Open Access

Inequality constraint in least-squares inversion of geophysical data

Earth, Planets and Space201451:BF03352229

DOI: 10.1186/BF03352229

Received: 24 August 1998

Accepted: 16 February 1999

Published: 6 June 2014


This paper presents a simple, generalized parameter constraint using a priori information to obtain a stable inverse of geophysical data. In the constraint the a priori information can be expressed by two limits: lower and upper bounds. This is a kind of inequality constraint, which is usually employed in linear programming. In this paper, we have derived this parameter constraint as a generalized version of positiveness constraint of parameter, which is routinely used in the inversion of electrical and EM data. However, the two bounds are not restricted to positive values. The width of two bounds reflects the reliability of ground information, which is obtained through well logging and surface geology survey. The effectiveness and convenience of this inequality constraint is demonstrated through the smoothness-constrained inversion of synthetic magnetotelluric data.