Source parameters for historical earthquakes worldwide are compiled to develop a series of empirical relationships among moment magnitude ( M ), surface rupture length, subsurface rupture length, downdip rupture width, rupture area, and maximum and average displacement per event. The resulting data base is a significant update of previous compilations and includes the additional source parameters of seismic moment, moment magnitude, subsurface rupture length, downdip rupture width, and average surface displacement. Each source parameter is classified as reliable or unreliable, based on our evaluation of the accuracy of individual values. Only the reliable source parameters are used in the final analyses. In comparing source parameters, we note the following trends: (1) Generally, the length of rupture at the surface is equal to 75% of the subsurface rupture length; however, the ratio of surface rupture length to subsurface rupture length increases with magnitude; (2) the average surface displacement per event is about one-half the maximum surface displacement per event; and (3) the average subsurface displacement on the fault plane is less than the maximum surface displacement but more than the average surface displacement. Thus, for most earthquakes in this data base, slip on the fault plane at seismogenic depths is manifested by similar displacements at the surface. Log-linear regressions between earthquake magnitude and surface rupture length, subsurface rupture length, and rupture area are especially well correlated, showing standard deviations of 0.25 to 0.35 magnitude units. Most relationships are not statistically different (at a 95% significance level) as a function of the style of faulting: thus, we consider the regressions for all slip types to be appropriate for most applications. Regressions between magnitude and displacement, magnitude and rupture width, and between displacement and rupture length are less well correlated and have larger standard deviation than regressions between magnitude and length or area. The large number of data points in most of these regressions and their statistical stability suggest that they are unlikely to change significantly in response to additional data. Separating the data according to extensional and compressional tectonic environments neither provides statistically different results nor improves the statistical significance of the regressions. Regressions for cases in which earthquake magnitude is either the independent or the dependent parameter can be used to estimate maximum earthquake magnitudes both for surface faults and for subsurface seismic sources such as blind faults, and to estimate the expected surface displacement along a fault for a given size earthquake.

New Empirical Relationships among Magnitude, Rupture Length, Rupture Width, Rupture Area, and Surface Displacement

The thermodynamic properties of 154 mineral end-members, 13 silicate liquid end-members and 22 aqueous fluid species are presented in a revised and updated data set. The use of a temperature-dependent thermal expansion and bulk modulus, and the use of high-pressure equations of state for solids and fluids, allows calculation of mineral–fluid equilibria to 100 kbar pressure or higher. A pressure-dependent Landau model for order–disorder permits extension of disordering transitions to high pressures, and, in particular, allows the alpha–beta quartz transition to be handled more satisfactorily. Several melt end-members have been included to enable calculation of simple phase equilibria and as a first stage in developing melt mixing models in NCKFMASH. The simple aqueous species density model has been extended to enable speciation calculations and mineral solubility determination involving minerals and aqueous species at high temperatures and pressures. The data set has also been improved by incorporation of many new phase equilibrium constraints, calorimetric studies and new measurements of molar volume, thermal expansion and compressibility. This has led to a significant improvement in the level of agreement with the available experimental phase equilibria, and to greater flexibility in calculation of complex mineral equilibria. It is also shown that there is very good agreement between the data set and the most recent available calorimetric data.

An internally consistent thermodynamic data set for phases of petrological interest

There is a special reason for reviewing this book at this time: it is the 50th edition of a compendium that is known and used frequently in most chemical and physical laboratories in many parts of the world. Surely, a publication that has been published for 56 years, withstanding the vagaries of science in this century, must have had something to offer. There is another reason: while the book is a standard fixture in most chemical and physical laboratories, including those in medical centers, it is not as frequently seen in the laboratories of physician's offices (those either in solo or group practice). I believe that the Handbook can be useful in those laboratories. One of the reasons, among others, is that the various basic items of information it offers may be helpful in new tests, either physical or chemical, which are continuously being published. The basic information may relate

Handbook of Chemistry and Physics

Preface 1. Basic tools 2. Elasticity and Hooke's law 3. Seismic wave propagation 4. Effective media 5. Granular media 6. Fluid effects on wave propagation 7. Empirical relations 8. Flow and diffusion 9. Electrical properties Appendices.

