Open AccessEmpirical 3‐D basis for the internal density of a planet
Author(s) -
Chambat Frédéric,
Ricard Yanick
Publication year - 2005
Publication title -
geophysical journal international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0956-540X
DOI - 10.1111/j.1365-246x.2005.02650.x
Subject(s) - planet , basis (linear algebra) , geophysics , uniqueness , kernel density estimation , gravitational field , operator (biology) , geology , physics , theoretical physics , mathematics , statistical physics , mathematical analysis , classical mechanics , geometry , astrophysics , statistics , biochemistry , chemistry , repressor , estimator , transcription factor , gene
SUMMARY Various papers have discussed the forward relationships between internal density anomalies of a planet and its external gravity field. The inverse modelling, i.e. finding the internal density anomalies from the external potential is known to be highly non‐unique. In this research note, we explain how a 3‐D basis can be built to represent the internal density variations that includes a subset that explicitly spans the kernel of the forward gravity operator. This representation clarifies the origin of the non‐uniqueness of the gravity sources and implies the existence of a natural minimal norm inverse for the internal density. We illustrate these ideas by comparing a tomographic model of the mantle to the minimal norm density.