Performance of the complete travel-time equation of state at simultaneous high pressure and temperature

The complete travel-time equation of state (CT-EOS) is presented by utilizing thermodynamics relations, such as; $$K_T = K_S (1 + \alpha \gamma T)^{ - 1} , \gamma = \frac{{\alpha K_S }}{{\rho C_P }}, \left. {\frac{{\partial C_P }}{{\partial P}}} \right)_T = - \frac{T}{\rho }\left[ {\alpha ^2 + \left. {\frac{{\partial \alpha }}{{\partial T}}} \right)_P } \right], etc.$$ The CT-EOS enables us to analyze ultrasonic experimental data under simultaneous high pressure and high temperature without introducing any assumption, as long as the density, or thermal expansivity, and heat capacity are also available as functions of temperature at zero pressure. The performance of the CT-EOS was examined by using synthesized travel-time data with random noise of 10^?5 and 10^?4 amplitude up to 4 GPa and 1500 K. Those test conditions are to be met with the newly developed GHz interferometry in a gas medium piston cylinder apparatus. The results suggest that the combination of the CT-EOS and accurate experimental data (10^?4 in travel time) can determine thermodynamic and elastic parameters, as well as their derivatives with unprecedented accuracy, yielding second-order pressure derivatives (?² M/?P ²) of the elastic moduli as well as the temperature derivatives of their first-order pressure derivatives ?² M/?P?T). The completeness of the CT-EOS provides an unambiguous criterion to evaluate the compatibility of empirical EOS with experimental data. Furthermore because of this completeness, it offers the possibility of a new and absolute pressure calibration when X-ray (i.e., volume) measurements are made simultaneously with the travel-time measurements.     

Effects of temperature and sliding rate on frictional strength of granite

Layers of artificial granite gouge have been deformed on saw-cut granite surfaces inclined 30° to the sample axes. Samples were deformed at a constant confining pressure of 250 MPa and temperatures of 22 to 845°C. The velocity dependence of the steady-state coefficient of friction (^ss) was determined by comparing sliding strengths at different sliding rates. The results of these measurements are consistent with those reported bySolberg andByerlee (1984) at room temperature andStesky (1975) between 300 and 400°C. Stesky found that the slip-rate dependence of (^ss) increased above 400°C. In the present study, however, the velocity dependence of (^ss) was nearly independent of temperature.     

Lees's topographic correction in heat flow and the geothermal flux in Tasmania

Summary Lees's topographic correction for a simple idealized hill is discussed and extended to a monoclinal structure. It is valuable as giving very simply the order of magnitude of the correction. A number of new measurements of temperature in Tasmanian boreholes has been made and the previous rather high value of over 2 cal/cm² sec for the heat flux has been confirmed. The variation of thermal conductivity through the thickness of a differentiated tholeiite sheet has been measured and found to be in reasonably good agreement with values calculated from chemical and modal analyses.     

Die Sonnenstrahlung und ihre Messung

Summary History and results of a 41/2-years-expedition to Argentine. A determination of the sun's «temperature» can only be given by the laws ofBoltzmann-Stefan andWien, because the temperature of the different layers is different. In the measurements of the sun's radiation the law ofBoltzmann-Stefan was introduced (T ⁴, where is a constant, andT the Kelvin-Temperature) while in the passed 100 years the difference between the sun's and the instruments radiation was taken as radiation, although this difference was arbitrariously variable with the instruments temperature. The effect of the vertical exchange of airmasses, on the radiation of the sun and the radiation of the air between the sun and the instrument was cleared. With these corrections one can not receive more as the difference between the so called solar constant and the albedo of the atmosphere. If the highest values are used (smallest albedo) the approximated value of the solar constant becomes 2.4, corresponding well to the value, derived from the supposed temperature of the sun.     

Seismic excitation of the polar motion, 1977–1993

The mass redistribution in the earth as a result of an earthquake faulting changes the earth's inertia tensor, and hence its rotation. Using the complete formulae developed byChao andGross (1987) based on the normal mode theory, we calculated the earthquake-induced polar motion excitation for the largest 11,015 earthquakes that occurred during 1977.0–1993.6. The seismic excitations in this period are found to be two orders of magnitude below the detection threshold even with today's high precision earth rotation measurements. However, it was calculated that an earthquake of only one tenth the size of the great 1960 Chile event, if happened today, could be comfortably detected in polar motion observations. Furthermore, collectively these seismic excitations have a strong statistical tendency to nudge the pole towards 140°E, away from the actually observed polar drift direction. This non-random behavior, similarly found in other earthquake-induced changes in earth rotation and low-degree gravitational field byChao andGross (1987), manifests some geodynamic behavior yet to be explored.     

