New measurements of compressional and shear wave velocities to hydrostatic pressures of 1 GPa are summarized for 678 rocks. Emphasis was placed on obtaining high-accuracy velocity measurements, which are shown to be critical in calculating Poisson's ratios from velocities. The rocks have been divided into 29 major groups for which velocities, velocity ratios, and Poisson's ratios are presented at several pressures. Observed Poisson's ratios for the monomineralic rocks compare favorably with theoretical Poisson's ratios calculated from single-crystal elastic constants. Plagioclase feldspar composition is important in understanding rock Poisson's ratios, since Poisson's ratio of albite increases from 0.28 to a predicted value of 0.31 for anorthite. Fe substitution for Mg in pyroxene and olivine also increases Poisson's ratio. Plotting rock compressional wave velocities versus Poisson's ratios reveals a triangular distribution bounded by quartzite with low compressional wave velocity and low Poisson's ratio, dunite with high compressional wave velocity and intermediate Poisson's ratio, and serpentinite with low compressional wave velocity and high Poisson's ratio. For common plutonic igneous rocks, there is a clear trend relating Poisson's ratio to composition, in which Poisson's ratio for granitic rocks increases from 0.24 to 0.29 as composition changes to gabbro and then decreases with decreasing plagioclase and increasing olivine contents to 0.25 in dunite. Changes in Poisson's ratio with progressive metamorphism of mafic and pelitic rocks correlate reasonably well with mineral reactions. There is no simple correlation between Poisson's ratio and felsic and mafic rock compositions; however, a linear correlation of increasing Poisson's ratio with decreasing SiO2 content is observed for rocks with 55 to 75 wt % SiO2. Average Poisson's ratios for continental and oceanic crusts are estimated to be 0.265 and 0.30, respectively.

Poisson's ratio and crustal seismology

We use new interior models of cold planets to investigate the mass-radius relationships of solid exoplanets, considering planets made primarily of iron, silicates, water, and carbon compounds. We find that the mass-radius relationships for cold terrestrial mass planets of all compositions we considered follow a generic functional form that is not a simple power law: log10 Rs = k1 + log10(Ms) - k2M for up to Mp ≈ 20 M⊕, where Ms and Rs are scaled mass and radius values. This functional form arises because the common building blocks of solid planets all have equations of state that are well approximated by a modified polytrope of the form ρ = ρ0 + cPn. We find that highly detailed planet interior models, including temperature structure and phase changes, are not necessary to derive solid exoplanet bulk composition from mass and radius measurements. For solid exoplanets with no substantial atmosphere we have also found the following: with 5% fractional uncertainty in planet mass and radius it is possible to distinguish among planets composed predominantly of iron or silicates or water ice but not more detailed compositions; with ~5% uncertainty water ice planets with 25% water by mass may be identified; the minimum plausible planet size for a given mass is that of a pure iron planet; and carbon planet mass-radius relationships overlap with those of silicate and water planets due to similar zero-pressure densities and equations of state. We propose a definition of "super-Earths" based on the clear distinction in radii between planets with significant gas envelopes and those without.

http://militzer.berkeley.edu/papers/34_seager_kuchner_hier-majumder_militzer_2007.pdf

Mass-Radius Relationships for Solid Exoplanets

Elasticity of Minerals, Glasses, and Melts

The mechanical resonant response of a solid depends on its shape, density, elastic moduli and dissipation. We describe here instrumentation and computational methods for acquiring and analyzing the resonant ultrasound spectrum of very small (0.001 cm3) samples as a function of temperature, and provide examples to demonstrate the power of the technique. The information acquired is in some cases comparable to that obtained from other more conventional ultrasonic measurement techniques, but one unique feature of resonant ultrasound spectroscopy (RUS) is that all moduli are determined simultaneously to very high accuracy. Thus in circumstances where high relative or absolute accuracy is required for very small crystalline or other anisotropic samples RUS can provide unique information. RUS is also sensitive to the fundamental symmetry of the object under test so that certain symmetry breaking effects are uniquely observable, and because transducers require neither couplant nor a flat surface, broken fragments of a material can be quickly screened for phase transitions and other temperature-dependent responses.

