Upward and downward continuation of gravity and magnetic data using linear programming

Upward and downward continuation of gravity and magnetic data can be computed by convolving the data with a set of weighting coefficients. Linear programming can be applied to calculating the weighting coefficients based on the desired frequency response. The objective function in the linear programming is defined as the summation of the weighting coefficients multiplied by an exponential-type function and is subject to the constraint that the error between the desired frequency response and the computed frequency response is less than a very small number. The exponential-type function can force the magnitudes of the coefficients to decrease gradually from the center element to the edges, making this approach more accurate than the straight minimization of the maximum error used in the "minimax" method. The technique of linear programming can be applied to a wide range of filter design problems.