Generalized Hilbert transforms of the effect of single magnetic sources

FERNANDO GUSPI; NOVARA IVAN

GEOPHYSICS

SOC EXPLORATION GEOPHYSICISTS

Año: 2011

0016-8033

The generalized Hilbert transforms of potential fields, particularly magnetic fields, provide a useful resource for improving the interpretation. Even though both x and y Hilbert transforms of a potential field on a plane are determined and can be approximately computed from the whole observed field, they are locally independent of the observations when considering restricted areas of the plane, and therefore can be combined with them to better constrain local inversions. The extended Euler deconvolution, based on Euler´s homogeneity equation, makes extensive use of this principle. In this work, we present closed form expressions for evaluating in the space domain the generalized x and y Hilbert transforms of magnetic fields generated by single point sources, given in the form of dipoles, monopoles, and Newtonian potential type sources. Apart from providing a way to calculate Hilbert transforms via equivalent sources, this approach can be applied to local inverse problems where the solution is modeled by point sources, because it enables to match to the observations not only the magnetic effect of the model, but also its Hilbert transforms, incorporating this way a stronger constraint. In a synthetic example with noisy data, it is shown the increased resolving power of this approach to locally outline the shape of a prismatic body. In an example with real data, the generalized Hilbert transforms of a magnetic anomaly over Sierra de San Luis, Argentina, are calculated from Newtonian equivalent sources, and used as a support to estimate from an extended Euler deconvolution, within certain limitations, the true magnetization direction within the causative structure.