Decomposição em valores singulares aplicada a dados de campo magnético

Abstract

The singular value decomposition of a matrix A, n x m, which represents a magnetic anomaly, can be seen as a bidimensional coherence filtering method which separates the correlated information from noncorrelated information in a magnetic data matrix A. The filter is defined by expansion of matrix A into eigenimages and singular values. Each eigenimage is constructed by the scalar product of the base vectors and eigenvectors, which are associated with the eigenvectors and eigenvalues of the covariance matrices ATA and AAT. This filtering method is based on the fact that the eigenimages, which are associated with large singular values, concentrate the major part of the correlated information present in the data, while the noncorrelated part, including noise caused by external magnetic sources, compilation errors, and shallow magnetic sources comprise the remaining eigenimages. This method was employed on many examples of synthetic and real data from PETROBRÁS' Carauari-Norte project (Solimões Basin) in order to investigate the utility of the method in the identification, elimination and attenuation of noise present on magnetic data and as a possible method for enhancing certain features generated by anomalies of shallow and deep origin. This work suggests the desirability of introducing both static and dynamic shift on magnetic lines to enhance the correlation (coherence) between the magnetic lines. This shift concentrates the correlated signal in the first few eigenimages. Another important aspect of this decomposition into eigenimages and eigenvalues is the savings gained in storage of a matrix A of n x m units. Memory requerements can be diminished considerably by using p autoimages, i. e. p x (n + m + 1) units without altering the form of the anomaly. We conclude that an appropriate choice of eigenimages generated by SVD decomposition shows good promise as a processing method in magnetic data.