Laboratory measurement of compaction-induced permeability change in porous rocks: Implications for the generation and maintenance of pore pressure excess in the crust

Permeability exerts significant control over the development of pore pressure excess in the crust, and it is a physical quantity sensitively dependent on the pore structure and stress state. In many applications, the relation between permeability and effective mean stress is assumed to be exponential and that between permeability and porosity is assumed to be a power law, so that the pressure sensitivity of permeability is characterized by the coefficient and the porosity sensitivity by the exponent . In this study, we investigate experimentally the dependence of permeability on pressure and porosity in five sandstones with porosities ranging from 14% to 35% and we review published experimental data on intact rocks, unconsolidated materials and rock fractures. The laboratory data show that the pressure and porosity sensitivities differ significantly for different compaction mechanisms, but for a given compaction mechanism, the data can often be approximated by the empirical relations. The permeabilities of tight rocks and rock joints show relatively high pressure sensitivity and low porosity sensitivity. A wide range of values for and have been observed in relation to the mechanical compaction of porous rocks, sand and fault gouge, whereas the porosity sensitivity for chemical compaction processes is often observed to be given by 3. We show that since the ratio / corresponds to the pore compressibility, the different dependences of permeability on porosity and pressure are related to the pore structure and its compressibility. Guided by the laboratory data, we conduct numerical simulations on the development of pore pressure in crustal tectonic settings according to the models ofWalder andNur (1984) andRice (1992). Laboratory data suggest that the pressure sensitivity of fault gouge is relatively low, and to maintain pore pressure at close to the lithostatic value in the Rice model, a relatively high influx of fluid from below the seismogenic layer is necessary. The fluid may be injected as vertically propagating pressure pulses into the seismogenic system, andRice's (1992) critical condition for the existence of solitary wave is shown to be equivalent to >1, which is satisfied by most geologic materials in the laboratory. Laboratory data suggest that the porosity sensitivity is relatively high when the permeability is reduced by a coupled mechanical and chemical compaction process. This implies that in a crustal layer, pore pressure may be generated more efficiently than cases studied byWalder andNur (1984) who assumed a relatively low porosity sensitivity of =2.     

On the asymmetric diurnal tide

Summary The response of the atmosphere to a diurnally oscillating thermal drive, asymmetric with respect to the equator, is investigated. It is found that the solutions ofLaplace's tidal equation do not form a complete set; all of them being orthogonal to the associated Legendre polynomial,P ₂ ¹ (cos ), being the latitude. As an extension ofLaplace's theorem for gravitationally excited ocean tides to thermally driven atmospheric tides, it is shown that a diurnal drive whose latitude dependence is given byP ₂ ¹ gives rise to no surface pressure oscillation.     

Composition of the core,II. Effect of high pressure on solubility of FeO in molten iron

An experimental and theoretical investigation of the effect of pressure on the solubility of FeO in molten iron has been carried out. Analyses of shock-wave compression data on iron oxides combined with measurements of the FeO bond length in “metallic” oxides suggest that the partial molar volume of FeO(V^*) dissolved in molten iron is substantially smaller than that of molten wüstite. Hence the effect of high pressure should be to increase the solubility of FeO in molten iron at a given temperature. This inference is confirmed by an experimental investigation of the effect of pressure on the position of the FeFeO eutectic. Thermodynamic calculations based on these experiments yield an estimate forV^* which is in reasonable agreement with the theoretical estimates. The experimental value ofV^* is used to calculate the effect of high pressure upon the FeFeO phase diagram. Solubility of FeO in molten iron increases sharply with pressure, the liquid immiscibility region contracts and disappears around 20 GPa and it is predicted that the FeFeO phase diagram should resemble a simple eutectic system above about 20 GPa. Analogous calculations predict that the solubility of FeO in molten iron in equilibrium with magnesiowüstite (Mg_0.8Fe_0.2)O at 2500°C increase from 14 mol.%(P = 0) to above 25 mol.% at 20 GPa. If the core formed by segregation of metallic iron originally dispersed throughout the earth, it seems inevitable that it would dissolved large amounts of FeO, thereby accounting for the observation that the density of the outer core is substantially smaller than that of pure iron under correspondingP, T conditions.     

