Shear modulus and Q of forsterite and dunite near partial melting from forced-oscillation experiments

An apparatus designed to determine the complex shear modulus of rock samples by forced torsion oscillations at high temperature and in the seismic frequency band 0.003–30 Hz is briefly described. Measurements were performed on natural dunite from Åheim (Norway) up to 1400°C and on polycrystalline forsterite up to 1500°C at 1 atm pressure. The two materials were chosen to study, by comparison, the effect of melt on the elasticity and anelasticity of mantle rocks.Between 1000 and 1200°C the absolute values of the shear modulus G are almost equal for both materials. Above 1200°C G for natural dunite decreases progressively with temperature and at 1400°C and 1 Hz reaches $\text{～}\text{1}\text{3}$ of its value at 1100°C. In contrast, G of pure forsterite depends little on temperature. For petrological reasons, supported by simultaneous measurements of the electric resistivity, there is strong evidence that the decrease of G in dunite above 1200°C is due to melt from the lower melting components of the dunite. Based on different models estimates of the melt fraction are made.At high temperature, in both materials Q^?1 is characterized by a monotonic decrease with frequency according to ω^?α, with α ≈ 0.25. An apparent activation energy of 38±5 kcal mol^?1 for forsterite and 48±8 kcal mol^?1 for dunite was found with no significant change in the regime of partial melting. From this it is concluded that Q^?1, even at partial melting, is dominated by solid state high temperature background absorption. There is no indication from these experiments for a constant-Q-band at low seismic frequencies or an increase of Q proportional to frequency as suggested by some seismologists. The present results are in good qualitative agreement with those for Young's modulus obtained previously by strain retardation experiments.     

Ultrasonic measurements of Vp and Qp: relaxation spectrum of complex modulus on basalt melts

Ultrasonic compressional wave velocity V_p and quality factor Q_p have been measured in alkali basalt, olivine basalt and basic andesite melts in the frequency range of 3.4–22 MHz and in the temperature range of 1100–1400°C. Velocity and attenuation of the melts depend on frequency and temperature, showing that there are relaxation mechanisms in the melts. Complex moduli are calculated from the ultrasonic data. The results fit well a complex modulus of Arrhenius temperature dependence with log-normal Gaussian distribution in relaxation times of attenuation. The analysis yields average relaxation time, its activation energy, relaxed modulus, unrelaxed modulus and width of Gaussian distribution in relaxation times. Relaxed modulus is smaller (17.5 GPa) for basic andesite melt of high silica and high alumina contents than for the other two basalt melts (18.1–18.4 GPa). The most probable relaxation times decrease from ～ 3 × 10^?10 s for basic andesite to ～ 10^?11 s for alkali basalt at 1400°C. Activation energies of attenuation, ranging from 270 to 340 kJ mol^?1 in the three melts, are highest in basic andesite. Longitudinal viscosity values and their temperature dependences are also calculated from V_p and Q_p data. The volume viscosity values are estimated from the data using the shear viscosity values. Longitudinal, volume and shear viscosities and their activation energies are highest in the basic andesite melt of the most polymerized structure.     

