the earth’s surface; and by measurements of joint and fault surfaces topography.

Partial melting in the upper mantle

The low velocity zone in tectonic and oceanic regions is too pronounced to be the effect of high temperature gradients alone. Partial melting is consistent with the low velocity, low Q and abrupt boundaries of this region of the upper mantle and is also consistent with measured heat flow values. The inferred low melting temperatures seem to indicate that the water pressure is sufficiently high to lower the solidus about 200 °C to 400 °C below laboratory determinations of the melting point of anhydrous silicates. The mechanical instability of a partially molten layer in the upper mantle is probably an important source of tectonic energy. The top of the low-velocity zone can be considered a self-lubricated surface upon which the top of the mantle and the crust can slide with very little friction. Lateral motion of the crust and upper mantle away from oceanic rises is counterbalanced by the flow of molten material in the low-velocity layer toward the rise where it eventually emerges as new crust. If this lateral flow of molten material is not as efficient as the upward removal of magma, then regions of extrusion, such as oceanic rises, will migrate.

Statistical physics approach to understanding the multiscale dynamics of earthquake fault systems

[1] Earthquakes and the faults upon which they occur interact over a wide range of spatial and temporal scales. In addition, many aspects of regional seismicity appear to be stochastic both in space and time. However, within this complexity, there is considerable self-organization. We argue that the occurrence of earthquakes is a problem that can be attacked using the fundamentals of statistical physics. Concepts of statistical physics associated with phase changes and critical points have been successfully applied to a variety of cellular automata models. Examples include sandpile models, forest fire models, and, particularly, slider block models. These models exhibit avalanche behavior very similar to observed seismicity. A fundamental question is whether variations in seismicity can be used to successfully forecast the occurrence of earthquakes. Several attempts have been made to utilize precursory seismic activation and quiescence to make earthquake forecasts, some of which show promise.

The frictional properties of a simulated gouge having a fractal particle distribution

The frictional properties of a layer of simulated Westerly granite fault gouge sandwiched between sliding blocks of Westerly granite have been measured in a high-speed servo-controlled double-direct shear apparatus. Most gouge layers were prepared to have a self-similar particle distribution with a fractal dimension of 2.6. The upper fractal limit was varied between 45 and 710 μm. Some gouges were prepared with all particles in the range between 360 and 710 μm. In each experiment the sliding velocity was cyclically alternated between 1 and 10 μms−1 and the coefficient of friction μm and its transient parameters a, b and Dc were measured as functions of displacement. In addition to the particle size distribution, the following experimental variables were also investigated: the layer thickness (1 and 3 mm), the roughness of the sliding surfaces (Nos 60 and 600 grit) and the normal stress (10 and 25 MPa). Some of the sample assemblies were epoxy impregnated following a run so the gouge structure could be microscopically examined in thin section. We observed that gouges which were initially non-fractal evolved to a fractal distribution with dimension 2.6. Gouges which had an initial fractal distribution remained fractal. When the sliding blocks had smooth surfaces, the coefficient of friction was relatively low and was independent of the particle distribution. In these cases, strong velocity weakening was observed throughout the experiment and the transient parameters a, b and Dc, remained almost constant. When the sliding blocks had rough surfaces, the coefficient of friction was larger and more dependent on the particle distribution. Velocity strengthening was observed initially but evolved to velocity weakening with increased sliding displacement. All three transient parameters changed with increasing displacement. The a and b values were about three times as large for rough surfaces as for smooth. The characteristic displacement Dc was not sensitive to surface roughness but was the only transient parameter which was sensitive to the normal stress. For the case of rough surfaces, the coefficient of friction of the 1 mm thick gouge was significantly larger than that for the 3 mm thick layers. Many of these observations can be explained by a micromechanical model in which the stress in the gouge layer is heterogeneous. The applied normal and shear stresses are supported by ‘grain bridges’ which span the layer and which are continually forming and failing. In this model, the frictional properties of the gouge are largely determined by the dominant failure mode of the bridging structures.