On waves generated by a moving pressure field,II: Cnoidal wave effects

Summary In a recent paperHunt andTanner [3]²) investigated the waves generated by a steadily moving two-dimensional pressure distribution, which was zero ahead of the disturbance and a constantp ₀, tehind it, these regions being joined smoothly by a cubic function. Only those solutions with supercritical flow in both regions were considered, these were found to lead to an asymmetric solitary wave.This result is now extended to take account of the possibility of subcritical flow in either or both the regions, that is when there is a cnoidal wave train either behind and or ahead of the main solitary wave crest.The wave profiles are determined by the iterative method employed in the previous paper. This together with the wave drag associated with each system is computed for various values ofp ₀/U ², where is the fluid density andU a typical velocity.     

Resolution of tidal high water anomaly

Summary As a preliminary calculation of the Equilibrium Theory of Tides, a fictitious Earth-Moon configuration is analyzed byThomson andTait [1]²), in which non-sphericity of oceans is attributed to the attraction exerted by a stationary Moon. A rise of level is found at the which Earth-Moon orbital motion is accounted. This feature, which is utterly contradictory to fact according toG. H. Darwin [2] prompted him to remark that the equilibrium theory is nearly as much wrong as possible, in respect to the time of high water. An elementary analysis is given which, in demonstrating an exactly opposite finding, suggests a manner of removing one of the long-standing obscurities of the Laplace theory, remarked upon byHough andAiry, and in recent times byC. Eckart [3].     

Pn residuals and station corrections

Summary This paper is an attempt towards determination of station adjustments for Shillong and Delly Observatories from considerations of a large number ofP _n residuals. Station adjustments toJeffreys-Bullen travel time tables for Shillong comes to about 4 seconds and for Delhi 2 seconds respectively for 20°.     

A relationship between phonon conductivity and seismic parameter Φ for silicate minerals

Summary The relationship between the phonon conductivity at room temperature (K _N ) and the seismic parameter () for silicate minerals is suggested. The considerations are based on the Debye model of thermal energy transport phenomena in solids and on the seismic equation of state for silicates and oxides given byAnderson (1967). The semiempirical relationship is the formK _N = 0.43^0.82 where is in km²/s² andK _N in mcal/cm s K, and the empirical relationship isK _N =(0.528±0.006) –(8.18±2.11). The laboratory data on thermal and elastic properties for several silicates were taken fromHorai andSimmons (1970).     

Instantaneous photochemical rates in the global stratosphere

Starting with the average actual distribution of ozone (Dütsch [15]) and temperature in the stratosphere, we have calculated the solar intensity as a function of wavelength and the instantaneous rates (molecules cm^–3 sec^–1) for each Chapman reaction and for each of several reactions of the oxides of nitrogen. The calculation is similar to that ofBrewer andWilson [5]. These reaction rates were calculated independently in each volume element in spherical polar coordinates defined by R=1 km from zero to 50, =5° latitude, and ø=15° longitude (thus including day and night conditions). Calculations were made for two times: summer-winter (January 15) and spring-fall (March 22). As input data we take observed solar intensities (Ackerman [1]) and observed, critically evaluated. constants for elementary chemical and photochemical reactions; no adjustable parameters are employed. (These are not photochemical equilibrium calculations.) According to the Chapman model, the instantaneous, integrated, world-wide rate of formation of ozone from sunlight is about five times faster than the rate of ozone destruction, and locally (lower tropical stratosphere) the rate of ozone formation exceeds the rate of destruction by a factors as great as 1000. The global rates of increase of ozone are more than 50 times faster thanBrewer andWilson's [5] estimate of the average annual transfer rate of ozone to the troposphere. The rate constants of the Chapman reactions are believed to be well-enough known that it is highly improbable that these discrepancies are, due to erroneous rate constants. It is concluded that something else besides neutral oxygen species is very important in stratospheric ozone photochemistry. The inclusion of a uniform concentration of the oxides of nitrogen (NO_x as, NO and NO₂) averaging 6.6×10^–9 mole fraction gives a balance between global ozone formation and destruction rates. The inclusion of a uniform mole fraction of NO_x at 28×10^–9 also gives a global balance. These calculations support the hypethesis (Crutzen [10],Johnston [24]) that the oxides of nitrogen are the most important factor in the global, natural ozone balance. Several authors have recently evaluated the natural source strength of NO_x in the stratosphere; the projected fleets of supersonic transports would constitute an artificial source of NO_x about equal to the natural value, thus promising more or less to double an active natural stratospheric ingredient.     