High-temperature anelasticity and elasticity of mantle peridotite

An apparatus has been devised which allows precise creep and relaxation measurements to be made on minerals and rocks at temperatures up to 1600°C and at very low deviatoric stresses (1 < σ < 300 bar). This paper is concerned with measurements on mantle peridotite (lherzolite) from Balmuccia (Zone of Ivrea, Italy).The reaction of the sample to a step-like increase in stress is called its “creep function”. It is shown that the creep function contains all the necessary information to derive the spectra of the quality factor Q(ω) and of Young's modulus E(ω), within the seismic range of frequencies, provided the material behaves as a linear system. This has been proven up to a strain of 5 × 10^?5.The Q^?1-spectra at 1200 and 1300°C, obtained by Fourier inversion from the creep function, show no pronounced peak in the frequency band 0.01 < tf < 1 Hz and exhibit a general tendency to decrease slightly with frequency. The creep function: ?(t) = ?_u · [1 + 3.7 · q · {(1 + 50t)^0.27 ? }], where q is related to Q, satisfactorily describes the data at high temperatures and leads to $\text{Q}{}^{\mathrm{?1}}\text{(ω, T) = 3 × 10}{}^3\text{· ω}{}^{\mathrm{<mtext>?0.27\; ·\; </mtext><mtext>exp</mtext>}}\text{(}\text{?30}\text{RT}\text{)}$E(ω) is related to Q(ω) by the material dispersion equation. Above 1100°C the unrelaxed Young's modulus decreases rapidly with temperature according to an activation energy of about 20 kcal/mole. A lowering of short period S-wave velocity by 40% and P-wave velocity by 10% occurs below the solidus. Therefore, no partial melting is required in the asthenosphere.Steady-state creep at low axial stresses (20 < σ < 100 bar), obtained from the same rock, follows the relation $\text{?}\text{?}\text{= 3 × 10}{}^7\text{· δ}{}^{1.4}\text{·}\text{exp}\text{(}\text{?125}\text{RT}\text{)}$ indicative of grain boundary diffusion or superplasticity. At higher stresses a power law $\text{?}\text{?}\text{= 45 · δ}{}^4\text{·}\text{exp}\text{(}\text{?125}\text{RT}\text{)}$ typical of dislocation creep, is found.The frequency dependence of Q and the ratio of the activation energies of Q and are indicative of so called “high-temperature background absorption”, as the dominant mechanism, and of a diffusion-controlled dislocation mobility common to both absorption and creep. From a, b, and c, relations between the effective viscosity η_f and Q of the form: $\text{log}\text{η}{}_{\mathrm{e??}}\text{=}\text{1}\text{α}\text{·}\text{log}\text{Q ? (n ? 1) ·}\text{log}\text{ω +}\text{log}\text{D}$ are derived, where α ～ 0.25, n is the power of σ, and D is a constant.     

Lead isotopes and age of Hawaiian lherzolite nodules

The reaction between enstatite (En_95.3Fs_4.7) and CaCO₃ has been studied at pressures between 23 and 77 kbars and at temperatures between 800° and 1400°C. At 1000°C enstatite and CaCO₃ react to form dolomite and diopside solid solutions at pressures below approximately 45 kbars and magnesite and diopside solid solutions at higher pressures. The curve for the reaction dolomite_ss + enstatite_ss ? magnesite_ss + diopside_ss lies between 40 to 45 kbars at 1000°C and between 45 and 50 kbars at 1200°C. It is very close to the graphite-diamond transition curve. These experimental results indicate that calcite (or aragonite) is unstable in the presence of enstatite, and that dolomite and magnesite are the stable carbonates at high pressures. The forsterite + aragonite assemblage is, however, stable to at least 80 kbars at 800°C. It is suggested that in the upper mantle where enstatite is present, dolomite is stable to depths of about 150 km and magnesite is stable at greater depths in the continental regions, assuming that the partial pressure of CO₂ is equal or close to the total pressure. It is also suggested that carbonate inclusions in pyroxene can be used as an indicator of the depth of their equilibration; dolomite inclusions in enstatite would be formed at depths shallower than 150 km and magnesite inclusions in diopside at greater depths. Eclogite and peridotite inclusions in kimberlite may be classified on this basis.     

A Dislocation Model of Seismic Wave Attenuation and Micro-creep in the Earth: Harold Jeffreys and the Rheology of the Solid Earth

—A microphysical model of seismic wave attenuation is developed to provide a physical basis to interpret temperature and frequency dependence of seismic wave attenuation. The model is based on the dynamics of dislocation motion in minerals with a high Peierls stress. It is proposed that most of seismic wave attenuation occurs through the migration of geometrical kinks (micro-glide) and/or nucleation/migration of an isolated pair of kinks (Bordoni peak), whereas the long-term plastic deformation involves the continuing nucleation and migration of kinks (macro-glide). Kink migration is much easier than kink nucleation, and this provides a natural explanation for the vast difference in dislocation mobility between seismic and geological time scales. The frequency and temperature dependences of attenuation depend on the geometry and dynamics of dislocation motion both of which affect the distribution of relaxation times. The distribution of relaxation times is largely controlled by the distribution in distance between pinning points of dislocations, L, and the observed frequency dependence of Q, Q, Q∝ω^α is shown to require a distribution function of P(L)∝L ^-m with m=4-2α The activation energy of Q ^?1 in minerals with a high Peierls stress corresponds to that for kink nucleation and is similar to that of long-term creep. The observed large lateral variation in Q ^?1 strongly suggests that the Q ^?1 in the mantle is frequency dependent. Micro-deformation with high dislocation mobility will (temporarily) cease when all the geometrical kinks are exhausted. For a typical dislocation density of ～ 10⁸ m^?2, transient creep with small viscosity related to seismic wave attenuation will persist up to the strain of ～ 10^?6, thus even a small strain (～ 10^?6?10^?4) process such as post-glacial rebound is only marginally affected by this type of anelastic relaxation. At longer time scales continuing nucleation of kinks becomes important and enables indefinitely large strain, steady-state creep, causing viscous behavior.     

