TL;DR: The present work is aimed at rapid reduction of the gravity and magnetic fields observed over an uneven surface to a horizontal plane by estimate the Fourier transform of the potential field over an imaginary horizontal plane lying entirely above the ground surface and impose boundary conditions.
Abstract: The present work is aimed at rapid reduction of the gravity and magnetic fields observed over an uneven surface to a horizontal plane. The approach suggested is to estimate the Fourier transform of the potential field over an imaginary horizontal plane lying entirely above the ground surface and impose boundary conditions; namely, the solution must satisfy the observed field over the ground surface and vanish over an infinite hemisphere. The desired Fourier transform is obtained in an iterating manner. A 2D FFT algorithm can considerably reduce the computational burden. The FFT approach cannot be used unless the discrete data is available on a rectangular grid. If the observations are scattered, interpolation to the nearest grid point will have to be carried out. Interpolation introduces marginal increase in the rms error. The iterating approach is about 10 times faster than the least squares approach. >
Abstract: In correlation filtering we attempt to remove that component of the aeromagnetic field which is closely related to the topography The magnetization vector is assumed to be spatially variable, but it can be successively estimated under the additional assumption that the magnetic component due to topography is uncorrelated with the magnetic signal of deeper origin The correlation filtering was tested against a synthetic example The filtered field compares very well with the known signal of deeper origin We have also applied this method to real data from the south Indian shield It is demonstrated that the performance of the correlation filtering is superior in situations where the direction of magnetization is variable, for example, where the remnant magnetization is dominant
Abstract: Accurate terrain corrections are important for all gravity surveying. In airborne surveys, a digital model of the terrain is constructed and terrain corrections are calculated at each airborne measurement point. Airborne gravity gradiometry is of high spatial resolution and is particularly sensitive to nearby topographic variations, placing particular requirements on the terrain corrections. A combination of mathematical analysis and simulation studies has led to quantification of the requirements: current on-shore, low-level gradiometer surveys require sub-metre accuracy in navigation and in digital terrain model heights; cell sizes (and therefore also topographic sampling) in the terrain model should be about one-third of the ground clearance. The choice of terrain correction density depends on the application and it is important that the interpreter of the corrected gravity data has the ability to test the impact of changes in this density. Accurate calculation of the gravity gradient field at the airborne sampling points may be achieved by a wide variety of either spatial or harmonic domain methods. Calculation in the harmonic domain is fast but assumes the data represent a periodic function on a planar surface. Padding methods for periodic extension and piecewise continuation away from a plane both add error and slow the calculation. Spatial domain methods are slower but can be sped up by the use of various approximations. In both cases, a clear understanding of accuracy requirements is essential for making an appropriate tradeoff between accuracy and speed.
Abstract: The problem of reduction of magnetic and gravity data, when observed on an arbitrary surface in a region of high topographic relief, is studied with equivalent source representation at the points of observation. It is shown that the analytical relationship between the total magnetic field or the gravity effect and equivalent magnetization or density on an arbitrary observational surface is given by a Fredholm integral equation of the second kind. A rapidly convergent iterative scheme is described for the solution of the integral equation, yielding the surface distribution of magnetization or density. With this distribution, the field at any other surface can be easily computed. Then it has been demonstrated with model examples that the gravity or magnetic field observed on a rough terrain can be accurately reduced to a horizontal plane for processing and interpretation.A new method has been suggested for minimization of terrain-induced anomalies on a magnetic or gravity map. This method is based on the concept that when the anomalous field observed on an arbitrary surface is continued to a surface parallel to the topography, the terrain effect in the continued field is sharply reduced relative to the field created by bodies of finite extent in the crust. Model examples are presented to show the accuracy and reliability of the method.
Abstract: An equivalent source algorithm is described for continuing either one‐ or two‐dimensional potential fields between arbitrary surfaces. In the two‐dimensional case, the dipole surface is approximated as a set of plane faces with constant moments over each face. In the one‐dimensional case, the plane faces of the dipole surface reduce to straight line segments. Application of the algorithm to model and field examples of aeromagnetic data shows the method to be effective and accurate even when the terrain has strong topographic relief and is composed of highly magnetic volcanic rocks.
"Fast reduction of potential fields ..." refers methods in this paper
...Hansen and Miyazaki [ 6 ] modified the method given in  for better accuracy....
Abstract: Conventional reductions of gravity and magnetic data do not lead to values that are effectively on the same horizontal plane, although it is common practice to regard them so. In regions of high topographic relief, failure to take into account local differences in vertical gradients can result in appreciable error. In this study a method is developed for reducing to a common level gravity or magnetic anomaly data observed at unevenly spaced stations at various elevations above a reference plane. The reduction is effected by means of finite harmonic series approximations in which the coefficients are determined by matrix methods and least squares. Traditional Fourier methods are not applicable because uneven station spacing and relative vertical displacement of stations preclude the use of the orthogonality properties of the trigonometric functions. The number of terms required to represent the data adequately is discussed in terms of “cutoff” wavenumbers empirically determined from residual variance estim...
"Fast reduction of potential fields ..." refers methods in this paper
...Henderson and Cordell [ 7 ] have used finite harmonic series expansion of the observed data and then, using the estimated coefficients, they were able to reduce the field to a plane surface....
Abstract: A new method for continuing two‐dimensional potential data upward from an uneven track is developed with special emphasis on solving a particular practical problem, that of magnetic data taken near the bottom of the ocean. The method is based on the use of the Schwarz‐Christoffel transformation, which maps the original, irregular track into a horizontal straight line. It has been found to be very fast computationally and to suffer none of the restrictions found in some earlier two‐dimensional algorithms.
Abstract: Summary This paper describes a method for the continuation of three-dimensional potential fields measured on an uneven surface; this method is based on a technique proposed earlier by the authors : first we represent potential functions as a sum of elementary interpolating functions; then an inversion technique gives the continued field as a very simple linear combination of the observed values. The method is of interest in several geophysical problems: for example, aeromagnetic surveys made at different altitudes can be joined with no edge effect. This case and others, both theoretical and real, are presented in the paper.