Off-Fault Secondary Failure Induced by a Dynamic Slip Pulse

We develop a 2D slip-weakening description of a self-healing slip pulse that propagates dynamically in a steady-state configuration. The model is used to estimate patterns of off-fault secondary failure induced by the rupture, and also to infer fracture energies G for large earthquakes. This extends an analysis for a semi-infinite rupture (Poliakov et al. , 2002) to the case of a finite slipping zone length L of the pulse. The dynamic stress drop, when divided by the drop from peak to residual strength, determines the ratio of L to the slip-weakening zone length R . Predicted off-fault damage is controlled by that scaled stress drop, static and dynamic friction coefficients, rupture velocity, principal prestress orientation, and poroelastic Skempton coefficient. All damage zone lengths can be scaled by ![Graphic][1] , which is proportional G /(strength drop)2 and is the value of R in the low-rupture-velocity, low-stress-drop, limit. In contrast to the Poliakov et al. (2002) case R / L = 0, the region that supports Coulomb failure reaches a maximum size on the order of ![Graphic][2] when mode II rupture speed approaches the Rayleigh speed. Analysis of slip pulses documented by Heaton (1990) leads to estimates of G , each with a factor-of-two model uncertainty, from 0.1 to 9 MJ/m2 (including the factor), averaging 2–4 MJ/m2; G tends to increase with the amount of slip in the event. In most cases, secondary faulting should extend, at high rupture speeds, to distances from the principal fault surface on the order of 1 to 2 ![Graphic][3] ≈ 1–80 m for a 100-MPa strength drop; that distance should vary with depth, being larger near the surface. We also discuss gouge and damage processes. [1]: /embed/inline-graphic-1.gif [2]: /embed/inline-graphic-2.gif [3]: /embed/inline-graphic-3.gif

Self-similar cataclasis in the formation of fault gouge

Particle-size distributions have been determined for gouge formed by the fresh fracture of granodiorite from the Sierra Nevada batholith, for Pelona schist from the San Andreas fault zone in southern California, and for Berea sandstone from Berea, Ohio, under a variety of triaxial stress states. The finer fractions of the gouge derived from granodiorite and schist are consistent with either a self-similar or a logarithmic normal distribution, whereas the gouge from sandstone is not. Sandstone gouges are texturally similar to the disaggregated protolith, with comminution limited to the polycrystalline fragments and dominantly calcite cement. All three rock types produced significantly less gouge at higher confining pressures, but only the granodiorite showed a significant reduction in particle size with increased confining pressure. Comparison with natural gouges showed that gouges in crystalline rocks from the San Andreas fault zone also tend to be described by either a self-similar or log-normal particle distribution, with a significant reduction in particle size with increased confining pressure (depth). Natural gouges formed in porous sandstone do not follow either a self-similar or a log-normal distribution. Rather, these are represented by mixed log-normal distributions. These textural characteristics are interpreted in terms of the suppression of axial microfracturing by confining pressure and the accommodation of finite strain by scale-independent comminution.

Long-range and long-term fault interactions in Southern California

Paleoseismological data suggest the occurrence of four bursts of seismic moment release in the Los Angeles region during the past 12,000 yr. The historic period appears to be part of an ongoing lull that has persisted for about the past 1000 yr. These periods of rapid seismic displacement in the Los Angeles region have occurred during the lulls between similar bursts of activity observed on the eastern California shear zone in the Mojave Desert, which is now seismically active. A kinematic model in which the faults of the greater San Andreas system suppress activity on faults in the eastern California shear zone, and vice versa, can explain the apparent switching of activity between the two fault networks. Combined with the observation that short-term geodetic and longer-term geologic rates co-vary on major southern California fault systems, this suggests that either (1) a temporal cluster of seismic displacements on upper-crustal faults increases ductile deformation on their downward extensions, or (2) rapid ductile slip in the lower crust beneath faults loads the upper crust, driving a seismic cluster. We suggest that alternating periods of rapid seismic displacement may be the expected mode of seismicity when two fault systems accommodate the same plate-boundary motion, and slip on one system suppresses slip on the other.