On the Causes of Frequency-Dependent Apparent Seismological Q

Variability of the Earth’s structure makes a first-order impact on attenuation measurements which often does not receive adequate attention. Geometrical spreading (GS) can be used as a simple measure of the effects of such structure. The traditional simplified GS compensation is insufficiently accurate for attenuation measurements, and the residual GS appears as biases in both Q ₀ and η parameters in the frequency-dependent attenuation law Q(f) = Q ₀ f ^η . A new interpretation approach bypassing Q(f) and using the attenuation coefficient χ(f) = γ + πf/Q _e(f) resolves this problem by directly measuring the residual GS, denoted γ, and effective attenuation, Q _e. The approach is illustrated by re-interpreting several published datasets, including nuclear-explosion and local-earthquake codas, Pn, and synthetic 50–300-s surface waves. Some of these examples were key to establishing the Q(f) concept. In all examples considered, χ(f) shows a linear dependence on the frequency, γ ≠ 0, and Q _e can be considered frequency-independent. Short-period crustal body waves are characterized by positive γ _SP values of (0.6–2.0) × 10^?2 s^?1 interpreted as related to the downward upper-crustal reflectivity. Long-period surface waves show negative γ _LP ≈ ?1.9 × 10^?5 s^?1, which could be caused by insufficient modeling accuracy at long periods. The above γ values also provide a simple explanation for the absorption band observed within the Earth. The band is interpreted as apparent and formed by levels of Q _e ≈ 1,100 within the crust decreasing to Q _e ≈ 120 within the uppermost mantle, with frequencies of its flanks corresponding to γ _LP and γ _SP. Therefore, the observed absorption band could be purely geometrical in nature, and relaxation or scattering models may not be necessary for explaining the observed apparent Q(f). Linearity of the attenuation coefficient suggests that at all periods, the attenuation of both Rayleigh and Love waves should be principally accumulated at the sub-crustal depths (~38–100 km).     

Seismic Wave Attenuation in the Greater Cairo Region, Egypt

In the present study, a digital waveform dataset of 216 local earthquakes recorded by the Egyptian National Seismic Network (ENSN) was used to estimate the attenuation of seismic wave energy in the greater Cairo region. The quality factor and the frequency dependence for Coda waves and S-waves were estimated and clarified. The Coda waves (Q _c) and S-waves (Q _d) quality factor were estimated by applying the single scattering model and Coda Normalization method, respectively, to bandpass-filtered seismograms of frequency bands centering at 1.5, 3, 6, 12, 18 and 24?Hz. Lapse time dependence was also studied for the area, with the Coda waves analyzed through four lapse time windows (10, 20, 30 and 40?s). The average quality factor as function of frequency is found to be Q _c?=?35?±?9f ^0.9±0.02 and Q _d?=?10?±?2f ^0.9±0.02 for Coda and S-waves, respectively. This behavior is usually correlated with the degree of tectonic complexity and the presence of heterogeneities at several scales. The variation of Q _c with frequency and lapse time shows that the lithosphere becomes more homogeneous with depth. In fact, by using the Coda Normalization method we obtained low Q _d values as expected for a heterogeneous and active zone. The intrinsic quality factor (Q _i ^?1 ) was separated from the scattering quality factor (Q _s ^?1 ) by applying the Multiple Lapse Time Domain Window Analysis (MLTWA) method under the assumption of multiple isotropic scattering with uniform distribution of scatters. The obtained results suggest that the contribution of the intrinsic attenuation (Q _i ^?1 ) prevails on the scattering attenuation (Q _s ^?1 ) at frequencies higher than 3?Hz.     

