WALDIM: A code for the dimensionality analysis of magnetotelluric data using the rotational invariants of the magnetotelluric tensor

In the magnetotelluric (MT) method, the analysis of geoelectric dimensionality has acquired special importance in the last years, because numerical codes have made it possible to model and invert data using either one-dimensional (1D), two-dimensional (2D) or three-dimensional (3D) approaches. We present a FORTRAN code termed WALDIM to perform the dimensionality analysis of a set of MT data, according to the WAL rotational invariants criteria. These criteria are based on the possible annulment of the invariants of the MT tensor, which allow retrieval of as much information as possible from this tensor, without taking any a priori dimensionality assumption. When determining the dimensionality of real and therefore noisy data, two problems arise. The first is due to the data errors, which propagate into the invariants values, and therefore, to the determination of the dimensionality. The second is the fact that the invariants are rarely precisely zero, and the definition of a threshold is necessary. To solve these problems, WALDIM takes into account the data errors. Additionally, the dimensionality results can be grouped into frequency bands. Thus, we provide a software utility that allows providing a robust description of the dimensionality, and the parameters necessary for data correction prior to modeling. Given its completeness at analyzing the MT tensor for both individual and bands of frequencies, this code is meant to be a practical tool for MT data analysis.