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The Rock Physics Handbook: Tools for Seismic Analysis of Porous Media

The thermodynamic properties of 254 end-members, including 210 mineral end-members, 18 silicate liquid end-members and 26 aqueous fluid species are presented in a revised and updated internally consistent thermodynamic data set. The PVT properties of the data set phases are now based on a modified Tait equation of state (EOS) for the solids and the Pitzer & Sterner (1995) equation for gaseous components. Thermal expansion and compressibility are linked within the modified Tait EOS (TEOS) by a thermal pressure formulation using an Einstein temperature to model the temperature dependence of both the thermal expansion and bulk modulus in a consistent way. The new EOS has led to improved fitting of the phase equilibrium experiments. Many new end-members have been added, including several deep mantle phases and, for the first time, sulphur-bearing minerals. Silicate liquid end-members are in good agreement with both phase equilibrium experiments and measured heat of melting. The new dataset considerably enhances the capabilities for thermodynamic calculation on rocks, melts and aqueous fluids under crustal to deep mantle conditions. Implementations are already available in thermocalc to take advantage of the new data set and its methodologies, as illustrated by example calculations on sapphirine-bearing equilibria, sulphur-bearing equilibria and calculations to 300 kbar and 2000 °C to extend to lower mantle conditions.

An improved and extended internally consistent thermodynamic dataset for phases of petrological interest, involving a new equation of state for solids

Measurements of the elastic constants and related pressure and temperature derivatives of ten compounds of interest to geophysical and geochemical theories are reported and analyzed. We discuss the corrections that are expected from effects of anisotropy and porosity and conclude that polycrystalline samples with porosities of 4% are not adequate for reliable acoustic measurements. We find that two anharmonic parameters, γth and δS, are independent of temperature at high temperature, and we use this result to estimate the temperature derivative of the bulk modulus at high temperatures. We present a number of correlations between the elastic constants and illustrate their use by attempting to predict the unmeasured elastic properties of fayalite.

Some elastic constant data on minerals relevant to geophysics

Earth's Deep Interior: Mineral Physics and Tomography From the Atomic to the Global Scale

Using a DIA-type, cubic-anvil, high-pressure apparatus (SAM-85) in conjunction with in situ X-ray diffraction, we have investigated phase relations between coesite and stishovite up to 12 GPa and 1530 °C using synthetic powders of the two phases as the starting materials. The phase transition between coesite and stishovite was identified by observing the first appearance of a phase that did not already exist or by a change in the relative intensity of the two patterns. In most experiments, the diffraction patterns on samples were collected within 10 minutes after reaching a pressure and temperature condition. On this time scale, two phase boundaries associated with the coesite-stishovite transition have been determined: (1) for the stishovite-to-coesite transition, observations were made in the temperature range of 950–1530 °C, and (2) for the coesite-to-stishovite transition from 500 to 1300 °C. These observations reveal that there exists a critical temperature of about 1000 °C to constrain the coesite-stishovite equilibrium phase boundary. Above this temperature, both boundaries are linear, have positive dP/dT slopes, and lie within a pressure interval of 0.4 GPa. Below this temperature, the dP/dT slope for the stishovite-to-coesite phase boundary becomes significantly larger and that for the coesite-tostishovite phase boundary changes from positive to negative. As a result, an equilibrium phase boundary can only be determined from the results above 1000 °C and is described by a linear equation P (GPa)=6.1 (4)+ 0.0026 (2) T (°C). This dP/dT slope is in good agreement with that of Zhang et al. (1993) but more than twice that of Yagi and Akimoto (1976). For the kinetics of the phase transition, preliminary rate data were obtained for the stishovite-to-coesite transition at 1160 and 1430 °C and are in agreement with the simple geometric transformation model of Avrami and Cahn.

In situ X-ray observations of the coesite-stishovite transition: reversed phase boundary and kinetics

The structure of pressure-densified vitreous ${\mathrm{SiO}}_{2}$ has been investigated using neutron-diffraction and molecular-dynamics techniques. After compression to 16 GPa at room temperature, recovered samples have densities 20% higher than normal vitreous ${\mathrm{SiO}}_{2}$ and show substantial changes in the first sharp diffraction peak (FSDP): an indication of modification in the intermediate-range order. The changes in the FSDP are due to increased frustration caused by the decrease in the Si-O-Si bond angle and a shift in the Si-Si and O-O correlations in the range of 4--8 \AA{} toward lower distances.

Robert C. Liebermann

Papers

Some elastic constant data on minerals relevant to geophysics

Earth's Deep Interior: Mineral Physics and Tomography From the Atomic to the Global Scale

In situ X-ray observations of the coesite-stishovite transition: reversed phase boundary and kinetics

Intermediate-range order in permanently densified vitreous SiO2 : a neutron-diffraction and molecular-dynamics study

P-V-T equation of state of (Mg, Fe)SiO3 perovskite: constraints on composition of the lower mantle