Francis Birch

Heat generation of plutonic rocks and continental heat flow provinces

Combined radioactivity and heat flow measurements in pluionie rocks at 38 localities in the United States define three heat flow provinces; the eastern United States, the Sierra Nevada, and a zone of high heat flow in the western United States which includes the Basin and Range province. In each of these provinces heat flow ( Q ) and heat production ( A ) are related by an equation of the form Q = a + bA . The simplest interpretation of this linear relation is that the radioactivity measured at the surface is constant from the surface to depth b but varies from place to place. Thus the fraction of heat flow from the lower crust and upper mantle, a , remains constant within a heat flow province while the variable upper crustal radioactivity generates the variable heat flow observed at the surface. In the eastern United States b = 7.5 km and a = 0.79 cal/cm 2 sec, in the Sierra Nevada b = 10.1 km and a = 0.40 cal/cm 2 sec, and in the Basin and Range province b = 9.4 km and a = 1.4 cal/cm 2 sec. The line characteristic of the eastern United States may have broad applicability to stable portions of continents and thus be considered the reference curve for normal continental heat flow. The similarity of all the slopes indicates that most local variability of heat flow is due to sources in the uppermost 7–11 km of the earths crust, and that the contribution from the lower crust and upper mantle is quite uniform over large regions. The intercept values can be used to infer the proportion of heat flow from the mantle and to map provinces with different mantle heat flow. These heat flow provinces correlate closely with surface geological provinces.

The Effect of Pressure Upon the Elastic Parameters of Isotropic Solids, According to Murnaghan's Theory of Finite Strain

Murnaghans theory of finite deformations is applied to a discussion of the effect of hydrostatic pressure upon the elastic coefficients of an isotropic body, for small strains superposed on the hydrostatic strain. Stress‐strain equations for the small strains, and the equations of small motion, are shown to have the same form as those of the classical theory, with elastic parameters which depend upon the pressure. Using a form of elastic potential identical with that of the classical theory, explicit results are found for the pressure coefficients of compressibility, Youngs modulus, rigidity and so on; these are compared with such experimental results as are available, with good agreement. A single‐constant formula is derived which gives the volume change of such compressible materials as sodium and cesium up to the highest experimental pressure, 45,000 kg/cm2, within the experimental error.

FLOW OF HEAT IN THE FRONT RANGE, COLORADO

Modern conceptions of the structure of the earth9s crust and of the distribution of radioactivity lead to an expectation of a greater flow of heat to the surface in mountains than in lowlands. An exceptional opportunity for testing this expectation is provided by the data obtained by the geologists of the Bureau of Reclamation during the construction of the Alva B. Adams Tunnel under Rocky Mountain National Park. This tunnel, 13 miles long, at a mean altitude of 8300 feet, passes under the Continental Divide, more than 12,000 feet above sea level. Some 70 observations of temperature have been reduced with the purpose of finding the flow of heat. Corrections have been applied for the topography on several different hypotheses regarding the physiographic history. The corrected vertical gradient of temperature lies between 24°C/km, on the assumption that the present topography has persisted indefinitely, and 20°C/km, on the assumption that the surface features have been derived from an old-age surface by erosion and by uplift of 7000 feet uniformly distributed over the last million years. If the time of evolution is taken as 4 million years, the corrected gradient is 22°C/km. An uncertainty of about 1°C/km results from lack of reliable data concerning the surface temperature. Thermal conductivity has been measured in the laboratory for 123 samples of rock from the tunnel; these rocks are chiefly granites, gneisses, and schists. The variations of conductivity with rock type and with position along the tunnel are found to be insignificant; the mean value of conductivity is 0.008 cal/cm·sec·deg. The heat flow is then computed as between 1.6 and 1.9 microcal/cm 2 ·sec, with a “best value” of 1.7 microcal/cm 2 ·sec. This is believed to differ significantly from the best values for a “normal” sea-level crust, which fall close to 1.1 microcal/cm 2 ·sec. With conventional assumptions as to thickness and density of the layers of the normal crust, the difference of heat flow may be accounted for in terms of mountain roots having a mean radioactivity of the same order as that of granites or intermediate rocks. The observed heat flow is consistent with the doctrine of mountain roots and with an approximately uniform distribution of radioactivity throughout the “granitic” layer. A few of the other possible interpretations are briefly discussed.

Speculations on the Earth's Thermal History

The gross structure of the Earths interior—mantle and core with their subdivisions—affords evidence of the thermal evolution. The principal event was the formation of a liquid iron core from an initially cool unsorted conglomerate after about 500 m.y. of heating by radioactivity and tidal friction. Core formation was accompanied by conversion of gravitational energy to heat, the deep interior reaching temperatures of 4000°–5000°; this process was completed about 4500 m.y. ago. Fractional melting of the mantle concentrated radioactive and “lithophile” elements in the upper mantle and transition zone, leaving the lower mantle devoid of radioactivity. Formation of stable continental crust became possible after this upward concentration and decay of radioactivity, beginning about 3500 m.y. ago. Further concentration of the radioactive elements in the continental crust has left the subcontinental mantle impoverished by comparison with the suboceanic mantle. Present temperatures are consequently higher in the suboceanic mantle than at the same depths beneath continents, approaching or reaching melting temperatures beneath the oceans while cooling continues beneath continents. The required concentrations of radioactive elements appear to be in reasonable agreement with existing measurements if the primitive undifferentiated Earth resembled the meteorite Orgueil in its radioactive content.

The Effect of Pressure on the Rigidity of Rocks. I

A dynamical method has been adapted to the measurement of the velocity of torsional waves in cylinders of rock exposed to pressures as high as

Elasticity of igneous rocks at high temperatures and pressures

4,000 kg/cm^{2}, at 30^{\circ} C

The Effect of Pressure on the Modulus of Rigidity of Several Metals and Glasses

. and at 100° C. From these results the rigidities of the rocks under these conditions are derived, as well as approximate values for the pressure and temperature coefficients of velocity and rigidity. Very large changes of rigidity are observed in many cases upon the application of the first few hundred atmospheres; at high pressure the change of rigidity with pressure becomes nearly linear and small. The following questions are discussed: stress conditions in aggregates of crystals, the effect of anisotropy upon velocity, the calculation of other elastic parameters from rigidity and compressibility, damping and dispersion in rocks, the effect of combined pressure and temperature on velocity in the earths crust, and the identification of materials in the crust by comparison with seismological data.

On the possibility of large changes in the Earth's volume

Elastic constants, derived from measured velocities of pulsed ultrasonic waves (10 to 20 Mc/sec) are given for three specimens of natural pyrite. For all specimens, the constant C12 is positive. The values for the crystal of best quality are: C11=3.818, C12=+0.310, C44=1.094, in units of 1012 dyn/cm2. An explanation for the negative values of C12 found by some observers is advanced. Ultrasonic double refraction for shear waves was also observed.