Theoretical Equations of State

The primary objective of theoretical equation-of-state work in geophysics has been to provide a framework with which the ultrasonic, X-ray compression, and shock data can be used in interpreting the seismic velocity and density profiles in the earth. Each of these experimental techniques falls short of the ultimate experiment of reproducing the temperature-pressure conditions at any depth in the earth and measuring V_p, V_s, and p of mantle-candidate mineral assemblages for direct comparison with the seismic profiles. The ultrasonic data give V_p, V_s, and p as a function of T and P, but the pressure range has been limited to ∼10 kb. This limit necessitates a large extrapolation for discussion of even the upper mantle. The X-ray static compression measurements have a pressure range to 300 kb, but are limited to room temperature and to only the pure compression properties K_T and p. Finally, although the shock-wave techniques can generate pressures comparable to those found throughout the earth's mantle and core, the shock-produced states are characterized by pressure and internal energy. Thus an E(T, P) equation of state is required before the data can effectively be used. Further, like static compression experiments, the shock technique now yields only K and p

Mechanical origin of power law scaling in fault zone rock

A nearest neighbor fragmentation model, previously developed to explain observations of power law particle distributions in 3D with mass dimension D 3 ≈ 2.6 (D 2 ≈ 2.6 in 2D section) in low-strain fault gouge and breccia, is extended to the case of large strains to explain recent observations of D 3 ≈ 3.0 (D 2 ≈ 2.0 in 2D section) in the highly strained cores of many exhumed fault zones. At low strains, the elimination of same-sized nearest neighbors has been shown to produce a power law distribution which is characterized by a mass dimension near D 3 ≈ 2.6. With increasing shear strain these isolated same-size neighbors can collide, in which case one of them fractures. The probability of two same size neighbors colliding and fragmenting in a simple shear flow is a function of the size and density of the two particles. Only for a power law distribution with D 3 = 3.0 is this collision probability independent of the size of the particles

The significance of seismic wavespeed minima and thermal maxima in the mantle and the role of dynamic melting

It is widely assumed that the boundary layer above the core is the source of intraplate volcanoes such as Hawaii, Samoa, and Yellowstone, and that the sub-plate boundary layer at the top of the mantle is thin and entirely subsolidus. In fact, this upper layer is thicker and has higher expansivity, buoyancy, and insulating power than the lower one, and may have higher potential temperatures. The observed seismic structure of the low-velocity zone (LVZ) including attenuation, anisotropy, sharp boundaries, and a reduction of both compressional and shear moduli can be taken as strong evidence for the ubiquitous presence of melt in the upper mantle. If the LVZ contains as little as 1%–2% melt, then it is the most plausible and accessible source for midplate magmas; deeply rooted active upwellings are unnecessary. The upper boundary layer is also the most plausible source of ancient isotopic signatures of these magmas and their inclusions

Quantitative characterization of the small-scale fracture patterns on the plains of Venus

The objectives of this research project were to (1) compile a comprehensive database of the occurrence of regularly spaced kilometer scale lineations on the volcanic plains of Venus in an effort to verify the effectiveness of the shear-lag model developed by Banerdt and Sammis (1992), and (2) develop a model for the formation of irregular kilometer scale lineations such as typified in the gridded plains region of Guinevere Planitia. Attached to this report is the paper 'A Tectonic Model for the Formation of the Gridded Plains on Guinevere Planitia, Venus, and Implications for the Elastic Thickness of the Lithosphere'

An experimental study of the effect of off-fault damage on the velocity of a slip pulse

The effect of off-fault damage on the speed of ruptures propagating on faults in photoelastic Homalite plates was measured using high-speed digital photography. The off-fault damage was composed of a network of fractures introduced by thermally shocking the Homalite in liquid nitrogen. The mode II rupture speed measured in damaged Homalite was significantly lower than the limiting Rayleigh speed of v_r = 0.92 v_s, even after the shear wave speed v_s was reduced to a value appropriate for the fracture-damaged Homalite. The additional slowing is most likely caused by frictional sliding on preexisting cracks, especially since we did not observe the generation of new fractures. The spatial extent of the interaction between the rupture and the off-fault damage was measured using samples in which the damage was limited to a band of width 2w centered on the fault and also using damaged samples containing a band of undamaged Homalite centered on the fault. By measuring the rupture velocity as a function of w, the interaction between the rupture and off-fault damage was observed to be limited to a distance of about 1 cm from the fault plane. This agrees with the spatial extent of Coulomb failure near the tip of a dynamic slip pulse predicted by the analytic model developed by Rice et al. (2005)

A Micromechanics Based Constitutive Model for Brittle Failure at High Strain Rates

The micromechanical damage mechanics formulated by Ashby and Sammis, 1990, “The Damage Mechanics of Brittle Solids in Compression,” Pure Appl. Geophys., 133(3), pp. 489–521, and generalized by Deshpande and Evans 2008, “Inelastic Deformation and Energy Dissipation in Ceramics: A Mechanism-Based Constitutive Model,” J. Mech. Phys. Solids, 56(10), pp. 3077–3100. has been extended to allow for a more generalized stress state and to incorporate an experimentally motivated new crack growth (damage evolution) law that is valid over a wide range of loading rates. This law is sensitive to both the crack tip stress field and its time derivative. Incorporating this feature produces additional strain-rate sensitivity in the constitutive response. The model is also experimentally verified by predicting the failure strength of Dionysus-Pentelicon marble over strain rates ranging from ~10^(−6) to 10^3s^(−1). Model parameters determined from quasi-static experiments were used to predict the failure strength at higher loading rates. Agreement with experimental results was excellent

Quantifying near-field and off-fault deformation patterns of the 1992 M_w 7.3 Landers earthquake

Coseismic surface deformation in large earthquakes is typically measured using field mapping and with a range of geodetic methods (e.g., InSAR, lidar differencing, and GPS). Current methods, however, either fail to capture patterns of near-field coseismic surface deformation or lack preevent data. Consequently, the characteristics of off-fault deformation and the parameters that control it remain poorly understood. We develop a standardized method to fully measure the surface, near-field, coseismic deformation patterns at high resolution using the COSI-Corr program by correlating pairs of aerial photographs taken before and after the 1992 M_w 7.3 Landers earthquake. COSI-Corr offers the advantage of measuring displacement across the entire zone of surface deformation and over a wider aperture than that available to field geologists. For the Landers earthquake, our measured displacements are systematically larger than the field measurements, indicating the presence of off-fault deformation. We show that 46% of the total surface displacement occurred as off-fault deformation, over a mean deformation width of 154 m. The magnitude and width of off-fault deformation along the rupture is primarily controlled by the macroscopic structural complexity of the fault system, with a weak correlation with the type of near-surface materials through which the rupture propagated. Both the magnitude and width of distributed deformation are largest in stepovers, bends, and at the southern termination of the surface rupture. We find that slip along the surface rupture exhibits a consistent degree of variability at all observable length scales and that the slip distribution is self-affine fractal with dimension of 1.56