Open AccessLateral Variations of Density in the Mantle
Author(s) -
ArkaniHamed Jafar
Publication year - 1970
Publication title -
geophysical journal of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0016-8009
DOI - 10.1111/j.1365-246x.1970.tb06085.x
Subject(s) - geology , mantle (geology) , geopotential , geophysics , structure of the earth , spherical harmonics , crust , core–mantle boundary , gravitational field , geoid , shear (geology) , geodesy , outer core , gravity anomaly , seismology , inner core , physics , petrology , classical mechanics , paleontology , quantum mechanics , oil field , measured depth
Summary The lateral variations of the Earth's gravitational field, deduced from orbital data of artificial satellites, indicate the existence of lateral density variations within the Earth. A density model is computed for the mantle with the following constraints: (1) the model presents perturbations to Gutenberg's earth model which are specified by spherical harmonics through the sixth order and degree; (2) the density anomalies are confined to the mantle and the crust; (3) the anomalies of the crust are determined for n = 2, …, 6 and m = 0, …, n from crustal thickness, crustal P wave velocity, and P n velocity, and those of the upper mantle for n = 2 and 3 and m = 0, …, n are related to the lateral variations of seismic travel‐time residuals; (4) the unknown density anomalies of the mantle are determined such that the total shear strain energy of the Earth is a minimum; (5) the gravitational potential of the deformed Earth (subject to the density anomalies) on its surface equals the first six orders of the spherical harmonic representation of the measured geopotential; and (6) an isotropic, elastic, and cold mantle, and a liquid core are assumed in the stress analysis. The density anomalies thus obtained exhibit a decreasing feature with depth. In the crust they are of the order of 0.3g cm −3 , in the upper mantle 0.1 g cm −3 , and in the lower mantle 0.04 g cm −3 , which are within the values deduced from independent seismic measurements. The lateral variations of the associated stress differences at shallow depths correlate with the surface feature of the Earth. This correlation disappears in the deep mantle.