Evaluation and developmental studies of possible active seismic experiments during the post-Apollo period

Seismic velocity studies pertinent to the lunar crust and mantle are briefly summarized. The compressional and shear wave velocities in loose aggregates are discussed along with the effects of temperature on seismic velocity in compacted powders. Abstracts of papers concerning the lunar structure are included

Analysis and testing of numerical formulas for the initial value problem

Three computer programs for evaluating and testing numerical integration formulas used with fixed stepsize programs to solve initial value systems of ordinary differential equations are described. A program written in PASCAL SERIES, takes as input the differential equations and produces a FORTRAN subroutine for the derivatives of the system and for computing the actual solution through recursive power series techniques. Both of these are used by STAN, a FORTRAN program that interactively displays a discrete analog of the Liapunov stability region of any two dimensional subspace of the system. The derivatives may be used by CLMP, a FORTRAN program, to test the fixed stepsize formula against a good numerical result and interactively display the solutions

Seismic Love waves [Book Review]

This monograph is devoted to a methodical mathematical study, using the spectral theory of linear differential operations, of surface Love waves. The authors are affiliated with the Institute of Chemical Physics and the Institute of Physics of the Earth of the Academy of Sciences of the USSR

Using the NAVSTAR Global Positioning System as a global timing system

The application of NAVSTAR GPS to the problems of PTTI dissemination is discussed. A short review of the GPS concept lead to a detailed description of the implementation of time transfer through NAVSTAR GPS. Time was followed from the U.S. Naval Observatory (USNO) through the ground control, satellite, and receiving segments of GPS to the user's clock system. The three options by which a user's system can receive from the GPS receivers, currently under development by the DOD, are defined in detail. The electrical/digital/mechanical interface parameters along with suggested methods for their use are outlined for each option. A detailed error model is also presented for the traceability of UTC (GPS) to UTC (USNO). Real time synchronization between stationary users on the time continent can be controlled to within a few nanoseconds, and absolute post processed time offset with UTC (USNO) measured within 25 nanoseconds or better. A discussion of some of the potential work around techniques and their applications are included

Universal dispersion tables III. Free oscillation variational parameters

The effect of a small change in any parameter of a realistic Earth model on the periods of free oscillation is computed for both spheroidal and torsional modes. The normalized partial derivatives, or variational parameters, are given as a function of order number and depth in the Earth. For a given mode it can immediately be seen which parameters and which regions of the Earth are controlling the period of free oscillation. Except for _oS_o and its overtones the low-order free oscillations are relatively insensitive to properties of the core. The shear velocity of the mantle is the dominant parameter controlling the periods of free oscillation and density can be determined from free oscillation data only if the shear velocity is known very accurately. Once the velocity structure is well known free oscillation data can be used to modify the average density of the upper mantle. The mass and moment of inertia are then the main constraints on how the mass must be redistributed in the lower mantle and core

Dispersion of Long-Period Love Waves in a Spherical Earth

Periods of torsional eigenvibrations have been computed for heterogeneous spheres corresponding to a variety of Earth models, and the periods of oscillation are used to calculate phase and group velocities for the fundamental and first higher modes of Love waves. A comparison is made between velocities for different spherical models, with the velocities calculated by use of equivalent flat Earth structures. The comparison shows that (1) the effect of sphericity on fundamental-mode Love waves is more complicated than for Rayleigh waves because of the efficient channeling of waves by low-velocity layers, and (2) the first higher Love mode is more affected by curvature than the fundamental mode. The variation with depth of the relative amplitude of the displacements indicates that the first higher Love mode for periods less than 90 sec is very sensitive to upper mantle structure in the vicinity of the low-velocity zone. Comparison of the theoretical results with recent phase-velocity and torsional- oscillation data shows that a Gutenberg-type velocity structure is more satisfactory than either the Lehmann or Jeffreys structures. The use of consistent densities with the Gutenberg model, rather than Bullen A densities, has a small but significant effect on the calculated velocities. For periods greater than 200 sec the calculated phase velocities for various oceanic and continental structures are all within 2% of each other. The calculated group velocities are within 1 1/2% of each other in the range 150 < T < 400 sec, thus confirming experimental results. Dispersion measurements must therefore be made to better than this accuracy in order to draw significant conclusions about details of Earth structure

Higher mode surface waves and their bearing on the structure of the earth's mantle

A detailed numerical investigation of surface wave dispersion and particle motion associated with the higher Love and Rayleigh modes over realistic earth models has been carried out as a preliminary to the routine use of these waves in studies of the crust-mantle system. The suggestion that the so-called channel waves, such as the Lg, Li, and Sa phases, can be interpreted by higher mode group velocity dispersion curves is verified in detail. Furthermore, Sa should have a higher velocity across shield areas than across normal continental areas and a higher velocity across continents than across oceans. Higher mode Rayleigh wave data are presented for long oceanic paths to Pasadena. The observed data favor the CIT 11 model of Anderson and Toksöz (1963) over the 8099 model of Dorman et al. (1960) and indicate that under the Pacific Ocean the low-velocity zone extends to a depth perhaps as deep as 400 km followed by an abrupt increase in shear velocity

The Internal Structure of the Moon and the Terrestrial Planets

The known internal structure of the Earth is the logical starting point for discussions of the terrestrial planets and the Moon. Until we have direct data, the most reasonable assumption regarding these bodies is that they are similar in composition to the Earth

Long-Period Love Waves in a Heterogeneous, Spherical Earth

Periods of torsional eigenvibrations have been computed for heterogeneous spheres corresponding to a variety of earth models, and the periods of oscillation are used to calculate phase and group velocities for the fundamental and first higher modes of Love waves. A comparison is made between velocities computed for different spherical models and for equivalent flat earth structures. The comparison shows (1) that the effect of sphericity is more complicated for fundamental mode Love waves than for Rayleigh waves because of the efficient channeling of waves by low-velocity layers and (2) that the first higher Love mode is more affected by curvature than the fundamental mode. The variation with depth of the relative amplitude of the displacements indicates that the first higher Love mode for periods less than 90 seconds is very sensitive to upper-mantle structure in the vicinity of the low-velocity zone. Comparison of the theoretical results with recent phase velocity and torsional oscillation data shows that a Gutenberg type of velocity structure is more satisfactory than either the Lehmann or Jeffreys structures. The use of consistent densities with the Gutenberg model, rather than Bullen A densities, has a small but significant effect on the calculated velocities. For periods greater than 200 seconds the calculated phase velocities for various oceanic and continental structures are all within 2 per cent of each other. The calculated group velocities are within 1½ per cent of each other in the range 150 < T < 400 sec, thereby confirming experimental results. Dispersion measurements must therefore be made with precision if significant conclusions are to be inferred about details of earth structure

The Interiors of the Terrestrial Planets

Conclusions regarding the internal constitution of the terrestrial planets are dependent on the assumption as to the nature of the earth's core. It has previously been supposed that if the terrestrial planets, Earth, Venus, and Mars, are of similar composition the material of the core must represent a phase change, but if the core material is chemically distinct the planets must differ in over-all chemical composition. An equation of state for the mantle and core based on recent free oscillation and shock wave data is used in developing models of the terrestrial planets. It is demonstrated that Earth, Venus, and Mars can be satisfied with the hypothesis of chemical uniformity and a chemically distinct iron-rich core, provided that the external radius of Mars is about 3310 km. The radius of Mars could be as large as 3325 km and could differ only slightly from the gross composition of the earth, i.e. 2% less iron. Astronomical data indicate that Mars must be an almost homogeneous body, but compositional identity with the earth can be maintained by mixing mantle and core material