Bernstein preprocessing for nonlinear least squares inversion of gravity and magnetic data

Nonlinear, nonlocal and adaptive optimization algorithms, now readily avail able, as applied to parameter estimation problems, require that the data to be inverted should not be very noisy. If they are so, the algorithm tends to fit them, rather than smoothening the noise component out. Here, use of Bernstein polynomials is proposed to prefilter noise out, before inversion with the help of a sophisticated optimization algorithm. Their properties a re described. Inversion of gravity and magnetic data for basement depth est imation, singly and jointly, and without and after Bernstein-preprocessing is conducted to illustrate that the inversion of Bernstein-preprocessed gra vity data alone may be slightly superior to the joint inversion of gravity and magnetic data.