Dispersion and attenuation of elastic waves due to multiple scattering from cracks

Multiple scattering from cracks is considered in the two-dimensional plane-strain condition. It is assumed that identical cracks are distributed uniformly in space and that the effective waves propagate normal to the crack surfaces. Then, the apparent dispersion and attenuation are calculated as functions of frequency for three independent modes of wave propagation: SV, P and SH.The calculated results show that, in each case, the attenuation coefficient Q^?1 takes a peak value when the wavelength is nearly twice the crack width, while phase velocity has a maximum deviation from the intrinsic value at a frequency lower than the peak frequency for Q^?1.     

Thermal expansion of stishovite

The thermal expansion of stishovite has been determined by an X-ray camera technique in a temperature range of 18 – 600°C at an atmospheric pressure. The thermal-expansion coefficients along the crystallographic a- and c-axes at 300 K are α_a = (6.0 ± 0.6) · 10^?6K^?1 and α_c = (1.4 ± 0.5) · 10^?6K^?1, respectively. The volume coefficient at 300 K is α_ν = (13.5 ± 0.6) · 10^?6K^?1.     

Spatial measurements of stream baseflow,a relevant method for aquifer characterization and permeability evaluation. Application to a hard‐rock aquifer,the Oman ophiolite

The structure, functioning and hydrodynamic properties of aquifers can be determined from an analysis of the spatial variability of baseflow in the streams with which they are associated. Such analyses are based on simple low‐cost measurements. Through interpreting the hydrological profiles (Q = f(A)) it is possible to locate the aquifer(s) linked to the stream network and to determine the type of interrelated flow, i.e. whether the stream drains or feeds the aquifer. Using an analytical solution developed for situations with a positive linear relationship, i.e. where the baseflow increases linearly with increasing catchment size, it is also possible to estimate the permeability of the aquifer(s) concerned at catchment scale. Applied to the hard‐rock aquifers of the Oman ophiolite, this method shows that the ‘gabbro’ aquifer is more permeable than the ‘peridotite’ aquifer. As a consequence the streams drain the peridotites and ‘leak’ into the gabbro. The hydrological profiles within the peridotite are linear and positive, and indicate homogeneity in the hydrodynamic properties of these formations at the kilometre scale. The permeability of the peridotite is estimated at 5 · 10^?7 to 5 · 10^?8 m/s. Copyright © 2004 John Wiley & Sons, Ltd.     

Short-period PKP phases and the anelastic mechanism of the inner core

Short-period seismograms are synthesized for PKP phases in anelastic Earth models. The synthetics were constructed using a synthetic technique valid at grazing incidence, a source-time function appropriate for deep-focus earthquakes, and an instrument response for either a short-period WWSSN or SRO seismograph. The agreement between predicted and observed amplitudes and spectral ratios requires neither a low-Q_α zone at 0.2–2 Hz nor a low or negative P-velocity gradient at the bottom of the outer core. Thin low-Q_α zones beneath the inner core boundary fit spectral ratio data that sample the upper 200 km of the inner core but fail to fit data that sample the lower inner core. Only a model having Q_α^?1?[0.003, 0.004] at 0.2–2 Hz, nearly constant with depth in the inner core, satisfies all of the spectral ratio and amplitude data. The assumption of a bulk viscosity of 10-10³ Pa s for the liquid phase of a partially molten inner core combined with the observation of low shear attenuation in the inner core at frequencies less than 0.005 Hz limit the physical parameters associated with two possible attenuation mechanisms: (1) fluid flow and viscous relaxation due to ellipsoidally shaped inclusions of melt, and (2) the solid-liquid phase transformation induced by the stress change during the passage of a seismic wave. Both mechanisms require an order of 0.1% partial melt to reproduce the observed Q_α^?1. In the outer core, the time constant of the mechanism of phase transformation is predicted to be 10⁴–10⁶ s. Confirmation of small shear attenuation in the inner core in the frequency band of seismic body waves would favor the mechanism of phase transformation.     

