The choice of an appropriate regularization parameter
enables the correct estimation of model parameters and
convergence of an inversion routine. The selection of the regularization
parameter in different inversion methods
determines/controls the local convergence, global convergence, or
both local and global convergence of the algorithms. This indicates
that the choice of regularization parameter estimation method plays
a crucial role in geophysical inversion. In this article, a comparison
of the effects of different regularization parameter approximation
techniques on the inversion of electrical resistivity and controlledsource
radiomagnetotelluric (CSRMT) data is tested. The constraining
equation defines the property of an inversion method;
therefore, different methods can have different constraining equations.
At this juncture, regularization parameters are calculated by
LASSO and elastic-net (a convex combination of L2 and L1 norm)
regression analyses. Also, the damping parameter for the Levenberg–
Marquardt method is computed using singular value
decomposition (SVD). In addition, a new empirical approach
developed for the estimation of regularization parameters is presented
in this paper and compared along with the above-mentioned
techniques. This exercise is performed on synthetic and field data
sets. The efficacy of different regularization parameter schemes is
analyzed for the isotropic and anisotropic joint inversion of electrical
resistivity and CSRMT data. In general, the elastic-net
regularization and the new empirical scheme work well. However,
the elastic-net solutions are slightly dependent on the choice of
convex combination regularization term. Additionally, the solutions
obtained with the damping parameter estimation using SVD
are dependent on the starting model. Elastic-net uses a combination
of L1 and L2 norm constraining equations, which is why in some
places it has shown better convergence and parameter reconstruction
than the Marquardt method. However, an appropriate ratio of
each (L1 and L2) norm is required to achieve optimal results with
this method. Consequently, the new empirical approach proved to
be optimal compared to other regularization parameter estimation
approaches discussed in this work.