Abstract
Abstract The problem of model recovering in the presence of impulse noise on the data is considered for the magnetotelluric (MT) inverse problem. The application of total variation regularization along with L1-norm penalized data fitting (TVL1) is the usual approach for the impulse noise treatment in image recovery. This combination works poorly when a high level of impulse noise is present on the data. A nonconvex operator named smoothly clipped absolute deviation (TVSCAD) was recently applied to the image recovery problem. This operator is solved using a sequence of TVL1 equivalent problems, providing a significant improvement over TVL1. In practice, TVSCAD requires the selection of several parameters, a task that can be very difficult to attain. A more simple approach to the presence of impulse noise in data is presented here. A nonconvex function is also considered in the data fitness operator, along with the total variation regularization operator. The nonconvex operator is solved by following a half-quadratic procedure of minimization. Results are presented for synthetic and also for field data, assessing the proposed algorithm’s capacity in model recovering under the influence of impulse noise on data for the MT problem.
Highlights
Electromagnetic sounding methods have been applied for a long time to investigate the interior of the Earth from depths of a few meters to hundreds of kilometers
In an effort to generate models with sharp boundaries, several techniques have been applied to this problem: piecewise continuous formulations as in ref. [4,5], l1 norm minimization [6,7,8], total variation penalizers in ref. [9] and [10], among others
We propose to apply the operator to the fitness term in (2), solving algorithm proposed by Geman and Yang [22]
Summary
Electromagnetic sounding methods have been applied for a long time to investigate the interior of the Earth from depths of a few meters to hundreds of kilometers. Only one unbiased estimate can be obtained at one site simultaneously using a magnetic field measurement at a remote site [13,14]. The latter can be used effectively only for uncorrelated noise between local and remote sites. The use of classical spectral analysis together with least-squares regression is warranted if data follow a stationary and Gaussian model. In this case, it is common to assume that residuals follow a multivariate normal probability distribution. Results are presented for the MT problem, but can be applied to other types of electromagnetic soundings
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