A Cubic B-Spline Approach for Inter-Transformation between Potential Field and Gradient Data


Traditionally, algorithms involving Fast Fourier Transforms (FFT) are used to calculate gradients from field data and vise versa. Because the popular FFT differentiation algorithms are prone to noise, expensive field campaigns are increasingly utilized to obtain gradient data. In areas with both field and gradient data, transformation facilitates comparison. In areas with only one kind of data, transformation facilitates interpretation by transforming the measured data into another form of data. We advance unified formulae for interpolation, differentiation and integration using cubic B-splines, and propose new space-domain approaches for 2D and 3D transformations from potential field data to potential-field gradient data and vice versa. We also advance spline-based continuation techniques. In the spline-based algorithms, the spacing can be either regular or irregular. Analyses using synthetic and real gravity and magnetic data show that the new algorithms have higher accuracy, are more noise-tolerant and thus provide better insights into understanding the nature of the sources than the traditional FFT techniques.

Meeting Name

AGU Fall Meeting (2008: Dec. 15-19, San Francisco, CA)


Geosciences and Geological and Petroleum Engineering

Keywords and Phrases

Computational methods: potential fields; Gravity methods; Magnetic and electrical methods; Geopotential theory and determination; Fourier analysis

Document Type

Article - Conference proceedings

Document Version


File Type





© 2008 American Geophysical Union (AGU), All rights reserved.

Publication Date

01 Dec 2008

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