The lunar fossil bulge hypothesis revisited

The lunar gravity field can be satisfactorily explained by relatively-small wavelength, density anomalies located near the lunar surface. The exceptions to this are the second degree harmonics and we postulate a dual origin for these terms; they are partly a consequence of the same near-surface anomalies as the remainder of the gravity field and partly a measure of a fossil bulge. This latter contribution represents an equilibrium condition preserved from a time when the synchronously rotating Moon was approximately 25 Earth-radii from the Earth. If this shape was acquired at some time soon after 4.0 · 10⁹ years ago, then the rate of dissipation of tidal energy in the Earth has been much lower in the past then it is now. The implications of this on the evolution of the Earth-Moon system are briefly discussed.     

A simple method for calculating displacements and stresses around tunnel openings an application for the microcomputer

SummaryA Simple Method for Calculating Displacements and Stresses Around Tunnel Openings — An Application for the Microcomputer The paper describes a program, written for an Apple-II/Plus Microcomputer, and designed to calculate the perimetral elastic deformations and tangential stresses around underground openings of non-circular section. The mathematical basis used in this program first appeared in a paper by Dr. E. Wisser, published in Rock Mechanics. The Appendix gives the list of the program and all instructions which a user, familiar with computers, may require.With 5 Figures     

Flexure of the ocean lithosphere from island uplift, bathymetry and geoid height observations: the Society Islands

Summary. The response of a stratified elastic medium can be conveniently characterized by the Green's tensor for the medium. For coupled seismic wave propagation ( P—SV or fully anisotropic), the Green's tensor may be constructed directly from two matrices of linearly independent displacement solutions. Rather simple forms for the Green's tensor can be found if each displacement matrix satisfies one of the boundary conditions on the seismic field. This approach relates directly to 'reflection matrix' representations of the seismic field.
For a stratified elastic half space the Green's tensor is used to give a spectral representation for coupled seismic waves. By means of a contour integration a general completeness relation is obtained for the 'body wave' and 'surface wave' parts of the seismic field. This relation is appropriate for SH and P–SV waves in an isotropic medium and also for full anisotropy.     

Optimized system to improve pumping rate stability during aquifer tests

Aquifer hydraulic properties are commonly estimated using aquifer tests, which are based on an assumption of a uniform and constant pumping rate. Substantial uncertainties in the flow rate across the borehole-formation interface can be induced by dynamic head losses, caused by rapid changes in borehole water levels early in an aquifer test. A system is presented that substantially reduces these sources of uncertainty by explicitly accounting for dynamic head losses. The system which employs commonly available components (including a datalogger, pressure transducers, a variable-speed pump motor, a flow controller, and flowmeters), is inexpensive, highly mobile, and easily set up. It optimizes the flow rate at the borehole-formation interface, making it suitable for any type of aquifer test, including constant, step, or ramped withdrawal and injection, as well as sinusoidal. The system was demonstrated for both withdrawal and injection tests in three aquifers at the Savannah River Site. No modifications to the control system were required, although a small number of characteristics of the pumping and monitoring system were added to the operating program. The pumping system provided a statistically significant, constant flow rate with time. The range in pumping variability (95% confidence interval) was from +/- 2.58 x 10(-4) L/sec to +/- 9.07 x 10(-4) L/sec, across a wide range in field and aquifer conditions.     

Effective bulk composition changes due to cooling: a model predicting complexities in retrograde reaction textures

Diffusive processes are a strong function of temperature. Thus, during cooling of rocks, mineral grains may develop zoning profiles as successively larger parts of the grain “close” to the diffusive exchange with the rock. One of the consequences of this process is that, during cooling, successively larger parts of zoned minerals (depending on grain size) are effectively removed from the reacting part of the rock volume. Thus, the effective bulk composition of metamorphic rocks changes during cooling and the rate of its change will be a function of grain size. Because the sequence of metamorphic reactions seen by a given rock is a strong function of its bulk composition, this process may have the consequence that two rocks of identical overall bulk composition, but of different grain size, may experience a different sequence of reactions. Qualitatively identical peak paragenesis may therefore react to form qualitatively different retrograde reaction textures. The model is applied to examples in the pelitic system. There, garnet is usually the slowest diffusing phase developing zoning profiles during cooling and the effective removal of garnet from the reacting rock volume will cause changes of the effective bulk composition. It is shown that, during cooling of pelitic rocks from amphibolite facies conditions, typical aluminous peak parageneses of garnet-muscovite-kyanite ± biotite may react to form either staurolite, chlorite or muscovite (or different combinations thereof), depending on grain size. During cooling from the granulite facies, aluminous peak parageneses of garnet-cordierite-sillimanite may form biotite, either on the expense of cordierite or garnet, also depending on grain size. The two examples are illustrated with a series of reaction textures reported for amphibolite and granulite terrains in the literature. Received: 12 March 1996 / Accepted: 7 April 1997