Prediction of concentrated flow width in ephemeral gully channels

Empirical prediction equations of the form W = aQ^b have been reported for rills and rivers, but not for ephemeral gullies. In this study six experimental data sets are used to establish a relationship between channel width (W, m) and flow discharge (Q, m³ s^?1) for ephemeral gullies formed on cropland. The resulting regression equation (W = 2·51 Q^0·412; R² = 0·72; n = 67) predicts observed channel width reasonably well. Owing to logistic limitations related to the respective experimental set ups, only relatively small runoff discharges (i.e. Q < 0·02 m³s^?1) were covered. Using field data, where measured ephemeral gully channel width was attributed to a calculated peak runoff discharge on sealed cropland, the application field of the regression equation was extended towards larger discharges (i.e. 5 × 10^?4m³s^?1 < Q < 0·1 m³s^?1). Comparing W–Q relationships for concentrated flow channels revealed that the discharge exponent (b) varies from 0·3 for rills over 0·4 for gullies to 0·5 for rivers. This shift in b may be the result of: (i) differences in flow shear stress distribution over the wetted perimeter between rills, gullies and rivers, (ii) a decrease in probability of a channel formed in soil material with uniform erosion resistance from rills over gullies to rivers and (iii) a decrease in average surface slope from rills over gullies to rivers. The proposed W–Q equation for ephemeral gullies is valid for (sealed) cropland with no significant change in erosion resistance with depth. Two examples illustrate limitations of the W–Q approach. In a first example, vertical erosion is hindered by a frozen subsoil. The second example relates to a typical summer situation where the soil moisture profile of an agricultural field makes the top 0·02 m five times more erodible than the underlying soil material. For both cases observed W values are larger than those predicted by the established channel width equation for concentrated flow on cropland. For the frozen soils the equation W = 3·17 Q^0·368 (R² = 0·78; n = 617) was established, but for the summer soils no equation could be established. Copyright © 2002 John Wiley & Sons, Ltd.     

Melting of hydrous upper mantle and possible generation of andesitic magma: An approach from synthetic systems

Phase equilibria in a portion of the system forsterite-plagioclase (An₅₀Ab₅₀ by weight)-silica-H₂O have been determined at 15 kbar pressure under H₂O-saturated conditions. The composition of the liquid pertinent to the piercing point forsterite + enstatite solid solution + amphibole + liquid + vapor is similar to that of calc-alkaline andesite. The electron microprobe analysis of the glass coexisting with the above three crystalline phases is very close to that of the piercing point determined by phase assemblage observations; however, the glass near (< 8 μm) forsterite crystals is significantly depleted in the normative forsterite component. With the addition of 10 wt.% KAlSi₃O₈, the composition of this piercing point becomes even closer to the compositions of calc-alkaline andesites. It is also shown that the liquid coexisting with forsterite and enstatite solid solution remains silica-rich (60–62 wt.%) over a wide (～ 100°C) temperature range. The present experimental studies support the view that liquids similar in composition to calc-alkaline andesites can be generated by direct partial melting of hydrous upper mantle at least at or near 15 kbar.     

Eutectic between wollastonite II and calcite contrasted with thermal barrier in MgO-SiO2-CO2 at 30 kilobars,with applications to kimberlite-carbonatite petrogenesis

In the join CaCO₃-CaSiO₃ at 30 kbars, calcite melts at 1615°C, wollastonite II at 1600°C, and a binary eutectic occurs at 1365°C with liquid composition 43 wt.% CaCO₃, 57 wt.% CaSiO₃. The eutectic liquid quenches to a glass with few quench crystals. In the join MgCO₃-MgSiO₃ at 30 kbars, magnesite melts at 1590°C, enstatite at 1837°C, and the fields for the primary crystallization of magnesite and enstatite are separated by a thermal barrier near 1900°C for the melting of forsterite in the presence of CO₂. Only about 10 wt.% MgSiO₃ dissolves in the carbonate liquid. These data, are considered together with incomplete results for joins CaMgSi₂O₆-CaMg(CO₃)₂, CaMgSi₂O₆-MgCO₃, CaMgSi₂O₆-CaCO₃, and other published data in the system CaO-MgO-SiO₂-CO₂. A thermal barrier separates the silicate and carbonate liquids in MgO-SiO₂-CO₂ but, in the quaternary system, silicate liquids with dissolved CO₂ can follow fractionation paths around the forsterite field to the fields for the primary crystallization of carbonates. This suggests that fractional crystallization of CO₂-bearing ultrabasic magma at 100 km depth can produce residual carbonatite magma.     

