1887

Abstract

We demonstrate that the solution of 3-D DC resistivity tomography has strong numerical artifacts if the inverse<br>problem is not properly regularized. With only few data points but a large number of model parameters<br>(unknowns), the nonlinear inverse problem is ill-posed. Many studies have shown that some kind of model<br>correlation must be constructed to stabilize the inversion. Among those, Tikhonov regularization takes a<br>more explicit approach by damping spatial derivatives of the model function as opposed to applying ,ad hoc<br>smoothing. However, we show evidence that not all smoothness criteria in the class of Tikhonov methods<br>are well-posed for 3-D DC resistivity inversion. In fact, only under the second- or higher-order derivative<br>regularization, 3-D DC resistivity tomography can produce a physically meaningful solution which has no<br>dependence on the model discretization. In adopting effective smoothness criteria, the solution approximates<br>a continuous function with no more structure than is necessary to fit the data. Further, we demonstrate<br>that using Tikhonov method to regularize the model stepsize rather than the model itself does not improve<br>the ill-posedness of the inverse problem. As the result, only the data misfit has been minimized and model<br>correlation is not constrained. Finally, we apply our tomography approach to model real data collected at the<br>Mojave Generating Station in Laughlin, Nevada. For different model discretization, our approach prbduces<br>similar subsurface image.

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/content/papers/10.3997/2214-4609-pdb.205.1996_075
1996-04-28
2021-12-02
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http://instance.metastore.ingenta.com/content/papers/10.3997/2214-4609-pdb.205.1996_075
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