Incompressibility at the earth's mantle-core boundary.

(1) Introduction.-In this paper, the values of variables at the base of the mantle and top of the core in the Earth models to be considered will be indicated by the subscripts 1 and 2, respectively; k and p will denote the incompressibility and density; let Ak = k2ki and Ap = p2 pi. In an earlier Earth model,1 Model A, k1 = 6.5 X 1012 dyn/cm2 and k2 = 6.2 X 1012 dyn/cm2, giving Ak = -0.3 X 1012 dyn/cm2 and Ak/kj -5 per cent. The values of k in Model A are derived from the density distribution and the seismically determined distributions of the P and S velocities a and ,3. These values of k do not depend on any theory or additional observational evidence relating to compressibility in the Earth. The sources of error contributing to the determination of Ak on the Model A procedures are listed in § (2). The fact that Ak/kj is so small in Model A, along with certain other evidence, 3 led to the formulation of a compressibility-pressure hypothesis, one important part of which is that k varies continuously through the Earth, as well as smoothly with respect to the pressure p, below 1000 km depth. The hypothesis need be considered to hold only as a useful first approximation to actual conditions in the Earth, but even so has several important implications, including, for example, being instrumental in providing the initial evidence that the Earth's inner core has significant rigidity. In 1950 an Earth model B was constructed4 in which the hypothesis was taken as a central feature, and which exhibits various characteristics of an Earth with a solid inner core. As a consequence of additions to older seismic data, including observations of the orbits of artificial satellites and of the periods of free Earth oscillations excited by the Chilean and Alaskan earthquakes of 1960 and 1964, as well as other evidence also essentially unconnected with compressibility theory, it is now possible to examine the assessment of Ak fairly closely, and so test one of the important items of evidence on which the k-p hypothesis rests. The purpose of the present paper is to examine the amendments needed to the previously assessed Ak and, in particular, to show how on current evidence k appears indeed5 to be practically continuous at the mantle-core boundary. (2) Corrections to Model A Estimate of Ak.-The 1Iodel A estimate of Ak is derived from the values taken for a and j3 and the values inferred for p over the period 1940-42 in the vicinity of the mantle-core boundary, N say. In the present paper, except to a small extent in § (6), errors in a and f8 near N will be disregarded as being probably small in their effect on Al1k compared with other errors in the Model A structure. The values of p nearN are tied up with the determination of the density distribution of the whole Earth. Thus corrections to the Model A estimate of Ak arise principally from corrections to the Earth's density distribution. The main sources of corrections needing to be considered are: