Análise da resolução do modelo de Hughes em sondagens magnetotelúricas

Abstract

In most geophysical exploration methods, the interpretation is carried out assuming an uniformily stratified Earth model. Due to the lack of uniqueness in the inversion of eletromagnetic data, all of the methods require theoretical modeling techniques to aid interpretation. In the literature data has usually been interpreted in terms of a one-dimensional conductivity structure; commoly the Earth is assumed to be horizontally uniform so that the conductivity is a function of depth only. In this work a new technique was developed to model a generic two-layer Earth in which the interface separating the layers can be represented by a Fourier series. The technique involves a pertubation method to find the effects of a sinusoidal boundary with small ondulations. Because the first-order pertubation solution is a linear one, we can use the overlap principle and combine solutions for several different sinusoids to form the solution for any two-layer in which the boundary is represented by a Fourier series. Comparison with the finite elements technique, the following conclusions can be drawing: • For one model of a flat, two-layer Earth, the layers separated by an interface whose depth varies sinusoidal in one diretion, the eletromagnetic response are more strong when the first layer tickness is of the order of skin depth of the eletromagnetic wave in the medium; • On the other hand, the aparent resistivity for this model is not affected by the change in the spatial frequency (v) of the boundary; • In case of using the general solution for any two layer Earth that can be developed in Fourier series, this technique produced good results when compared to finite elements technique. The lineralization restrict the application of the technique to small structure, nevertheless, a lot of structure can be model in simple way and the computational time is very fast; • When the dimension of the first layer has the same order of magnitude of the structure, this technique is not recommended because for some particular sounding position, the apparent resistivity curves obtained show a small shift when compared to the curves obtained by finite elements.