Near-source attenuation of high-frequency body waves beneath the New Madrid Seismic Zone

Attenuation characteristics in the New Madrid Seismic Zone (NMSZ) are estimated from 157 local seismograph recordings out of 46 earthquakes of 2.6?≤?M?≤?4.1 with hypocentral distances up to 60 km and focal depths down to 25 km. Digital waveform seismograms were obtained from local earthquakes in the NMSZ recorded by the Center for Earthquake Research and Information (CERI) at the University of Memphis. Using the coda normalization method, we tried to determine Q values and geometrical spreading exponents at 13 center frequencies. The scatter of the data and trade-off between the geometrical spreading and the quality factor did not allow us to simultaneously derive both these parameters from inversion. Assuming 1/R ^1.0 as the geometrical spreading function in the NMSZ, the Q _P and Q _S estimates increase with increasing frequency from 354 and 426 at 4 Hz to 729 and 1091 at 24 Hz, respectively. Fitting a power law equation to the Q estimates, we found the attenuation models for the P waves and S waves in the frequency range of 4 to 24 Hz as Q _P?=?(115.80?±?1.36) f ^{(0.495?±?0.129)} and Q _S?=?(161.34?±?1.73) f ^{(0.613?±?0.067)}, respectively. We did not consider Q estimates from the coda normalization method for frequencies less than 4 Hz in the regression analysis since the decay of coda amplitude was not observed at most bandpass filtered seismograms for these frequencies. Q _S/Q _P?>?1, for 4?≤?f?≤?24 Hz as well as strong intrinsic attenuation, suggest that the crust beneath the NMSZ is partially fluid-saturated. Further, high scattering attenuation indicates the presence of a high level of small-scale heterogeneities inside the crust in this region.     

Spatial and Temporal Dependence of Temperature Variations Induced by Atmospheric Pressure Variations in Shallow Underground Cavities

Pressure-induced temperature (PIT) variations are systematically observed in the atmosphere of underground cavities. Such PIT variations are due to the compressibility of the air, damped by heat exchange with the rock surface. It is important to characterize such processes for numerous applications, such as the preservation of painted caves or the assessment of the long-term stability of underground laboratories and underground waste repositories. In this paper we thoroughly study the spatiotemporal dependence of the PIT response versus frequency using vertical and horizontal profiles of temperature installed in an abandoned underground quarry located in Vincennes, near Paris. The PIT response varies from about 20 × 10^?3°C hPa^?1 at a frequency of 2 × 10^?4 Hz to 2–3 × 10^?3°C hPa^?1 at a frequency of one cycle per day. An analytical expression based on a simple heat exchange model accounts for the observed features of the PIT response and allows for correcting the measured time series, having standard deviations of about 10^?2°C, to residual variations with a standard deviation of about 2 × 10^?3°C. However, a frequency-dependent attenuation of the response, corresponding to a reduction in amplitude with a factor varying from 2 to 3, is observed near the walls. This effect is not included in the simple analytical expression, but it can be accounted for by a one-dimensional differential equation, solved numerically, where temperature variations in the atmosphere are damped by an effective radiative coupling with the rock surface, complemented by a diffusive coupling near the walls. The TIP response is observed to remain stable over several years, but a large transient enhancement of about a factor of two is observed near the roof at one location from July to October 2005. In a cavity located below the Paris Observatory, an additional contribution is identified in the PIT response function versus frequency for frequencies smaller than 2 × 10^?5 Hz. This contribution can be described using a modified analytical expression that includes the effect of heat diffusion into the surrounding rock. Using this expression, in this case also, the temperature time series can then be corrected, giving a residual standard deviation smaller than 1.6 × 10^?3°C. Transient temporal variations of the PIT response are observed in all sites, with possible nonlinear components in the PIT. Such effects are not properly understood at this stage, and limit the reduction of time series to standard deviations of the order of 2 × 10^?3°C, and consequently limit the search for new transient or seasonal temperature signals, for example due to the presence of tiny heat sources in the cavity or to geodynamical effects.     

Studies in diffusion,II. Oxygen in phlogopite mica

Self-diffusion of oxygen in a natural phlogopite mica (annite 4%) has been measured under hydrothermal conditions at 2000 bars pressure and from 500 to 800°C using water enriched in¹⁸O. Diffusional transport is dominantly parallel to the c crystallographic axis. A linear Arrhenius plot was obtained with a pre-exponential term = (1.03 ± 0.38) × 10^?9cm²sec^?1 a and an activation energy of 29 ± 2kcal/g-atom O. The difference in transport rate between oxygens in the OH groups and those in tetrahedral sites is small to non-existent unless the OH oxygens diffuse much more slowly than the other oxygens, which we consider unlikely. A typical phlogopite crystal, 0.2 mm thick by 1 mm across will lose radiogenic argon faster than it will exchange oxygen at temperatures above 435°C, but the reverse holds at lower temperatures if the diffusion mechanism can be extrapolated to temperatures below 500°C. Such a crystal will lose only 5% of its argon if held at 380°C for 1 m.y., but could exchange 27% of its oxygen in that time. The rate at which phlogopite will undergo deformation by diffusional creep does not appear to be controlled by oxygen diffusion.     

