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Two dimensional Fourier transform can be used for the upward continuation of gravity or magnetic field dataacquired at given altitude over a rectangular area. Earth’s curvature is often neglected in most potential field continuations,however, it should be considered over several hundred kilometer field area. In this study, we developed a new methodretaining terms of Earth’s curvature to better perform the continuation of potential field on spherical patch area.Keywords: gravity or magnetic field, upward continuation, Fourier transform:             ,   2    .       ,        .      /   .: , ,  Introduction Gravity and magnetic fields are two potential fields, whichhave been widely used for important reconnaissance surveysin geophysical prospecting. Recently, the data acquisitions ofthese fields are often done by airborne or on-satellite mea-surements. These modern techniques enable us to cover largerarea more easily than ever. With the measurement at givenheight, the upward/downward continuation of potential fieldis a powerful method to investigate the distribution and prop-erties of sources at depth or other features at different heights.If the whole globe is under consideration, spherical harmonicseries would be the relevant one to describe the global field.Upward continuation of gravity or magnetic field has gener-ally been done by two dimensional Fourier transforms on rect-angular and flat areas.Although the flat Earth had been normally assumed in thepotential field continuation, it is desirable to consider the cur-vature of the Earth, when data area exceeds a few degrees oflatitude and longitude. In this study, we derive a new algo-rithm for upward continuation of gravity or magnetic field ona spherical patch area (Fig. 1). Both the field and its potentialcan be continued by similar ways with only different expo-nents for radial dependence.

Upward Continuation of Potential Field on Spherical Patch Area