Information theory lateral density distribution for Earth inferred from global gravity field

Abstract

Information theory inference, better known as the maximum entropy method, is used to infer the lateral density distribution inside the earth. The approach assumes that the earth consists of indistinguishable Maxwell‐Boltzmann particles populating infinitesimal volume elements and follows the standard methods of statistical mechanics (maximizing the entropy function). The GEM 10B spherical harmonic gravity field coefficients, complete to degree and order 36, are used as constraints on the lateral density distribution. The spherically symmetric part of the density distribution is assumed to be known. The lateral density variation is assumed to be small in comparison with the spherically symmetric part. The resulting information theory density distribution for the cases of no crust removed, 30 km of compensated crust removed, and 30 km of uncompensated crust removed all give broad density anomalies extending deep into the mantle, but with the density contrasts being the greatest toward the surface (typically ±0.004 g cm−3 in the first two cases and ±0.04 g cm−3 in the third). None of the density distributions resemble classical organized convection cells. The information theory approach may have use in choosing standard earth models, but the inclusion of seismic data into the approach appears difficult.

Inferring the viscosity and the 3-D density structure of the mantle from geoid, topography and plate velocities

“…Hide & Horai 1968). More complex methods have also been applied, minimizing the shear strain energy (Kaula 1963) or using the maximum entropy approach (Rubincam 1982). In all cases, the geophysical meaning of the assumptions leading to the inversion is, to the least, debatable.…”

On inversion for mass distribution from global (time-variable) gravity field

“…of moments (n + 1)(n + 2)/2 Degree of deficiency n(n − 1)/2 0 1 (monopole) 1 (total mass) 0 1 3 (dipole) 3 (center of mass) 0 2 5 (quadrupole) 6 (inertia tensor) 1 3 7 (octupole) 10 (3rd moment) 3 4 9 15 6 5 1 1 2 1 1 0 6 1 3 2 8 1 5 100 201 5151 4950 the physical condition of minimum shear energy in the mantle, Kaula (1963) determined a unique lateral density distribution for the Earth. Rubincam (1982) achieved the unique solution by employing the mathematical constraint of maximum entropy. Likewise, it can be shown that minimizing the norm-2 variance for the lateral distribution also leads to unique solutions.…”

Geomagnetic variation anomalies in northern England: processing and presentation of data from a non-simultaneous array

“…This is the approach generally adopted in the maximum entropy inference. Some recent examples are Rietsch (1977), Gull & Daniell (1978), Rubincam (1979Rubincam ( , 1981 and Berrill & Davis (1980). Since Shannon's entropy is defined relative to the arbitrarily chosen independent variable, the probability distribution generated from the principle will be parameter-dependent.…”