Open AccessA matrix representation of the potential second‐rank gradient tensor for local modelling
Author(s) -
Soler Tomás
Publication year - 1985
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.1985.tb06406.x
Subject(s) - gradiometer , rank (graph theory) , tensor (intrinsic definition) , cartesian tensor , matrix (chemical analysis) , representation (politics) , spherical harmonics , cartesian coordinate system , point (geometry) , mathematics , mathematical analysis , geometry , computer science , physics , tensor field , tensor density , materials science , magnetometer , combinatorics , quantum mechanics , politics , magnetic field , political science , law , composite material , exact solutions in general relativity
Summary. This paper introduces a new matrix computational approach to the local determination of gravity gradients, convenient for comparing with gradient signals from moving base gradiometer systems or calculating topographic effects at instrument heights. The method represents a practical alternative to the more conventional spherical harmonics formulation, primarily global in nature, and it may be considered as an extension to other previously used local representations, such as point masses. Important characteristics of the analytical development outlined herein are its conceptual simplicity and the possibility of obtaining at once, up to a certain order n , and in an arbitrary Cartesian coordinate system, the symmetric point gradient tensor of second rank.