The influence of oxidation state on the electrical conductivity of olivine

The electrical conductivity of a single crystal of San Carlos olivine (Fo₉₂, 0.16 wt.% Fe₂O₃) has been measured as a function of temperature and oxygen fugacity (fO₂). After heating to 1338°C at fO₂ = 10^?12 atm., the conductivity at 950°C was 10^?5 (ohm-m)^?1, almost 3 orders of magnitude less than that measured in air. This decrease is due to the reduction of Fe³⁺ to Fe²⁺. Further heating to 1500°C at fO₂ = 10^?14 atm., decreased the electrical conductivity at 950°C to 10^?6 (ohm-m)^?1. When recovered at room temperature, the speciment had Fo₉₆ composition and contained small, opaque blebs distributed throughout the crystal. Derivations of temperature profiles for the earth's mantle from conductivity-depth models must take account of the important role played by iron oxidation state in the electrical conductivity of olivine.     

Seismic Attenuation Computed from GLIMPCE Reflection Data and Comparison with Refraction Results

—Instantaneous frequency matching has been used to compute differential t* values for seismic reflection data from the Great Lakes International Multidisciplinary Program on Crustal Evolution (GLIMPCE) experiment. The differential attenuation values were converted to apparent Q ^?1 models by a fitting procedure that simultaneously solves for the interval Q ^?1 values using non-negative least squares. The bootstrap method was then used to estimate the variance in the interval Q ^?1 models. The shallow Q ^?1 structure obtained from the seismic reflection data corresponds closely with an attenuation model derived using instantaneous frequency matching on seismic refraction data along the same transect. This suggests that the effects of wave propagation and scattering on the apparent attenuation are similar for the two data sets. The Q ^?1 model from the reflection data was then compared with the structural interpretation of the reflectivity data. The highest interval Q ^?1 values (>0.01) were found near the surface, corresponding to the sedimentary rock sequence of the upper Keweenawan. Low Q ^?1 values (<0.0006) are found beneath the Midcontinent rift’s central basin. In addition to structural interpretation, seismic attenuation models derived in this way can be used to correct reflection data for dispersion, frequency and amplitude effects, and allow for improved imaging of the subsurface.     

A study of Guptkashi,Uttarakhand earthquake of 6 February 2017 (<Emphasis Type="Italic">M</Emphasis><Subscript><Emphasis Type="Italic">w</Emphasis></Subscript>5.3) in the Himalayan arc and implications for ground motion estimation

The 2017 Guptkashi earthquake occurred in a segment of the Himalayan arc with high potential for a strong earthquake in the near future. In this context, a careful analysis of the earthquake is important as it may shed light on source and ground motion characteristics during future earthquakes. Using the earthquake recording on a single broadband strong-motion seismograph installed at the epicenter, we estimate the earthquake’s location (30.546° N, 79.063° E), depth (H?=?19 km), the seismic moment (M₀?=?1.12×10¹⁷ Nm, M _w 5.3), the focal mechanism (φ?=?280°, δ?=?14°, λ?=?84°), the source radius (a?=?1.3 km), and the static stress drop (Δσ _s ~22 MPa). The event occurred just above the Main Himalayan Thrust. S-wave spectra of the earthquake at hard sites in the arc are well approximated (assuming ω^?2 source model) by attenuation parameters Q(f)?=?500f^0.9, κ?=?0.04 s, and f_max?=?infinite, and a stress drop of Δσ?=?70 MPa. Observed and computed peak ground motions, using stochastic method along with parameters inferred from spectral analysis, agree well with each other. These attenuation parameters are also reasonable for the observed spectra and/or peak ground motion parameters in the arc at distances ≤?200 km during five other earthquakes in the region (4.6?≤?M _w ?≤?6.9). The estimated stress drop of the six events ranges from 20 to 120 MPa. Our analysis suggests that attenuation parameters given above may be used for ground motion estimation at hard sites in the Himalayan arc via the stochastic method.