The Application of TSVD in MT Inversion with Improved MSE as Determination of the Regularization Level

The total mean-square error (MSE) of the estimated model, defined as the sum of the standard model variance and the bias variance, is used to define the truncation level of the singular-value decomposition to give a reasonable balance between model resolution and model variance. This balance is determined largely by the data and no further assumptions are necessary except that the bias terms are estimated sufficiently well. This principle has been tested on the ID magnetotelluric inverse problem with special emphasis on high-frequency magnetotelluric (MT) data. Simulations clearly demonstrate that the method provides a good balance between resolution and variance. Starting from a homogeneous half-space, the best solution is sought for a fixed set of singular values. The model variance is estimated from the sum of the inverse eigenvalues squared, up to a certain threshold, and the bias variance is estimated from the model projections on the remaining eigenvectors. By varying the threshold, the minimum of the MSE is found for an increasing number of fixed singular values until the number of active singular values becomes greater than or equal to the estimated number.