# Documentation¶

The flexure of elastic plates is a central concept in the theory of plate tectonics,
where the Earth’s lithosphere (crust and uppermost mantle) reacts to transverse applied loads
by bending, a process referred to as flexural isostasy. Estimating the *effective*
elastic thickness (\(T_e\)) of the lithosphere (thickness
of an equivalent ideal elastic plate) gives important clues on the rheology of the
lithosphere and its thermal state. Estimating \(T_e\) is typically done by
modeling the cross-spectral properties (admittance and coherence) between
topography and gravity anomaly data, which are proxies for the distribution of
flexurally compensated surface and subsurface loads.

This package contains `python`

and `fortran`

modules to calculate the wavelet spectral
and cross-spectral quantities of 2D gridded data of topography and gravity anomalies.
Once obtained, the wavelet cross-spectral quantities (admittance and coherence) are
used to determine the parameters of the effectively elastic plate, such as the
effective elastic thickness (\(T_e\)), the initial subsurface-to-surface
load ratio (\(F\)) and optionally the initial phase difference between
surface and subsurface loads (\(\alpha\)).
The estimation can be done using non-linear least-squares or probabilistic (i.e., bayesian)
inference methods. The analysis can be done using either the Bouguer or Free air gravity anomalies, and
over land or ocean areas. Computational workflows are covered in the Jupyter
notebooks bundled with this package. The software contains methods to make
publication-quality plots using the seaborn package.

Note

The cross-spectral quantities calculated here are the real-valued admittance and squared-real coherency, as discussed in the references