Coseismic slip in the 1964 Prince William Sound earthquake: A new geodetic inversion

The 1964 Prince William Sound earthquake (March 28, 1964;M _w =9.2) caused crustal deformation over an area of approximately 140,000 km² in south central Alaska. In this study geodetic and geologic measurements of this surface deformation were inverted for the slip distribution on the 1964 rupture surface. Previous seismologic, geologic, and geodetic studies of this region were used to constrain the geometry of the fault surface. In the Kodiak Island region, 28 rectangular planes (50 by 50 km each) oriented 218°N, with a dip varying from 8^o nearest the Aleutian trench to 9^o below Kodiak Island, define the rupture surface. In the Prince William Sound region 39 planes with variable dimensions (40 by 50 km near the trench, 64 by 50 km inland) and orientation (218°N in the west and 270°N in the east) were used to approximate the complex faulting. Prior information was introduced to constrain offshore dip-slip values, the strike-slip component, and slip variation between adjacent planes. Our results suggest a variable dip-slip component with local slip maximums occurring near Montague Island (up to 30 m), further to the east near Kayak Island (up to 14 m), and trenchward of the northeast segment of Kodiak Island (up to 17m). A single fault plane dipping 30°NW, corresponding to the Patton Bay fault, with a slip value of 8 m modeled the localized but large uplift on Montague Island. The moment calculated on the basis of our geodetically derived slip model of 5.0×10²⁹ dyne cm is 30% less than the seismic moment of 7.5×10²⁹ dyne cm calculated from long-period surface waves (Kanamori, 1970) but is close to the seismic moment of 5.9×10²⁹ dyne cm obtained byKikuchi andFukao (1987).     

Differential scanning calorimetry in a piston-cylinder apparatus: Design and calibration

We have designed and calibrated a piston-cylinder cell assembly suitable for conductingin situ measurements of enthalpies of phase transitions at elevated pressures by heat-flux differential scanning calorimetry (DSC). The high-pressure DSC detector consists of a Pt-Pt13%Rh thermopile wrapped around a frame of fired pyrophyllite. Four thermocouple junctions, arranged radially around the sample capsule, are connected in series, with four reference thermocouple junctions located 3–4 mm above the sample and embedded in thermally inert ceramic. A W-W25%Re control thermocouple is situated directly above the top of the sample; the whole detector assembly is enclosed in a 1.5 mm thick cylindrical ceramic sleeve located at the center of a 8–10 mm long hot-zone in the tapered graphite furnace. Using this detector design and cell assembly, we have observed the thermal signal associated with the fusion of Au at 0.5 and 1.2 GPa, and have calculated a calibration factor (K) for this detector based on the gold melting curve ofMirwald andKennedy (1979). Detector sensitivity decreases by a factor of four over this pressure-temperature interval. The reproducibility of the enthalpy of fusion of gold at 0.5 GPa suggests that detector geometry is reproducible from one experiment to the next, and thus confirms the viability of this particular detector design for quantitative DSC measurements. Subsequent experiments will assess the dependence of (K) on temperature and pressure by measuring the enthalpies of fusion of additional metals (e.g., Ag, Cu, Al, Ge) and salts (e.g., NaCl, CsCl).     

Research note: the effect of strain amplitude produced by ultrasonic waves on its velocity

The effect of the amplitude of ultrasonic waves propagating through a sample is not often taken into account in laboratory experiments. However, ultrasonic waves can produce relatively large strain inside the sample, and thus change the properties of the sample. To investigate the effect of strain amplitude on the P-wave velocity, a series of ultrasonic wave propagation experiments were carried out on three different media. All measurements were performed at 1 MHz central frequency and at the strain levels inside propagating waves of  ∼3.0 × 10⁻⁶ to 6.0 × 10⁻⁵ without applying confining pressure to the sample. Strains in the waves were measured by a laser Doppler interferometer upon wave arrival on a free surface of the sample. The ultrasonic velocities were measured by a pair of P-wave transducers located at the same measuring point as the laser beam of the LDI. The effect of strain on P-wave velocity varied for different material. The P-wave velocity was calculated using both a first arrival and a first maximum peak at different applied voltage. The P-wave velocity remained unchanged for a pure elastic medium (aluminium); however, the velocity increased continuously with the increasing of the strain for polymethylmethacrylate and Gosford sandstone. For Gosford sandstone, velocity increases up to 0.8% with strain increase from 7.0 × 10⁻⁶ to 2.0 × 10⁻⁵. This effect of velocity increase with the strain induced by an ultrasonic wave can be explained by the in-elasticity of both the polymethylmethacrylate and Gosford sandstone samples.     

