Journal ArticleDOI
A scattered equivalent-source method for interpolation and gridding of potential-field data in three dimensions
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TLDR
In this article, the inverse distance Newtonian potential function is used to interpolate geophysical data observed at scattered discrete points in three dimensions by relating the point data to a continuous function of equivalent discrete point sources, located beneath some of the data points at a depth proportional to distance to the nearest neighboring data point.Abstract:
Potential‐field geophysical data observed at scattered discrete points in three dimensions can be interpolated (gridded, for example, onto a level surface) by relating the point data to a continuous function of equivalent discrete point sources. The function used here is the inverse‐distance Newtonian potential. The sources, located beneath some of the data points at a depth proportional to distance to the nearest neighboring data point, are determined iteratively. Areas of no data are filled by minimum curvature. For two‐dimensional (2-D) data (all data points at the same elevation), grids calculated by minimum curvature and by equivalent sources are similar, but the equivalent‐source method can be tuned to reduce aliasing. Gravity data in an area of high topographic relief in southwest U.S.A. were gridded by minimum curvature (a 2-D algorithm) and also by equivalent sources (3-D). The minimum‐curvature grid shows strong correlation with topography, as expected, because variation in gravity effect due to...read more
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The historical development of the magnetic method in exploration
Misac N. Nabighian,V.J.S. Grauch,R. O. Hansen,Thomas R. LaFehr,Yaoguo Li,J. W. Peirce,Jeffrey D. Phillips,M. E. Ruder +7 more
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Historical development of the gravity method in exploration
Misac N. Nabighian,Mark E. Ander,V.J.S. Grauch,R. O. Hansen,T. R. LaFehr,Yaoguo Li,W. C. Pearson,J. W. Peirce,Jeffrey D. Phillips,M. E. Ruder +9 more
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Sub-ice geology inland of the Transantarctic Mountains in light of new aerogeophysical data
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Journal ArticleDOI
The equivalent data concept applied to the interpolation of potential field data
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REGCONT: A Matlab based program for stable downward continuation of geophysical potential fields using Tikhonov regularization
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References
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Journal ArticleDOI
Machine contouring using minimum curvature
TL;DR: In this article, Finite difference equations are deduced from a principle of minimum total curvature, and an iterative method of solution is outlined, based on which the spline fit has well defined smoothness properties.
Journal ArticleDOI
The equivalent source technique
TL;DR: In this article, the authors synthesize an equivalent source of discrete point masses on a plane of arbitrary depth below the surface by keeping the depth of the plane within certain limits relative to the station spacing, and then the synthesized field closely approximates the true gravity field in the region close to and above the terrain.
Journal ArticleDOI
Continuation of potential fields between arbitrary surfaces
R. O. Hansen,Y. Miyazaki +1 more
TL;DR: In this article, an equivalent source algorithm is described for continuing either one-dimensional or two-dimensional potential fields between arbitrary surfaces, where the dipole surface is approximated as a set of plane faces with constant moments over each face.
Journal ArticleDOI
Some general properties of potential fields in space and frequency domain: A review
TL;DR: In this article, the amplitudes of different frequencies synthesizing a potential field signal are limited by an upper bound given by a fixed constant multiplied by exp ( − Hs), where H is the depth to the top of the source and s, the frequency.