On the uniqueness of the inverse potential problem for homogeneous polyhedrons
SIAM Journal on Applied Mathematics
Singularity detection and processing with wavelets
IEEE Transactions on Information Theory - Part 2
Potensoft: MATLAB-based software for potential field data processing, modeling and mapping
Computers & Geosciences
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We start from the general inverse problem for potential fields and discuss the validity and suitability of using not only horizontal variations of them, but also their vertical ones. Hence multilevel data sets are considered, being they obtained either from measured data at different levels or by measuring the field just at the lower level and then generating by upward continuation the data at the remaining upper levels. In the latter case the upward continued data must be considered as the true ones plus some errors due to experimental errors and to the fact that they are generated from a discrete data set known on a finite survey area. Several forms of a priori information, such as that assuming the source can be represented by a fault or a sheet sandwich model, may allow the information contained in multilevel data to be effectively used for the interpretation of gravity and magnetic data. Recently established techniques of analysis, such as the continuous wavelet transform, are applied successfully to potential fields using implicitly the information contained in multilevel data. Assuming a block model for the source domain, the upward continuation formula may help to improve the solution of either 1D, 2D or 3D inverse problems enlarging the system with the equations related to the vertical variations of the fields, thereby reducing the algebraic ambiguity. Meaningful and computationally suitable quantities, such as weighted averages of potential fields, are also closely related to the use of multilevel data, providing useful insights for the determination of the depth distribution of the sources.