Resumen:
We propose two fast equivalent-layer techniques for processing large gravity gradient and magnetic datasets. Based on the equivalent-layer principle, we assume that potential-field data produced by arbitrary geological sources can be approximated by a linear combination of harmonic functions defined by a fictitious physical-property distribution on a planar layer. The computational efficiency of our methods are attained by the symmetric structure in block-Toeplitz Toeplitz-block (BTTB) of the sensitivity matrices when we use a regular grid of data. Although processing gravity-gradient data using the classical equivalent-layer technique allows a convenient way to maintain the physical consistency among the gravity-gradient components, it requires a computationally costly linear inversion. Hence, this restricts the applicability of the classical technique for processing the gravity gradient components from large datasets. To overcome this problem, we have developed a fast equivalent-layer method for processing gravity-gradient data. Our method consists in estimating a single equivalent layer that reproduces all the gravity gradient components. Additionally, this methodology allows the use of data from different acquisition systems. For processing magnetic data, the first step consists in using a rapid iterative approach to reproduce total-field anomaly data that may be irregularly disposed on an uneven surface. In the second step, we transform the estimated distribution obtained by the iterative approach into a magnetic moment distribution to perform transformations with phase change. Our methods are able to reduce by orders of magnitude the total number of floating-point operations to estimate the physical property distribution on the equivalent layer if compared with the classical approach. Applications to synthetic and real data show that our methods are computationally efficient alternative to deal with large data sets.