/pdf/resonant-ultrasound-spectroscopic-techniques-for-measurement-wt0fciyopd.pdf

Resonant ultrasound spectroscopic techniques for measurement of the elastic moduli of solids

We compile a worldwide catalog of shallow (depth < 70 km) and large ( Ms ≥ 7) earthquakes recorded between 1900 and 1989. The catalog is shown to be complete and uniform at the 20-sec surface-wave magnitude Ms ≥ 7.0. We base our catalog on those of Abe (1981, 1984) and Abe and Noguchi (1983a, b) for events with Ms ≥ 7.0. Those catalogs, however, are not homogeneous in seismicity rates for the entire 90-year period. We assume that global rates of seismicity are constant on a time scale of decades and most inhomogeneities arise from changes in instrumentation and/or reporting. We correct the magnitudes to produce a homogeneous catalog. The catalog is accompanied by a reference list for all the events with seismic moment determined at periods longer than 20 sec. Using these seismic moments for great and giant earthquakes and a moment-magnitude relationship for smaller events, we produce a seismic moment catalog for large earthquakes from 1900 to 1989. The catalog is used to study the distribution of moment released worldwide. Although we assumed a constant rate of seismicity on a global basis, the rate of moment release has not been constant for the 90-year period because the latter is dominated by the few largest earthquakes. We find that the seismic moment released at subduction zones during this century constitutes 90% of all the moment released by large, shallow earthquakes on a global basis. The seismic moment released in the largest event that occurred during this century, the 1960 southern Chile earthquake, represents about 30 to 45% of the total moment released from 1900 through 1989. A frequency-size distribution of earthquakes with seismic moment yields an average slope ( b value) that changes from 1.04 for magnitudes between 7.0 and 7.5 to b = 1.51 for magnitudes between 7.6 and 8.0. This change in the b value is attributed to different scaling relationships between bounded (large) and unbounded (small) earthquakes. Thus, the earthquake process does have a characteristic length scale that is set by the downdip width over which rupture in earthquakes can occur. That width is typically greater for thrust events at subduction zones than for earthquakes along transform faults and other tectonic environments.

Seismic moment catalog of large shallow earthquakes, 1900 to 1989

Measurements of the nine adiabatic elastic constants of single-crystal forsterite are reported for the temperature range 300–1700 K at ambient pressure. The measured room temperature Cijs and their first temperature derivatives at ambient conditions are generally consistent with previous measurements, which were taken over a narrower temperature range. Slight nonlinear behavior is observed in the temperature dependence of the C11s, C22s, and C33s moduli. The resulting Hill-averaged bulk and rigidity moduli Ks and G are lower at 1700 K than predicted by linear extrapolation of low-temperature data. At 1700 K the new data give Ks = 103.8 ± 1.1 GPa and G = 61.3 ± 0.5 GPa. Isotropic elastic wave velocities have been calculated using the Hill averaging scheme over the range of temperatures measured. At T = 1700 K and ambient pressure we find vp = 7.79 ± 0.04 km s−1 and vs = 4.48 ± 0.03 km s−1. The parameter (∂lnvs/∂lnvp)P is near to 1.2 and independent of temperature. Calculations are presented for elastic properties and other parameters important for the equations of state and anharmonicity of forsterite. Recent high-temperature thermal expansion measurements on a forsterite specimen from the same boule are used in this analysis. Effects of uncertainties in high-temperature thermal expansion data on these parameters have been evaluated and are discussed.

Elasticity of single‐crystal forsterite measured to 1700 K

By holding the rectangular parallelepiped specimen between long, thin alumina buffer rods, we can detect the resonance vibration of a specimen even at temperatures above 1800 K. This new technique, in combination with the theory for the calculation of the resonance frequency spectrum of a rectangular parallelepiped specimen, enables us to determine the high‐temperature elastic properties of single‐crystal materials. The first application of this new device was to determine the elastic stiffness constants of single‐crystal corundum up to 1825 K.

Takayasu Goto

Papers

Elasticity of single‐crystal forsterite measured to 1700 K

Apparatus for measuring elastic constants of single crystals by a resonance technique up to 1825 K

Measurement of elastic constants of mantle-related minerals at temperatures up to 1800 K