Heat flow in the Upper Silesian coal basin

Summary The paper presents results of heat flow measurements made in 6 deep bores in the Czechoslovakian part of the Upper Silesian coal basin. The heat flow measured was in the range from 1.74 to 1.87 cal/cm²s. The undisturbed period before the temperature measurement in the bore is discussed and results of repeated temperature measurements carried out 0.1, 1,5 and 36 days after cessation of drilling in one of the bores NP-522, are also given. Although the temperature in the bore still differs considerably from equilibrium, it is possible to determine the temperature gradient with an accuracy better than 5% as soon as 5 days after drilling was finished.     

Abschätzungen über einige Quellen des atmosphärischen Aerosols

Zusammenfassung Die vonLettau berechnete Produktion von Aitkenkernen durch Großstädte und die Abschätzung über die weltweite Wirkung von Vegetationsbränden und anderen Trübungsquellen werden diskutiert.-Nach gleichzeitigen Sonnenstrahlungsmessungen in und ausserhalb von Großstädten nimmt in der über den Städten befindlichen Luft der TrübungsfaktorT um 4 . 10^–4 sec^–1 zu. Durch Vergleich der Bevölkerungsdichten wird dieser Wert der anthropogenen Trübungsproduktion auf die Trübungszunahme der Luft über grösseren Gebieten umgerechnet. Für drei günstige Hochdrucklagen mit schwachen Winden über Mitteleuropa werden die Strahlungsmessungen von vier Stationen bearbeitet; die beobachtete Trübungszunahme (dT=0.15 bis 0.4 pro Tag) stimmt mit der errechneten gut überein. Die Rauchtrübung durch Vegetationsbrände dürfte im Mittel der Nordhalbkugel etwas geringere Wirksamkeit als Industrietrübung haben. Auf die Wichtigkeit einer Abschätzung der Trübungsproduktion aus der Gasphase, die in wolkenreichen Luftmassen eine wesentliche Rolle spielen dürfte, wird hingewiesen.

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Summary A discussion is given ofLettau's calculation of the Aitken nuclei production by towns and the estimations of the world wide effect of vegetation fires and of other nuclei sources. Sunradiation measurements, made simultanously inside and outside from cities, show that the turbidity factor of the air over towns increases by 4 . 10^–4 per sec. From consideration of the population densities, the value of anthropogeneous turbidity production is calculated for greater areas. Radiation measurements of four stations at high pressure weather situations with weak winds over Europe show a good agreement with the calculations. It seems that the mean turdidity over the northern hemisphere produced by smokes from vegetation fires has not so great effect as anthropogeneous aerosol. The attention is made to the importance of an estimation of the turbidity production from the gaseous phase, that may play an essential role in cloudy air masses.

     

The rate of quasi-steady growth and evaporation of small drops in a gaseous medium

Summary The intensity of steady diffusion flux onto a sphere absorbing particles with a known probability is determined at arbitrary Knudsen number. New expression for the concentration jump is given. The accuracy of the well known -method developed byN. A. Fuchs is estimated. The formula is derived for the rate of slow condensation growth (or evaporation) of drops of any size in a vapour-gas mixture at low vapour content. The results of different authors are compared.     

Effects of collision-induced breakup on drop size distributions in steady state rainshafts

New equations and techniques for dealing with drop breakups are developed and applied to the modelling of the evolution of raindrop spectra in rainshafts. Breakup experiments byMcTaggart-Cowan andList (1975) served as data base.No matter what the original size distribution, the spectrum evolution will always lead to a Marshall-Palmer type equilibrium di tributionN=N ₀e^–D, with =constant andN ₀ proportional to the rainfall rateR. (D stands for raindrop diameter.) ForR29 mm h^–1 and an original Marshall-Palmer distribution, the required fall height to reach equilibrium is 2 km.The equilibrium distributions are characterized by linear relationships betweenR, the radar reflectivity factorZ, the liquid water content LWC and theN ₀ of the Marshall-Palmer distribution. Possible explanations for the discrepancy with observations are given.The fact that the all-water processes cannot produce drops withD2.5 mm (as confirmed by observations) leads to the conclusion that observed large raindrops withD5 mm represent melted hailstones and have not yet reached an equilibrium distribution. These latter conclusions were reached within the original assumption of videspread, steady state precipitation.